DIAGNOSING STUDENTS’ MASTERY PROFILE OF ALGEBRAIC THINKING ABILITY: AN APPLICATION OF MIXED HIERARCHICALLY STRUCTURED COGNITIVE DIAGNOSTIC MODELS

Date

2023-6-22

Author

ERDOĞAN, MELEK

Metadata

Show full item record

This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Item Usage Stats

74
views

49
downloads

Cite This

In education, there has been a high demand for testing that offers strong diagnostic information. This demand is also notable in mathematics education. Considering this expectation, this study aimed to construct a multidimensional multiple-choice test within the framework of Cognitive Diagnostic Models (CDM) and to determine the mastery profile of the algebraic thinking ability of the students by the end of middle school. A framework reflecting algebraic thinking ability was defined based on Stephens et al. (2017) and structured on the core aspects and strands of algebraic thinking (Kaput, 2008) and core practices (Blanton et al., 2011). By utilizing this framework, three 20-item diagnostic multiple-choice tests (Test A, Test B, and Test C) were developed and implemented. The obtained response pattern from a sample of 2600 ninth-grade students in Çankaya District of Ankara was analyzed using Cognitive Diagnostic Models offering information about the characteristics of the item parameters and the mastery profiles of the students. Different structural models were tested, and the Mixed Hierarchically Structured GDINA model was selected as the best-fitted model for the response data. According to this structural model obtained from the answers given to the tests, quantitative reasoning has been determined as the prerequisite of generalized arithmetic and generalized arithmetic as the prerequisite of functional thinking abilities. On the other hand, regarding core practices, representation has been determined as the prerequisite for generalizing and generalizing as the prerequisite for justifying abilities. This structure has been identified as important by showing the direction of the interaction between algebraic thinking abilities. Through this structural model, the algebraic thinking ability mastery levels of the whole groups and subgroups were examined. The prominent items in the test were also examined according to different responding situations. Implications of the findings for diagnosing and developing algebraic thinking skills were discussed.

Subject Keywords

Algebraic Thinking Ability, Cognitive Diagnostic Assessment, Hierarchically Structured Cognitive Diagnostic Models, GDINA Model

URI

https://hdl.handle.net/11511/105142

Collections

Graduate School of Natural and Applied Sciences, Thesis