Math Manipulatives

This semester, two of my five classes are methods courses, or courses that are dedicated to exactly how to teach a specific subject to early childhood grades. I am taking Teaching Language Arts and Teaching Math and Technology. In my TMT class, we have been discussing the importance of using manipulatives, or physical and visual aids, when teaching math and technology to young students. As I interact with students now, I can see how important this is and I wanted to bring in some examples.

We had an assignment where we had to watch first grade students answer a word problem regarding (11 x 4). Then, each of the students answered it in their own way, using their own strategy. The thing that stood out for me in this video clip was how most of the featured students used some sort of visual aid or physical process to find the solution to the question.

There were no students shown who sat down and wrote the numeral eleven four times and then added the ones up on either side and got 44. This is the way I would have solved the problem, and the way most practice worksheets are formatted, so it was interesting to see that the majority of these students appear to learn best when they have manipulatives or visual aids present.

Some of these aids included counting beads, groupings of manipulatives, white boards where they could draw pictures, etc. This observation gives a lot of insight into the minds of first graders, which can be extended to include first grade mathematics students all over the country. Teachers can then take this information and apply it to their teaching to ensure that their students get the most out of each math lesson.

I think one of the largest advantages for students who learn mathematics in this way is that they can actually see the physical number in front of their eyes -- that there are concrete representations within the classroom, usually constructed by the students themselves, which depict the solution. This is a great advantage because abstract concepts are hard for students in the early grades to grasp; therefore, by employing concrete images, concepts are more likely to stick in students’ brains.

Another advantage of such teaching is the instilling of independence in students. The students we watched were not coddled by the teacher, but simply scaffolded in a very balanced way. If a student needed help, the teacher was there to repeat the question, but you did not see the teacher rearranging manipulative groupings or interrupting a conversation between two students. This is a very realistic and helpful way of teaching, since over-teaching will only create dependence in students.

Finally, a third advantage of this teaching is that students can see many different ways of solving problems. There were four or five students who came up with their own way of solving the problem; this too is realistic and illustrates that a problem may have only one solution, but that there are many ways of getting to that end result.

One disadvantage of such learning is that students may have a hard time translating their concrete manipulatives into abstract numbers. For example, after learning the value of eleven times four, or forty-four, using blocks, a student may be unable to come up with the answer without the blocks. Somewhat of a dependence may result from the constant use of manipulatives.

Another disadvantage for students who learn in this way is that they may work with groups a lot, and may be passive and overshadowed by their group-mates. Although a community of co-learners is a good thing to create, a teacher must ensure that all of her students are having the same amount of time to share and do the work. Otherwise, some students are going to fall behind, whether or not they actually know the material.

Interesting stuff...at least for a nerd like me, haha.