Manipulatives Blog

I have come to understand manipulatives more through this class. I cannot remember a time that I used manipulatives in math growing up in school. I am very enthusiastic about using manipulatives in my classroom because I feel that they assist the student in deepening their understanding of mathematical concepts and gives them a visual representation that will further their knowledge. I believe that what you hear, you'll forget; what you see, you'll remember; what you do, you learn. I think that all three of these steps are vital to a students' learning experience, but the latter is often forgotten to be made part of their curriculum.

1. How do you know students deepen their understanding while using manipulatives?
You know the students deepen their understanding while using manipulatives by their interactions and conversations while they are participating in the activity. As the students are working through manipulative activities, they should be talking out their processes and you can usually tell when a student is confused by the look on their faces. The students are more likely to have the "aha!" moment when using manipulatives because they can connect the mathematical ideas that they know in their mind with the experience and visual representation. Students understand more by doing what they are learning.

2. How do you know if the students can transfer their understanding from manipulatives to other situations?
You will be able to know if the students can transfer their understanding from manipulatives to other situations by asking them guiding questions where they will have to think through practical, real world application questions. They will then problem solve and communicate through discussion ways that they can take what they are learning by using the manipulatives and connect it with the real world.

3. How can you assess that understanding or growth?
You can assess their growth by requiring reflection to be a part of their activities. This way, the students will be incorporating the communication process standard and you can easily tell what their thought processes are about math. You can then assess their ability to utilize their mathematical language in an appropriate manner. Their understanding and growth can be assessed by setting up activities that are meaningful to their learning. A teacher can tell if the student is growing and learning based on their interactions with other students in working together using critical thinking skills to problem solve.

4. When students work in groups, how do you hold each youngster accountable for learning?
When students work in groups, I think that it is important that students have individual work to show that they were working and putting forth effort that is acceptable and contributes to their learning. I would have the students document what they are learning as they go through the different activities. I would also have the student not only write about what they are doing (methods), but what they are learning, and also what observations they make along the way. I would then have the students write a synthesis of their information in the form of a reflection that includes conclusions that they reached from their observations and also their thoughts about it.
5. When students work in groups, how do you assess each youngster's depth of understanding?
When students work in groups, their depth of understanding is critical as manipulatives should deepen their understanding, not provide a way to do simply hands on activities without any academic gain. Teachers should pay close attention as they are engaging in the activities and also take time to go around the room to ask the students questions that are thought provoking for the student which will cause them to give more than a surface/product answer. The student should be able to explain the process and make conjectures of how what they are doing relates not only within mathematics, but also interdisciplinary.


6. How are you improving students' problem solving skills with the manipulatives?
Students will need to know how to think critically in problem solving not just in math or in school, but as it relates to their daily lives and futures as professionals. Students learn to problem solve when working with manipulatives because they are activating their mind to think beyond what seems obvious. Students have to use manipulatives to solve problems and this causes the students to learn how to use many approaches and a variety of strategies to solve problems. There is usually more than one way to do things and this is true for problem solving. There is usually more than one way to solve a problem and some ways work better than others. Using manipulatives also helps students to refine their skills of determining the best strategy to problem solve and sometimes through guess and check/trial and error.

7. Why do they say not "hands - on" but "hands - on; minds - on"?
If activities are hands on only, students aren't learning to the depth at which their potential is. Activities need to be thought provoking and engaging of the mind as they work with their hands so that they can correlate knowledge/information to experience. A teacher should ensure that they are promoting equity within the education they are giving to the student in that they need to give the students solid instruction that give the student a firm foundation from which to build upon. If the students don't have good instruction and are given manipulatives, they will end up confused and won't get the max out of what they are supposed to be learning. They won't be able to make the connections and conclusions that are intended for them. Manipulatives must be coupled with strong teaching.

8. How do the process standards relate to the use of manipulatives?
Problem Solving:
Manipulatives incorporates the use of every process standard. Students exercise criticial thinking skills when using manipulatives in that they have to think beyond what is "expected or obvious" to come up with creative solutions. Students use a variety of problem solving strategies to come to a solution. Manipulatives also focuses more on the process rather than the product which is important when it comes to deepening mathematical understanding.
Communication
Students naturally use the process standard of communication when working with manipulatives/activities, especially when working with groups. As the students are encouraged to talk through their mathematical thought processes to reach a solution they are furthering their ability to communicate using the language of math. Their communication skills are sharpened as they engage in discussion and written reflection.
Reason and Proof
Students are asked to give rationale for their thinking when working with these activities. They should be talking through their processes, making conjectures and testing their predictions to see if they have understanding. Students should be working through problems that are meaningful and lend to explanation and justification of their work.
Representation
manipulatives are a great way to incorporate representation. Students can use manipulatives to represent data, mathematical equations, shapes, patterns, etc.
Connections
Students can make connections especially with the real world as they problem solve and work with manipulative activities. They are able to connect mathematical ideas together to see how mathematics is a coherent whole.

In class today, Monique and I did three different manipulatives which I thought were good. We did the snap blocks, unifix cubes and pattern blocks. I would have liked to experiment with the other manipulatives but we ran out of time. I really liked the snap blocks because they were so versatile and had many colors. It was easy to find activities that could be incorporated at every grade level with these. I also really liked the pattern blocks as there were a lot of things you could do with them. I thought with the pattern blocks; however, that it could be helpful to have many colors of the same shape (e.g. triangles would have yellow, green, orange, red, blue) so that if a student wanted to do representation of a pie graph for data analysis, it would be less confusing. I do understand that it is also important for them to be the same color. I also appreciated our discussion in class about what to do when students had deficiency in fine motor skills and thought that the suggestions were very good and insightful.

I really have enjoyed learning more about manipulatives in this class and I'm excited to purchase my own and implement them in the classroom.