By Teachers, For Teachers
When I was a kid, math instruction consisted learning all the important steps and rules. I was not handed manipulatives, given an explanation for the rules, or the meanings behind the math. You did fractions “this way” because that was the way to do it, multiplication tables were memorized because the teacher said to memorize them. It was just that way. The“old school” way.
Today this is not the case. With new calculators, assistive technology and innovative approaches to math instruction, there is a new math in town.
Now, math instruction focuses on understanding math concepts through the use of hands-on activities, manipulatives, real life applications, and “how to” essays. A far cry from the days of “copy the board and do page 65!” Students are more actively engaged in learning math and group problem solving while in previous years we were given the task and expected to complete independent of others.
In trying to keep up with new teaching methods, I read many articles about the integration of manipulatives in teaching math to elementary grades. I have also learned there are new methods of using manipulatives to teach various math concepts.Ways I didn't even know existed!
This got me thinking...
What Are Manipulatives?
Manipulatives are defined as concrete objects (things you can touch and move around) that aid in classification, patterning, counting, equations, fractions, multiplication, and other math tasks. They include attribute blocks, geometric shapes, base ten blocks, unifix cubes, fraction bars, and plastic counting cubes. They may also include everyday items such as buttons, soda caps, bingo chips, beans, dice, straws, craft sticks, food items such as jelly beans, and marbles.
Virtual manipulatives can come in endless varieties such as pictures, puzzles, and games. Virtual manipulatives may include engaging colors and sounds and most virtual manipulatives create a game out of the math, which tends to keep the student's interest alive while teaching concepts that may seem too challenging.
The National Council of Teachers of Mathematics (NCTM) strongly advocates the use of manipulatives in the classroom. The NCTM believes manipulatives allow students to actively construct their own understanding of math.
While I absolutely agree with the value manipulatives play in the classroom and have used them, I am concerned that manipulatives may prevent students from learning abstract thinking skills.
Struggling students are found to benefit from instruction that is explicit and systematic. Not all children learn in the same way or react to physical materials in the same way. What works for one may not work for all.
What if more time is spent on the manipulative while less time is spent on the abstract thinking part of math?
Would students still be able to both understand math concepts, and complete pencil to paper computations? I am all for math being “fun” but overuse of the manipulative could cause students to become too accustomed to the activities of the lesson and forget the actual lesson.
What about virtual manipulatives that can be accessed almost anywhere? Is it possible that students might learn to become too reliable on using objects to solve a problem? What happens when they are in a situation where they need to solve an problem quickly, and they do not have the tools with them to do so?
Also, not all concepts can be related in concrete form. Students should still learn how to problem solve, calculate, and think abstractly. How do we transition from manipulatives to abstract thinking without causing more confusion?
I suppose the first step to answering this question would be to ensure we are using the manipulatives properly. Many teachers (including myself) are not properly trained to use manipulatives. At no fault of their own, it just was not a main focus in college math classes in earlier years.
If manipulatives are used improperly, it could confuse the students. There are hundreds if not thousands of resources online as well teacher guides and other resource books that will list methods and examples of using manipulatives.
Here are some things to consider as you're planning manipulatives for your math class:
After reading the various pros and cons and studies completed on teaching math using manipulatives, I am still not completely sold on manipulatives as being the BEST method to teaching and learning math skills, but it is a growing trend in the education world and certainly has its benefits.
I admit, I am still a little “old school” in my methods of teaching math, but it is only because I want to ensure my students can think both abstractly and concretely. However, if this can be accomplished through pencil and paper as well as the use of manipulatives, then I am definitely open to learning how to properly use ALL the tools in my math toolbox.
What are your thoughts to using manipulatives in the classroom? How do you transition from concrete teaching to abstract teaching? What steps do you use? Share in the comments section!