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Abstract Middle school students (n = 144) worked with an applet specially designed to introduce the concept of function without using algebraic representations. The purpose of the study was to examine whether the applet would help students understand function as a relationship between a set of inputs and a set of outputs and to begin to develop a definition of function based on that relationship. Results indicate that, by focusing on consistency of the outputs, the students, at a rate of approximately 80%, are able to distinguish functions from nonfunctions. Also, students showed some promise in recognizing constant functions as functions, a known area of common misconceptions. Students' main conceptual difficulty, likely caused by the context, was accepting nonintuitive outputs even if those outputs were consistent.
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A Dual‐Purpose Model for Binary Data: Estimating Ability and Misconceptions
Abstract Most existing diagnostic models are developed to detect whether students have mastered a set of skills of interest, but few have focused on identifying what scientific misconceptions students possess. This article developed a general dual‐purpose model for simultaneously estimating students' overall ability and the presence and absence of misconceptions. The expectation‐maximization algorithm was developed to estimate the model parameters. A simulation study was conducted to evaluate to what extent the parameters can be accurately recovered under varied conditions. A set of real data in science education was also analyzed to examine the viability of the proposed model in practice.
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- Award ID(s):
- 2150601
- PAR ID:
- 10485267
- Publisher / Repository:
- Wiley-Blackwell
- Date Published:
- Journal Name:
- Journal of Educational Measurement
- Volume:
- 61
- Issue:
- 2
- ISSN:
- 0022-0655
- Format(s):
- Medium: X Size: p. 179-197
- Size(s):
- p. 179-197
- Sponsoring Org:
- National Science Foundation
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