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.