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Thursday, February 22, 2018

Innovative ways to teach math

Arizona Math Partnership robots

Arybe Campillo, left, and Logan Hatch work on programming their LEGO robots to execute four consecutive 90-degree turns. Photos by Daniel Friedman.

A week of Math Camp at Grand Canyon University (GCU) for a group of middle school students ages 12 to 14 involved math projects that went a bit further than your typical math instruction.

The Arizona Mathematics Partnership (AMP) organized the camp to give teachers the opportunity to teach some lessons they might not have the time or resources to do during the regular school year.

Some of the 102 students who participated stayed overnight in the GCU dorms to get a taste of college life. Parents came to GCU the last day  to see the outcome of the various projects.

Innovation over tradition

The purpose behind AMP is to explore new ways to help teachers teach math concepts versus basic arithmetic algorithms. Though started before Common Core standards were adopted in Arizona, the AMP project math aligns with Common Core, says principal investigator April Strom. Strom organized Math Camp and is the project manager behind AMP research to find better ways to teach middle school mathematics.

Arizona Math PArtnership cipher

To learn about inverse functions, a student at AMP Math Camp cuts out wheels to create a cipher wheel used to encrypt messages.

Strom explained how AMP encourages teachers to think of math as a continuous progression of learning rather than compartmentalizing the teaching of discrete skills.

Strom says students should know why their answers are correct and how various formulas and operations will yield solutions. They need to be able to convince others of their approach to problem-solving instead of simply relying on the algorithm.

For instance, “borrowing” in subtraction requires a thorough understanding of place value. Just teaching the algorithm to solve 23 minus 17 is an example of compartmentalized math learning.

In one class, students used the Pythagorean Theorem to calculate the time it would take to walk to a taco stand along the hypotenuse or the two legs of a right triangle. They had the distance figured out—325 feet—and the walking speed—two feet per second—so divide the distance by the feet per second to get the time, right? That’s correct, but can you explain how you know division is the proper operation to get the answer?

The correct explanation, given by eighth grader Lauren Anderson of Scottsdale, is that division will find how many groups of two there are in 325 by repeated subtraction. Division, as illustrated by the long division algorithm, is repeated subtraction.

Arizona Math Partnership mean absolute deviation

Donovan Bloom shoots a paint-tipped dart at a target.

Explaining how you know something requires a deep understanding of math concepts, but also a command of language. AMP stresses that this is the direction in which math teaching needs to go—not just because it is part of Common Core, but because Americans have fallen behind other countries in math proficiency.

The need for a deeper conceptual understanding in mathematics was discussed at length when I started taking my teaching certification classes at Arizona State University in 1991. The wheels of educational progress turn a lot slower than two feet per second, it seems.

Math bulls-eye!

Another project involved shooting paint-covered darts at a two-dimensional Cartesian system, or what most students know as the X and Y axes. The bulls-eye would be (0,0), but shots landed in all four quadrants.

The average of the coordinate points determined the quality of the students’ marksmanship. They used the averages to find the “mean absolute deviation.” I don’t know exactly this means, but Matt Perales, who teaches math in Florence, told me this. He and colleague Ashley Morris, who teaches in San Tan Valley, devised this project.

I suggested that averaging the coordinates would find a coefficient of accuracy for each group of dart shooters, to which Perales agreed. He may have just been humoring me, but I felt like I fit in for a second.

Mystery messages and robots

Another class was using ciphers to learn about inverse functions. Students used a cipher to encrypt a message. The inverse of the cipher decrypted the message.

Arizona Math Partnership target

The target, a two-dimensional Cartesian system.

Another class was programming LEGO robots to drive around a course. Then they were programming the robot to turn. First they had to figure out how many revolutions of the wheel was needed to turn the robot 90 degrees.

Amanda McCloud, who teamed up with Lauren, concocted a formula that—given the circumference of the wheel—determined the precise number of wheel revolutions necessary to turn the robot a specified number of degrees.

It turns out she found the exact formula the teachers were going to provide to the students to solve the robot-turning problem. One of the AMP team members, Chandler-Gilbert professor Scott Adamson, told me later that this never happens.

Perhaps my “friending” Amanda and Lauren on Facebook might be a good career move?

Read more about what the Arizona Mathematics Partnership is doing to prepare teachers for Common Core standards.

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Daniel Friedman

Daniel Friedman is a staff writer and photographer.

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