Improving Measurement and Geometry in Elementary Schools

Teaching Strategies

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Reflect on teaching and learning

Metacognitive strategies, which essentially involve "thinking about thinking," increase students' learning. By helping students to reflect on and communicate what they learn and what is still unclear, teachers have a unique opportunity to aid their students. There are a number of ways to help manage or help students to manage their thinking by:

One way of accomplishing this kind of reflection is through the use of student-created portfolios. Even the process of selection that goes into making portfolios helps the student to build self-awareness and ultimately gives the student more control over her or his own learning. By shifting the focus of the teacher's role from instructor to facilitator of learning, the process gives students the responsibility to determine what they need to know. These projects support students in looking at mathematics in different ways and in seeing value of the content of mathematics.

Writing is another way to encourage students to analyze, communicate, discover, and organize their growing knowledge. Facilitating classroom dialogues and other interactions and helping students to develop reasoning skills makes it possible for them to evaluate their own and others' thinking.

Teacher Reflection: A Vignette about Perimeter and Area

During a class discussion of the relationship between perimeter and area, several students in Janet's class stated that increasing the perimeter would have to increase the area. None of the other students questioned these statements. That evening, Janet reflected on why her students developed this misconception. In reviewing the activities that she had asked the students to do prior to the discussion, she discovered that in every instance when the student increased the perimeter the area also increased. The students were justified in assuming this would always happen. She had decided that during the discussion she needed to do more than state that increasing the perimeter did not always increase the area. The students' belief structure had to be challenged by examples that did not fit their misconception.

After looking at several options, Janet decided to have the students work in groups using a geoboard. She would ask students to use Pick's Theorem to find as many triangles as they could with area equal to 1. For each triangle, the students would measure the sides and calculate the perimeter. She would then ask them to create a table showing the perimeter and area of each triangle found, arranging the table from smallest perimeter to largest perimeter. She would then ask them to reflect on the relationship between perimeter and area, asking, "Does increasing the perimeter always yield a larger area?"

Student Reflection Example