Manipulating Math

I hear and I forgot

            I see and I remember

                        I do and I understand

                                            -       Confucius

This week in class, we explored the topic of implementing manipulatives in the classroom. As a group, we (the teacher candidates) had the opportunity to solve various mathematical problems using objects such as candy, ropes and algebra tiles. Although we are a very competent and intelligent group of future math educators, it was evident that the use of manipulatives fostered engagement and success. Manipulatives are not just useful for elementary students, students whom are struggling or those in the lower streams of math; manipulatives are for everyone!

So why manipulatives?

Manipulatives are concrete objects used as a teaching tool that allow students to explore a concept in an active, hands-on approach. Traditionally, manipulatives are used in the classroom to introduce, practice or reinforce a concept. Common classroom manipulatives include: algebra tiles, base ten blocks, connecting cubes, pattern blocks and so many more. The use of manipulatives allows students to reach a deeper level of understanding because they are constructing their own cognitive models for abstract ideas and processes. More importantly, manipulatives engage students both visually and physically.

An article from Hand2mind discusses how manipulatives move students through the three stages of learning (concrete to representational to abstract). Students begin using concrete materials to solve problems by looking for patterns or generalizations. In the representational stage, students record their work by sketching representations of their manipulative models. Lastly, students move to the abstract stage where the objects and pictures are connected to the abstract numbers and signs of arithmetic. While moving through these stages, students gain an understanding of the mathematical problems through their direct experiences in the concrete and representational stages.

Movingwithmath.com

What are the benefits?

Which sounds more interesting: passively copying down the problems your teacher is writing on the board, or collaborating with your classmates using three-dimensional shapes to determine the surface area and volume? Manipulatives can be used both individually or amongst a group of students. When implemented through a collaborative approach, students engage in conversations where they are able to verbalize their mathematical reasoning using a common language. As students work through the problems, they gain self-confidence and pride through the process of solving the problem using a method that “works” for them. As I mentioned in my last post, I believe building confidence amongst students is one of the most important steps in achieving student success. I came across this video on using manipulatives for multiplication and thought it was a great demonstration of a student strengthening their understanding. 

https://www.youtube.com/watch?v=UKlz2aWa_Mg

From personal experience, the constant use of paper and pencil assignments in math class can become very tedious and boring. Manipulatives are fun and for some students they represent “play” as opposed to work. In class, we had a worksheet that involved counting candies and chocolates with their associated cost. Without realizing it, we were in fact solving a system of linear equations. As a future educator, I intend to use an ample amount of manipulatives that apply to all students. We live in a very technological based society, and thus manipulatives could also include technology (another aspect of my teaching I hope to further develop).

Ispeakmath.org

Personally, I wish I had the opportunity throughout my educational experience to use more manipulatives. As a student in the academic stream, many of my teachers possessed the preconceived notion that our class did not require manipulatives to aid our learning. This past year, I had first hand-expereince with the result of using manipulatives. I was tutoring a younger student in algebra and we were working on collecting and multiplying like terms. Without the use of manipulatives, the student had great difficulty grasping the concept. With the use of the algebra tiles, her engagement and motivation immediately shifted. It was clear she was a visual learner and the use of algebra tiles significantly increased her understanding. I can only assume that this outcome would be very similar for many other students. Algebra tiles can also be used for factoring, completing the square, etc. Edugain explains the use of many different manipulatives and provides activities and tip sheets for each type. 

Of course, it is important to note that educators should not over-use manipulatives in their classroom. As this course continues, I am looking forward to further developing my knowledge on the use of manipulatives. I am excited to have this as one of the tools in my teaching toolbox. 

That’s all for now,
Rachelle

Why Teach Mathematics with Manipulatives? (2016) Retrieved from http://www.hand2mind.com/resources/why-teach-math-with-manipulatives