MATH LIMITS

MATH LIMITS - by Renee M. Hamilton-Newman

Publication: 2e Newsletter, November/December 2014 [View Newsletter)

Thirty-one years ago I entered college with a full scholarship at the University of Wisconsin—Madison. In a room with four student advisors, I was asked jokingly, “So, what do you want to be when you grow up?” Without hesitation, I said, “An engineer.” Abruptly, they all burst out laughing.

Shocked and embarrassed, I asked, “What’s so funny?” One of the advisors, trying to be serious, replied, “Well, let’s assume you were struck by lightning and could suddenly do math. It would take you seven years to get your four-year degree.” Dejected, I asked, “Well, what can I do without math?” They had two answers, “Journalism or prelaw.” Reasoning that I love to write, but that journalists get no respect, I said, “Okay, I choose pre-law.” I majored in Integrated Liberal Studies, which provided an amazing intellectual adventure before the age of personal computers and the Internet; but I still was required to pass one college algebra class.

Despite being in high school honors classes and scoring very well on all standardized tests, as well as taking college classes from age 14, I flunked algebra in college. In the past, I’d gotten a mercy grade from sympathetic math teachers, aware of my sheer determination, perseverance, and extraordinary effort; but this was college. I tried everything — bought Algebra Programmed from the university bookstore, went to daily tutoring, did my math in the lounge of the engineering union (where the math brains were), regularly got assistance through my tears — but nothing helped. I failed every test, and tests were all that counted.

In distress, I begged my TA (teaching assistant) to let me retake the class under direct supervision during tests. As it turned out, I could do the work on the board in front of the TA if I could talk aloud while reasoning; but I couldn’t remember how to repeat my performance later on a test taken in silence. He agreed, and I took my tests on the board, talking as I worked. The TA watched intently, pointing things out like, “You just said 56, but look what you wrote.” I finally got an A.

The Early Years

Back in seventh grade, my teacher tried to save me. We had a deal. For a Snicker’s bar, Ms. Cousino worked with me each day through lunch period. She’d say, “Look, I’m not so great at spelling. Of course, I’m not supposed to admit that! You’re not so great at math. So what? Benjamin Franklin got pulled out of school because he was bad at math. Keep doing your best.”

I wanted to believe that I could do it. After all, everything else came easily. But, in spite of willing myself to like math, psyching myself up, and relaxing like it didn’t matter, I still couldn’t get my locker opened in time and I mixed-up my multiplication facts. I still added by counting the dots I made on the paper, chronically got lost, and couldn’t remember my class schedule without checking the copy I pasted to the cover of every notebook. Come on! I read Atlas Shrugged at the age of 12. What was my problem?

Understanding and Helping Students with Dyscalculia

For students with dyscalculia, teaching and learning must occur in a tight framework of properly sequenced scaffolding, as in the CLSO system, which stands for concepts, language, symbols, and operations. (See the free learning resources on dyscalculia.org for more information.) All instructors should be both familiar with the characteristics of dyscalculic learners and aware of strategies that can help them. The following table provides an overview of learner characteristics and key strategies.

Learning Disability?

I had never heard of a learning disability until I was almost finished with college. My advisor at Michigan State University insensitively said, “If you have dyscalculia and your fiancé has dyslexia, I’d hate to see what your kids will be like.” Hence, when I got married, I made it my business to learn all I could about both. I discovered a whole field of scientists seeking the neurological origins of these paradoxical syndromes that leave individuals with extraordinary talents and perplexing inabilities.

What I also discovered was that I could do math, but it had to be on my terms. All the switching of operations and directions within even simple problems overwhelmed me, so I learned to use different colors to remind myself what operation I was performing — green for adding, red for subtracting, blue for multiplying, and black for division. I used a pen that had all four ink colors. I talked aloud to remind myself what I was doing and why. To reason my way through word problems, I drew pictures to illustrate them. I used a calculator or chart to double check my fact recall. I read aloud the numbers three times to make sure I saw them the same way.

Understanding Dyscalculia

Inquiry into the brain origins of dyscalculia is taking place all over the world. Researchers have found that the brains of dyscalculics are structurally different in the areas responsible for math processing, and that their brains light up in different areas when thinking about math than brains that have no difficulty with numbers. These findings show that while trying harder may not prove an effective strategy, trying differently can result in success. Like the blind learn by relying on their other senses, dyscalculics must likewise use their intact abilities to think about, reason, interact with, manipulate, and communicate mathematically. Since most are good with language, this means becoming fluent in the contextual language of math.

Computer apps, as well, offer dyscalculics other ways of learning. Researchers are developing programs to correct the fundamental skill deficits underlying math disability. Some programs help users develop automatic number sense, or the ability to instantly associate a visual quantity with a number or digit. Other programs build fast and accurate math-fact recall, visual-spatial skills, and directional sense. (See the table “Understanding and Helping Students with Dyscalculia.”)

Living with Dyscalculia

It’s still a struggle. For instance, a day after I make a purchase, it’s hard for me to remember if I paid, $238, $328, or $283 — as if my brain doesn’t think numbers are important enough to remember them exactly. This ambiguity is equally true for time, dates, sequences, and the physical layout of everything.

Of course, I’d rather not admit I have these embarrassing brain glitches. By putting them out there, I hope others learn from my experiences, search out causes and solutions, and are inspired to invent and evolve until they’re able to achieve what once seemed impossible.

Renee Hamilton-Newman’s expertise is in the areas of instructional design, learning disabilities (dyslexia, dyscalculia, and dysgraphia), educational technology, assessment, and remedial programming. She runs the nonprofit http://www.dyscalculia.org/. It provides a host of free information and tools for students, parents, and professionals of all ages and schools.

Permission Statement

This article first appeared in the November, 2014, issue of 2e: Twice-Exceptional Newsletter and is used here with permission.

This article provides information on understanding and helping students with dyscalculia.

by Renee M. Hamilton-Newman

Publication: 2e Newsletter, November/December 2014

Thirty-one years ago I entered college with a full scholarship at the University of Wisconsin—Madison. In a room with four student advisors, I was asked jokingly, “So, what do you want to be when you grow up?” Without hesitation, I said, “An engineer.” Abruptly, they all burst out laughing.

Shocked and embarrassed, I asked, “What’s so funny?” One of the advisors, trying to be serious, replied, “Well, let’s assume you were struck by lightning and could suddenly do math. It would take you seven years to get your four-year degree.” Dejected, I asked, “Well, what can I do without math?” They had two answers, “Journalism or prelaw.” Reasoning that I love to write, but that journalists get no respect, I said, “Okay, I choose pre-law.” I majored in Integrated Liberal Studies, which provided an amazing intellectual adventure before the age of personal computers and the Internet; but I still was required to pass one college algebra class.

Despite being in high school honors classes and scoring very well on all standardized tests, as well as taking college classes from age 14, I flunked algebra in college. In the past, I’d gotten a mercy grade from sympathetic math teachers, aware of my sheer determination, perseverance, and extraordinary effort; but this was college. I tried everything — bought Algebra Programmed from the university bookstore, went to daily tutoring, did my math in the lounge of the engineering union (where the math brains were), regularly got assistance through my tears — but nothing helped. I failed every test, and tests were all that counted.

In distress, I begged my TA (teaching assistant) to let me retake the class under direct supervision during tests. As it turned out, I could do the work on the board in front of the TA if I could talk aloud while reasoning; but I couldn’t remember how to repeat my performance later on a test taken in silence. He agreed, and I took my tests on the board, talking as I worked. The TA watched intently, pointing things out like, “You just said 56, but look what you wrote.” I finally got an A.

The Early Years

Back in seventh grade, my teacher tried to save me. We had a deal. For a Snicker’s bar, Ms. Cousino worked with me each day through lunch period. She’d say, “Look, I’m not so great at spelling. Of course, I’m not supposed to admit that! You’re not so great at math. So what? Benjamin Franklin got pulled out of school because he was bad at math. Keep doing your best.”

I wanted to believe that I could do it. After all, everything else came easily. But, in spite of willing myself to like math, psyching myself up, and relaxing like it didn’t matter, I still couldn’t get my locker opened in time and I mixed-up my multiplication facts. I still added by counting the dots I made on the paper, chronically got lost, and couldn’t remember my class schedule without checking the copy I pasted to the cover of every notebook. Come on! I read Atlas Shrugged at the age of 12. What was my problem?

Understanding and Helping Students with Dyscalculia

For students with dyscalculia, teaching and learning must occur in a tight framework of properly sequenced scaffolding, as in the CLSO system, which stands for concepts, language, symbols, and operations. (See the free learning resources on dyscalculia.org for more information.) All instructors should be both familiar with the characteristics of dyscalculic learners and aware of strategies that can help them. The following table provides an overview of learner characteristics and key strategies.

Learning Disability?

I had never heard of a learning disability until I was almost finished with college. My advisor at Michigan State University insensitively said, “If you have dyscalculia and your fiancé has dyslexia, I’d hate to see what your kids will be like.” Hence, when I got married, I made it my business to learn all I could about both. I discovered a whole field of scientists seeking the neurological origins of these paradoxical syndromes that leave individuals with extraordinary talents and perplexing inabilities.

What I also discovered was that I could do math, but it had to be on my terms. All the switching of operations and directions within even simple problems overwhelmed me, so I learned to use different colors to remind myself what operation I was performing — green for adding, red for subtracting, blue for multiplying, and black for division. I used a pen that had all four ink colors. I talked aloud to remind myself what I was doing and why. To reason my way through word problems, I drew pictures to illustrate them. I used a calculator or chart to double check my fact recall. I read aloud the numbers three times to make sure I saw them the same way.

Understanding Dyscalculia

Inquiry into the brain origins of dyscalculia is taking place all over the world. Researchers have found that the brains of dyscalculics are structurally different in the areas responsible for math processing, and that their brains light up in different areas when thinking about math than brains that have no difficulty with numbers. These findings show that while trying harder may not prove an effective strategy, trying differently can result in success. Like the blind learn by relying on their other senses, dyscalculics must likewise use their intact abilities to think about, reason, interact with, manipulate, and communicate mathematically. Since most are good with language, this means becoming fluent in the contextual language of math.

Computer apps, as well, offer dyscalculics other ways of learning. Researchers are developing programs to correct the fundamental skill deficits underlying math disability. Some programs help users develop automatic number sense, or the ability to instantly associate a visual quantity with a number or digit. Other programs build fast and accurate math-fact recall, visual-spatial skills, and directional sense. (See the table “Understanding and Helping Students with Dyscalculia.”)

Living with Dyscalculia

It’s still a struggle. For instance, a day after I make a purchase, it’s hard for me to remember if I paid, $238, $328, or $283 — as if my brain doesn’t think numbers are important enough to remember them exactly. This ambiguity is equally true for time, dates, sequences, and the physical layout of everything.

Of course, I’d rather not admit I have these embarrassing brain glitches. By putting them out there, I hope others learn from my experiences, search out causes and solutions, and are inspired to invent and evolve until they’re able to achieve what once seemed impossible.

Renee Hamilton-Newman’s expertise is in the areas of instructional design, learning disabilities (dyslexia, dyscalculia, and dysgraphia), educational technology, assessment, and remedial programming. She runs the nonprofit http://www.dyscalculia.org/. It provides a host of free information and tools for students, parents, and professionals of all ages and schools.

Permission Statement

This article first appeared in the November, 2014, issue of 2e: Twice-Exceptional Newsletter and is used here with permission.