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Using the Rasch Model to Measure the Extent to which Students Work Conceptually with Mathematics.

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This study introduces a new instrument to measure conceptual mathematics work in students. The Rasch calibrated tool identifies how well students connect mathematical concepts rather than just applying rules.

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Area of Science:

  • Mathematics Education
  • Educational Measurement

Background:

  • The distinction between procedural and conceptual mathematical understanding is established.
  • Procedural work involves rule application without deep comprehension.
  • Conceptual work requires building interconnected knowledge structures.

Purpose of the Study:

  • To develop and validate a measurement instrument for assessing conceptual mathematical work.
  • To provide a tool for researchers and educators to quantify conceptual understanding.

Main Methods:

  • The study employed Rasch calibration to develop a measurement instrument.
  • Data were collected from 133 student teachers and 185 Civil Engineering students.
  • Item analysis identified 20 effective items for measurement.

Main Results:

  • A reliable and valid Rasch calibrated instrument was developed.
  • The instrument effectively measures the degree of conceptual work in mathematics.
  • 20 items were validated for their measurement capabilities.

Conclusions:

  • The presented instrument offers a robust method for measuring conceptual mathematical engagement.
  • This tool can aid in understanding student learning and informing pedagogical strategies.
  • Further research can utilize this instrument to explore conceptual understanding across different student populations.