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The Making of a Mathematical Mind: 1 Step at a Time

The views expressed are those of the author and are not necessarily those of Scientific American.

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One time when I was in the third grade, I got sick and missed a week of school. My dad wanted me to keep up with my schoolwork, so he brought my assignments and books home. I did the required work in the math workbook quickly, or so the story goes, and went on to complete many additional pages in the book. My rate of progress during this bout of illness inspired my father to embark on a long-term parenting project to accelerate his children in math.

worksheet for times 5

Courtesy of jimmiehoseschoolmom via Flickr

As a result of these ambitions, my younger brother and I ended up years ahead in math. I am not especially gifted at manipulating or thinking about numbers, and yet it required only about three hours per week (and a lot of nagging on my father’s part) for me to learn enough to enter first year algebra at age 11. My brother was right with me…at age 9. My brother is probably an outlier in terms of ability, but the idea that there is big potential for kids to move faster in math than schools require is hardly foreign to me.

Enter John Mighton, a mathematician at the Fields Institute for Research in the Mathematical Sciences in Toronto. I met him at the Aspen Brain Forum in 2011. He runs a charity called JUMP Math that enables not just reasonably well-to-do, bright kids to excel in math, but also accelerates students who are having a lot of trouble with the subject, some of them due to disadvantaged circumstances. Many of the kids Mighton tutored—originally, his charity was a tutoring service—started years behind grade level. His experience with such children led him to painstakingly build a system of instruction, grade by grade, that could transform a struggling math student into a strong one. In a controlled study, students in math classes using Mighton’s program progressed twice as fast as those in comparison classes taught using standard techniques.

I approached Mighton in Aspen and asked him to write an article for Scientific American Mind about his program. Happily, he agreed. In “New Techniques Make Math Fun for All,” which appears in our September/October 2013 issue, Mighton describes JUMP Math’s key elements. These include breaking down math instruction into very small steps, providing lots of practice and quickly correcting errors. The brilliance of the program lies not only in these important principles but also in the details of its execution. (For an example of a step-by-step, or “scaffolded,” JUMP lesson, read Mighton’s blog, “How to Teach Long Division through Guided Discovery.”) Mighton’s patience and persistence led him to decipher the confusions of the kids he taught and translate them into a program that prevents them. To hear the whole story, listen to the podcast, “Kids JUMP for Math [John Mighton’s Junior Undiscovered Math Prodigies]”

My father believed that low standards contributed to underachievement in math among many, if not most, kids in the U.S. (For more on his ideas and tips, see Math Coach: A Parent’s Guide to Helping Children Succeed in Math, Berkley Trade, 2001.) Mighton has developed a method that not only backs up that belief, but expands the ability to rapidly master math to virtually all children. His ideas and techniques also sow the seeds of a social revolution of sorts, as children who begin to succeed in math develop confidence in their ability to learn in general. Math is supposed to be a difficult subject, after all. In addition, young people begin to have faith in the role of effort in achievement, a mindset that, according to work by psychologist Carol Dweck of Stanford University, could alter the course of their lives. See the video below to hear Mighton chat with Dweck about this important topic.

Ingrid Wickelgren About the Author: Ingrid Wickelgren is an editor at Scientific American Mind, but this is her personal blog at which, at random intervals, she shares the latest reports, hearsay and speculation on the mind, brain and behavior. Follow on Twitter @iwickelgren.

The views expressed are those of the author and are not necessarily those of Scientific American.

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  1. 1. MariaDroujkova 9:43 am 08/16/2013

    I’ve been experimenting on algebraic ideas with kids as young as three. If you want to go that young, there are more adaptations to make. Here are a few:
    - Use large objects and gross motor skills
    - Switch to the qualitative from the quantitative
    - Use sets of objects to show numbers, and keep the numbers small
    - Pretend-play with characters that matter to your child
    - Tell a story of what’s going on in the problem, and why
    - Use computer models, especially touch technology

    Let me know if you would like to learn more. The site for my early math community is

    Link to this
  2. 2. PapaTango72 3:40 pm 08/16/2013

    Actually, linear algebra can be introduced in grade school along with set theory. One revolution that can be brought about that is overlooked is the process of conceptualization. Rather than forcing memorization techniques upon students, a process-based learning model that advances through the concepts of mathematical reasoning with a logical progression of a combination of skills and theory that positively reinforce learning patterns would be more beneficial. The sooner we do away with the current “teaching to the test” “educational” system that we have in this country, the better for our children, as well as our own future.

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  3. 3. TheUniter 5:53 pm 08/16/2013

    Any methodolgy to push maths is a good idea certainly.

    For more on how the mind actually deal with streams of consciousness as it were, I would suggest a perusal of my thesis here


    PS. If you live Lower Mainland area of BC and particularly Vancouver you might want o be amused or annoyed slightly:

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  4. 4. TheUniter 5:54 pm 08/16/2013

    PapaTango72 I had issues when I was trying to learn linear algebra in college and teaching it earlier sounds like an excellent idea indeed.

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  5. 5. Kathy K. 10:19 pm 08/16/2013

    I totally agree with PapaTango72′s comments. Math reasoning and conceptualization is not being taught at an early enough age and many kids learn to hate math from the repetitive paper/pencil drills that have no context or meaning to them.

    Link to this

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