Yay for Manipulatives!

Hi everyone!

Today, I wanted to introduce the topic of manipulatives, and address some of the misconceptions that we may have around this subject. 

What are manipulatives? 

Manipulatives are tools that students can use to help them approach and solve math problems. They are concrete items that students can move and explore. Even though math is the "universal" language, sometimes it is difficult to understand or decipher, so students can use manipulatives to represent math in a new way that makes sense to them. 

What are some of the benefits of manipulatives? 

• Manipulatives decrease math anxiety because it offers students a concrete way to interact with abstract concepts 
• They are fun to explore! Math doesn't always need to be represented on paper!
• They can be used in all grade levels and streams. Yes, that's right; they can be used in both ACADEMIC and APPLIED. Manipulatives do not just apply to one particular stream or age group, since they can be used in Grade 12 and College/University. 
• They provide both a visual and kinesthetic approach to mathematics, so they are a great way to offer differentiated instruction to all learning types. 
• In order to save money and provide more manipulatives for your students to work with, you can make your own! 
• I was able to make my own algebra tiles by gluing a piece of red and blue construction paper together, and cutting it into different shapes (long, thin rectangles represent the x term; and small squares represent the constant term 1). This cost me a total of 60 cents, since I only used 4 sheets of construction paper.    

Construction paper Algebra Tiles

Algebra tiles can be used for a number of different algebraic concepts, such as factoring, adding and subtracting expressions, multiplying and dividing expressions, and completing the square! (Who knew!) I focused on using algebra tiles to collect like terms, which I have included in a video below. I hope this helps for anyone who is new to using algebra tiles! 

Are there any problems with manipulatives?

Personally, I don't see a problem with manipulatives because they allow students to learn at their own pace and discover new ways of representing and understanding mathematics. 

However, there tends to be a problem when students are unable to use them during a test, when they previously had access to them during lessons and homework sessions. I understand that teachers want to see if students are able to demonstrate their work using the abstract procedures shown in class, but how are students able to display this level of abstract thinking, when they need a concrete tool to help them understand? Tests already place a heavy amount of pressure on students, especially when these students have math anxiety. 

Taking away their manipulatives during a test, might be the equivalent of throwing them into an ocean without a life jacket. No wonder students have a growing fear of math. 

Some students will use their manipulatives during class in order to help them understand an abstract concept, but will no longer need them for the test because they have grasped the abstractness. However, others will depend on their manipulatives to help them through a stressful assessment; we should not be taking that away from them. I believe that a student should be able to use any strategy or tool to arrive at an answer, and they should not be penalized based on their chosen strategy. As long as students are able to express their answers and explain the procedure they used, then they have effectively demonstrated their learning. 

My final critique on manipulatives is that some teachers lack the training to use them in the classroom. Often times, the Ministry deems that manipulatives should be implemented in the classroom (which is great!), but they do not provide teachers with the proper training to effectively incorporate them in their lessons. This lack of training may cause confusion for students, frustration for teachers, and the benefits of manipulatives to not be reaped. I think that an easy fix to this potential problem would be to provide teachers with PD days that would help them learn more about the manipulatives, and provide examples and suggestions on how to use them in their lessons. 

Overall, manipulatives are a great tool for teacher's to have in their toolbox. We just need to know how to incorporate them in our lessons in order for them to be effective!

Thank you all for reading, and I hope you have a great day!

Dayna