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doi:10.7282/t3-097p-7m92

This session was recorded in the first two days during which a group of students explore the concepts of surface area and volume. On camera there are four students; Brian, Michael, Romina, and Michelle. These events display the use of student’s mathematical language as they progress throughout the session while working on problems of surface area and volume. The mathematical language that students use include; units of surface area, units of volume, the discussion of formulas for both surface area and volume, and vocabulary of dimensions (ends, faces, length, width). As we progress through the session, more questions are posed, and students formalize their language and formula’s for surface area. They use manipulatives called Cuisenaire rods through the entire lesson as they generate these understandings with the group. Students begin the session by using the Cuisenaire rods to come up with a general formula for surface area. They are then directed to work on volume where Romina comes up with the formula L=V. Students question this and suggest a different formula, V=L^3. When Romina hears this, she assumes the length should be cubed to get volume. Students pose this formula L=V to Researcher Maher, and then clarifies to students that this is not a true statement, and length and volume are two distinct units. she further advises that students work on their mathematical language. Students go back to the question of surface area and Brian suggests the formula for surface area = the quantity ‘length times four plus two’ times the number of rods. Michelle claims that the hidden faces would not be counted and suggests a different way of finding the surface area. The other students agree with this and ask researcher Maher if it is acceptable. Researcher Maher asks sudents to clarify the meaning behind the terms they chose to use, and further suggests they use square units rather than the term faces. She additionally specifies again the difference in the units used for volume and surface area. The use of stamping is suggested to students to find surface area, as suggested earlier in the session. Finally, Michael comes up with a formula that worked using precise language and all other students agree with this statement.

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