When I was a student in high school, I did a lot of peer tutoring. It was when I figured out I wanted to be a math teacher. I was struggling to get a peer to understand how to solve a one step equation. I used the method I saw my teachers use, basically just talking about inverse operations, but it wasn't working; no matter how many times I said it. I asked my teacher at the time if there was another way, but was disappointed when I was told there wasn't. I was also skeptical of this answer. How can there not be another way? Fast forward to my early teaching career. I found Algebra Tiles in the cupboard, where they were stashed away from the previous teacher, never used. I tried to make sense of them, but got confused and stashed them back in the cupboard. Fast forward another couple of years. I went to a workshop by Nancy Berkas and Cyntha Pattison in my northwest corner of Minnesota. They introduced Algeblocks (the 3D version of Algebra Tiles). As they explained their use, a lightbulb burst on and lit the path for the rest of my career. I found the "other" way to teach solving equations and more. I found a way that all students can grasp an abstract concept and succeed. I also found a way to get my smarty pants students to think differently and challenge their tendencies to take the easy road of memorizing steps. So, here is the idea, give students something physical that they can manipulate to make sense of the operation/concept you are teaching. They do it frequently in the elementary with base ten blocks. I have yet to meet a math teacher that would condone teaching without base ten blocks in the elementary, but it is difficult to find math teachers that have the same philosophy for the Algebra class. And yet, we complain when students make 2x + 3 into 5x. They do this because they don't understand what 2x is and what 3 is. They need to understand what they are in order to do the operation correctly. Before I continue, let me describe Algeblocks. (I have nothing against Algebra Tiles, they work the same). Constants are represented just like you would with base ten blocks. The kit comes with green centimeter cubes. The number 3 is represented by getting out 3 green cubes, we call them the "Green Guys". X is represented with a yellow stick, it is 1 centimeter by 1 centimeter by a little over 3 centimeters. There are also blocks that stand for y, xy, x^2, y^2, x^3, y^3, xy^x, and yx^2, I think that covers them all. It is always interesting to start a lesson asking students to show me 2x. If this is the first time they have used Algeblocks, I often see two green cubes with a yellow stick to the right of them. If you have Algeblocks or Algebra tiles, try it (after introducing and defining them). It is a huge eye opener that they don't understand what 2x means! It is also interesting to represent x/2, they often put a yellow stick above and 2 green cubes below it. Sometimes they even use another yellow stick in between to represent the fraction bar. I do many things with manipulatives. This post is to just introduce manipulatives in general. I will have future posts to discuss specific uses and lessons. I love how using manipulatives gives me a place to go with students who are struggling, but also gives me a way to challenge students' thought processes when I feel they are just memorizing steps. I use many different manipulatives, not just Algeblocks. I use Base Ten Blocks, Balance Scales, XY Axis Pegboards, Geosolids, Linking Cubes, 1in Square tiles, and Anglegs; all in the high school classroom. I also use digital manipulatives, my favorite being Demos. One of the most difficult parts of using manipulatives is giving up the time to do them. Lots of time is a key factor to teaching with them! But, I promise, teaching with manipulatives saves time in the end. You don't have to take time to reteach misconceptions. Plus, your students actually UNDERSTAND what they are doing, which is always a positive. But be warned, they are not magical. There is a process you need to use (see next post). I often fear when I see an article or blog criticizing the use of manipulatives. But when I read them, I agree with their arguments. You need to know what you are doing. But when done right, they can open doors to understanding! I wouldn't teach without them now that I have experienced what they can do.
1 Comment
Helene
1/14/2020 06:22:46 am
Hi,
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AuthorI teach mathematics for grades 7-12. Teaching mathematics is my passion. Archives
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