This site was designed for assisting secondary teachers and students in the teaching and use of technologies in a mathematics classroom. The goal was to find programs, websites, and other technologies that could be beneficial for both teaching and learning. While the focus has been strictly on secondary education, a quick glance and with some use of these technologies it is reasonable to suggest that many of these resources could span across grade levels- perhaps elementary or high school.
The first section of this site is entitled "Online Resources" and it contains an ongoing list of technological resources that are available to mathematics teachers and students. With each resource listed is a small description of what the technology is all about, as well as a link to visit the resource. These are all resources that could potentially be useful in the classroom and deserve a closer look by visiting and trying the site links.
The second section of this site is entitled "Online Resources Evaluations" and it contains ten resources which have been evaluated in detail as to their usefulness, affordance, and relation to the NCTM Principles and Standards of Mathematics. These are sites that have had a critical analysis and offer more information about the technology than in the previous section.
Finally, on the sidebar of this website, the sites have been organized by labels as related to the NCTM Principles and Standards of Mathematics. Resources for a particular standard can easily be shown on one webpage by clicking on a given standard. Also included on the sidebar is quick link reference to each resource presented on this site, in alphabetical order. Each link will take you to a given resource.
Please feel free to leave any comments about any of the resources, evaluations, or this site in general. Any contributions (technologies that could be a worthwhile addition to the site) are welcomed.
Online Resources
ABCya!- Fraction Tiles
This resource allows students to virtually manipulate a set of fractions tiles. In secondary education there is a strong focus on fractions and the relationships between fractions. Students are asked to find equivalent fractions, common factors, etc. Using an applet that provides students with fraction tiles is beneficial in that it offers students a chance visual for the fractions they are working with. Being able to see that four 1/4s equal one whole is an important step in the understanding of how fractions work and are related.
Arithmetic Four
This applet provides students with a game that is very similar to “Connect Four” in which students are doing computations in order to get game pieces in which they can play on a virtual game board to get “four in a row”. This multiplayer game allows for students to compete against one another while practicing computational skills with both whole numbers and integers.
Balloon Pop Math
This program offers students the opportunity to show their knowledge of fraction values and their ability to compare and order fractions. In this program students must identify fraction values written on balloons and "pop" the balloons from the lowest value to the greatest value with their cursor-pin. Students are racing against a timer for points in order to become the high-scorer, all the while practicing and learning about comparing fraction values.
Cabri Jr.: Exploring the Diameter and Circumference of a Circle
Students will be learning how pi is determined and its relationship to the circumference and diameter of a circle using a graphing calculator. Students will also be learning how to correctly graph circles, measure and draw a circle’s diameter, and measure a circle’s circumference using the Cabri Jr. program on the TI-84 calculator.
Circle 0
http://nlvm.usu.edu/en/nav/frames_asid_122_g_3_t_1.html?open=instructions&from=topic_t_1.html
The purpose of this applet is to promote addition, logic, and problem solving skills. The goal of the activity is to find sums of 21 using the integers that are given in a set of circles that are intertwined. Students who successfully can makes sums of 21 in each of the circles complete the activity.
http://nlvm.usu.edu/en/nav/frames_asid_122_g_3_t_1.html?open=instructions&from=topic_t_1.html
The purpose of this applet is to promote addition, logic, and problem solving skills. The goal of the activity is to find sums of 21 using the integers that are given in a set of circles that are intertwined. Students who successfully can makes sums of 21 in each of the circles complete the activity.
Create a Graph
This applet is a showcase of the many different types of graphs available to display data. Students are choosing and manipulating a graph of their preference- inputting data to display and correctly labeling the different pieces and parts of a graph. What the program aims to show is that there are many types of graphs that can show and represent a set of data accurately. This program serves as a great tool for allowing students to quickly and accurately create graphs.
Death to Decimals
This program offers students the chance to show their knowledge of converting fractions to decimals. This unique and engaging program allows students to be a superhero that saves cities from around the world from the attacks of decimals. Students must "shoot" down decimals that are equivalent to a given fraction that are falling from the sky in order to save the city that is being attacked. The program is fast paced and quick, and student knowledge of fractions and decimal conversions will truly be tested.
Dividing Fractions by Fractions
This applet provides practice of dividing fractions by fractions using the division of fractions algorithm. The program offers a small explanation on how to divide fractions by fractions, as well as three “game” settings that allows students to practice dividing fractions by fractions against a timer.
Dueling Calculators
http://nlvm.usu.edu/en/nav/frames_asid_312_g_4_t_1.html?from=topic_t_1.html
“Dueling Calculators” an applet allows students to visually and numerically see the differences calculator truncating and rounding can play in mathematics. When a calculator truncates (due to the size of its viewing window), answers are not usually effected greatly. Over time, however, repeated truncation can drastically change the solutions and results we get. This applet provides a resource for students to see that change.
http://nlvm.usu.edu/en/nav/frames_asid_312_g_4_t_1.html?from=topic_t_1.html
“Dueling Calculators” an applet allows students to visually and numerically see the differences calculator truncating and rounding can play in mathematics. When a calculator truncates (due to the size of its viewing window), answers are not usually effected greatly. Over time, however, repeated truncation can drastically change the solutions and results we get. This applet provides a resource for students to see that change.
Escape from KNAB
Escape from KNAB is a program that connects real-world situations, like filling out a tax form, in a make-belief, out-of-this-world, story. Students will analyze different situations, like choosing between two job offers that have varying benefits, and decide on which conditions will allow them to make the most money to be able to afford a return flight home from the distant planet, KNAB. Students problem solving skills will be practiced as they try and earn and save money.
First in Math
http://www.firstinmath.com
"First in Math" is an online version of the game, '24'. 24 is a popular card game in which students must make a total of 24 using four numbers on a given card. This site promotes the practice and increase in skill of mental computational fluency. The varying levels of difficulty (from whole numbers to fractions to integers to even algebra!) offer students of all abilities to find this site beneficial. Students can earn virtual stickers for completing various activities, and their is even a ranking and leader board of student sticker count, from the school level all the way to a nationwide leader board.
http://www.firstinmath.com
"First in Math" is an online version of the game, '24'. 24 is a popular card game in which students must make a total of 24 using four numbers on a given card. This site promotes the practice and increase in skill of mental computational fluency. The varying levels of difficulty (from whole numbers to fractions to integers to even algebra!) offer students of all abilities to find this site beneficial. Students can earn virtual stickers for completing various activities, and their is even a ranking and leader board of student sticker count, from the school level all the way to a nationwide leader board.
Function Machine
http://nlvm.usu.edu/en/nav/frames_asid_191_g_3_t_2.html?from=category_g_3_t_2.html
This technology plays to the common metaphor that functions are like “machines”- you put a number in (input), you get a number out (output). This applet allows students to put a given set of numbers into the function “machine” and have the machine generate an output. Students must also try and decipher the function “rule” in order to determine missing outputs for inputs.
http://nlvm.usu.edu/en/nav/frames_asid_191_g_3_t_2.html?from=category_g_3_t_2.html
This technology plays to the common metaphor that functions are like “machines”- you put a number in (input), you get a number out (output). This applet allows students to put a given set of numbers into the function “machine” and have the machine generate an output. Students must also try and decipher the function “rule” in order to determine missing outputs for inputs.
Genius Boxing
http://www.mrnussbaum.com/geniusboxing.htm
http://www.mrnussbaum.com/geniusboxing.htm
"Genius Boxing" is a program that allows students to compare numbers. In the middle grades, students are using inequality symbols to compare numbers and are writing sentences with inequalities. This program allows students to practice this skill in a fun and engaging manner. Students are boxing against a famous opponent (like Bill Gates or Albert Einstein), and can score a knockout by answering questions correctly. Incorrect answers result in a punch from the opponent. Students can win the game by successfully knocking out all challengers, but to do so will have to answer increasingly difficult questions.
Geometry Hidden Picture
This technology is a geometry applet for students whose main goal is to identify geometric shapes based on their characteristics and properties in order to reveal pieces to a hidden picture. Students are successful when correctly identify the given geometric figures and they completely uncover the mystery picture that was hidden.
Half-Court Rounding
This program is designed to help students with rounding skills. The program allows students to play a basketball game, giving the students the opportunity to make a one, two, or three point shots based on the level of difficulty of the problem that they choose. If a student answers the problem correctly, they make a basket, and if they are incorrect, they miss the shot. The program keeps track of the students score, and after ninety seconds gives students a final score for the game. It's a fun and competitive program that keeps students engaged and practicing their rounding skills.
Math Baseball
This applet allows students to practice their addition, subtraction, multiplication, and division facts by performing basic computations. They are rewarded for correct answers (the harder the problem, the greater the reward- a home run, for example), and punished for an incorrect answer (an out) in a baseball game format.
Mystery Picture: Integer Order of Operations
This applet allows students to not only practice their integer operations, but to also solve expressions correctly by following the order of operations. This duel learning experience makes this program worthwhile, as students are solving integer expressions in order to uncover a hidden mystery picture. This can be used as an assessment tool for students to showcase their integer operation skills.
Number Balls
http://www.sheppardsoftware.com/mathgames/Numberballs_algebra_I/numberballsAlgebraI.htm
http://www.sheppardsoftware.com/mathgames/Numberballs_algebra_I/numberballsAlgebraI.htm
The program allows students to practice their algebra skills by having them solve one-step equations that are written inside "number balls". Once students solve each equation, they must put each answer from least to greatest order. They then will click each ball going from least to greatest in order. Students get points for correctly clicking on a ball, and lose points for incorrectly choosing a ball. All-time high scores are saved and posted, giving this applet replay value and motivation for students to do well.
Pearson SuccessNet
Pearson SuccessNet was created to assist both teacher in the classroom and for students at home. The site contains online videos that teachers can use in the classroom to introduce or explain a given concept (all secondary math concepts), while also providing students with online tutorials, videos, and practice problems that students can access from their home computer with a log-in identification. This program offers assistance to students who may need it outside the classroom, while providing technology to teachers inside the classroom. This is a pay site.
Penguin Waiter Tip Game
This applet provides students the chance to use their percent and decimal skills in a real-life, everyday math situations. The "penguin waiter" will give students a problem that asks them to calculate the tip for a given bill, offering all the parameters necessary to do the computations ("What would be a 20% tip on a $20.00 bill?). Students have to correctly compute the tip in order to move on to the next problems. The applet provides practice with percents, decimals, and multiplication skills while giving a common real-life problem.
This applet provides students the chance to use their percent and decimal skills in a real-life, everyday math situations. The "penguin waiter" will give students a problem that asks them to calculate the tip for a given bill, offering all the parameters necessary to do the computations ("What would be a 20% tip on a $20.00 bill?). Students have to correctly compute the tip in order to move on to the next problems. The applet provides practice with percents, decimals, and multiplication skills while giving a common real-life problem.
Rounding Decimals
http://www.321know.com/g6-dec-round.htm
This applet gives students the chance to practice their rounding skills with decimal numbers. Students can practice rounding given decimal numbers to certain decimal place values. There are also three variety of games that students can play that test their knowledge of decimal rounding. Students can race against the clock to see how many problems they can get right in sixty seconds, time themselves to see how long it takes them to get twenty answers correct, or they can earn extra time to add to a running timer for correct answers as they try to answer as many questions as possible before the timer runs out.
http://www.321know.com/g6-dec-round.htm
This applet gives students the chance to practice their rounding skills with decimal numbers. Students can practice rounding given decimal numbers to certain decimal place values. There are also three variety of games that students can play that test their knowledge of decimal rounding. Students can race against the clock to see how many problems they can get right in sixty seconds, time themselves to see how long it takes them to get twenty answers correct, or they can earn extra time to add to a running timer for correct answers as they try to answer as many questions as possible before the timer runs out.
The Secret World of Cookie Man
This program was designed as an engaging activity for secondary students to practice using basic formulas, like distance and area. Students have to help “Cookie Man” in his adventure, solving problems along the way. Students must be able to set up formulaic equations correctly, substitute values for variables, as well as solve for missing amounts. The program offers amusing and laughable problems that make solving them fun and engaging for all students.
Specialist Calculators
This program is a tool that students can use that automates and simplifies measurement conversion tasks. The program offers students a variety of calculators that can do multiple simultaneous measurement conversions- from capacity to length to weight, or even polygon measurements, like length of diagonals and angle measures.
Stick or Switch
http://nlvm.usu.edu/en/nav/frames_asid_117_g_3_t_5.html?from=category_g_3_t_5.html
This program is a math version of the old game show, “Let’s Make a Deal” in which students have the choice of one of three doors, but behind only one of them is the grand prize. The object of the program is to showcase that by staying with your initial choice throughout the game (not switching your pick), you have lowered your probability of winning. The greater probability of winning is when students switch their picks after the first door is revealed. This program is centered on discovery based learning and potential for stimulating discussion on probability.
http://nlvm.usu.edu/en/nav/frames_asid_117_g_3_t_5.html?from=category_g_3_t_5.html
This program is a math version of the old game show, “Let’s Make a Deal” in which students have the choice of one of three doors, but behind only one of them is the grand prize. The object of the program is to showcase that by staying with your initial choice throughout the game (not switching your pick), you have lowered your probability of winning. The greater probability of winning is when students switch their picks after the first door is revealed. This program is centered on discovery based learning and potential for stimulating discussion on probability.
Toon University: Prime Factoring
This applet allows students to test their knowledge of prime factors. This fun game allows students to "shoot" cartoon birds with prime factors written on them with their cartoon character. Students have to correctly identify the prime factor of a given number, or determine which of the numbers written on a bird is not a prime factor of a given number. There are three levels of difficulty, offering a chance for differentiation amongst students.
Online Resource Evaluations
Geometry Hidden Picture
http://www.aplusmath.com/cgi-bin/games/geopicture
Description
This technology is a geometry applet for students whose main goal is to identify geometric shapes based on their characteristics and properties in order to reveal pieces to a hidden picture. Students are successful when correctly identify the given geometric figures and they completely uncover the mystery picture that was hidden.
Evaluation
What mathematics is (potentially) being learned?
NCTM Standard(s) addressed?
- Geometry, 6-8: Students will be able to analyze characteristics and properties of two-dimensional shapes.
What is the nature of the mathematics?
The concepts being shown are analyzing the geometric characteristics and properties of two-dimensional shapes. Students are analyzing given shapes for specific characteristics and properties in order to successfully identify them by their geometric name.
How does learning take place?
Learning takes place as students try to identify the characteristics and properties of two-dimensional shapes. For example, if a student must find the shape of an obtuse triangle, students will have to analyze the given shapes for the properties and characteristics that are indicative of an obtuse triangle. Misconceptions can also be cleared up as students use the technology. If a student had the misconception that an equilateral triangle had only two congruent sides, by clicking an isosceles triangle students would be able to see that they were incorrect and had to fix their definition of what equilateral meant. Through analysis and reflection, significant learning can take place.
What role does technology play?
The technology affords students the chance to represent their geometric knowledge and thinking by identifying the correct properties and characteristics of two-dimensional shapes in order to reveal a hidden picture.
The technology will ask students to identify a particular geometric shape or characteristic (a right triangle, a radius, parallel lines, etc.). Students will then click on the shape they feel is best representative of what the applet is asking them to identify. If the student answers correctly, a piece of the missing picture is revealed. An incorrect answer by the student will result in another question and no piece revealed. The student “wins” when the hidden picture is revealed. Once completed, the technology offers many other hidden pictures for students to uncover in which they will have to identify even more geometric characteristics and properties.
How does it fit within existing school curriculum?
This applet is to be used as a supplement to a secondary geometry unit. This is not meant to teach students about the characteristics or properties of geometric shapes, but rather tests their knowledge. Thus this program can be used as an assessment piece for students to show their geometric knowledge. Older grades (late-secondary, high school) could use the program to review prior knowledge.
How does the technology fit or interact with the social context of learning?
This activity can be done individually or with a partner, depending on a teacher’s preference. As noted above, this applet can be of great use as an assessment piece for representing student knowledge, but it could also promote strong mathematical discussions about geometry if done in pairs. If a student misunderstood the meaning of an equilateral triangle, having a partner to work with would help clear up any misconceptions or confusions through social interaction. Also, pairing students who are struggling with the characteristics and properties of geometric shapes would be beneficial in allowing them to discuss answers together before making choices.
What do teachers and learners need to know?
Once the students discover the hidden picture, there is little replay value. While the technology offers students the opportunity to uncover a different picture, it does repeat a lot of the same geometric shapes. For instance, in the span of three games I had to identify a pentagon in all three games. For some students the reinforcement may be beneficial, but for most it will probably be repetitive and tiresome.
http://www.aplusmath.com/cgi-bin/games/geopicture
Description
This technology is a geometry applet for students whose main goal is to identify geometric shapes based on their characteristics and properties in order to reveal pieces to a hidden picture. Students are successful when correctly identify the given geometric figures and they completely uncover the mystery picture that was hidden.
Evaluation
What mathematics is (potentially) being learned?
NCTM Standard(s) addressed?
- Geometry, 6-8: Students will be able to analyze characteristics and properties of two-dimensional shapes.
What is the nature of the mathematics?
The concepts being shown are analyzing the geometric characteristics and properties of two-dimensional shapes. Students are analyzing given shapes for specific characteristics and properties in order to successfully identify them by their geometric name.
How does learning take place?
Learning takes place as students try to identify the characteristics and properties of two-dimensional shapes. For example, if a student must find the shape of an obtuse triangle, students will have to analyze the given shapes for the properties and characteristics that are indicative of an obtuse triangle. Misconceptions can also be cleared up as students use the technology. If a student had the misconception that an equilateral triangle had only two congruent sides, by clicking an isosceles triangle students would be able to see that they were incorrect and had to fix their definition of what equilateral meant. Through analysis and reflection, significant learning can take place.
What role does technology play?
The technology affords students the chance to represent their geometric knowledge and thinking by identifying the correct properties and characteristics of two-dimensional shapes in order to reveal a hidden picture.
The technology will ask students to identify a particular geometric shape or characteristic (a right triangle, a radius, parallel lines, etc.). Students will then click on the shape they feel is best representative of what the applet is asking them to identify. If the student answers correctly, a piece of the missing picture is revealed. An incorrect answer by the student will result in another question and no piece revealed. The student “wins” when the hidden picture is revealed. Once completed, the technology offers many other hidden pictures for students to uncover in which they will have to identify even more geometric characteristics and properties.
How does it fit within existing school curriculum?
This applet is to be used as a supplement to a secondary geometry unit. This is not meant to teach students about the characteristics or properties of geometric shapes, but rather tests their knowledge. Thus this program can be used as an assessment piece for students to show their geometric knowledge. Older grades (late-secondary, high school) could use the program to review prior knowledge.
How does the technology fit or interact with the social context of learning?
This activity can be done individually or with a partner, depending on a teacher’s preference. As noted above, this applet can be of great use as an assessment piece for representing student knowledge, but it could also promote strong mathematical discussions about geometry if done in pairs. If a student misunderstood the meaning of an equilateral triangle, having a partner to work with would help clear up any misconceptions or confusions through social interaction. Also, pairing students who are struggling with the characteristics and properties of geometric shapes would be beneficial in allowing them to discuss answers together before making choices.
What do teachers and learners need to know?
Once the students discover the hidden picture, there is little replay value. While the technology offers students the opportunity to uncover a different picture, it does repeat a lot of the same geometric shapes. For instance, in the span of three games I had to identify a pentagon in all three games. For some students the reinforcement may be beneficial, but for most it will probably be repetitive and tiresome.
Stick or Switch
http://nlvm.usu.edu/en/nav/frames_asid_117_g_3_t_5.html?from=category_g_3_t_5.html
Description
This program is a math version of the old game show, “Let’s Make a Deal” in which students have the choice of one of three doors, but behind only one of them is the grand prize. The object of the program is to showcase that by staying with your initial choice throughout the game (not switching your pick), you have lowered your probability of winning. The greater probability of winning is when students switch their picks after the first door is revealed. This program is centered on discovery based learning and potential for stimulating discussion on probability.
Evaluation
What mathematics is (potentially) being learned?
NCTM Standard(s) addressed?
- Data Analysis and Probability, 6-8: Students will be able to collect and analyze data in order to formulate questions about probability.
What is the nature of the mathematics?
The main concept addressed with this program is probability. Students are working with fractions to represent probabilities: “There is a 1/3 chance of getting the grand prize by sticking with my initial choice.” Students are also analyzing data their ‘wins’ and ‘losses’ from a table that is provided by the technology in order to determine the best method, or the highest probability, for getting the grand prize.
How does learning take place?
The technology uses its own version of “Let’s Make a Deal” to show students that being aware of probabilities of events can be beneficial in situations. Students, by trial and experimentation, discover that by switching their first choice of prize to the alternate choice actually increases their chances of winning the grand prize. As students begin to make this discovering, there is a set of questions that students can answer in the “strategy” portion of the game that help bring their findings to light. This experimentation and reflection is the basis for a potential discussion on probability and how having a great probability means a more likely chance. The discussion can also build to why switching their first choice of prize to the alternate has a higher chance of probability.
What role does technology play?
This technology affords students the opportunity to communicate and collaborate with peers, as well as provides access to information and automates tasks to support student learning. The technology purpose is to serve as a jumping point for a discussion about probability, using created data from the game “Let’s Make a Deal” as a basis. Because of this, the technology provides access to information for students about probability in a “strategy” portion of the program and it keeps track of student data by automatically updating a chart that displays whether the student “won” or loss. This way the students are better informed and can focus on communication and collaboration.
How does it fit within existing school curriculum?
This program would be a beneficial supplement to be used in any probability or data analysis unit. It could be a great pre-assessment tool for teachers to see what knowledge of probability their students currently have.
How does the technology fit or interact with the social context of learning?
The technology’s biggest draw is the fact that it isn’t meant to assess or necessarily teach students about probability, but rather to promote discussion amongst peers and as a class. The technology offers a jumping point for debate: Is it better to stick with your original choice of door, or change it midway through the process? By using the technology the students can bolster their explanations and knowledge to make meaningful contributions to a discussion on probability.
What do teachers and learners need to know?
Some students may not be familiar with the game, “Let’s Make a Deal.” Therefore it might be beneficial for teachers to explain how the game works in detail before kids use the technology and become confused with the directions or objective.
http://nlvm.usu.edu/en/nav/frames_asid_117_g_3_t_5.html?from=category_g_3_t_5.html
Description
This program is a math version of the old game show, “Let’s Make a Deal” in which students have the choice of one of three doors, but behind only one of them is the grand prize. The object of the program is to showcase that by staying with your initial choice throughout the game (not switching your pick), you have lowered your probability of winning. The greater probability of winning is when students switch their picks after the first door is revealed. This program is centered on discovery based learning and potential for stimulating discussion on probability.
Evaluation
What mathematics is (potentially) being learned?
NCTM Standard(s) addressed?
- Data Analysis and Probability, 6-8: Students will be able to collect and analyze data in order to formulate questions about probability.
What is the nature of the mathematics?
The main concept addressed with this program is probability. Students are working with fractions to represent probabilities: “There is a 1/3 chance of getting the grand prize by sticking with my initial choice.” Students are also analyzing data their ‘wins’ and ‘losses’ from a table that is provided by the technology in order to determine the best method, or the highest probability, for getting the grand prize.
How does learning take place?
The technology uses its own version of “Let’s Make a Deal” to show students that being aware of probabilities of events can be beneficial in situations. Students, by trial and experimentation, discover that by switching their first choice of prize to the alternate choice actually increases their chances of winning the grand prize. As students begin to make this discovering, there is a set of questions that students can answer in the “strategy” portion of the game that help bring their findings to light. This experimentation and reflection is the basis for a potential discussion on probability and how having a great probability means a more likely chance. The discussion can also build to why switching their first choice of prize to the alternate has a higher chance of probability.
What role does technology play?
This technology affords students the opportunity to communicate and collaborate with peers, as well as provides access to information and automates tasks to support student learning. The technology purpose is to serve as a jumping point for a discussion about probability, using created data from the game “Let’s Make a Deal” as a basis. Because of this, the technology provides access to information for students about probability in a “strategy” portion of the program and it keeps track of student data by automatically updating a chart that displays whether the student “won” or loss. This way the students are better informed and can focus on communication and collaboration.
How does it fit within existing school curriculum?
This program would be a beneficial supplement to be used in any probability or data analysis unit. It could be a great pre-assessment tool for teachers to see what knowledge of probability their students currently have.
How does the technology fit or interact with the social context of learning?
The technology’s biggest draw is the fact that it isn’t meant to assess or necessarily teach students about probability, but rather to promote discussion amongst peers and as a class. The technology offers a jumping point for debate: Is it better to stick with your original choice of door, or change it midway through the process? By using the technology the students can bolster their explanations and knowledge to make meaningful contributions to a discussion on probability.
What do teachers and learners need to know?
Some students may not be familiar with the game, “Let’s Make a Deal.” Therefore it might be beneficial for teachers to explain how the game works in detail before kids use the technology and become confused with the directions or objective.
Cabri Jr.: Exploring the Diameter and Circumference of a Circle
http://education.ti.com/educationportal/activityexchange/Activity.do?cid=US&aId=6865
Description
Students will be learning how pi is determined and its relationship to the circumference and diameter of a circle using a graphing calculator. Students will also be learning how to correctly graph circles, measure and draw a circle’s diameter, and measure a circle’s circumference using the Cabri Jr. program on the TI-84 calculator.
Evaluation
What mathematics is (potentially) being learned?
NCTM Standard(s) addressed?
-Geometry, Grades 6-8: Students will use visualization (drawing geometric objects with specified properties) and analyze characteristics to understand relationships.
What is the nature of the mathematics?
This program allows students to discover the origination of the number, pi, through discovery-based learning. Using Cabri Jr., students must create a circle and manipulate the length of its circumference and diameter in order to examine the ratios that exist that show the originations of pi.
How does learning take place?
The learning takes place as students examine different measures of different circles and begin to explore the relationship between the diameters and circumferences of each. Students are also learning how to construct circles using a graphing calculator. In higher level math classes in high school and beyond many students will use graphing calculators regularly in their classrooms. It’s important that students not only know how to use the basic functions on a graphing calculator, but to also be able to explore some of the more advanced functions available.
What role does technology play?
The Cabri Jr. program offers two types of affordances of technology that support student learning. One is that it automates, simplifies, and transforms tasks. This is evident in the construction of circles, as well as the measuring of the diameter and circumference. Students do not have to spend time creating circles using compasses and measuring lengths with tape measures, as the task is done by the command of the student in the program. This also ensures accurate measurements and “perfectly” constructed circles by all students in the classroom. A second affordance is that Cabri Jr. represents knowledge and thinking. The Cabri Jr. program is on a graphing calculator, which allows students to display constructed circles, diameters, and measurements. Cabri Jr. provides the opportunity for students to show their abilities to create and measure circles, thus showing their knowledge of the properties of a circle, as well as their abilities to use Cabri Jr. and the graphing calculator effectively.
How does it fit within existing school curriculum?
This technology is not intended to replace any current technologies or curriculum designs. It is to be used by teachers and students as a resource for uncovering the derivation of pi, and therefore should be used by teachers and students as a supplement to an existing curriculum unit on geometry. It offers a new and different avenue for learning that is engaging and exciting for students, and could be useful for any secondary and high school classroom.
How does the technology fit or interact with the social context of learning?
This is an activity done individually, but does allow for some group collaboration in the sharing of data, results, and ideas. The technology is a tool used to promote learning, and it is the responsibility of the teacher to use the technology in the manner most beneficial to their particular classroom.
What do teachers and learners need to know?
There is an assumption that students are already familiar with the basic uses and functions of the graphing calculator (they know where the buttons are) and have worked in Cabri Jr. in previous classroom activities (This is not an activity intended for a class that has not used graphing calculators before). Students must also know relevant terms, like circle, diameter, circumference, pi, and measure. These are all terms that students have used in prior elementary grade levels, but may need refreshing before starting this activity.
What is also missing from the technology, however, is any sort of table or place to record results, make and write conjectures, and explore conclusions. This is something neither the website nor the technology provides, and is imperative to include with the lesson, as it is difficult for student learning to occur without careful examination of the relationships between multiple circles. The technology can only allow students to construct one circle at a time in its viewing window, and while it allows for the manipulation of that circle (the changing of its size), it does not allow multiple circles to be represented simultaneously. Because of which, a resource to record observations and data is needed. As stated in the PSSM, “With well-designed activities, appropriate tools, and teachers' support, students can make and explore conjectures about geometry and can learn to reason carefully about geometric ideas.” The Cabri Jr. technology offers an appropriate tool, but the teacher still needs to offer the support so students learning can occur and for the activity to be well-designed.
http://education.ti.com/educationportal/activityexchange/Activity.do?cid=US&aId=6865
Description
Students will be learning how pi is determined and its relationship to the circumference and diameter of a circle using a graphing calculator. Students will also be learning how to correctly graph circles, measure and draw a circle’s diameter, and measure a circle’s circumference using the Cabri Jr. program on the TI-84 calculator.
Evaluation
What mathematics is (potentially) being learned?
NCTM Standard(s) addressed?
-Geometry, Grades 6-8: Students will use visualization (drawing geometric objects with specified properties) and analyze characteristics to understand relationships.
What is the nature of the mathematics?
This program allows students to discover the origination of the number, pi, through discovery-based learning. Using Cabri Jr., students must create a circle and manipulate the length of its circumference and diameter in order to examine the ratios that exist that show the originations of pi.
How does learning take place?
The learning takes place as students examine different measures of different circles and begin to explore the relationship between the diameters and circumferences of each. Students are also learning how to construct circles using a graphing calculator. In higher level math classes in high school and beyond many students will use graphing calculators regularly in their classrooms. It’s important that students not only know how to use the basic functions on a graphing calculator, but to also be able to explore some of the more advanced functions available.
What role does technology play?
The Cabri Jr. program offers two types of affordances of technology that support student learning. One is that it automates, simplifies, and transforms tasks. This is evident in the construction of circles, as well as the measuring of the diameter and circumference. Students do not have to spend time creating circles using compasses and measuring lengths with tape measures, as the task is done by the command of the student in the program. This also ensures accurate measurements and “perfectly” constructed circles by all students in the classroom. A second affordance is that Cabri Jr. represents knowledge and thinking. The Cabri Jr. program is on a graphing calculator, which allows students to display constructed circles, diameters, and measurements. Cabri Jr. provides the opportunity for students to show their abilities to create and measure circles, thus showing their knowledge of the properties of a circle, as well as their abilities to use Cabri Jr. and the graphing calculator effectively.
How does it fit within existing school curriculum?
This technology is not intended to replace any current technologies or curriculum designs. It is to be used by teachers and students as a resource for uncovering the derivation of pi, and therefore should be used by teachers and students as a supplement to an existing curriculum unit on geometry. It offers a new and different avenue for learning that is engaging and exciting for students, and could be useful for any secondary and high school classroom.
How does the technology fit or interact with the social context of learning?
This is an activity done individually, but does allow for some group collaboration in the sharing of data, results, and ideas. The technology is a tool used to promote learning, and it is the responsibility of the teacher to use the technology in the manner most beneficial to their particular classroom.
What do teachers and learners need to know?
There is an assumption that students are already familiar with the basic uses and functions of the graphing calculator (they know where the buttons are) and have worked in Cabri Jr. in previous classroom activities (This is not an activity intended for a class that has not used graphing calculators before). Students must also know relevant terms, like circle, diameter, circumference, pi, and measure. These are all terms that students have used in prior elementary grade levels, but may need refreshing before starting this activity.
What is also missing from the technology, however, is any sort of table or place to record results, make and write conjectures, and explore conclusions. This is something neither the website nor the technology provides, and is imperative to include with the lesson, as it is difficult for student learning to occur without careful examination of the relationships between multiple circles. The technology can only allow students to construct one circle at a time in its viewing window, and while it allows for the manipulation of that circle (the changing of its size), it does not allow multiple circles to be represented simultaneously. Because of which, a resource to record observations and data is needed. As stated in the PSSM, “With well-designed activities, appropriate tools, and teachers' support, students can make and explore conjectures about geometry and can learn to reason carefully about geometric ideas.” The Cabri Jr. technology offers an appropriate tool, but the teacher still needs to offer the support so students learning can occur and for the activity to be well-designed.
Function Machine
http://nlvm.usu.edu/en/nav/frames_asid_191_g_3_t_2.html?from=category_g_3_t_2.html
Description
This technology plays to the common metaphor that functions are like “machines”- you put a number in (input), you get a number out (output). This applet allows students to put a given set of numbers into the function “machine” and have the machine generate an output. Students must also try and decipher the function “rule” in order to determine missing outputs for inputs.
Evaluation
What mathematics is (potentially) being learned?
NCTM Standard(s) addressed?
-Algebra, 6-8: Students will be able to understand patterns, relations, and functions through analysis of data and input-output tables.
What is the nature of the mathematics?
The main concept being shown is functions. Students are going to recognize functions as “machines” that process inputs and outputs. Students will also become familiar with reading and using an input-output table and analyzing an input-output table for patterns.
How does learning take place?
Learning takes place as students begin to analyze the outputs of the function machine for patterns. Using the input-output table, students have the opportunity to analyze the values the function machine has produced. By doing this, a pattern will begin to emerge (for example, for every input, the output is the input plus three). Using this pattern will help determine the nature of the function and allow the students to figure out the three missing outputs that are omitted from the input-output table. By analyzing the function’s data, examining relationships between the inputs and outputs, and recognizing patterns, student learning of functions can occur.
What role does technology play?
This technology allows students to physically move inputs into the function machine. This plays to the metaphor of functions being a “machine” as it brings the metaphor to life. The technology also generates the outputs for the student, and places both the inputs and outputs into an input-output table that is presented. The applet also allows for students to enter the values for three missing outputs in the table, which the students must determine from the pattern of the function.
This technology affords students the opportunity to represent knowledge and thinking based upon the student’s ability to show the recognition of a function’s pattern by naming the three missing outputs to the applet’s function. The technology also automates and simplifies the task, as students do not have to do any work in figuring out the first four outputs of the input-output table (the function machine does that for them) and do not have to fill out must of the input-output table (the applet fills out the first four input-output pairs for the students).
How does it fit within existing school curriculum?
This technology works well as an introduction to functions. Students in secondary schools will see this technology as beneficial as they are familiar with functions being termed “machines”. This applet would crystallize this image for them, as well as provide an engaging and interactive activity for students to practice recognizing patterns, filling out input-output tables, and learning about functions. This technology is to be used as a supplement to algebra lessons dealing with patterns and functions.
How does the technology fit or interact with the social context of learning?
There are some functions that involve non-numeric outputs. For example, in one particular function an input of ‘one’ will result in an output of ‘F’. This abstract thinking tests students’ abilities to think outside the box as well as think critically about patterns. Because some of the patterns aren’t as easily recognizable as others, for beginning classes first dealing with functions, it is recommended that students pair together and work with this function machine together.
What do teachers and learners need to know?
An understanding of functions is a must for students. This technology is not to be used as an introduction to a unit or the concept of functions, but rather as an assessment or skill builder. It is important for students to understand the terminology associated with functions to give this technology more meaning and purpose.
http://nlvm.usu.edu/en/nav/frames_asid_191_g_3_t_2.html?from=category_g_3_t_2.html
Description
This technology plays to the common metaphor that functions are like “machines”- you put a number in (input), you get a number out (output). This applet allows students to put a given set of numbers into the function “machine” and have the machine generate an output. Students must also try and decipher the function “rule” in order to determine missing outputs for inputs.
Evaluation
What mathematics is (potentially) being learned?
NCTM Standard(s) addressed?
-Algebra, 6-8: Students will be able to understand patterns, relations, and functions through analysis of data and input-output tables.
What is the nature of the mathematics?
The main concept being shown is functions. Students are going to recognize functions as “machines” that process inputs and outputs. Students will also become familiar with reading and using an input-output table and analyzing an input-output table for patterns.
How does learning take place?
Learning takes place as students begin to analyze the outputs of the function machine for patterns. Using the input-output table, students have the opportunity to analyze the values the function machine has produced. By doing this, a pattern will begin to emerge (for example, for every input, the output is the input plus three). Using this pattern will help determine the nature of the function and allow the students to figure out the three missing outputs that are omitted from the input-output table. By analyzing the function’s data, examining relationships between the inputs and outputs, and recognizing patterns, student learning of functions can occur.
What role does technology play?
This technology allows students to physically move inputs into the function machine. This plays to the metaphor of functions being a “machine” as it brings the metaphor to life. The technology also generates the outputs for the student, and places both the inputs and outputs into an input-output table that is presented. The applet also allows for students to enter the values for three missing outputs in the table, which the students must determine from the pattern of the function.
This technology affords students the opportunity to represent knowledge and thinking based upon the student’s ability to show the recognition of a function’s pattern by naming the three missing outputs to the applet’s function. The technology also automates and simplifies the task, as students do not have to do any work in figuring out the first four outputs of the input-output table (the function machine does that for them) and do not have to fill out must of the input-output table (the applet fills out the first four input-output pairs for the students).
How does it fit within existing school curriculum?
This technology works well as an introduction to functions. Students in secondary schools will see this technology as beneficial as they are familiar with functions being termed “machines”. This applet would crystallize this image for them, as well as provide an engaging and interactive activity for students to practice recognizing patterns, filling out input-output tables, and learning about functions. This technology is to be used as a supplement to algebra lessons dealing with patterns and functions.
How does the technology fit or interact with the social context of learning?
There are some functions that involve non-numeric outputs. For example, in one particular function an input of ‘one’ will result in an output of ‘F’. This abstract thinking tests students’ abilities to think outside the box as well as think critically about patterns. Because some of the patterns aren’t as easily recognizable as others, for beginning classes first dealing with functions, it is recommended that students pair together and work with this function machine together.
What do teachers and learners need to know?
An understanding of functions is a must for students. This technology is not to be used as an introduction to a unit or the concept of functions, but rather as an assessment or skill builder. It is important for students to understand the terminology associated with functions to give this technology more meaning and purpose.
Arithmetic Four
http://www.shodor.org/interactivate/activities/ArithmeticFour/
Description
This applet provides students with a game that is very similar to “Connect Four” in which students are doing computations in order to get game pieces in which they can play on a virtual game board to get “four in a row”. This multiplayer game allows for students to compete against one another while practicing computational skills with both whole numbers and integers.
Evaluation
What mathematics is (potentially) being learned?
NCTM Standard(s) addressed?
-Numbers and Operations, 6-8: Students will be able to compute fluently using addition, subtraction, multiplication, division with both whole numbers and integers.
What is the nature of the mathematics?
This applet allows students to show their understanding of the basic operations by computing given problems. The program allows students to not only practice their computational skills, but to also compete against a friend in a competitive game manner. There is also a time limit placed on problems, so it is important that students begin to show the ability of being able to do computations in a reasonable time frame.
How does learning take place?
This applet is a technology designed for practice in the basic computations of integers and whole numbers. The type of operation and level of difficulty can be adjusted for each new game; however, both players must play at the same level/with the same type of operation. Users may add, subtract, multiply or divide with only whole numbers or with positive/negative integers. In general there is only enough time to use mental math when computing, so users are practicing their mental strategies for computing.
What role does technology play?
This technology affords students the opportunity to collaborate with their peers and represent their knowledge on adding, subtracting, multiplying, and dividing integers through an interactive version of the game "Connect Four". Students take turns solving given problems in order to receive game pieces that will allow them to attempt to get "four in a row" in order to win the game. The applet also allows teachers the opportunity to discuss integer operations with students, while also providing access to various integer computation worksheets and activities. This technology automates and simplifies the process of playing a flashcard-type math game. It provides the math problems, and can be customized to the desired level/need of the players.
How does it fit within existing school curriculum?
This technology would fit wonderfully into a secondary or high school math curriculum. At the secondary level students are beginning to work with integers, with a focus on being able to compute fluently with negative numbers. As stated in the NCTM’s standard for Numbers and Operations Grades 6-8, students, “should also develop and adapt procedures for mental calculation and computational estimation with fractions, decimals, and integers.” This applet is a practice tool for doing quick, mental math computations with integers.
How does the technology fit or interact with the social context of learning?
This is a multiplayer game that involves two students, thus communication and collaboration is a key element of this technology. Being able to discuss methods and solutions when doing whole number and integer computations, even in a competitive game setting, is beneficial to the students in becoming fluent in their computational skills. It also makes the technology more engaging, as it provides interaction not only with the applet, but with a fellow peer as well.
How are important differences among learners taken into account?
The technology is separated into categories, which allows players the opportunity to work on computations with whole numbers, or with integers. Students can choose the level they feel most comfortable with, or the level in which they need the most practice. Varying game levels means increased levels of participation from classrooms with differing levels of ability. Since the technology itself determines correct or incorrect answers, as well as if an answer was given in time, this removes the need for a 3rd party referee or the need for one of the players to know the correct answer.
What do teachers and learners need to know?
Students need to have a basic understanding of integer operation rules. Without the previous knowledge of such rules it would be difficult for any student have success while playing the game or for the technology to have any real meaning to the student. Teachers must make students aware of the differences between doing computations with whole numbers and computations with integers.
http://www.shodor.org/interactivate/activities/ArithmeticFour/
Description
This applet provides students with a game that is very similar to “Connect Four” in which students are doing computations in order to get game pieces in which they can play on a virtual game board to get “four in a row”. This multiplayer game allows for students to compete against one another while practicing computational skills with both whole numbers and integers.
Evaluation
What mathematics is (potentially) being learned?
NCTM Standard(s) addressed?
-Numbers and Operations, 6-8: Students will be able to compute fluently using addition, subtraction, multiplication, division with both whole numbers and integers.
What is the nature of the mathematics?
This applet allows students to show their understanding of the basic operations by computing given problems. The program allows students to not only practice their computational skills, but to also compete against a friend in a competitive game manner. There is also a time limit placed on problems, so it is important that students begin to show the ability of being able to do computations in a reasonable time frame.
How does learning take place?
This applet is a technology designed for practice in the basic computations of integers and whole numbers. The type of operation and level of difficulty can be adjusted for each new game; however, both players must play at the same level/with the same type of operation. Users may add, subtract, multiply or divide with only whole numbers or with positive/negative integers. In general there is only enough time to use mental math when computing, so users are practicing their mental strategies for computing.
What role does technology play?
This technology affords students the opportunity to collaborate with their peers and represent their knowledge on adding, subtracting, multiplying, and dividing integers through an interactive version of the game "Connect Four". Students take turns solving given problems in order to receive game pieces that will allow them to attempt to get "four in a row" in order to win the game. The applet also allows teachers the opportunity to discuss integer operations with students, while also providing access to various integer computation worksheets and activities. This technology automates and simplifies the process of playing a flashcard-type math game. It provides the math problems, and can be customized to the desired level/need of the players.
How does it fit within existing school curriculum?
This technology would fit wonderfully into a secondary or high school math curriculum. At the secondary level students are beginning to work with integers, with a focus on being able to compute fluently with negative numbers. As stated in the NCTM’s standard for Numbers and Operations Grades 6-8, students, “should also develop and adapt procedures for mental calculation and computational estimation with fractions, decimals, and integers.” This applet is a practice tool for doing quick, mental math computations with integers.
How does the technology fit or interact with the social context of learning?
This is a multiplayer game that involves two students, thus communication and collaboration is a key element of this technology. Being able to discuss methods and solutions when doing whole number and integer computations, even in a competitive game setting, is beneficial to the students in becoming fluent in their computational skills. It also makes the technology more engaging, as it provides interaction not only with the applet, but with a fellow peer as well.
How are important differences among learners taken into account?
The technology is separated into categories, which allows players the opportunity to work on computations with whole numbers, or with integers. Students can choose the level they feel most comfortable with, or the level in which they need the most practice. Varying game levels means increased levels of participation from classrooms with differing levels of ability. Since the technology itself determines correct or incorrect answers, as well as if an answer was given in time, this removes the need for a 3rd party referee or the need for one of the players to know the correct answer.
What do teachers and learners need to know?
Students need to have a basic understanding of integer operation rules. Without the previous knowledge of such rules it would be difficult for any student have success while playing the game or for the technology to have any real meaning to the student. Teachers must make students aware of the differences between doing computations with whole numbers and computations with integers.
Circle 0
http://nlvm.usu.edu/en/nav/frames_asid_122_g_3_t_1.html?open=instructions&from=topic_t_1.html
Description
The purpose of this applet is to promote addition, logic, and problem solving skills. The goal of the activity is to find sums of 21 using the integers that are given in a set of circles that are intertwined. Students who successfully can makes sums of 21 in each of the circles complete the activity.
Evaluation
What mathematics is (potentially) being learned?
NCTM Standard(s) addressed?
-Numbers and Operations, 6-8: Students will be able to compute integers fluently using addition skills.
-Problem Solving, 6-8: Students will be able to apply and reflect on strategies that help solve a mathematical problem (Circle 21).
-Reasoning and Proof, 6-8: Students will be able to make and investigate mathematical conjectures by reasoning which numbers would be best to make 21 in a given circle and then testing said conjectures.
What is the nature of the mathematics?
This program crosses multiple standards set forth by the NCTM. While on the surface the game appears to only be a simple addition game with integers, there is much more mathematics involved than at first glance. Students are practicing “logic analysis” by making examining the set of numbers that are given in order to determine the best placement for each number in a circle. Students are also using reasoning skills (“Well if I put a -3 here, then I have to put a four there.”) while solving the problem.
How does learning take place?
Learning takes place as students begin to investigate their conjecture on what three numbers it would take to make circle’s sum zero. Students are making and testing conjectures while analyzing the results to figure out the correct solution to the puzzle. With continued practice of integer addition skills the puzzle provides, students will begin to increase their computational fluency with integer computations.
What role does technology play?
This applet allows students to show and test their knowledge of adding integers while also allowing students to apply logic and reasoning skills to solve a mathematical puzzle.
This applet is a fun and challenging way for students to practice adding integers in a game/puzzle format. When students are able to make twenty-one in a circle by dragging the given numbers into a circle, the technology turns the circle a tan color, representing the students were correct in making twenty-one. When all the intertwining circles have twenty-one inside of them, the technology turns all the circles red, meaning the students have won the game. The technology also provides students with multiple “Circle 0” games, meaning students who finish one can move onto another, or if a student is stuck on one game can try a different one.
How does it fit within existing school curriculum?
This technology would work well in a secondary setting as students practice their adding of integer skills, as well as their problem solving and logic skills. This program is not designed to teach students how to add integers or think logically, and does not offer any hints on how to solve the puzzle, but it does allow student to practice all these skills in fun and engaging format. Hence the technology should be used as a supplement to an existing curriculum and unit on integer computation.
How does the technology fit or interact with the social context of learning?
The technology is designed to be done individually, however the applet could be used as a partner activity. As suggested on the “teacher page” of the applet, students could partner together and “race” against one another to see who can make zero the fastest. This would allow interaction to occur as well as motivation when completing the puzzle.
How are important differences among learners taken into account?
For students that struggle with integer addition, there are two similar applets, “Circle 21” and “Circle 99” that follow the same rules as “Circle 0”, but allow students to work with adding just whole numbers (smaller whole numbers in “Circle 21”, larger whole numbers in “Circle 99”). While students are not increasing their computational fluency by adding integers, they are still applying problem solving strategies as well as logic and reasoning skills, making the activity worthwhile.
What do teachers and learners need to know?
Because this activity involves doing a lot of computations, it is recommended that student come prepared with a paper and pencil to work out computations. The applet does not provide a calculator or any place to work through computations. Students that try to do the math mentally may open themselves up for more mistakes, so depending on the level of student the teacher should make sure that the students have a pencil and paper handy.
http://nlvm.usu.edu/en/nav/frames_asid_122_g_3_t_1.html?open=instructions&from=topic_t_1.html
Description
The purpose of this applet is to promote addition, logic, and problem solving skills. The goal of the activity is to find sums of 21 using the integers that are given in a set of circles that are intertwined. Students who successfully can makes sums of 21 in each of the circles complete the activity.
Evaluation
What mathematics is (potentially) being learned?
NCTM Standard(s) addressed?
-Numbers and Operations, 6-8: Students will be able to compute integers fluently using addition skills.
-Problem Solving, 6-8: Students will be able to apply and reflect on strategies that help solve a mathematical problem (Circle 21).
-Reasoning and Proof, 6-8: Students will be able to make and investigate mathematical conjectures by reasoning which numbers would be best to make 21 in a given circle and then testing said conjectures.
What is the nature of the mathematics?
This program crosses multiple standards set forth by the NCTM. While on the surface the game appears to only be a simple addition game with integers, there is much more mathematics involved than at first glance. Students are practicing “logic analysis” by making examining the set of numbers that are given in order to determine the best placement for each number in a circle. Students are also using reasoning skills (“Well if I put a -3 here, then I have to put a four there.”) while solving the problem.
How does learning take place?
Learning takes place as students begin to investigate their conjecture on what three numbers it would take to make circle’s sum zero. Students are making and testing conjectures while analyzing the results to figure out the correct solution to the puzzle. With continued practice of integer addition skills the puzzle provides, students will begin to increase their computational fluency with integer computations.
What role does technology play?
This applet allows students to show and test their knowledge of adding integers while also allowing students to apply logic and reasoning skills to solve a mathematical puzzle.
This applet is a fun and challenging way for students to practice adding integers in a game/puzzle format. When students are able to make twenty-one in a circle by dragging the given numbers into a circle, the technology turns the circle a tan color, representing the students were correct in making twenty-one. When all the intertwining circles have twenty-one inside of them, the technology turns all the circles red, meaning the students have won the game. The technology also provides students with multiple “Circle 0” games, meaning students who finish one can move onto another, or if a student is stuck on one game can try a different one.
How does it fit within existing school curriculum?
This technology would work well in a secondary setting as students practice their adding of integer skills, as well as their problem solving and logic skills. This program is not designed to teach students how to add integers or think logically, and does not offer any hints on how to solve the puzzle, but it does allow student to practice all these skills in fun and engaging format. Hence the technology should be used as a supplement to an existing curriculum and unit on integer computation.
How does the technology fit or interact with the social context of learning?
The technology is designed to be done individually, however the applet could be used as a partner activity. As suggested on the “teacher page” of the applet, students could partner together and “race” against one another to see who can make zero the fastest. This would allow interaction to occur as well as motivation when completing the puzzle.
How are important differences among learners taken into account?
For students that struggle with integer addition, there are two similar applets, “Circle 21” and “Circle 99” that follow the same rules as “Circle 0”, but allow students to work with adding just whole numbers (smaller whole numbers in “Circle 21”, larger whole numbers in “Circle 99”). While students are not increasing their computational fluency by adding integers, they are still applying problem solving strategies as well as logic and reasoning skills, making the activity worthwhile.
What do teachers and learners need to know?
Because this activity involves doing a lot of computations, it is recommended that student come prepared with a paper and pencil to work out computations. The applet does not provide a calculator or any place to work through computations. Students that try to do the math mentally may open themselves up for more mistakes, so depending on the level of student the teacher should make sure that the students have a pencil and paper handy.
Math Baseball
http://www.funbrain.com/math/
Description
This applet allows students to practice their addition, subtraction, multiplication, and division facts by performing basic computations. They are rewarded for correct answers (the harder the problem, the greater the reward- a home run, for example), and punished for an incorrect answer (an out) in a baseball game format.
Evaluation
What mathematics is (potentially) being learned?
NCTM Standard(s) addressed?
- Numbers and Operations, Grades 6-8: Students must be able to compute fluently to use this applet. Students must use appropriate methods for calculations.
What is the nature of the mathematics?
This program is designed for one or two students to practice their computations of whole numbers. The players may choose to do any of the four operations or a mixture of the four, on whole numbers only. For increased difficulty the players can choose algebra mode where the answer is given, but one of the factors/addends, etc. is missing. In the course of a game, a student will be given many practice problems, and can move on to harder levels or operations if the game becomes too easy.
How does learning take place?
Learning takes place through the continual practice of mathematical computations. Students will strengthen their computational skills through repeated practice. The applet provides a variety of problems with different operations which allows students to focus on more than just one particular operation. By also introducing basic algebra concepts, the applet is preparing students for higher-level computations.
What role does technology play?
The technology turns math computation into a competitive game. The applet allows students to participate in computational practice problems individually or with a partner by creating a math baseball game in which students answer questions correctly in order to get hits and runs. The game provides motivation to succeed in solving problems, as well as reinforces concepts learned in the classroom. It allows for a player to compete against the computer or another human player. It also allows players to instantly change the type of operation they’re playing with and the difficulty level. Little time is wasted on a skill that is too easy or too hard, with just a few clicks. The game can be adjusted to all students so that it is at an appropriate level.
This technology allows students to represent their knowledge of basic addition, subtraction, multiplication, and division computational problems in either an individual or peer setting. The game automates flash card practice, and gives instant feedback about correct/incorrect answers. It offers incentive for correct answers, as that is how the player advances in the game (around the base paths) and ultimately wins (scoring the most runs). The peer setting allows students to communicate while solving problems, even though they may be on opposite teams. They could confer about an answer before entering it- comparing methods of solving and having to justify to one another on how an answer was reached. Even without multiple players on a team, players view one another's successes and mistakes and are essentially getting twice the practice while only being responsible for half of the work.
How does it fit within existing school curriculum?
Computational practice can be a beneficial addition to any school’s curriculum. Students from of any age and grade level can benefit from increased practice. At the middle school level, according to the NCTM’s Numbers and Operations standard, students, "Students should also develop and adapt procedures for mental calculation". The "Math Baseball" applet is a valuable tool for achieving this goal.
How does the technology fit or interact with the social context of learning?
This technology could be used as a partner activity. The applet allows for peers to compete against one-another, allowing for collaboration. It may also be used for individual practice, perhaps for the student that is struggling with their computations and need the extra practice, or for the learner who finishes their work early and "needs something to do". It provides flexibility for the teacher as it offers two game modes that the teacher can use.
How are important differences among learners taken into account?
One of the most beneficial aspects of the game is that it allows for students to choose the most appropriate difficulty level. This allows for all levels of learners the ability to learn and be successful. The game won’t be "too hard" or "too easy" for any student in the classroom. It offers challenges to all students who play.
http://www.funbrain.com/math/
Description
This applet allows students to practice their addition, subtraction, multiplication, and division facts by performing basic computations. They are rewarded for correct answers (the harder the problem, the greater the reward- a home run, for example), and punished for an incorrect answer (an out) in a baseball game format.
Evaluation
What mathematics is (potentially) being learned?
NCTM Standard(s) addressed?
- Numbers and Operations, Grades 6-8: Students must be able to compute fluently to use this applet. Students must use appropriate methods for calculations.
What is the nature of the mathematics?
This program is designed for one or two students to practice their computations of whole numbers. The players may choose to do any of the four operations or a mixture of the four, on whole numbers only. For increased difficulty the players can choose algebra mode where the answer is given, but one of the factors/addends, etc. is missing. In the course of a game, a student will be given many practice problems, and can move on to harder levels or operations if the game becomes too easy.
How does learning take place?
Learning takes place through the continual practice of mathematical computations. Students will strengthen their computational skills through repeated practice. The applet provides a variety of problems with different operations which allows students to focus on more than just one particular operation. By also introducing basic algebra concepts, the applet is preparing students for higher-level computations.
What role does technology play?
The technology turns math computation into a competitive game. The applet allows students to participate in computational practice problems individually or with a partner by creating a math baseball game in which students answer questions correctly in order to get hits and runs. The game provides motivation to succeed in solving problems, as well as reinforces concepts learned in the classroom. It allows for a player to compete against the computer or another human player. It also allows players to instantly change the type of operation they’re playing with and the difficulty level. Little time is wasted on a skill that is too easy or too hard, with just a few clicks. The game can be adjusted to all students so that it is at an appropriate level.
This technology allows students to represent their knowledge of basic addition, subtraction, multiplication, and division computational problems in either an individual or peer setting. The game automates flash card practice, and gives instant feedback about correct/incorrect answers. It offers incentive for correct answers, as that is how the player advances in the game (around the base paths) and ultimately wins (scoring the most runs). The peer setting allows students to communicate while solving problems, even though they may be on opposite teams. They could confer about an answer before entering it- comparing methods of solving and having to justify to one another on how an answer was reached. Even without multiple players on a team, players view one another's successes and mistakes and are essentially getting twice the practice while only being responsible for half of the work.
How does it fit within existing school curriculum?
Computational practice can be a beneficial addition to any school’s curriculum. Students from of any age and grade level can benefit from increased practice. At the middle school level, according to the NCTM’s Numbers and Operations standard, students, "Students should also develop and adapt procedures for mental calculation". The "Math Baseball" applet is a valuable tool for achieving this goal.
How does the technology fit or interact with the social context of learning?
This technology could be used as a partner activity. The applet allows for peers to compete against one-another, allowing for collaboration. It may also be used for individual practice, perhaps for the student that is struggling with their computations and need the extra practice, or for the learner who finishes their work early and "needs something to do". It provides flexibility for the teacher as it offers two game modes that the teacher can use.
How are important differences among learners taken into account?
One of the most beneficial aspects of the game is that it allows for students to choose the most appropriate difficulty level. This allows for all levels of learners the ability to learn and be successful. The game won’t be "too hard" or "too easy" for any student in the classroom. It offers challenges to all students who play.
Dividing Fractions by Fractions
http://www.321know.com/div66ox2.htm
Description
This applet provides practice of dividing fractions by fractions using the division of fractions algorithm. The program offers a small explanation on how to divide fractions by fractions, as well as three “game” settings that allows students to practice dividing fractions by fractions against a timer.
Evaluation
What mathematics is (potentially) being learned?
NCTM Standard(s) addressed?
-Numbers and Operations, 6-8: Students will be able to analyze the algorithm necessary for division of fractions. Students will also be able to “work flexibly” with fractions to understand fraction computation problems and to increase computational fluency.
What is the nature of the mathematics?
Students will be dividing fractions by fractions. Students must be able to apply the algorithm for dividing fractions correctly, while also being able to multiply fractions and simplify fractions completely. The combination of these skills is a must, as the applet does not go into any explanations of why a student is incorrect if they get an answer wrong.
How does learning take place?
This applet focuses solely on the division of fractions by other fractions. It tells students to use the algorithm of inverting the second fraction, then multiplying numerators and denominators to get a fraction as their answer. They should then simplify the answer by dividing numerator and denominator by a common factor, until it is reduced completely.
What role does technology play?
This technology allows students access to information on how to divide fractions by fractions. After reading, students have the opportunity to represent their knowledge of dividing fractions by fractions by answering questions against a timer.
This technology gives students a chance to learn/review how to divide fractions by fractions using an algorithm. It also gives students the opportunity to play games that involve solving dividing fraction by fraction problems against a timer. The technology is used to give instant feedback for practicing fraction division. It is also used to motivate students to increase their efficiency with this computation.
How does it fit within existing school curriculum?
This program would fit nicely into a fraction unit. It is not meant to teach students the concept of dividing fractions, but it does offer practice problems for students to increase their computational fluency. It is meant to be used as a supplement to fraction units. It is also important to recognize that the program does not show ‘why’ the algorithm of dividing fractions works, so it may be less useful for those classrooms unfamiliar with the concept of dividing fractions (early secondary).
How does the technology fit or interact with the social context of learning?
I have personally used this applet as a whole-class group experience. I set a goal for my students using the timer application the program has. I may challenge my class to see if they can solve 20 problems in less than 3 minutes. When I start the timer, students try and solve the problems and I will randomly choose a student to give me the answer, from which I will plug into my computer to see if they’re right. I have the whole program displayed using an LCD projector, so students can visually see the timer, problem, and whether they are correct or incorrect. The primary use of the program is also tailored for individual practice, which is always good for practicing the skill individually.
How are important differences among learners taken into account?
Unfortunately, differences are not taken into account. The program offers very little in terms of differentiation. There is no adjustment to skill level- all students of every level get the same problems. This can be problematic for the student that “doesn’t get it” or for the student who thinks the problems are “too easy”. There is a written review at the beginning of the program that does allow students to refresh their memories on the algorithm for dividing fractions, which may be beneficial to some of the lower students.
What do teachers and learners need to know?
This program is not designed for a “deep understanding” of division of fractions. While the algorithm is an easy way to do division of fraction problems quickly and efficiently, it does not answer the essential question of why the algorithm works. Meaning, why do we invert the numerator and denominator of the second fraction when we are dividing? Why are we changing the division sign to a multiplication sign? These questions are left unanswered, and thus it is the teacher’s responsibility to create understanding, preferably before use of this applet. Learners need to realize that this program is to be used to help them compute fluently division of fraction problems, and not develop a deeper understanding of the concept.
http://www.321know.com/div66ox2.htm
Description
This applet provides practice of dividing fractions by fractions using the division of fractions algorithm. The program offers a small explanation on how to divide fractions by fractions, as well as three “game” settings that allows students to practice dividing fractions by fractions against a timer.
Evaluation
What mathematics is (potentially) being learned?
NCTM Standard(s) addressed?
-Numbers and Operations, 6-8: Students will be able to analyze the algorithm necessary for division of fractions. Students will also be able to “work flexibly” with fractions to understand fraction computation problems and to increase computational fluency.
What is the nature of the mathematics?
Students will be dividing fractions by fractions. Students must be able to apply the algorithm for dividing fractions correctly, while also being able to multiply fractions and simplify fractions completely. The combination of these skills is a must, as the applet does not go into any explanations of why a student is incorrect if they get an answer wrong.
How does learning take place?
This applet focuses solely on the division of fractions by other fractions. It tells students to use the algorithm of inverting the second fraction, then multiplying numerators and denominators to get a fraction as their answer. They should then simplify the answer by dividing numerator and denominator by a common factor, until it is reduced completely.
What role does technology play?
This technology allows students access to information on how to divide fractions by fractions. After reading, students have the opportunity to represent their knowledge of dividing fractions by fractions by answering questions against a timer.
This technology gives students a chance to learn/review how to divide fractions by fractions using an algorithm. It also gives students the opportunity to play games that involve solving dividing fraction by fraction problems against a timer. The technology is used to give instant feedback for practicing fraction division. It is also used to motivate students to increase their efficiency with this computation.
How does it fit within existing school curriculum?
This program would fit nicely into a fraction unit. It is not meant to teach students the concept of dividing fractions, but it does offer practice problems for students to increase their computational fluency. It is meant to be used as a supplement to fraction units. It is also important to recognize that the program does not show ‘why’ the algorithm of dividing fractions works, so it may be less useful for those classrooms unfamiliar with the concept of dividing fractions (early secondary).
How does the technology fit or interact with the social context of learning?
I have personally used this applet as a whole-class group experience. I set a goal for my students using the timer application the program has. I may challenge my class to see if they can solve 20 problems in less than 3 minutes. When I start the timer, students try and solve the problems and I will randomly choose a student to give me the answer, from which I will plug into my computer to see if they’re right. I have the whole program displayed using an LCD projector, so students can visually see the timer, problem, and whether they are correct or incorrect. The primary use of the program is also tailored for individual practice, which is always good for practicing the skill individually.
How are important differences among learners taken into account?
Unfortunately, differences are not taken into account. The program offers very little in terms of differentiation. There is no adjustment to skill level- all students of every level get the same problems. This can be problematic for the student that “doesn’t get it” or for the student who thinks the problems are “too easy”. There is a written review at the beginning of the program that does allow students to refresh their memories on the algorithm for dividing fractions, which may be beneficial to some of the lower students.
What do teachers and learners need to know?
This program is not designed for a “deep understanding” of division of fractions. While the algorithm is an easy way to do division of fraction problems quickly and efficiently, it does not answer the essential question of why the algorithm works. Meaning, why do we invert the numerator and denominator of the second fraction when we are dividing? Why are we changing the division sign to a multiplication sign? These questions are left unanswered, and thus it is the teacher’s responsibility to create understanding, preferably before use of this applet. Learners need to realize that this program is to be used to help them compute fluently division of fraction problems, and not develop a deeper understanding of the concept.
Dueling Calculators
http://nlvm.usu.edu/en/nav/frames_asid_312_g_4_t_1.html?from=topic_t_1.html
Description
“Dueling Calculators” an applet allows students to visually and numerically see the differences calculator truncating and rounding can play in mathematics. When a calculator truncates (due to the size of its viewing window), answers are not usually effected greatly. Over time, however, repeated truncation can drastically change the solutions and results we get. This applet provides a resource for students to see that change.
Evaluation
What mathematics is (potentially) being learned?
NCTM Standard(s) addressed?
-Numbers and Operations, 6-8: Students will be able to understand large numbers (numbers with many digits) as they are written in calculator notation.
-Data Analysis, 6-8: Students will be able to interpret data in a table as well as in a graph and understand the connection between the two.
-Communication, 6-8: Students will able to clearly communicate their ideas using mathematical language about rounding and truncating.
What is the nature of the mathematics?
The concepts being displayed are calculator truncating, rounding, and the limitations of calculators. These concepts are displayed in the technology using two calculators, a table of created data, and a graph of the data. The students must interpret the data through discussion and collaboration with peers to gain understanding of the concepts displayed.
How does learning take place?
Learning takes place through meaningful discussion with peers. While the technology provides great data for analysis and visuals for interpretation, what the technology does not do is offer answers or conclusions for the data presented. Thus it is the students’ responsibility, through careful thinking and fruitful discussion, to use what is provided in the technology to reach conclusions about calculator truncation and rounding in general, and their effects on a data set.
What role does technology play?
The technology shows two calculators that are set side by side, one that displays nine-digits and the other that displays eight-digits. The technology allows students to set an input that is the same for each calculator, and the calculators put the input into a given function (provided by the technology), and display an output, which is truncated to the last spot in each calculator’s display. The calculators then take their truncated output and put them back into the original function as inputs. Because of truncation, the outputs for each calculator begin to change, and students have the opportunity to see the change both in numerical data displayed, as well as in a visual graph.
This technology affords peers the opportunity for communicating and collaborating with one another. The technology acts as a starting point for a discussion on the effects of rounding and calculator truncating. By interpreting the data presented in a table and on a graph provided by the technology through discussion, students are able to reach conclusions about calculator truncation and the effects rounding have on numbers.
How does it fit within existing school curriculum?
This technology would be a great beginning of the year activity. Some students nowadays are becoming too reliant on technologies, calculators especially, and are becoming weak in computational skills. By discussing the pitfalls of relying on calculators entirely and examining their limitations, students will begin to understand that complete reliance on calculators can be a detriment to their learning. It is also a fantastic introduction to some math vocabulary, like “truncate”, and provides a great visual of what it means for a calculator to truncate a number.
How does the technology fit or interact with the social context of learning?
This program can be a great tool for leading a whole-class discussion on the cautions of technologies. What is problematic about relying on technology completely? What do users have to know when using a technology? What limitations do calculators have? Teachers can even move to a discussion on rounding. How does rounding affect a set of data? This technology is designed to stimulate discussion and communication amongst students and the classroom.
What do teachers and learners need to know?
While students do not need have a particular knowledge of the functions the program provides (some may be a little abstract for early-secondary students) or how to graph the functions, students and teachers must be able to interpret the graph the technology generates and compare the two sets of data generated by the two calculators. A basic understanding of how functions work (there is an output for every input) is essential.
http://nlvm.usu.edu/en/nav/frames_asid_312_g_4_t_1.html?from=topic_t_1.html
Description
“Dueling Calculators” an applet allows students to visually and numerically see the differences calculator truncating and rounding can play in mathematics. When a calculator truncates (due to the size of its viewing window), answers are not usually effected greatly. Over time, however, repeated truncation can drastically change the solutions and results we get. This applet provides a resource for students to see that change.
Evaluation
What mathematics is (potentially) being learned?
NCTM Standard(s) addressed?
-Numbers and Operations, 6-8: Students will be able to understand large numbers (numbers with many digits) as they are written in calculator notation.
-Data Analysis, 6-8: Students will be able to interpret data in a table as well as in a graph and understand the connection between the two.
-Communication, 6-8: Students will able to clearly communicate their ideas using mathematical language about rounding and truncating.
What is the nature of the mathematics?
The concepts being displayed are calculator truncating, rounding, and the limitations of calculators. These concepts are displayed in the technology using two calculators, a table of created data, and a graph of the data. The students must interpret the data through discussion and collaboration with peers to gain understanding of the concepts displayed.
How does learning take place?
Learning takes place through meaningful discussion with peers. While the technology provides great data for analysis and visuals for interpretation, what the technology does not do is offer answers or conclusions for the data presented. Thus it is the students’ responsibility, through careful thinking and fruitful discussion, to use what is provided in the technology to reach conclusions about calculator truncation and rounding in general, and their effects on a data set.
What role does technology play?
The technology shows two calculators that are set side by side, one that displays nine-digits and the other that displays eight-digits. The technology allows students to set an input that is the same for each calculator, and the calculators put the input into a given function (provided by the technology), and display an output, which is truncated to the last spot in each calculator’s display. The calculators then take their truncated output and put them back into the original function as inputs. Because of truncation, the outputs for each calculator begin to change, and students have the opportunity to see the change both in numerical data displayed, as well as in a visual graph.
This technology affords peers the opportunity for communicating and collaborating with one another. The technology acts as a starting point for a discussion on the effects of rounding and calculator truncating. By interpreting the data presented in a table and on a graph provided by the technology through discussion, students are able to reach conclusions about calculator truncation and the effects rounding have on numbers.
How does it fit within existing school curriculum?
This technology would be a great beginning of the year activity. Some students nowadays are becoming too reliant on technologies, calculators especially, and are becoming weak in computational skills. By discussing the pitfalls of relying on calculators entirely and examining their limitations, students will begin to understand that complete reliance on calculators can be a detriment to their learning. It is also a fantastic introduction to some math vocabulary, like “truncate”, and provides a great visual of what it means for a calculator to truncate a number.
How does the technology fit or interact with the social context of learning?
This program can be a great tool for leading a whole-class discussion on the cautions of technologies. What is problematic about relying on technology completely? What do users have to know when using a technology? What limitations do calculators have? Teachers can even move to a discussion on rounding. How does rounding affect a set of data? This technology is designed to stimulate discussion and communication amongst students and the classroom.
What do teachers and learners need to know?
While students do not need have a particular knowledge of the functions the program provides (some may be a little abstract for early-secondary students) or how to graph the functions, students and teachers must be able to interpret the graph the technology generates and compare the two sets of data generated by the two calculators. A basic understanding of how functions work (there is an output for every input) is essential.
The Secret World of Cookie Man
http://www.learningwave.com/preview/integers/cm1.html
Description
This program was designed as an engaging activity for secondary students to practice using basic formulas, like distance and area. Students have to help “Cookie Man” in his adventure, solving problems along the way. Students must be able to set up formulaic equations correctly, substitute values for variables, as well as solve for missing amounts. The program offers amusing and laughable problems that make solving them fun and engaging for all students.
Evaluation
What mathematics is (potentially) being learned?
NCTM Standard(s) addressed?
-Algebra, 6-8: Students will be able to represent and analyze situations with equations and will be able to solve equations using given values.
-Numbers and Operations, 6-8: Students will be able to develop and analyze methods for solving problems.
-Measurement, 6-8: Students will be able to understand and convert between different units of measurement.
What is the nature of the mathematics?
The nature of the mathematics is to be able to read and analyze a word problem, extract useful data, and to be able to successfully apply the data using a given formula. The problems are all in word form and students are expected to use problem solving skills to solve them. Students are using the area formula for a rectangle, the distance formula, as well as simple conversion methods to solve the word problems.
How does learning take place?
Learning takes place as the student apply strategies to find the missing values requested in each of the problems. Students are substituting values into equations and correctly and evaluating them for a numeric answer. Students are able to check their answers in the solution box, as an incorrect answer will lead them to the next problem, while an incorrect will keep them on the same problem. This ensures that the students will have to complete each problem and achieve success in order to make it through the entire program.
What role does technology play?
The technology affords students the opportunity to represent their knowledge and thinking by solving complex equations and applying useful formulas. Students’ knowledge is represented as they make their way through the “Cookie Man” program, solving each given problem.
The technology itself provides the students with an engaging backdrop to complete word problems dealing with algebraic concepts. While the story presented by the technology is silly and goofy, the problems themselves are excellent examples for using formulas and equations in mathematics. The technology offers the students these problems to students while keeping them interested with an funny story.
How does it fit within existing school curriculum?
This program fits well into any secondary school curriculum. At the secondary level students are being introduced to many algebraic concepts, like equations, variables, and using formulas. “Cookie Man” promotes all of these in a manner that engages students. “Cookie Man” would be a wonderful supplement to any algebra unit, or even used as an assessment of students learning by teachers.
How does the technology fit or interact with the social context of learning?
The program itself does not offer much in the way of a “hint” to students. The problem solving is done strictly by the students themselves- which is rigorous work. Because of the nature of the problems, “Cookie Man” is a fantastic program to do in partners. Students analyzing the problems in partners would have opportunity to discuss their methods for solving with one another, thus leading to some fruitful mathematic discussion.
How are important differences among learners taken into account?
Differences amongst learners are not addressed with the program, as it is one of its downfalls. The program lacks any levels of difficulty or assistance to lower-level learners. If students have poor reading skills they are almost certain to struggle comprehending the story and problems presented. Another problem with the program is that there is only one set of problems- once students have correctly answered the problems there is nothing else for them to do. Once the program is completed once, there is no use for using it again.
What do teachers and learners need to know?
This program is part of a preview for a website, http://www.learningwave.com/, which is devoted to creating engaging online activities for secondary students. Many of the activities are designed by teachers for classroom use, including “Cookie Man”. “Cookie Man” is one of the preview programs available to teachers for free.
Students need to be prepared to have a pencil and paper (or calculator) handy as they go through the “Cookie Man” program. The program does not offer much assistance in the solving of each problem, so students have to be persistent and patient, especially those of lower levels. Reading skills are also very important for this program, as all of the problems and story is reading based.
http://www.learningwave.com/preview/integers/cm1.html
Description
This program was designed as an engaging activity for secondary students to practice using basic formulas, like distance and area. Students have to help “Cookie Man” in his adventure, solving problems along the way. Students must be able to set up formulaic equations correctly, substitute values for variables, as well as solve for missing amounts. The program offers amusing and laughable problems that make solving them fun and engaging for all students.
Evaluation
What mathematics is (potentially) being learned?
NCTM Standard(s) addressed?
-Algebra, 6-8: Students will be able to represent and analyze situations with equations and will be able to solve equations using given values.
-Numbers and Operations, 6-8: Students will be able to develop and analyze methods for solving problems.
-Measurement, 6-8: Students will be able to understand and convert between different units of measurement.
What is the nature of the mathematics?
The nature of the mathematics is to be able to read and analyze a word problem, extract useful data, and to be able to successfully apply the data using a given formula. The problems are all in word form and students are expected to use problem solving skills to solve them. Students are using the area formula for a rectangle, the distance formula, as well as simple conversion methods to solve the word problems.
How does learning take place?
Learning takes place as the student apply strategies to find the missing values requested in each of the problems. Students are substituting values into equations and correctly and evaluating them for a numeric answer. Students are able to check their answers in the solution box, as an incorrect answer will lead them to the next problem, while an incorrect will keep them on the same problem. This ensures that the students will have to complete each problem and achieve success in order to make it through the entire program.
What role does technology play?
The technology affords students the opportunity to represent their knowledge and thinking by solving complex equations and applying useful formulas. Students’ knowledge is represented as they make their way through the “Cookie Man” program, solving each given problem.
The technology itself provides the students with an engaging backdrop to complete word problems dealing with algebraic concepts. While the story presented by the technology is silly and goofy, the problems themselves are excellent examples for using formulas and equations in mathematics. The technology offers the students these problems to students while keeping them interested with an funny story.
How does it fit within existing school curriculum?
This program fits well into any secondary school curriculum. At the secondary level students are being introduced to many algebraic concepts, like equations, variables, and using formulas. “Cookie Man” promotes all of these in a manner that engages students. “Cookie Man” would be a wonderful supplement to any algebra unit, or even used as an assessment of students learning by teachers.
How does the technology fit or interact with the social context of learning?
The program itself does not offer much in the way of a “hint” to students. The problem solving is done strictly by the students themselves- which is rigorous work. Because of the nature of the problems, “Cookie Man” is a fantastic program to do in partners. Students analyzing the problems in partners would have opportunity to discuss their methods for solving with one another, thus leading to some fruitful mathematic discussion.
How are important differences among learners taken into account?
Differences amongst learners are not addressed with the program, as it is one of its downfalls. The program lacks any levels of difficulty or assistance to lower-level learners. If students have poor reading skills they are almost certain to struggle comprehending the story and problems presented. Another problem with the program is that there is only one set of problems- once students have correctly answered the problems there is nothing else for them to do. Once the program is completed once, there is no use for using it again.
What do teachers and learners need to know?
This program is part of a preview for a website, http://www.learningwave.com/, which is devoted to creating engaging online activities for secondary students. Many of the activities are designed by teachers for classroom use, including “Cookie Man”. “Cookie Man” is one of the preview programs available to teachers for free.
Students need to be prepared to have a pencil and paper (or calculator) handy as they go through the “Cookie Man” program. The program does not offer much assistance in the solving of each problem, so students have to be persistent and patient, especially those of lower levels. Reading skills are also very important for this program, as all of the problems and story is reading based.
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