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

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.