“Abstraction is only a sort of trickery and deflection of the mind if it doesn’t constitute the crowning stage of a series of previously concrete actions. The real cause of failure in formal education is therefore essentially the fact that one begins with language instead of beginning with real and material action.” -Jean Piaget, 1976

After reading this quote from Jean Piaget, I am reminded of babies learning to walk, babies don’t just walk, there are steps to get there, crawling, balance, and more. When you think of it, you might not think of all these steps. I think the same can be said with learning math, without learning the smaller steps grasping abstract concepts can be futile. Looking back at my own experience with math, I can remember teachers helping me to grasp concrete actions before moving on to more abstract ideas. Making sure I was understanding the concepts before moving on helped to create the pieces that I would then use to grasp abstract concepts in older grades. Word problems are a good example of progression into using abstraction. At a certain point, students, don’t need the concrete or representational objects in front of them, they can take the data from the word problem to find their answer. Lessons that start with concrete actions might be lessons that utilize blocks to represent number sentences, this can progress into students knowing what the numbers and symbols represent and will eventually complete automatically without attaching concrete example to them.

I loved your example of babies learning to walk. I feel like that it applies perfectly to learning about math. Without learning the little steps, like addition and subtraction, how are we supposed to move on to more complex skills. We don’t just know how to do math, we are taught several little skills along the way.

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Hi Joelle-

Well said! Piaget is saying that without understanding the building blocks of math, an individual won’t be able to grasp its more abstract operations. The analogy between babies learning to walk and children learning math explains how important the small steps are. Thank You!

Alex 🙂

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Hi Joelle,

I enjoyed reading your reflection on Piaget’s statement. You made your response very clear in his message. I agree with you completely. We need to learn the baby steps before they are running. I, too, remembering being taught conceptually. I hope that there are still teachers using the same method.

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Hello Joelle, I enjoyed your response. I like how you made a clear understanding about concrete of abstract. Teachers really need to keep using this method. Great work!

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