Student G was an elementary school student. He was in grade 6 when we started tutoring classes. He did not know multiplication table, and consequently, he could not learn how to divide numbers. He could not complete the academic requirements of grade 6 and the school decided to put him into the special education class with other weak students that require extra help.
The whole story:
I started to teach the multiplication table. I gave him all tips and tricks on memorizing multiplication facts. I explained how to use some facts that he remembers to calculate multiplication facts he doesn’t.For example, whenever we need 9x8 we can use 10x8=80 and 80-8=72 because 10x8 is a sum of 10 eights, while 9x8 has only 9 eights. Another example: if you need to figure out how much is 6x7 you can use 6x6=36, which is very easy to remember. The next multiplication fact you are looking for, 6x7, will equal to 36 + extra 6. His mom was helping him at home while he was doing the homework I assigned.
We have tried that for more than 2 months. He was learning and understanding well everything during the lesson, and forgetting on the next day.
This situation would continue forever if at some point I hadn’t realize that he is tricking us by playing “weak memory” game because we are accepting his weaknesses and offering our help again and again.
I remember that when I was at elementary school all my classmates memorized multiplication table pretty quickly, simply because not memorizing it for months was not an option for my very strict teacher. I still remember her severe voice when she was saying: “You need to memorize it so well that if I wake you up in the middle of the night you have to be able to answer how much is 7x8!”
I realized that I have tried everything except for my teacher’s method – putting very strict deadlines and boundaries on for how long he can keep forgetting. With the support of his mom, I told him that he has ONLY one week to memorize multiplication table completely and I do not care if it takes him to practice for 5-6 hours per day. No more explanations and repetitions will be provided. I made a strict face and repeated my teacher’s mantra about middle of the night. He started to cry horrified by our cruelty, but we (me and his Mom) have remained adamant.
And, imagine, by the next week session 80% of the multiplication table was memorized. Even though he was forgetting some facts but he was using the methods that I was teaching him. After one more week he memorized everything and we could move to learning division.
Very often problems in Mathematics are due to low demands on students, very loose boundaries, and the absence of discipline. I met many high school students that do not know how to study to succeed in mathematics. They do not check their answers when practicing questions at home, do not self assess themselves to identify the weaknesses. Many can not plan their studies, leaving all practice on the night before the test.
When I ask students which way they memorize things, for example poems, formulas, definitions, very often they are telling me that they don’t know because they have never memorized anything. The majority of teachers provide formulas sheets and students do not need to remember them. On the other hand, our education, in any area, is based on remembering facts, methods, concepts, procedures and students have to train their memory to be able to complete successfully the courses.
By the way, knowing the formulas in physics and mathematics contributes greatly to understanding, simply because you can’t memorize the majority of them without understanding the development, the logical structure, the meaning of each symbol in it.
In the situations like the case above I recall the words of the main character from Davies Robertson’s “Deptford trilogy”:
“...I gained skill, because I had a great master. And that means very often an exacting, hot-tempered, and impatient master, because whatever my great countrymen Pestalozzi and Froebel may have said about the education of commonplace people, great things are not taught by blancmange methods ….”
To some extends and for some people it is true, in my opinion.