You say memorizing is not a good way for students to learn math. Why?
It’s not that memorizing is bad; it’s just that many students try to memorize 100% of the math. MathCubed students know they only need to memorize about 5% of the math and focus on understanding the other 95%.
A student’s success in math is directly dependent on how much they understand, not how much they memorized (exceptions described below*). Math tests assess a student’s understanding, so if a student wants to do well in math, they must understand the math.
The following are some of the PROBLEMS memorization, without understanding, can cause:
Memorization without understanding has no staying power: the student doesn’t retain the math concept over time. In other words, he or she will inevitably forget it.
Also, not being able to retain the math means the student has to keep learning it over and over again, either when studying for their final exam or when they haven’t taken math for a summer, a term, or a year. Having to re-learn the same thing repeatedly quickly leads to frustration, which causes self-doubt and discouragement.
When a student memorizes math, they memorize one form of a question. So if the question is presented even slightly differently on their homework or a test, they don’t know how to do it.
Memorizing each math concept in isolation, as though it has no connection with a simpler version of itself from lower-level math, is an overwhelming and inefficient task. There is a continuum to each math concept, from its most basic form (usually taught in elementary school) to its most advanced. The more quickly a student can see the connection between a math concept they are currently trying to learn and the simpler version of the same concept that they already know, the more quickly they will understand the “new” math concept. For example, there is a big difference between memorizing 2 x 3 = 6 versus understanding why 2 x 3 = 6. If a student knows why 2 x 3 = 6, then when they are introduced to the more advanced form of that concept in Algebra, as in 2(x+3), they can make sense of it quickly.
Word problems are another reason it’s so important to understand, not memorize, math. If a student doesn’t know why they are doing what you’re doing in math, word problems become extremely challenging. A student can’t memorize word problems since they are never the same (see the third point above). Memorization is the #1 reason students struggle with word problems.
A student’s math marks can plummet in grade 9 if they have relied exclusively on memorization in grades 7 and 8, even if they were getting good marks. Why? Because memorizing may work at the lower grade levels but it does not work in high school math. If a student relies exclusively on memorizing math in high school, the odds are they will either barely pass the course or fail it! And, if a student barely passes a course this year, the odds are they will fail it next year.
*Important to know: There are two exceptions to when a student can excel by memorizing:
1) If a student has an exceptional, or photographic, memory, they will be able to do well at math without making the effort to understand it.
2) If a student is willing to spend up to 3 hours every single day studying math, they will probably do well. This intensive form of studying is popular in many cultures; the learning takes place as questions are done again and again and again until they are all memorized.
In summary, if a student does not have a photographic memory, or is not willing to study math for up to 3 hours every single day, then memorization won’t work. If that’s the case, then there is only one option left (and it’s a very good option) - understanding the math.