As a high school physics teacher, I frequently notice that some of my students’ math skills seem to stop developing at a certain level. As a result, chemistry and physics courses that require students to utilize their math skills to solve problems turn into Mission Impossible. There are probably many reasons for this, but I believe a major cause is that many school districts no longer expect students to memorize the multiplication table. Some education experts in this country believe that requiring students to memorize things stifle their imagination and creativity. This idea can be misleading and harmful in math education if students are not requested to remember anything.
When we learn to read, we start with the alphabet. After we memorize all the letters in the alphabet, we learn short words like cat, bat, pat to memorize how letter “a” is pronounced in them. Only afterwards, do we know how phonetics work, allowing us to tackle longer and less common words... Similarly, our math skills are accumulated step by step. We learn to count first before we try to add. We learn subtraction only after we have mastered addition. We will not learn multiplication before we grasp both addition and subtraction. However, because many students do not memorize the multiplication table since that is not required, they don’t have a solid foundation to learn the next math skill: division. When they struggle with multiplying and dividing of whole numbers, how can we expect them to master decimal numbers and their operations? The concept of fraction is based on division and closely related to decimal numbers. On top of that, we can build the skill of fraction operations. Then we learn ratios, percentage, and other useful math skills. All math concepts and skills the children learn in 4th grade and up depend on the basic skills of adding, subtracting, multiplying, and dividing whole numbers, just like higher floors are based on the ground floor and foundation of a building.
I have heard many people say that they were good at math until the third grade, when math somehow became more and more incomprehensible. I think a big reason is that they haven’t really mastered multiplication and are unable to perform simple multiplication without a calculator. The foundation of their math skills has holes and needs reinforcement. Trying to learn fraction without mastering multiplication and division is like trying to write an essay without knowing any three letter words.
If you want your students to feel comfortable with math after third grade, encourage them to learn the multiplication table. There are many educational games on Amazon.com that can make it fun. I prefer real board games to online games for young students, but if you need free online resources, there are some math games at https://www.multiplication.com/games .