Toward a Better Understanding of the Nature of Pedagogical Content Knowledge for Fractions: The Role of Experience

ABSTRACT

Mathematical knowledge for teaching (MKT) is a professional knowledge crucial for effective mathematics instruction, encompassing both content knowledge (CK) and pedagogical content knowledge (PCK). The purpose of this study is to investigate the hierarchical structure of PCK for fractions by seeking further evidence for the PCK-Fractions assessment. The PCK-Fractions measure is designed to examine the effectiveness of teacher education program and field experiences in facilitating preservice teachers’ (PSTs) PCK for children’s fraction reasoning in grades 4–6. Emplying165 undergraduate students, the research investigates how different levels of coursework and field experience influence PCK-Fractions scores. Results suggest that both completing coursework in a teacher education program and having grades 4–6 field experience each led to higher PCK-Fractions scores. Additionally, this study provides further evidence supporting the validity of the PCK-Fractions measure as a reliable indicator of PSTs’ proficiency in teaching fractions. Implications for mathematics teacher education and educational research are discussed.

KEYWORDS:

• Field experience, elementary school
• fractions
• pedagogical content knowledge
• validity argument

Acknowledgments

Research reported here received support from the National Science Foundation (NSF) through DRK-12 Grant (1908159). Any opinions, findings, and conclusions or recommendations expressed in this article are those of the author(s) and do not necessarily reflect the views of NSF.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Notes

¹ It is worthy to note that some individuals had additional test items included on their version of PCK-Fractions, but these extra items were not included within this current analysis.

² Although the highest score in this range was −.13, recall that these were first semester PSTs. Thus, a score of −.13 was considered relatively high for a PST at this stage of their professional education.

³ We excluded 3^rd grade field experience as informal feedback from participants revealed little experience with fractions in such placements.

⁴ We tested this hypothesis and simulated an additional 30 participants with higher scores on PCK-Fractions measure. After analyzing the simulation, we found the person reliability increased to .70.

Additional information

Funding

The work was supported by the National Science Foundation [1908159].