Exploring U.S. Prospective Lower Secondary Teachers' Mathematical Content Knowledge

• In Event: 65.066 - Mathematics Teacher Education: Results and Implications of an International Study

Abstract

Purpose
The purpose of this study was to investigate the mathematical content knowledge (MCK) of prospective lower secondary teachers (PLSTs) in the U.S. as reported in the Teacher Education and Development Study in Mathematics (TEDS-M; Tatto et al., 2012). The TEDS-M study reported that the PLSTs scored a scaled mean score of 471 on a scale with a mean of 500 and a standard deviation of 100. With regard to international exams in general, the U.S. performs about average. Therefore, with a score 29 points lower than the mean, which areas of MCK did PLSTs find most difficult?

Theoretical Framework
The theoretical framework for this study came from the TEDS-M study’s conceptual framework (Tatto, Schwille, Senk, Ingvarson, Peck, & Rowley, 2008). The measure of prospective teachers’ MCK consisted of their performance on mathematics items. Each item in the TEDS-M study was categorized by content domain (number, algebra, geometry, and data), cognitive domain (knowing, applying, and reasoning), and curricular domain (novice, intermediate, and advanced) (Tatto, 2013).

Methods
In order to understand the performance of the PLSTs on the MCK instrument compared to the other programs, I calculated the difference in scores between the U.S. and the top performing country on each item. Then, I separated the MCK items into their content domains. Next, I subdivided the items into their cognitive and then their curricular domains. After that, I grouped the items by subcategory and found the average difference in performance per item.

Results
In the number domain, the average percent below the top performing countries for the knowing items was 38%, 14% for the applying items, 33% for the reasoning items, 32% for the novice items, 36% for the intermediate items, and 15% for the advanced items. For algebra, the average percent below the top performing countries for the knowing items was 16%, 23% for the applying items, 13% for the reasoning items, 24% for the novice items, 26% for the intermediate items, and 13% for the advanced items.
With regard to geometry, the average percent below the top performing countries for the knowing items was 25%, 24% for the applying items, 21% for the reasoning items, 27% for the novice items, 22% for the intermediate items, and 13% for the advanced items. There were only a few data items which did not have any differences above 20%.
There were relative challenges in knowing and reasoning with number concepts, applying algebraic concepts, and all cognitive domains with geometry. For number, algebra, and geometry, PLSTs struggled with novice and intermediate items. The full paper includes more detailed analyses.

Scholarly Significance
This study points to areas of focus for PLSTs during their teacher preparation programs. Bolstering PLSTs’ skills in the aforementioned cognitive and curricular topics will help address areas of weakness for PLSTs. The Mathematical Education of Teachers II (CBMS, 2012) makes similar recommendations for the mathematical education of PLSTs. Having better-prepared PLSTs is a social justice issue to improve the mathematics education of all children.

Author

• Shawn Broderick, Keene State College