Examining Math Manipulatives

1. How do you hold every student accountable for learning while using manipultives?

Teachers must put purposeful effort into holding each student accountable for their learning with manipulatives. There are a number of effective ways to do so. First, you could have students record some or all of the work that they do with the manipulatives onto a sheet of looseleaf paper or onto a teacher made "record sheet". This is different from a work sheet in that students are recording what they do with the manipulatives, not simply using the manipulatives to solve teacher made problems. Another way to hold students accountable is to have students journal after using manipulatives. Journal topics may vary and may include things such as "what did you learn at this center?", "What was your favorite and least favorite thing you did at this center?", or "did this manipulative help you with a math concept? Explain how it did or did not, and which concept". Finally, teachers could have students share what they have learned through using the manipulatives with the class. This is a great way to get students talking about math.

2. Why is the new emphasis on "Hands on, Minds on", instead of simply "Hands on".

All manipulatives are hands-on by nature. However, this does not mean that because students are using the manipulative, they will learn math. Manipulatives should be used as a tool for instruction, the key word being instruction. Students should be instructed or guided in some fashion in order that they are using the manipultive to help them meet the math objectives of the lesson. Only then is the activity both hands on and minds on. Handing first graders a set of base-ten blocks does not guarantee that they will use the manipulative in any way involving math. In fact, I would predict that given this situation (with no prior instruction using base 10 blocks) many first graders would build intricate buildings and towers. Building towers has educational value, though it is not mathematics and likely does not meet the learning standards of the lesson. In order to achieve a true hands on, minds on experience for students, teachers must couple good instructional strategies with the use of manipulatives. Similarly, as stated above teachers must hold all students accountable for their learning while using manipulatives.

3. How are the process standards used with the use of manipulatives?

Representation immediately sticks out to me when considering the use of the process standards in learning with math manipulatives. The nature of a manipulative is such that the manipulative itself is a way to represent math concepts. Showing students multiple representations, including 3 dimensional objects, is a key to a solid understanding for many students. Communication can very easily be incorporated into the use of manipulatives by having students work together in small groups to explore math concepts with manipulatives. Also, sharing ideas and findings with the class after an investigation activity using manipulatives is a way to improve students' communication of math concepts. Manipulatives can also incorporate the process standard of connections. This can be done especially with real world manipulatives, such as money. Problem solving is included in the use of manipultives when the teacher allows students to investigate how to use the manipulative to solve a problem, rather than providing direct step-by-step instructions on what to do and how to do it. Lastly, students should use manipulatives as tools to explain their reasoning of and to show proof that they have the correct answer.