Investigating Pre-service Preschool Teachers’ Math Teaching Knowledge of Numerical Relations

• In Event: Poster Session 09
  In Poster Session: PS 09 Topic - Education, Schooling

Abstract

Few studies have measured preschool teachers’ knowledge of teaching mathematics, despite evidence of positive long-term impacts of high-quality early childhood education. Acknowledging that pre-service teachers have lower math content knowledge and math pedagogical content knowledge compared with in-service teachers (Shahbari, 2017), the present study concerns pre-service preschool teachers’ math teaching knowledge in the domain of numerical relations. The construct of math teaching knowledge in this study has three components, adopted from Ball and colleagues (2008): 1) specialized content knowledge (SCK) that entails unpacked and differentiated knowledge in specific content areas; 2) knowledge of content and students (KCS) that includes knowledge of children’s development trajectories and common errors/misconceptions; 3) knowledge of content and teaching (KCT) that teachers demonstrate when proposing appropriate tasks/strategies to help correct a child’s errors or advance the child’s learning. This set of explicit teaching knowledge impacts the quality of pedagogical interactions in the early childhood classroom.
Forty-four pre-service preschool teachers answered a researcher-designed questionnaire composed of three scenarios. Each scenario depicts a math game played by a teacher and a group of children. After each scenario, participants answer open-response and multiple-choice questions that target either SCK, KCS, or KCT. SCK is measured by participants’ ability to identify key concepts in the scenario; KCS is measured by participants’ ability to identify a child’s errors/difficulties; KCT is measured by participants’ ability to propose tasks that address the child’s difficulties. Reported in this proposal are data from the open response questions following a scenario depicting a number comparison game (N = 37).
The data were analyzed qualitatively by an author-created coding system. Reliability was established for 38% of the dataset between two raters (κ = .65). For SCK, the analysis revealed that 85% of participants identified at least one skill that the scenario was targeting, which was either the primary concept--comparing numbers or the secondary concept--number order; the highest frequency of incorrect responses mentioned cardinality and verbal counting. Regarding KCS, 38% of participants correctly identified at least one of the child’s mathematical strengths and weaknesses; for the child’s weakness, 38% of participants identified the child’s primary difficulty, which is either naming numbers less than another number or comparing numbers greater than 4 or 5. The most common incorrect responses did not include reference to the child’s mathematical thinking. For KCT, the analysis revealed that the majority of participants targeted one of the child’s two areas of weakness (65%), wrote a somewhat detailed response (43%), did not include hands-on or visual materials (60%), and suggested a task somewhat likely to help a child compare numbers (44%). Furthermore, a Friedman test indicated a significant difference between the three components of math teaching knowledge, χ2(2) = 34.92, p < .001. Pairwise comparisons indicated that SCK was significantly higher than both KCS and KCT. The present study provides insights into the degree to which pre-service preschool teachers are aware of the key numerical relation concepts, children’s mathematical thinking regarding numerical relations, and the strategies that support them.

Authors

• Xia Li, Brooklyn College CUNY
  Non-Presenting Author

• Colleen Uscianowski, University of Cincinnati
  Presenting Author

• Colleen O'Donnell Oppenzato, Columbia University
  Non-Presenting Author