How Chinese and U.S. Preservice Teachers Ask Different Questions When Teaching Conceptual and Procedure Understanding of Geometry Topics

• In Event: Teacher Education in Comparative Perspective: Instructional Understanding, Relational Agency, and Equity

Proposal

Purposes and Rationale
Geometry is a key curriculum topic essential for developing students' spatial and visual thinking skills, number concepts, and quantitative ideas (Clements & Sarama, 2011). Teachers' effective use of questions helps support students' geometry learning (DeJarnette et al., 2020). Chinese students tend to understand geometry better than U.S. students (Wang & Lin, 2009, 2013). Chinese teachers also show a deeper understanding of mathematics (Ma, 1999; Zhou et al., 2005) and develop stronger content- and context-focused questions (Perry et al., 1993) compared to U.S. teachers.
In this study, we explore how well Chinese and U.S. preservice teachers use different types of questions to highlight the conceptual and procedural aspects of their geometry lessons, focusing on two questions. How effectively do Chinese and U.S. preservice teachers use various question types to emphasize the conceptual focus in their geometry lessons? How effectively do they use different questions to emphasize the procedural focus in their geometry lessons?
Theoretical Frameworks
Common Content Knowledge for Mathematics Teaching
Mathematics common content knowledge is a crucial area of mathematics content knowledge for teaching (Ball et al., 2008). It includes mathematical concepts and procedures that all educated adults are expected to understand and use when solving various problems. Such understanding is important for elementary geometry instruction (Clements & Sarama, 2011) and guided the development of coding systems to identify the conceptual and procedural focuses of participants' geometry lessons.
Question Types in Teaching
Teachers ask different types of questions in teaching mathematics (DeJarnette et al., 2020), which influence students' understanding of mathematics in various ways (Mason, 2000). These questions can be categorized as: 1) "yes-no" questions, asking students to confirm or reject an idea or process, 2) "what" questions, asking students to explain specific mathematics ideas or processes, 3) "how" questions, prompting students to describe steps or procedures leading to mathematical ideas, and 4) "why" questions, encouraging students to justify particular mathematical ideas and procedures. This framework guides the development of a coding system to identify the types of questions for participants' geometry lessons.
Methodology
Participants and Context
This study involved five Chinese and five U.S. preservice teachers. They were selected from different mathematics methods courses at a Chinese university and a U.S. university's elementary program, based on whether they taught geometry lessons during their practicum experiences.
Data Sources and Analysis
This study collected the geometry lessons from each Chinese and U.S. participant. Each lesson was videotaped and transcribed. Chinese lesson transcripts were also translated into English. We coded the conceptual and procedural focuses in each geometry lesson and calculated their mean scores for each group. Then, we coded each lesson for different types of questions, grouped similar questions, and calculated their averages for each group.
To answer the first question, we performed correlation tests to investigate the relationship between the mean scores of conceptual focuses and each type of question in each group's geometry lessons. To answer the second question, we used correlation tests to see how the mean scores of procedural focuses and each type of question are related in each group's geometry lessons.
Findings
Associations Between Conceptual Focuses and Questions
Chinese and U.S. participants did not significantly improve any of the four types of questions. These questions included "yes-no," "what," "why," and "how" questions, focusing on their concepts during the geometry lessons.
For Chinese participants, the insignificant correlations are observed between the mean scores of conceptual focuses and "yes-no" questions, rₛ=-.033, n=121, p>.05; between the mean scores of conceptual focuses and "what" questions, rₛ=.054, n=121, p>.05; between the mean scores of conceptual focuses and "how" questions, rₛ=.051, n=121, p>.05; and between the mean scores of conceptual focuses and "why" questions, rₛ=.089, n=121, p>.05.
Similarly, for U.S. participants, insignificant correlations are observed between the mean scores of conceptual focuses and "yes-no" questions, rₛ=.173, n=80, p>.05; between the mean scores of conceptual focuses and "what" questions, rₛ=.092, n=80, p>.05; between the mean scores of conceptual focuses and "how" questions, rₛ=.003, n=80, p>.05; and between the mean scores of conceptual focuses and "why" questions, rₛ=.038, n=80, p>.05.
Associations Between Procedural Focuses and Questions
U.S. participants used significantly more "what" questions than their Chinese peers when demonstrating procedural aspects of their geometry lessons. The results show a significant positive correlation between the mean scores of procedural aspects and "what" questions for U.S. participants, rₛ=.448, n=80, p<.001. However, there is no significant correlation between these measures for Chinese participants, rₛ=-.03, n=121, p＞.05.
Chinese and U.S. participants did not significantly develop "yes-no," "why," and "how" questions in their procedural focuses during their geometry lessons. For Chinese participants, the insignificant correlations are observed between the mean scores of procedural focuses and "yes-no" questions, rₛ=.211, n=80, p＞.05, between the mean scores of procedural focuses and "how" questions, rₛ=.1, n=80, p＞.05, and between the mean scores of procedural focuses and "why" questions, rₛ=-0.141, n=121, p＞.05. Similarly, for U.S. participants, the insignificant correlations are also identified between the mean scores of procedural focuses and "yes-no" questions, rₛ=.026, n=121, p＞.05, between the mean scores of procedural focuses and "how" questions, rₛ=.1, n=80, p＞.05, and between the mean scores of procedural focuses and "why" questions, rₛ=-0.134, n=80, p＞.05.
Discussions and Conclusions
This study offers several insights into our questions. Chinese and U.S. preservice teachers can use "yes-no" and "what" questions similarly. It questions the idea that Chinese teachers ask significantly more questions about content and context than U.S. teachers (Perry et al., 1993), providing a preservice-level contrasting example.
Chinese preservice teachers can use any of the four types of questions similarly when demonstrating conceptual focus in their geometry lessons. It is the case when they develop procedural focuses, except that U.S. preservice teachers might ask more "what" questions to demonstrate procedural focus in geometry lessons. These findings provide new empirical insights into how Chinese and U.S. preservice teachers use different question types to promote conceptual and procedural understanding. Therefore, it is important to investigate further into why these similarities and differences exist.

Authors

• Xuan He, Texas Tech University

• Jian Wang, Texas Tech University

• Raymond Flores, Texas Tech University

• Xiaofang Zeng, Dallas Independent School District

• Leah Osborne, Leander ISD