I asked on my Facebook page what people thought of this article "Memorizers are the lowest achievers and other Common Core math surprises".
Here are some of the comments so far:
Deborah Shalibo Skroch Certain "building blocks" like multiplication tables must be internalized. That is the big puzzle to me. What is the best way for students to have worked with them enough to truly digest them enough that they become a part of their brain chemistry. When you think of 100, for example, can you picture it as variations of groups of cubes (10 groups of 10, 4 groups of 25, etc). Is your mind "math flexible"? To me, there is a difference between this and "memorization". Kids who never get to this point are the ones who continue to struggle bc they always get caught up in the things they never "internalized" and they can't use those building blocks to puzzle things out when they get stuck.
Tim Koschmann I'll be honest I think it needs to be a mixture of memorization and problem solving.
It's like laying the foundation to building a house. You have to lay the foundation before moving forward with the construction. Sadly I see too many kids today still missing the foundation.
Willow Drummer I think the ability to figure out a problem is the most important ability. Rote memorization of facts is not a higher order thinking skill, and demanding that students learn "math facts" can hold back kids with great problem solving abilities, but processing issues. Calculators can only solve what the student puts into it.
Deborah Shalibo Skroch But trying to solve a problem with incorrect basic assumptions will never get you to a workable solution.
Tom Jackie If you can't factor a number quickly, your math fluency is greatly hampered. Quick factoring requires knowledge of multiplication facts! There are after all only a few if you go up to the 12's. I agree with Tim.
John T. Duffin How does one teach the curiosity necessary for inquiry, or achieve the comprehension required for anything but the most situational reasoning? I'd love to figure those things out. I certainly agree that the structure of public school favours memorization.
Mixsy Trinidad Curiosity is inherent and must be developed. Turning away from "what answer did you get" to "HOW did you get that answer?" "Why does it make sense?". Opening up the classroom to discussions around context questions rather than arithmetic gets conversations going. Cultivation of a safe classroom environment where all are encouraged and expected to contribute. While this takes time, it is 100% worth it!
John T. Duffin I understand the basics, of course... I think of the kids who hit 8th grade without a positive experience to speak of; in particular, those students who haven't picked up the reasoning or even application associated with something like multiplication. Engaging twenty such students in a class of thirty... I've achieved more resentment than result.
Mixsy Trinidad Yes, John T. Duffin, and it's because by 8th grade they've been indoctrinated into "get the results, quickly" and are resistant to change. This is why this change needs to happen before kindergarten, the inquiry approach to learning has to be fostered by everyone in the child's life.
It's a monumental effort that needs to occur, how? I don't know, but it needs to change.
Deborah Shalibo Skroch I have maintained for a long time that a big part of our problem lies in having more elementary educators who embrace mathematics. Unfortunately, too many teachers are uncomfortable with math, so how are our children going to develop a love of the subject?
Melissa June P Memorization through real world, applicable practice makes the best sense. After all, if you need a skill, then you will want to practice and retain it. If you don't need that skill often, then know how to look up the answer on the rare occasions when you do need it. This is how unschooling was born.
Mixsy Trinidad YES!!!! Memorization only gets you so far because the content is taught in isolation and connections aren't made. Having taught at the collegiate level and in the elementary education mathematics program I can attest from the countless journals that students want the unpacking of the procedures. They want to understand the "why" behind the concepts. Often they say "had I known all of this sooner I would have gotten further in math in high school.". To me this speaks VOLUMES!!
We also have to educate our parents and others as to why the methods behind common core can work if delivered appropriatly. There is no such thing as "common core math" for example. What we want is for students to develop a richer understanding of a beautiful subject and learn to think and ponder and walk away saying "This answer makes sense because....."
Lesley Beddard Holley Amen.
Kathrine Box not a surprise
Let me know what you think, join the conversation here!
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