When I reflect back on my experiences as a student in the math classroom, flashbacks of constant memorization fill my mind. As a primary ELL (English Language Learner), I struggled to retain math concepts from grade to grade and became very anxious during math class. I became a silent student that would rarely participate and quickly learned that if I stayed silent long enough, teachers would eventually give up and stop asking me math questions. However, whatever I lacked in comprehension, I made up for in effort and memorization.
I found a way to cope in the math classroom and realized that if I memorized hard enough and followed the steps demonstrated by my teacher, I would be able to do the math. Sure enough, as I approached the junior grades, I would show up to school in September and would still know my “multiplication facts”. I remembered to ‘carry’ the number when adding, ‘borrowing’ from number to the left when subtracting, and writing a zero when multiplying multi-digit numbers. I didn’t know why I had to carry or borrow or write a zero but it didn’t matter because I could do the math. That just drove me to memorize even more and found myself studying hours in preparation for math unit tests. I eventually evolved into a master of memorization and memorized anything that I couldn’t understand (cross multiplication, dividing fractions, integer operations, area formulas etc). By the time I reached the intermediate grades, I was getting A’s in math and was considered a great math student by my teachers. I thought I was a pretty darn good math student too. However, my perception of math at the time may have been a bit skewed. I thought math was all about studying hard, memorizing the facts, procedures, and formulas. In grades nine and ten, I was on top of the math world and I equated success in math to achieving math marks in the 90’s. By that time, I had mastered the art of deciphering the high school math textbook. If there was a word problem that I was confused with, I would just find the similar sample problem in the textbook with the different numbers or I would look to the answer key at the back of the textbook, find the solution to the problem and try a variety of procedures or formulas hoping that one of them would eventually lead to the correct answer. I knew how to play the game and was I winning… until I reached senior math.
As I was introduced to the world of trigonometry, calculus, derivatives, vectors, logarithms, I could feel the old but familiar sense of anxiety that I experienced as a primary student slowly creeping back into my mind and eating away at my confidence. I became desperate when my A average fell to a C average and did the only thing I knew how, I memorized harder, pulled all nighters and took summer school. I was still able to graduate from secondary school with an A average with great effort and memorization but as I remember and reflect on my entire math education I realized that I wasn’t really “doing” math, I was “memorizing” math.
I’m not trying to imply that I never learned or understood the math that I was taught. I’m saying that the way I was taught math and learned math was very inefficient. My perception of math was repeating and applying standard algorithms and formulas that I never really understood. I was never asked to try and solve a problem using my own invented algorithms. I was never exposed to mental math strategies for the basic operations. I never used tools like the open number line or an array to add or multiply. Problem solving wasn’t embedded in the curriculum when I learned math but rather a unit that was also taught very procedurally. Math solutions were expected to look identical to the teacher examples and marks were deducted for missing a step or forgetting an equal sign. It took me a long time to realize and accept the fact that my perception of math was false and that I was a product of procedural teaching and it was a hard pill to swallow. Memorizing is not a mathematical process and not an ideal way to acquire an understanding of math concepts and skills. Math in the classroom is about problem solving, reasoning and proving, reflecting, selecting a variety of tools and strategies, making connections, representing , and communicating.
Roflections 
I think many kids have similar experiences going through school. I can remember asking some top math students in a school I worked in before this one some questions about math, but phrased differently than the kids were used to. They couldn’t answer anything about math unless I carefully worded it in the fashion they were used to.
I definitely was one of those students that had trouble adapting to math problems that were worded differently or didn’t follow the problems that were assigned in class. I was the student that could fire off the multiplication facts up to 12 x 12 but would get stuck if a teacher asked me 15 x 12. At this point, I would draw in the air and try to solve it with my finger using the standard algorithm. Classic case of the standard algorithm not being the most efficient strategy for multiplication.
Isn’t it funny how often ‘success’ in school is actually failure in learning?
I think the pseudo ‘success’ that you’re referring to is students memorizing standard algorithms and formulas for a unit test, getting an A or a B but then forgetting the steps to the algorithms and the formulas a few weeks later thus not really learning any math at all and frustrating their teachers next year saying, “we never learned that last year”. When you think about it, there’s some truth to that phrase.
I think that most of us started learning mathematics that way. I know that I did. I also understand that it turns some people off. There came a time for me, personally, that I started to get insights and appreciate the beauty of mathematics. I wish I could figure why and how it happened.
Growing up my household, math was a subject that was focused on more than any other subject. My parents would often bring home math workbooks for me to work on during the school year and the summer and taking math all the way through secondary school was also an expectation. I didn’t really appreciate math growing up because it was practically embedded in my life. I never developed an appreciation for math until I went to university and took math courses with classmates that had a true passion for math and learning from some passionate math professors. I also developed a true passion for math in education when I became a math facilitator and worked with some of the most enthusiastic math educators I’ve ever met.
Math became meaningful for me during 2nd year of university, when we branched out into set theory and number theory. Before that, it was all memorization of facts and procedures. I think that’s why I developed a strong bias towards using computers for doing calculations and for performing algorithms, and using brains for modeling, imagination, and creativity.
Funny, there have been so many math facts that, years later, suddenly made sense to me. An example is 2 divided by 1/2. So simple, yet never modeled until years later, while teaching high school math.
I’m interested in watching students who use DreamBox. It’s only available for primary students right now. It involves students in activities where the math isn’t always obvious. It’s more conceptual.
I was taught math via rules rather than learning concepts first. It seems to me that learning the concepts first and gradually learning to apply the math would lead to more real success.
I’m not sure not sure why you felt the need to memorize in math. while it took time to learn the multiplication facts, algorithms unfolded logically and were predictive. Do not wrongly assume that to be successful in math, memorization is required. proficiency comes with practice as does learning. Recall of math facts is rapid when they have been used repeatedly. Doing a single word problem in a math class and discussing it’s various possible solution does not promote numeracy skills but rather communication skills. for kids to get good at math they need to do math. playing board games or card games where scores are calculated and computations made promotes mathematical literacy (ie numeracy). Those who are math phobic need to simplify the task and practise more. Avoiding math will only increase the problem.