Knowing Vs. Understanding

Is knowing something memorizing it? This was a topic of debate in class last week. There were basically three sides to this debate:

  1. Yes, students need to memorize times tables in order to know multiplication. 
  2. No, students don't need to memorize times tables in order to know multiplication, they only need to know how multiplication works. 
  3. A bit of both; students should understand what multiplication is but also memorize the tables so they can actually solve multiplication questions. 
My opinion is that memorization does not represent knowing something. Quite the opposite, in fact. I can't memorize anything - if something has no meaning then I will forget. Instead, why don't we teach students a strategy for solving multiplication? There are so many! Then, they can solve any multiplication question they face without memorizing anything. They 'know' how to do multiplication if they can solve a question. Nowhere does it say we need to do math quickly. 

The video below is a great example of knowing how to do math without memorizing anything. None of these students memorized how to multiply 18 x 5 - instead, they know strategies for solving multiplication questions.


This method of 'number talks' is also a great one since it helps students identify the meat of what they're learning: the method not the solution. 

Comments

  1. David Celebre17 September 2016 at 14:10

    Excellent points Megan.

    A common misconception of learning is that memorization is everything. However, how can you memorize something you don't understand? Is that very effective in terms of learning abilities? I think not. Students who memorize ONLY tend to forget why exactly they are memorizing a topic in the first place. If they were to focus on UNDERSTANDING the topic ahead of memorization, then they will have a better grasp on the topic which in turn should lead to simple memorization.

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  2. Anonymous19 September 2016 at 14:45

    Hey Megan,

    Great post! I appreciate your comment "memorization does not represent knowing something" because it sparked an idea in my mind. I personally think there should be a balance between memorizing and learning the processes/procedures for doing math. I like how you have approached the topic with factual evidence that you can use when teaching your students or explaining your position to other educators. Great work!

    ReplyDelete
  3. Ms.Gujadhur19 September 2016 at 22:36

    Hi Megan,
    I like the points your post highlights, and enjoyed the video you shared! During this discussion, and reflecting back on my experience of learning multiplication I remember doing weekly 'Math Drills' in grade 4 and grade 5. It was a test of 50 equations, related to curriculum expectations involving addition, subtraction, multiplication and division. This test was timed and really stressed on just the knowledge portion of the questions as well as ones ability to answer quickly. Personally I learned to memorize my times-tables in order to complete the test in under a minute, but neglected truly understanding the math concepts because of the pressure to produce a speedy answer. I agree with you in that math does not have to be done at swift pace, and as we shift away from this train of thought and focus more on the understanding portion of math concepts, students can receive a more meaningful learning experience.

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