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7 minutes reading time (1335 words)

Math Word Problems

For many students, math word problems are the bane of their existence. High school math teachers tell me that a number of their students just refuse to even try to solve such problems—perhaps because of years of failure and unwillingness to subject themselves to further failure. Many other students manage to “get by” through memorization of rules of thumb such as “of” means “times” while “and” often means “plus.” They have little understanding of what they are doing, or how it relates to solving “real world” problems.

I have recently revised and updated my 27-page IAE-pedia document on Math Word Problems (Moursund, 2016a). My target audience is K-12 teachers and parents of students in these grade levels. Unfortunately for struggling students, there is no “magical solution” to solving word problems in this document. However, it contains considerable useful information.

Often students face the difficulty that some of the math word problems they encounter are completely divorced from their (“personal, real”) world (Moursund, 2016b). Such word problems seem to the student to be made-up puzzles of no inherent interest. They just don’t “get it.” That is a sad situation, since a major goal in math education is to help students to recognize and solve math problems that they might (or do) encounter at play, at home, at school, and (sometime in the future) on a job.

The Heart of Every Discipline of Study

Recognizing and communicating about problems, solving problems, and accomplishing challenging tasks lie at the heart of every field of study. In our everyday lives we continually recognize and solve problems. For example, think of the problem of carrying on a conversation with a friend. Hearing, deciphering, and understanding the sounds of a spoken language is a very challenging problem. The very best of modern computers are making progress on this problem—but have a long way to go. Somewhat similarly, recognizing the face of a friend in a crowd is an amazing problem-solving achievement that most of us readily accomplish. (Some people, like your author, have face blindness. Due to a small defect in my brain, I cannot recognize people by their faces.) It is only fairly recently that computers have gotten reasonably good at face recognition.

My point is that humans have tremendous innate and/or learned problem-solving capabilities in areas essential to the survival of humanity. However, individuals vary considerably in their abilities to learn and to develop a reasonable level of problem-solving expertise in various areas. My own abilities in math have stood me well, and it is certainly a good thing that I did not have to make a living in music, art, dance, or competitive sports! Some students have more inherent ability in math than do others. A lower level of inherent ability to learn and use math should not prevent a student from getting a good overall education and succeeding in graduating from high school.

Math

My personal opinion is that our educational system places far too much emphasis on math. I am quite uncomfortable with the over-emphasis that began with the “algebra for all” movement and continues with the requirement of three or four years of high school math for graduation. It isn’t that such math is not useful. Rather, a great many students cannot master such math at a level of actually understanding what they are doing and being able to apply their math knowledge and skills. Moreover, the average level of math performance of adults in our country is at approximately the 7th to 8th grade level. In essence, life in our country is designed so that this level of math knowledge and skills suffices for a very large number of people.

In our everyday lives we encounter math problems that can be solved by computer systems, and these computer systems are gradually getting better. For the most part, our math education system is dragging its feet in the widespread implementation of routine student use of such computer capabilities. In addition, computer-assisted learning systems are getting better. I routinely wonder why we are not providing all students with high-quality computer-assisted learning systems for routine use throughout the curriculum. And, of course, these computer systems can be designed to provide instruction on how to make effective use of the problem-solving software that can solve and/or help solve problems in math and in other disciplines.

What You (a Teacher of Math) Can Do

This blog entry began with an emphasis on math word problems and then slipped into consideration of our whole math education system. Teachers today face unreasonably large class sizes and a great many different kinds of diversity (e.g., cultural, economic, linguistic, preparation) in their students. They face possible changes suggested by educational research and progress in cognitive neuroscience. Students have changed through growing up in a high-tech entertainment and communications environment. In addition, there has been a steady barrage of new and improved technological aids to teaching, learning, and using math.

Every math teacher is caught between top-down approaches to improving the entire math education system in the country or in their state, and the individual changes they personally feel would improve the results they are producing. Within whatever top-down approaches and pressures you work in, you still have considerable freedom to develop and make use of personal teaching skills and to work with students in a manner that you believe will be most beneficial to them. Here are some of my suggestions that might help to guide your individual efforts.

  1.  Place increased emphasis on math word problems—and, especially, on "good, realistic" math word problems. Learn to distinguish the good from the not so good, and significantly decrease use of the "not so good" word problems that are so prevalent in math textbooks and from other sources such as the Web.
  2. Use math word problems as a vehicle (as an environment) in which to help students gain in math maturity (Moursund, 2014). Make math maturity one of the ideas you hold in mind as you prepare math lesson plans and teach math classes.
  3. Strive to strike a “better balance” between emphasis on rote memorization versus emphasis on learning for understanding and for tackling novel, challenging problems. Help your students learn to make use of modern technology as an aid to representing and solving math problems.
  4. Use math word problems to increase the emphasis on math modeling, computer modeling, and other aspects of computational thinking routinely used by people who use math outside of the setting of being a student in school (Moursund, 2015). You may enjoy reading about the idea of folk math—think about folk music and then carry this idea over into math learning used by people to fit their practical needs and interests (Moursund, 2013).
  5. At the current time, many people have come to believe that the number one goal in math education is to prepare students to do well on high-stakes math tests. I believe that this is a very wrong-headed and sad situation, because such tests are weak in what is called authenticity. An authentic test measures what we want students to be able to actually do with the knowledge and skills they are being taught (Indiana University, 2016). One of my favorite questions is to ask adults, “When was the last time you were carry on in your everyday life and you encountered the need to solve a quadratic equation?” Please do not let yourself be steamrollered into believing that the main purpose of math education is to prepare students to do well on state, national, and international tests.

References and Resources

Indiana University (2016). Authentic assessment. Retrieved 3/23/2016 from http://citl.indiana.edu/resources_files/teaching-resources1/authentic_assessment.php.

Moursund, D. (2016a). Math word problems. IAE-pedia. Retrieved 3/22/2016 from http://iae-pedia.org/Word_Problems_in_Math.

Moursund, D. (2016b). Math word problems divorced from reality. IAE-pedia. Retrieved 3/22/2016 from http://iae-pedia.org/Math_word_problems_divorced_from_reality.

Moursund, D. (2016c). Math methods for preservice elementary teachers. IAE-pedia. Retrieved 3/22/2016 from http://iae-pedia.org/Math_Methods_for_Preservice_Elementary_Teachers.

Moursund, D. (2015). Computational thinking. IAE-pedia. Retrieved 3/22/2016 from http://iae-pedia.org/Computational_Thinking.

Moursund, D. (2014). Math maturity. IAE-pedia. Retrieved 3/22/2016 from http://iae-pedia.org/Math_Maturity.

Moursund, D. (2013). Folk math. IAE-pedia. Retrieved 3/22/2016 from http://iae-pedia.org/Folk_Math.

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Saturday, 17 April 2021

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