Helping Students Develop Math Understanding Beyond Memorization

Posted by Reed Howard on Sep 11, 2013 3:25:00 PM

One of my favorite movies, Only Yesterday, is centered around a young woman reminiscing about her days in elementary school. The young woman's name is Taeko and one of her memories involves a failing grade she received on a math test that required her to divide fractions.

Steering away from "Just remember to take the reciprocal and multiply..."

deeper math understandingWhen questioned by her sister on why she did so poorly on the test, Taeko asks, “What is dividing a fraction by a fraction, anyway? Two-thirds of an apple divided by a quarter is like asking to divide it between four people, right?” She draws a picture of two-thirds of an apple, then divides it into four pieces. “That’s one-sixth each, right?”

Her sister pauses for a moment, then shakes her head. “No, no, no. That’s multiplication.”

“How come it’s less when you multiply?” Taeko asks.

Her sister sighs and takes away the drawing. “Forget about apples. Just remember to take the reciprocal and multiply.”

Video: A Discussion on Teaching Math (from Only Yesterday)

Taeko's story is a familiar one. Math is often taught as a series of rules with no meaning. Many times, students are asked to arrive at the correct answer without understanding what they’re doing, or even why. One of my goals when writing a Wowzers lesson is to steer students away from pure memorization, and towards deeper understanding.

Answering "When will I ever use this?" with manipulatives and real-world scenarios

When students learn how to divide fractions in Wowzers, they are reminded that dividing six by two is simply asking, “How many groups of two can we make?" They are presented with a visual model that walks them through dividing a group of six objects into groups of two: something they are undoubtedly familiar with.

straight angle gameUsing the same visual process, the students digitally interact and manipulate objects on screen to divide two-thirds of a square into groups of one-fourth. Before ever introducing the concept of taking the reciprocal of the second fraction and multiplying, the students use virtual manipulatives in order to divide fractions.

The concept is also presented in a real world scenario: if a garden is five-eighths of a meter long, and the flowers need to be planted one-fifth of a meter apart, how many flowers could be planted in the garden? By relating the math to a situation such as this, it allows the students to visualize what it means to divide a fraction by a fraction, something Taeko struggled with. Providing a concrete example of each math concept also prevents the age old question of, “When will I ever use this?

Although Wowzers takes place in a creative digital world where anything is possible, math is never presented as a magical process that cannot be explained. It is my goal that no student who plays Wowzers should ever feel like Taeko.
 


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Topics: Wowzers Tales

Wowzers is a comprehensive online math program covering all Common Core State Standards for grades K-8. The research-based program adapts to each learner and allows for an individualized path through the curriculum. Content is presented in multiple ways, and appeals to tactile, auditory, and visual learners. Assessments mirror those found on high-stakes achievement tests and provide teachers and administrators with the information that they need to personalize learning for each student.

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