What good is memorization? Shouldn't we have the students understand rather than memorize? Let's see what would happen if we only focused on memorization or only focused on understanding. | Fast Fact Sequence for fourth - eighth grade coming soon to TPT - Check us out at mathNERDS |
Memorization Only Picture this: Memorize every word in the English language so that you can read a book. That's a lot of Memorization. Picture this: Memorize all the numbers and how they are represented (without understanding place value this could be difficult). - That's an infinite amount to memorize. It could take us awhile. | Understanding Only Picture this: Understand how the letters work together to make sounds, but you can't remember which letter makes which sound. How can you put the sounds together, if you can't remember which letter goes with which sound? Picture this: Understand how to count, but don't bother remembering the order of the place values or digits - that's part of memorizing. |
Memorization is the first way we learn.
Some memorization must take place, but is that all there is to learning?
Obviously not!
Have you ever witnessed a geometry student try to memorize all the different volume formulas? Surface area? If we tried to do this without understanding where the formulas came from, we would not be able to use them well or come up with new ones that we previously did not know. Math is full of connections that students who memorize without understanding never get. These connections are what mathematicians use to come up with new theorems and ideas.
Teach a student to look at the basic shape of an object and build the equations from there. To do this easily though, certain formulas should be memorized already.
For example:
For finding the volume of a prism or cylinder, all you need to understand is that the area of the base is stacked up to a certain height. Now, if you have the formula for the area of the base memorized, you can find the volume of any prism or cylinder. Remembering that the area of a circle is pi r squared is easier than remembering that the volume of a cylinder is pi r squared h.
Knowing that you are looking for the areas of the net of an object is a lot easier than memorizing the surface area of each different type of object. Now you just need to know how to find the areas of 2D shapes. Finding the surface area becomes easier when you have the 2D areas memorized.
Memorization of multiplication tables, factor pairs, prime numbers, and perfect squares can be so helpful when students get up to algebra and beyond. Knowing the factor pairs and prime numbers helps with reducing fractions, which in turn helps with solving equations. Prime factorizations can also help with this. Knowing the perfect squares through 20 is great for when students get to square roots, and knowing factor pairs and prime factorizations is great when it comes to finding imperfect roots.
In my own classroom, I have implemented a series of fast facts that have helped the students master concepts that make the higher level material and understanding easier.
The problem with most sets of fast facts is that it is the same thing over and over again. This series allows the student to continue on to something different after succeeding on the first set. It still allows them practice with the previous set of facts because the next set is based off of the previous. For example, division comes after multiplication. Factor pairs comes after division. These go through imperfect roots.
Last year, I had students that easily understood the concept of imperfect roots and how to find their exact value because of this two minute program at the beginning of class. As a student would move on I would quickly describe the new concept, which was easy to understand because of the build toward it with the other facts. More advanced students got to learn concepts that are usually understood in a later class. These were 6th grade and under. Knowing how to do this makes the approximation of imperfect roots easier when they are required to do them in 8th grade - I don't think finding the exact value is part of the core curriculum until much later. In this case memorization led to understanding more difficult concepts!
Some memorization must take place, but is that all there is to learning?
Obviously not!
Have you ever witnessed a geometry student try to memorize all the different volume formulas? Surface area? If we tried to do this without understanding where the formulas came from, we would not be able to use them well or come up with new ones that we previously did not know. Math is full of connections that students who memorize without understanding never get. These connections are what mathematicians use to come up with new theorems and ideas.
Teach a student to look at the basic shape of an object and build the equations from there. To do this easily though, certain formulas should be memorized already.
For example:
For finding the volume of a prism or cylinder, all you need to understand is that the area of the base is stacked up to a certain height. Now, if you have the formula for the area of the base memorized, you can find the volume of any prism or cylinder. Remembering that the area of a circle is pi r squared is easier than remembering that the volume of a cylinder is pi r squared h.
Knowing that you are looking for the areas of the net of an object is a lot easier than memorizing the surface area of each different type of object. Now you just need to know how to find the areas of 2D shapes. Finding the surface area becomes easier when you have the 2D areas memorized.
Memorization of multiplication tables, factor pairs, prime numbers, and perfect squares can be so helpful when students get up to algebra and beyond. Knowing the factor pairs and prime numbers helps with reducing fractions, which in turn helps with solving equations. Prime factorizations can also help with this. Knowing the perfect squares through 20 is great for when students get to square roots, and knowing factor pairs and prime factorizations is great when it comes to finding imperfect roots.
In my own classroom, I have implemented a series of fast facts that have helped the students master concepts that make the higher level material and understanding easier.
The problem with most sets of fast facts is that it is the same thing over and over again. This series allows the student to continue on to something different after succeeding on the first set. It still allows them practice with the previous set of facts because the next set is based off of the previous. For example, division comes after multiplication. Factor pairs comes after division. These go through imperfect roots.
Last year, I had students that easily understood the concept of imperfect roots and how to find their exact value because of this two minute program at the beginning of class. As a student would move on I would quickly describe the new concept, which was easy to understand because of the build toward it with the other facts. More advanced students got to learn concepts that are usually understood in a later class. These were 6th grade and under. Knowing how to do this makes the approximation of imperfect roots easier when they are required to do them in 8th grade - I don't think finding the exact value is part of the core curriculum until much later. In this case memorization led to understanding more difficult concepts!
Let's understand what we are memorizing, and use our memorization to further our understanding!