This button links to a Geogebra "app" that we designed and used in our research to describe how children learn to structure 3D collections of unit cubes to build rectangular prisms and find the volume of those prisms (a study reported briefly at PME/NA 2017, and in preparation).
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A Crosswalk connecting the CCSSM standards, NCTM Standards, Length LT, Area LT and Volume LT level notes, excerpted from: A Pleasure to Measure (2017)
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Link to: A Pleasure to Measure book, through the online NCTM Catalog
The link at left, "www.learningtrajectories.org", presents work by Douglas Clements and Julie Sarama related to Early Childhood Mathematics, especially the Building Blocks and TRIAD project outcomes. |
The following button opens a video clip showing how a triangle can be equivalent in area measure to a circle.
It illustrates a transformation, using clay strips and re-arrangement, to open up the concentric rings forming a circle shape into a triangle shape having altitude taken from the circle radius, and base length the circumference of the circle, with its top vertex at the center of the former circle. Notice that the two shapes are formed from the same component "pieces".
It illustrates a transformation, using clay strips and re-arrangement, to open up the concentric rings forming a circle shape into a triangle shape having altitude taken from the circle radius, and base length the circumference of the circle, with its top vertex at the center of the former circle. Notice that the two shapes are formed from the same component "pieces".
Video segments to accompany published papers:
First, there is a paper published in the Journal for Research in Mathematics (Cullen, et al., 2018) focused on area measurement, comparing 3 instructional interventions;
The following video clips show three related interventions we have used in research to describe how children learn to structure arrays to measure rectangle area, as reported in the Journal for Research for Mathematics Education, (Cullen et al., 2018) and in the Journal for Mathematical Behavior, (Clements et al., 2018). These 3 video segments present the pattern for our clinical interviews. We used video clips following this pattern to support the learning of area measurement for rectangles. Our findings suggest that the left most and center video clip intervention pattern were productive and supportive of students with typical ways of thinking about area for many students in grades 2 through 4. They made advances in their understanding of the formula for measuring area with rectangles.
Iteration Intervention Video
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Subdivision Intervention Video |
Comparison Intervention Video |
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Second, there is a paper to be published in the journal, School Science and Mathematics (in press), on children's estimation of area for rectangular regions:
The following two videos complement our report in School Science and Mathematics (Eames et al., In press as of July 9, 2019). The first is an example of our pre-test clinical interview format involving the use of a computer macro built with Geometer's Sketchpad software. The second, lower video segment is an example of our instructional interview format. Both are narrated by a member of the research team: Cheryl Eames (July, 2019).
The following two videos complement our report in School Science and Mathematics (Eames et al., In press as of July 9, 2019). The first is an example of our pre-test clinical interview format involving the use of a computer macro built with Geometer's Sketchpad software. The second, lower video segment is an example of our instructional interview format. Both are narrated by a member of the research team: Cheryl Eames (July, 2019).
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Pre-Test and Post-Test Interview format, with commentary notes.
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Instructional Interview format, with commentary notes.
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Please follow the next link for another website providing access to the video clips.
morgridge.du.edu/marsico-institute/projects/
Two related websites with resources describing research and support for teachers as they prepare instruction on geometric measurement topics:
www.learningtrajectories.org
and
dreme.stanford.edu/news/math-talk-measurement-home
prek-math-te.stanford.edu/measurement-data
morgridge.du.edu/marsico-institute/projects/
Two related websites with resources describing research and support for teachers as they prepare instruction on geometric measurement topics:
www.learningtrajectories.org
and
dreme.stanford.edu/news/math-talk-measurement-home
prek-math-te.stanford.edu/measurement-data
Further resources for classroom work with students learning geometric measurement: