Maria Pena’s Strategies For Learning Mathematics—From the Perspective of a Graduate Student With Severe Right Hemisphere Dysfunction
Or…
How to Learn Math When Your Eyes Lie to You
SOME BACKGROUND
In order to understand how my brain fails to learn math via conventional means, it is of benefit to have some background as to what my math history is, with respect to a Non-Verbal Learning Disability (NVLD), or severe right hemisphere dysfunction. Hopefully I will not bore you with a summary of my educational history, but I do want you to come away from reading this paper with some understanding about what students like me endure when it comes to learning the language of math.
My childhood and youth academic experiences were a treacherous path, laden with ironies. Teachers could not understand how I was so verbal, had a terrific vocabulary, yet I would get lost finding my classroom from the Special Education Trailers (that was where I went due to my EMR diagnosis) on the other side of the school, and was still working on basic math for two straight years. I could not remember left from right, could not draw geometric shapes (or anything for that matter), and could never remember the sequence to doing a long division problem.
Couple my math inabilities with the emotional baggage of abusive teachers. My Fifth grade teacher thought I was faking, when I could not do a test of long division problems; her solution was to take a big red marker and mark the exam with a big bold red X; she gave me a clean test paper, and told me I could not get up from my desk until the exam was correct and complete – but here was the punishment – my desk was moved outside with my chair on to the patio, and when I sat down, she closed the big metal and glass patio doors with a clang – all the while the students in the class were laughing – the sad part was, that I still did not know how to do long division, and ended up sitting there in the same spot for the entire day.
High school was a nightmare. I repeated math classes a few times to no avail. Algebra was incomprehensible to me; I took geometry twice, as the school thought if I failed algebra, I might do well in geometry (great reasoning, right?). I had an instructor in geometry, who would belittle me constantly. I would memorize all the postulates, axioms, and properties; but when I was sent to the chalkboard to do a proof, it was like a piece of my mind was missing. It was dehumanizing when the teacher would not let me sit down like the other students who had finished their problems; he would lecture, then periodically stop and ask me it I had figured it out, and then would ask if I would ever figure it out. By the time I finished high school I was emotionally damaged goods.
College was difficult, but El Camino College literally saved me, as I realized that I could do college work, yet I suffered to get through the math requirements. My anger, determination and perseverance eventually led me to finish a degree at UCSD, then on to graduate school. I received my Learning Disability “diagnosis” my second year of graduate school, and with accommodations, my abilities started to become more apparent in my work.
So this is what you deal with emotionally when you go through school with a NVLD. This is what a DSPS professional deals with on a daily basis, when a student walks in their door on the verge of a breakdown, because they have taken the lowest level of math three times, and cannot seem to pass the class. Not only do you have to repair a broken psyche, you have to attempt to help them learn a language, all the while knowing that even if they succeed, math will always be traumatic for them.
So what can a student do to learn math, when their eyes give them faulty information?
The methods I used in some respects are unconventional. You may scratch your head, and ask if this idea, or that method really works – for me it did and to this day it does work. It did not take me from F’s to A’s, but it helped me along so that I could pass the math classes (sometimes barely pass), concentrate and develop what few strengths I had to get an education and a career.
The methods I use depend on what type of math you are doing; you may have heard of them from me or someone else before, but for students who feel math is hopeless, a change from a failing grade to a D grade is movement in the right direction, and I guess it is worth the time to at least consider what I am talking about.
Math Strategies: Some of these ideas you may already implement when working with students, so please forgive me if you have heard this/read this all before.
I will take you through from start to finish; I feel that to learn a subject that is arduous and scary for the student you have to look at the whole picture.
Environment: The environment is extremely important. I am an auditory learner; at the time in my life that I took math, I literally thought I was a moron. – I had no LD diagnosis, no ADHD diagnosis, and no accommodations– so I learned what to do by trial and error.
The student needs to be in a clutter free environment. There should be only the books, calculator, multiplication table, pencils, and scratch paper on the desk. The backpack, rolling duffle, purse, cell phone (Turn it off) and other unnecessary stuff should be under the desk, put away. To the right of the supplies on the desk, should be a very simple kitchen timer (I will explain that one later). The student should not take phone calls, play with their IPOD or PDA, or do anything else but math, and this is why the desk has to be clutter free with only the necessities on it. Water, soda, and coffee are okay to have on the desk.
There are some other things needed close by in the environment – highlighters – as many colors as possible, colored pencils, a small tape recorder, 2 large safety pins, and two tubes of scented lip balm – like fruit scented Chap-Stick, a cherry and grape or whatever scent the student can get.
No music (if they are auditory learners, they will get into what they are hearing, not math), no friends, no study buddies. Subconsciously, the student will try to get out of devoting their full attention to math – I know this first –hand, because I would always go to study groups with the best intentions, and end up talking, laughing and going out for pizza, accomplishing absolutely nothing. Solo was the best way for me to study with no distractions.
The timer on the right side of the desk is there as a task -master. I realized early on that the extent of my concentration was correlated positively or negatively to my like/dislike of the subject. I remember saying how long and hard I would study, and I probably and truthfully did put in long hours, but I was understanding very little of a subject that was almost impossible for me to master. The timer became my study buddy. I developed the 15 / 5 style. My concentration for math lasts maybe about 15 minutes at a time, so what I would do is study for 15 minutes; when the timer rang, I would get up out of the chair, re-set the timer for five minutes, then for that five minutes I would stare at a wall, put my head down on the desk and cat nap, get a snack, use the restroom, etc. – when the timer rang again, I would re-set it for the 15 minutes, sit down and resume what I was doing.
MATH PROBLEMS
NUMBERS and SIGN ERRORS:From the time I began to learn basic math in elementary school, numbers and especially signs were a big problem for me. Part of the issue is that if a teacher quizzed me on individual signs, I would do okay; put them together with numbers, and I was lost. I figured out two main things about numbers and signs: my eyes were lying to me – first, I had good vision, but when I would look at a math problem, it was if I had processing blindness, like my brain was protecting me from the trauma of what I was learning, and blocked part of the problem out of my processing line of sight. The second thing was that although I could learn a single concept about a number or a sign, I was unable to retain the concept and apply it into a more complex problem. It is like learning a foreign language, where you can conjugate all the verbs, but are unable to write a sentence.
My answer to number and sign errors was color-coding. I would use brightly colored pencils, and assign a color to each number or sign I was missing, or made errors with in my homework and exams. For example, in college, quadratic equations were a nightmare for me – I would work out the problem and literally block out the smaller equation, in the denominator under the vinculum (fraction bar). So fraction bars took on a color, from which I never deviated. My order of operations was completely color coded, so that when I worked out a math problem I would begin to designate what the order was by the color more than remembering the actual order. I would use brightly colored highlighters in division problems, and in long division I would line up the columns with colors, because I could not keep my columns straight.
I never could use multiplication tables effectively, because they involved tracking with the eyes; so if I had to use one, I would get out the colors and highlight each row a different color. When I still had trouble tracking, then the brightly colored index card would come out and I would glide the card across the table, as if I was reading a book across its page. This was not a panacea, but it helped me negotiate the table. To this day, anything in a table or chart-like formation I color-code automatically; even histograms, because I can only negotiate them using color to help my processing.
THEORIES, POSTULATES, AXIOMS AND MEMORIZATION
If there are properties, theories, axioms, postulates or anything in words that need to be memorized; I would record it onto cassette tape, then listen back to it over and over again until I started to memorize what I was learning. This works great for learning formulas too. The only caveat is that just because I memorized it, does not mean I can apply it in a problem – that is what I meant when I said earlier that when doing a geometric proof, it was like a piece of my mind was missing.
WORD PROBLEMS
It was a very rare occurrence when I got a word problem correct on a test.I have come to realize that there are two types of difficulties students with learning disabilities have when working a word problem: The first is when they read a word problem, they could probably successfully solve it, but they do not understand what the question is asking them to do (usually this is a left hemisphere LD, i.e. dyslexia); The second type of difficulty is that the student understands the problem and what it is asking them to do, but cannot retain nor process the sequence, concepts or values of the variable – in other words, they cannot translate what the question is asking in English to Mathlish (this is the type of right-hemisphere LD that has plagued me all these years).
Again, I look at the question, read it aloud to myself (or if in a test with a reader, while I follow along). The first thing I do is to highlight the parts of the word problem in one color that are not needed to solve the problem, and I make a concerted effort to ignore that color. Then I take what I think is/are the important part(s) of the question and assign two highlighted colors to them: the first color I use to highlight tells me what I think the question is asking, the second part is what information I will need to do the set-up. I apply the colored pencils to all the signs, and assign different colors to the variables, I will mumble out loud to myself the necessary steps to give me some auditory reinforcement as to what I have learned and how to apply it in the problem.
Once I have completed that task, I attempt to write out using the colors and solve the problem. What few problems I did solve in College, I did use this method of set-up.
GRAPHS AND GRAPHING
This has always been a nightmare for me, so please forgive me if my method sounds unconventional. I suffered through intermediate algebra, college algebra, and baby calculus, and repeated the courses many times. Without any kind of accommodation I was left to my own devices. In Calculus, Limits were the worst; “as H approaches 0” – that was gibberish to me.
Concave up and concave down were so confusing to me.
When I try to do graphing, I take out all my highlighters, colored pencils, with the addition of the two big safety pins and the Chapstick tubes.To memorize concave up from concave down in calculus, I would first draw each graph on a piece of graphing paper. I would color the line I drew with a specific color, and then write its identification next to it. The next thing I would do is get my olfactory and kinesthetic senses involved: I would take the safety pin, open it and make pin impressions along the line I had drawn and colored; then I would apply the chapstick over the line, each one with a different scent. I would study the graphing to identify it by running my finger over the impressions, while saying what the formation was called out loud, and then I would smell the graph over and over, until it was burned into my memory, and believe it or not, it worked! It also worked out great when I had to learn which were the Y-axis and the X-axis too. It would probably work for students who need to learn the positive side and negative side of the number line.
When I read a graph, it is difficult for me, even when I color-code all of it. When I have to read a graph to discern what it is trying to convey I will usually talk it out to myself using the colors and working through it very slowly. The time factor can be problematic because it does (and always will) take me much longer than the average “normie” to figure it out.
Well, that is all I can think of for now. It is my sincere hope that if this strategies info can help one student, it will have been worth my time to help my colleagues in the field help an LD student through a math class with a passing grade.
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