Manipulatives

1. How do you hold every student accountable?
Initially I think it is important to allow every student to play and handle the manipulatives. It is natural to want to play with new things. College students have trouble with this sort of thing. Thus, I strongly feel that it is unreasonable of teachers to put manipulatives in front of students and expect them to overcome the urge to play. Furthermore, I feel that it sends the wrong message to tell students to play. Lifelong learning comes from a desire to explore and understand. Yet, teachers are insistent on stomping these behaviors out of children.


After the students have been allowed a period of exploration and play I feel that the teacher should take some time to model and introduce the materials. This is an important step as it will start to show students they ways that the materials can be applied to the mathematics content. This is the point when the teacher can ask guiding questions and get students vocalizing their thoughts and ideas. Students will build their vocabulary and ability to talk about the manipulatives only through hearing the teacher speak about the manipulatives. I feel that it is unreasonable to expect the students to use communication effectively if the teacher has not first modeled this step.

I don’t know that I know all the ways that teachers can make students accountable and find an observable way to measure the students learning using manipulatives. However, these are some of the ideas I have. Hands-on activities and group work activities lend themselves very well to observation and checklists. Watching students work through a problem when they are required to use communication and teamwork is a perfect opportunity for the teacher to take an observation role. In the older grades it might even be appropriate for the teacher to “interview” each student and ask them to explain their reasoning in a formal manner.

Another technique that a teacher might consider would be to have the students produce some kind of product. The students might journal on their experiences. Older students might consider blogging about their problem solving and thought processes. Students could draw a picture, type their work into a word processing software, capture a screen shot of their work, or even produce a project, poster or brochure.

I also think that a series of steps, guiding questions or a guided handout might be useful for keeping students on-task and engaged with the material. I saw a very interesting program that had students experimenting with pattern blocks. The teacher had created a series of questions that corresponded with a power point. Each question was multiple choice and as the students used the pattern blocks to determine the answer they answered with automatic clickers. The clicker software immediately polled the class and showed the data as a bar graph. Then the teacher asked the students with the correct answer to explain how they reached their conclusion. I felt that this was one great example of how to make mathematics education everything it can be. The students were using the manipulatives in a systematic and directed fashion; they were using technology in a meaningful way. Students were accountable for their work and they were talking about their problem solving and reasoning.

2. I have already addressed “hands-on” and “hands-on, minds-on” in the previous question. When the students are playing and becoming oriented with the materials they are “hands-on.” However, at that stage there knowledge is undirected. It takes purpose and guidance for students to progress to the level when they are “hands-on, minds-on.” Again, it is the difference between good teaching and poor teaching. Manipulatives are not enough and without strong instruction they are all useless as worksheets. I would even go as far to say that a teacher’s classroom management makes a big difference with their ability to successfully employ manipulatives in the classroom. I can easily see a lesson going wrong simply because the teacher doesn’t have assertive discipline and clearly defined boundaries in the classroom. Finally, when working with manipulatives a teacher is going need to be especially sensitive to the special needs in the classroom as well as the gifted students.

3. Process Standards
Problem Solving- I feel that it is fairly evident how students are using problem solving as they work with math manipulatives. Manipulatives allows students to easily and quickly engage in guess and check. It is especially important in this day and age that students get feedback as they work. Students who play video games and use technology frequently are accustomed to offering input every ten to fifteen seconds and accustomed to some level of feedback every twenty to thirty seconds. Manipulatives offer this level of engagement and can easily supplement activities that would otherwise leave students unengaged and disinterested.
Reasoning & Proof- Reasoning and proof doesn’t just happen as students work with manipulatives. Rather, they emerge in the way that the teachers couple the manipulatives with other work. When students must defend their work and document their proof this process standard becomes a natural part of the activity.
Communication- Communication is another process standard that flows naturally with the activity. However, the danger is that the students don’t use the correct terms and vocabulary. Thus, it runs the risk that the students are able to work through the activity but cannot explain what they did, how they did it or why they did it. It takes the teachers active modeling for students to learn the correct habits. Teachers should not assume that students will learn this on their own. As a result, communication becomes one of the valuable indicators of whether or not the instruction is effective or not.
Connections- Students have a remarkable ability to make connections between mathematics and other experiences in their lives. However, I feel that the teacher must be the facilitator in helping the students to realize the connections within mathematics.
Representation- Representation and math manipulatives go hand in hand. However, I feel that students abilities to utilize representation is sometimes far more capable than my own. Student’s creativity and cleverness is a constant surprise to me. The ways that they think about mathematics and problem solving should be nurtured and encouraged through the careful and deliberate use of math manipulatives.