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Prediction assessments: Using video-based predictions to assess prospective teachers’ knowledge of students’ mathematical thinking

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Abstract

In order to evaluate the effectiveness of an experimental elementary mathematics field experience course, we have designed a new assessment instrument. These video-based prediction assessments engage prospective teachers in a video analysis of a child solving mathematical tasks. The prospective teachers build a model of that child’s mathematics and then use that model to predict how the child will respond to a subsequent task. In this paper, we share data concerning the evolution and effectiveness of the instrument. Results from implementation indicate moderate to high degrees of inter-rater reliability in using the rubric to assess prospective teachers’ models and predictions. They also indicate strong correlation between participation in the experimental course and prospective teachers’ performances on the video-based prediction assessments. Such findings suggest that prediction assessments effectively evaluate the pedagogical content knowledge that we are seeking to foster among the prospective teachers.

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Acknowledgments

The research reported in this paper was supported by a DR-K12 grant from the National Science Foundation (NSF), under grant number DRL-0732143. The authors wish to thank all the members of the IMB research team, as well as Dionne Cross, who collaborated with us in collecting data.

Author information

Authors and Affiliations

  1. Department of Mathematics (0123), Virginia Tech, Blacksburg, VA, 24061, USA

    Anderson Norton

  2. Penn State, 268 Chambers Building, University Park, PA, 16802, USA

    Andrea McCloskey

  3. University of Southern Indiana, 8600 University Blvd, SC 3261, Evansville, IN, 47712, USA

    Rick A. Hudson

Authors
  1. Anderson Norton
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  2. Andrea McCloskey
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  3. Rick A. Hudson
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Corresponding author

Correspondence to Andrea McCloskey.

Appendix: prediction assessment rubric

Appendix: prediction assessment rubric

  • Content knowledge:

  • 0: Incorrectly solved the problem

  • 1: Correctly solved the problem

  • Model:

  • 0: Does not use evidence (descriptions of student actions or statements) to describe what or how the student is thinking

  • 1(a): Uses evidence to support an explanation of what the student knows or thinks, but not how the student is thinking

  • 1(b): Explains how the student is thinking but does not provide explicit evidence to support this explanation.

  • 2: Uses evidence to support a reasonable explanation for how the student is thinking

  • Prediction (accuracy and detail):

  • 0: Makes no prediction relevant to the situation

  • 1: Makes an inaccurate prediction with some detail relevant to the situation, but not enough to unambiguously envision what the student might have done or said in response to the task/question

  • 2(a): Makes an inaccurate prediction, but with enough relevant detail to envision what the student might have done or said in response to the task/question

  • 2(b): Makes a prediction that might be correct, but remains too vague to determine

  • 3(a): Makes an accurate prediction with some detail relevant to the situation, but not enough to unambiguously envision what the student would do or say in response to the task/question

  • 3(b): Makes multiple predictions, one of which accurately describes what the student would do or say

  • 4: Makes an accurate prediction with sufficient detail to envision what the student would do or say in response to the task/question

  • Use of model:

  • 0: There is no evidence (or there is counter-evidence) that the PST teacher used an explanation of the students’ thinking (model) to form any of the predictions

  • 1: There is some evidence that the PST used a model to form some of the predictions

  • 2: The PST clearly used a model to form most or all of the predictions

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Norton, A., McCloskey, A. & Hudson, R.A. Prediction assessments: Using video-based predictions to assess prospective teachers’ knowledge of students’ mathematical thinking. J Math Teacher Educ 14, 305–325 (2011). https://doi.org/10.1007/s10857-011-9181-0

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  • DOI: https://doi.org/10.1007/s10857-011-9181-0

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