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Memorization and Mathematics

Mathematics has always come easy to me. I excelled in it at school, it was integral in every job I had as a younger man, and plays a large role in my current line of work. I learned my single-digit addition and multiplication tables at an early age. I understood the concepts of adding and multiplying, so putting them to memory wasn't that difficult for me.

I went to a small private school and when they quizzed us on these math facts (“math facts” is what the kids call them nowadays), they gave us 10 minutes to answer 10 questions. I was usually finished before the teacher got back to her desk. I knew my math facts as well as I knew my own name.

When they started teaching us two-digit multiplication problems, I caught on quickly, but I noticed that most of my classmates struggled. Many of them took a long time to finish, and they got a lot of answers wrong. I didn’t understand why it took them so long, until the day when our teacher called a student up to the blackboard to solve 84×61.

The boy stacked up the numbers, multiplied 1×4, put it below, then multiplied 1×8, put it below, then put the 0 as a placeholder before multiplying the second line of numbers. (He had executed the problem perfectly up to that point.) Then, he put the chalk down, looked down at his hands, and started to count his fingers. After 10-15 seconds, he picked up the chalk again, put a 6 down below and carried a 2 on top. He had miscalculated 4×6, getting 26 instead of 24.

All of a sudden, everything made sense… Many of my classmates did not memorize their math facts. That’s why it took them so long to solve the problems, and that’s why they were getting a lot of wrong answers. They knew the method for multiplying two-digit numbers, but they didn’t memorize the single-digit math facts within the method. It finally added up (no pun intended). I’m not sure that the teacher saw the root of the problem. She merely corrected the boy, and when he got to 6×8, she told him that it was 48, in order to keep the class from stagnating further.

During the past five years, the number of students who know their math facts before our first session, has dwindled to roughly 50%. This goes for 3rd graders through 9th graders. They all have good memories; they know all the lyrics to songs, they know all of their family’s and friends' birthdays, and they definitely know the dates of school holidays. But they choose not to use their memory for math.

I explain to the them that, until they know their math facts, they will struggle more and more as they go forward in school, and that it’s possible that they might be left back a year. Most of them get the message, and memorize them. The few who need more convincing, all have the same defense… “Why do we have to memorize our math facts when we can just use a calculator?” My pat answer is always, ”You won’t be allowed to use calculators on tests, so if you don’t know your math facts by heart, then you won’t have enough time to finish the tests.”

Well… Unfortunately, I cannot use that answer for every student anymore. I currently have two Freshman students who are allowed to use calculators during exams. Their schools even provide calculators to the kids who forget to bring theirs. To give parents some solace… These particular students will indeed learn their math facts (as do all of my students). There will be some who will never recognize the importance of them, but I recognize it, and everyone who hires me knows that I put the children’s best interests far ahead of mine. Calculators or not, I don’t intend to change my method of tutoring. And, if someone disagrees with my methods, then I suppose I’ll cross that bridge when I come to it … Nobody’s disagreed with me yet.

--Editor, Tutor Pros

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Daniel Dayan of Tutor Pros

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