Author ORCID Identifier

Date Available


Year of Publication


Degree Name

Doctor of Philosophy (PhD)

Document Type

Doctoral Dissertation




Education Sciences

First Advisor

Dr.Xin Ma


Studies in recent years have explored the methods of identifying the turning points when dealing with the non-linear relationship. Four approaches applied by researchers, the eyeball approach, the establishment approach, the theory-driven approach, and the data-driven approach, are all under the traditional piecewise regression framework when seeking turning points. Thus, the purpose of this study is to introduce a multilevel piecewise regression model to identify the turning point beyond the traditional piecewise regression, as a completely non-linear approach.

Data used for this study is TIMSS 2019 United States sample. TIMSS is a project guided by the International Association for the Evaluation of Educational Achievement (IEA) (TIMSS 2007 Technical Report). In the United States, the sample size of fourth graders was 8,776 students from 287 schools. Students enrolled in the fourth grade have four years of schooling, and the average age in the United States sample is 10.2 years.

Under the present approach, the empirical findings confirmed the results in the literature review of previous research that certain factors impacted achievement. In this case, Students Like Learning Mathematics (SLM), Student Confidence in Mathematics (SCM), and Self-Efficacy for Computer Use (SEC) had a positive effect on mathematic achievement, but also indicated the different patterns of the effect change with and without control of the student and school factors. Students with the highest level of SLM, SCM, and SEC did not conclusively demonstrate the highest mathematics achievement. When students' SLM, SCM, and SEC reached a certain degree, their mathematics achievement progress slowed down, indicating after the turning point, more effort invested to increase the SLM, SCM, and SEC measurement level for higher mathematic outcomes might not effective.

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