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Angeliki Kolovou, Marja van den Heuvel-Panhuizen, and Olaf Köller

This study investigated whether an intervention including an online game contributed to 236 Grade 6 students' performance in early algebra, that is, solving problems with covarying quantities. An exploratory quasi-experimental study was conducted with a pretest-posttest-control-group design. Students in the experimental group were asked to solve at home a number of problems by playing an online game. Although boys outperformed girls in early algebra performance on the pretest as well as on the posttest, boys and girls profited equally from the intervention. Implications of these results for educational practice are discussed.

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Tutita M. Casa

This instructional tool helps students engage in discussions that foster student reasoning, then settle on correct mathematics.

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Jennifer Noll and J. Michael Shaughnessy

Sampling tasks and sampling distributions provide a fertile realm for investigating students' conceptions of variability. A project-designed teaching episode on samples and sampling distributions was team-taught in 6 research classrooms (2 middle school and 4 high school) by the investigators and regular classroom mathematics teachers. Data sources included survey data collected in 6 research classes and 4 comparison classes both before and after the teaching episode, and semistructured task-based interviews conducted with students from the research classes. Student responses and reasoning on sampling tasks led to the development of a conceptual lattice that characterizes types of student reasoning about sampling distributions. The lattice may serve as a useful conceptual tool for researchers and as a potential instructional tool for teachers of statistics. Results suggest that teachers need to focus explicitly on multiple aspects of distributions, especially variability, to enhance students' reasoning about sampling distributions.

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Katie L. Anderson

Teachers share success stories and ideas that stimulate thinking about the effective use of technology in K–grade 6 classrooms. This article describes a set of lessons where sixth graders use virtual pattern blocks to develop proportional reasoning. Students' work with the virtual manipulatives reveals a variety of creative solutions and promotes active engagement. The author suggests that technology is most effective when coupled with worthwhile mathematical tasks and rich classroom discussions.

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Derek A. Stiffler

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Luann Voza

Arm your students for victory in the age-old battle to master subtraction with regrouping.

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Johnnie B. Wilson

It is easy to fall into the trap of thinking that teaching mathematics should greatly differ from teaching language arts. The subjects are usually scheduled separately in the school day. Classroom teachers at Munich International School in Starnberg, Bavaria, Germany, did not pay much attention to what language means to learning and teaching mathematics—until their geometry students offered language surprises that reminded their teachers how important language is.

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Kathy A. Bacon

Presented with a variety of palatable, inquiry-based, creative learning choices in geometry, this teacher and her fifth graders found tremendous satisfaction in meeting target goals for reasoning skills and taking important “next steps” in learning.

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Carolyn M. Jones

Connecting mathematical thinking to the natural world can be as simple as looking up to the sky. Volunteer bird watchers around the world help scientists gather data about bird populations. Counting all the birds in a large flock is impossible, so reasonable estimates are made using techniques such as those described in this problem scenario. Scientists draw on these estimates to describe trends in the populations of certain species and to identify areas for further research.