Manipulative Reflection

How do you know if students deepen their understanding while using manipulatives?
I believe that a teacher can see if a student is deepening their understanding through the use of manipulatives through observation and questioning. The teacher can watch students to see if they are correctly utilizing the manipulatives they are working with. If this is not happening, the teacher can intervene to help the student and suggest alternative methods. The teacher can also see if students are deepening their understanding while using manipulatives by posing questions on the students. The teacher could ask students to represent something specific, explain their representation, and justify their representation. This could help the teacher gain insight on whether or not the student is really taking away meaning from the utilization of manipulatives.

How do you know if the students can transfer their understanding from manipulatives to other situations?
One way to see if students have the ability to transfer their understanding of an idea from manipulatives to other situations would be to ask the students to think about the manipulatives in their minds, or draw them out on paper. This would eliminate the actual use of the manipulatives, but the students could still utilize ideas they learned from the use of them. An example of this would be giving students the option of drawing base 10 pieces while solving a math problem. Although physical manipulatives would not be used, drawings could still help the student to solve the problem.

How can you assess that understanding or growth?
A teacher could assess the understanding or growth a student takes from the utilization of manipulatives by asking them to verbally explain their use of manipulatives, and what their manipulatives stand for. In addition, the teacher could ask students to write their explanation of their use of manipulatives and write also what the manipulatives stand for. These are two options for assessing student understanding of manipulatives. Another option would be for the teacher to provide manipulations on the SmartBoard or overhead projector, and ask students to explain the manipulations and their meaning to a partner, or ask students to share their ideas with the entire class. This could gauge whether or not students have true understanding of their use of manipulatives.

When students work in groups, how do you hold each youngster accountable for learning?
First of all, I think that any group work in the classroom should be done in very small groups of students, maybe 2 to 3 children in each group. When group sizes become too large, there are almost always students left out of discussions or students who feel they can "get away with" not participating. This is not acceptable, and really takes away from the overall point of group work in the first place. Having small groups should make all members of the group members participate and share their ideas. If a teacher notices a group member slacking or not participating, the teacher should pull that student aside and explain that their participation is not optional, and that their group members need their help and input during group work. I am not a huge believer in punishments, but I do believe that privileges should be taken away from students who do not participate in group work. All of these modifications will help students to be accountable for their learning, and promote participation and effort during group work instances.

When students work in groups, how do you assess each youngster's depth of understanding?
Assessment of students working in groups can be a difficult task, but I think there are two things that a teacher can use to help with this. The first item that can be used are checklists. Checklists can be used for individual students to monitor their progress and understanding throughout an activity or project that has students working in groups. While students are working, the teacher can observe and monitor student progress, behavior, participation, and understanding. The teacher can monitor understanding by asking students questions and trying to make sense of their responses. This may gauge whether or not the student is understanding the topic at hand. Conversation is a very effective tool for assessment, and a teacher can make great use of it during group work assessment. Another thing teachers can do to assess students during group work would be, if applicable, to have every student complete a handout or product. This ensures that all of the students in a group are participating and completing the task, and the teacher has something to look at for each and every student.

How are you improving students' problem solving skills with the manipulatives?
Manipulatives allow students to be hands on and visualize the mathematics they are carrying out. Many students need visualizations in order to understand mathematics, so manipulatives can be very useful. In addition, when using manipulatives, students can find errors and then fix those errors more easily. This can help lessen student frustration in problem solving. Manipulatives also provide a more concrete way of problem solving for students.