The Beauty of Manipulatives

Throughout my elementary and secondary school education, I had never enjoyed working with manipulatives. I thought that it was not the most efficient way to learn a new concept and consequently, I did not put much effort into using these tools. My teachers would explain exactly how to use the objects and I believe that this took away from the beauty of using manupulatives. 

In university, I was given another opportunity to work with manipulatives. We were asked to create a presentation about the use of a certain manipulative. My group chose geoboards and I realize now that we did not use the tool in an exciting way for the students. We used the manipulative in the exact way that it should be used and did not think of a way to creatively present it to the students. I believe that if I used the lesson that we created in a classroom, students would not have been very interested in the material. This reminds me of how I felt about using manipulatives throughout my education. 

This past week, I was introduced to four activities that involved the use of manipulatives. Two activities used mathematic manipulatives and two activities used objects that aren't specifically related to mathematics. I found the activities that used non-mathematical objects particularly interesting and therefore, I will be reflecting on my experience with this activity.

The first activity involved candy, chocolate and pennies (or some type of counter since pennies are now obsolete). As a lover of candy and chocolate, I was already intrigued by this activity and I was excited to work through this problem. I believe students will also be excited about this problem because it does not seem like you are solving a ‘mathematics’ problem. We were told that this activity was about solving linear equations. However, as we worked through this problem, I did not realize that we were using this mathematics concept at all. We were having FUN and I can imagine that students would feel the same way while completing this activity. As I reflect on this experience, it is evident that the manipulative served as a ‘mask’ of the mathematical concept and I believe it can encourage students to use mathematical skills without even realizing it. 

As demonstrated in the picture, the second activity involved ropes of various lengths and thicknesses. This activity asked the students to find relationships between the lengths of the ropes after multiple knots were tied.

Similarly to the activity using candy and chocolate, this activity was extremely different from what students are usually using in mathematics classrooms. In a traditional classroom, students usually read a question and filter the numbers that are provided in a formula in order to find the answer. However, the rope activity provides the students with an active learning environment where they are encouraged to find the numbers through investigation. This was a very hands on activity and can be especially useful to assist kinaesthetic learners. 

I now see the importance of manipulative in classrooms. I not only feel this way because my opinion of manipulatives has changed, but also because all students deserve the opportunity to learn in different ways. If presented properly, manipulatives provide students with the opportunity to be active members of their learning through exploration activities. I believe that these activities are much more likely to grab the students attention compared to pen and paper activities and may also increase student engagement with the mathematical content.

Problem Solving in the Mathematics Classroom

This past week, I was introduced to the activity 'skyscrapers' which is demonstrated in the picture below. Our facilitator asked us to get into groups of about four individuals, handed out some math-link cubes, and briefly explained how this activity worked. 

At first, we were all very confused and could not seem to understand the instructions. We could not figure out how this activity worked and even began saying things like “this is impossible”. I found myself feeling discouraged because I could not figure out how to complete the activity. Instead of giving up, we pushed through the phase of being discouraged and we began thinking of other ways that this activity may be solved. Without realizing it at the time, we used many strategies to try to find the answer. For example, we discussed other possible options, tried to make connections to our prior knowledge, reasoned with each other, and used representations to show our peers our ideas. I realize now that we were all using the mathematical processes in order to solve this problem. 

Earlier in the class, we discussed the seven mathematical processes. As outlined in the Ontario Mathematics Curriculum, the mathematical processes are problem solving, reasoning and proving, reflecting, selecting tools and computational strategies, connecting, representation, and communication. After completing this activity, it is evident that most, if not all, of these processes allowed our group to find the correct way to solve this problem. Since we had found the answer ourselves, we were excited to complete the activity and moved onto the more difficult problems. As I reflect on this experience, I can see the importance of allowing students to work through problems without providing them with step by step instructions. For example, if we were told exactly how to solve this activity, I believe we would not have been as excited to find the correct way to solve the problem.

This activity reminded me of using inquiry-based learning in classrooms. Inquiry-based learning begins with posing a question or problem to the class, rather than providing the students with all of the knowledge about a specific subject. This type of learning encourages the students to think beyond what they know in order to be critical and creative thinkers. It also encourages them to use the mathematical processes to solve the problem. I plan to use inquiry-based learning in my classroom because it allows students to solve problems in their own way. For example, some students may use manipulatives, whereas, some students may reason through the problem orally. As a future mathematics teacher, I know that my students may arrive at the same answer in different ways. I plan on celebrating those differences and encouraging my students to think outside the box when trying to solve a problem. 

Introduction

Hello everyone! My name is Laura Gravina and I am a Teacher Candidate at Brock University. I look forward to completing my final year of the concurrent education program as I learn through experience in my placement classrooms. My teachable subjects are mathematics and physical education and I am looking forward to teaching both of these subjects in the future. Since mathematics is my first teachable, I am extremely passionate about this subject and as a future educator, I hope to make the content meaningful for my students. Throughout my final year, I hope to learn unique and creative ways to engage my students in the content and also ways to teach that will allow all students to learn through differentiated instruction. The purpose of this blog is to reflect on my experiences throughout my teacher education year and I look forward to reading your responses and feedback!