Manipulative Reflection

How do you know if students deepen their understanding while using manipulatives?
Students deepen their understanding while using manipulatives because they have something physical and real to relate their ideas to while working with a mathematical concept. If you were to simply give students an example on paper and ask them to apply the concept they have just been taught moments ago without any real-life relation or physical manipulative work, it would be extremely hard for the student to understand what they were writing and working with. Using manipulatives helps give students real and tangible proof that the concept they're working with has reason and meaning.

How do you know if the students can transfer their understanding from manipulatives to other situations?
Teachers can begin to check on their students' abilities to transfer their understanding from manipulatives to other situations by slowly working away from the manipulatives towards real-life situations. For example, a teacher could start with 3D shape manipulatives while working with area, then move to having the students draw the shapes themselves or use the Smart Board, and then finally having students find objects of these 3D shape in or outside of the classroom to work with for a real-life connection.

How can you assess that understanding or growth?
Teachers can first assess the understanding and growth by asking students to give reasoning and proof of why and how they are using their manipulatives. We can also assess growth beyond this by having discussions about what their manipulatives can relate to in the real-world, and the importance of understanding that connection and the connection to the mathematical concept they are working with. If students are able to relate to these ideas, they will have shown their understanding and growth beyond working with simple manipulatives. 

When students work in groups, how do you hold each youngster accountable for learning?
An activity that I like to do with students working in groups is having students assign themselves a "job" for that group discussion/activity. Whether it be simply through discussion or writing down what is happening in their group, each student will have the opportunity and responsibility to participate. For example, if I had students in a group of 3 working on problems with manipulatives, one student may have the job of discussion leader, another might be a connector, and the other student may be asked to represent the work, etc.
When students work in groups, how do you assess each youngster's depth of understanding?
As I had stated before, if students were to have specified jobs in their groups, it would be beneficial for the students to come up with some written work of what they accomplished during the group work as somewhat of a reflection and checklist for understanding. Once the students had done their own write up or reflection, there could be a discussion or group write up of how their parts all came together and what they understand of the overall concept that would be beneficial.

How are you improving students' problem solving skills with the manipulatives?
Manipulatives greatly help students with their problem solving skills as it gives them physical objects to work with while learning and practicing various mathematical concepts. It also helps students begin to make connections with the manipulatives to real-world situations, and thus will lead them to work with this practice throughout higher levels of mathematics.