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Wednesday / April 24

Rethinking the Math Problems We Ask

“The evidence overall suggests that the status quo with respect to learning outcomes from high school mathematics is unacceptable (p.3).”

– Catalyzing Change in High School Mathematics (2018)

“Today, it seems as if nearly everyone agrees that high school mathematics needs to change. For far too long high school mathematics has not worked for far too many students: too many students leave high school unprepared for college or a career, particularly a STEM career; too many students do not see how math is useful in their lives; too many students leave high school without an affinity for doing math; too many students leave high school without the quantitative skills necessary to make sound decisions in their personal life and in our society which is increasingly quantitative in nature.”

– Matt Larson, NCTM Past-President, “Bringing Needed Coherence and Focus to High School Mathematics” (October 25, 2016)

As technology from phone apps to websites permeates education, this call for change in high school math is even more needed. For example, apps like photomath, wolframalpha and Chegg.com can easily solve (or show solutions) to high school mathematics problems that ask students to solve, factor, simplify and/or rationalize. These verbs/skills focus on algebraic manipulation of variables. Are these skills that still form the majority of high school mathematics antiquated?

In fact, should we not question why we assign any problem that Google can quickly solve (or show the solution to)? Certainly, our students question such as they quickly turn to technology for the solution to those problems. Given the call for change from NCTM, Dr. Larson’s quote, and the impact of technology on math education, maybe our focus should turn to innovative and authentic problem solving that Google cannot quickly solve. Three such examples are below.

1. Split 25.

(A simple problem that all students can understand, but the answer is not obvious.)

Take the number 25 and break it up into as many pieces as you want, such as:

25 = 10 + 10 + 5

25 = 2 + 23

25 = 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1

What is the biggest product you can make if you multiply those pieces together?

See more examples like this at: https://playwithyourmath.com/

2. Remove the numbers.

(Google will not help here!)

Place whole numbers 1 through 9 at most once in the empty boxes below to create an equation such that the solution is closest to zero.

See more examples like this at: http://www.openmiddle.com/

3. Deeper Problem Solving.

Two students met online and arrange for a blind date between 5:00 and 6:00pm. A week later, however, neither of them remembers the exact meeting time. As a result, each person arrives at a random time between 5:00 and 6:00 and waits exactly 10 minutes for the other person. When the 10 minutes have passed, each person leaves if the other person has not come. What is the probability the two students will actually meet?


Such change will most likely take place slowly as encroaching on the traditional algebraic symbolic manipulation strangle hold on mathematics will not be easy. Hopefully, though, more math educators, leaders, and policy makers will begin to realize that mathematical literacy in the 21st Century is much different and requires deeper problem solving and reasoning in addition to quantitative literacy.

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Written by

Dr. Eric Milou is a professor of mathematics at Rowan University in Glassboro, NJ. Dr. Milou has taught at Rowan for the past 20 years and served six terms as the President of the Rowan University Senate from 2007 to 2013. He previously served as President as the Association of Mathematics Teachers of New Jersey, the program chairperson of the 2007 NCTM annual meeting and has extensive speaking experience on standards based reform in mathematics. He is one of the authors of digits, EnVisions 6-8 and EnVisions A|G|A (published by Pearson) and was the recipient of the Max Sobel Outstanding Mathematics Educator Award in 2009.

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