Different Questions Developed by Chinese and U.S. Preservice Teachers to Teach Conceptual and Procedural Understanding of Word Problems

• In Event: Policy Meets Practice: Comparative Insights on Teacher Development and Curriculum Reform

Proposal

Purposes and Rationales
Strong conceptual and procedural understanding is crucial for solving math problems (Verschaffel, Depaepe, & Van Dooren, 2020). Teachers' effective use of questions helps support students’ word problem solving (DeJarnette, Wilke, & Hord, 2020). Chinese students tend to solve word problems better than U.S. students (Wang & Lin, 2009, 2013). Chinese teachers have a better understanding of mathematics (Ma, 1999; Zhou, Peverly, & Lin, 2005) and create stronger content- and context-focused questions (Perry, VanderStoep, & Yu, 1993) than 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 word problem lessons using two questions. To what extent do Chinese and U.S. preservice teachers vary in their use of different questions to develop the conceptual focus of their lessons? To what extent do they differ in their use of questions to develop the procedural focus in their word problem lessons?
Theoretical Frameworks
Common Content Knowledge for Mathematics Teaching
Mathematics common content knowledge is a key component of mathematics content knowledge for teaching (Ball, Thames, & Phelps, 2008). It encompasses mathematical concepts and procedures that all educated adults are expected to understand and apply when solving different problems. This understanding is crucial for teaching elementary word problems (Carpenter, 2013; Fuchs et al., 2021; Powell, 2011) and has guided the development of coding systems to assess the conceptual and procedural focus of participants’ word problem lessons.
Questions Used in Teaching
Teachers ask different types of questions in teaching mathematics (DeJarnette et al., 2020), which influence students' understanding of mathematics differently (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, prompting students to explain specific mathematics ideas or processes; 3) “how” questions, encouraging students to describe steps or procedures leading to mathematical ideas; and 4) “why” questions, urging students to justify particular mathematical ideas and procedures. This framework guides the development of a coding system to identify the types of questions in participants’ word problem lessons.
Methodology
Context and Participants
This study included 18 Chinese and 18 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 word problems during their practicum experiences.
Data Sources and Analysis
This study collected the word-problem lessons taught by each Chinese and U.S. participant. Each lesson was videotaped and transcribed. Chinese lesson transcripts were translated into English. We coded the conceptual and procedural focuses in each word problem lesson and calculated their average frequency scores for each group. We then 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 see how the mean scores of conceptual focuses and each type of question are related in each group’s word problem lessons. To answer the second question, we used the correlation tests to examine how the mean scores of procedural focuses and each type of question are related for each group.
Findings
Associations Between Conceptual Focuses and Questions
Chinese and U.S. participants developed similar “yes-no” and “what” questions significantly when demonstrating conceptual focuses. The significant and positive correlations exist between conceptual focuses and “yes-no” questions, rₛ=.262, n=558, p<.001 and rₛ=.243, n=466, p<.001 and between conceptual focuses and “what” questions with rₛ=.377, n=558,p < .001 and rₛ=.376, n= 466, p< .001, for Chinese and U.S. participants, respectively.
Chinese participants used “how” questions more than their U.S. peers when developing conceptual focuses. A significant and positive correlation exists between the mean scores of conceptual focuses and “how” questions for Chinese participants, rₛ=.193, n=558, p<.001. However, an insignificant correlation exists between the mean scores of conceptual focuses and “how” questions for U.S. participants, rₛ=.128, n=466, p>.005.
U.S. participants used “why” questions more than their Chinese peers in demonstrating conceptual focuses. The correlation results indicate a significant and positive correlation between the mean scores of why questions and conceptual focuses for U.S. participants, rₛ=.223, n=466, p <.001. However, an insignificant correlation exists between these measures for Chinese participants, rₛ=.196, n=558, p<.001.
Associations Between Procedural Focuses and Questions
Chinese and U.S. participants used similar “yes-no” and “what” questions significantly when teaching procedural fluency. The significant and positive correlations exist between the means scores of between procedural focuses and yes-or-no questions, rₛ=.216, n=558, p<.001 and rₛ=.234, n =466, p <.001, between the means scores of between procedural focuses and “what” questions, rₛ=.438, n=558, p<.001 and rₛ=.364, n= 466, p< .001, for Chinese and U.S. participants, respectively.
Chinese participants also used more “how” and “why” questions in developing procedural fluency than their U.S. peers. The significant and positive correlations exist between the mean scores of procedural fluency and “how” questions, rₛ=.244, n=558, p<.001, and between the mean scores of procedural fluency and “why” questions, rₛ=.141, n=558, p< .001for Chinese participants. In contrast, insignificant correlations exist between the mean scores of procedural fluency and how questions, rₛ=.107, n=466, p>.005, and between the mean scores of procedural fluency and “why” questions, rₛ=.114, n=466, p>.005, for U.S. participants.
Discussions and Conclusions
This study provides several insights into our questions. Chinese and U.S. preservice teachers can use “yes-no” and “what” questions in similar ways. It challenges the idea that Chinese teachers ask significantly more questions about content and context than U.S. teachers (Perry et al., 1993), with a preservice-level contrasting example.
Chinese preservice teachers tend to ask more “how” questions, while their U.S. counterparts might ask more “why” questions when developing the conceptual focus of word problem lessons. In contrast, Chinese preservice teachers may ask both “how” and “why” questions more frequently than their U.S. peers when focusing on procedural understanding. These findings offer new empirical insights into how Chinese and U.S. preservice teachers use different types of questions to promote conceptual and procedural understanding. Therefore, it is important to investigate further why these differences exist.

Authors

• Jian Wang, Texas Tech University

• Xuan He, Texas Tech University

• Raymond Flores, Texas Tech University

• Yesira Alhassan Alolo

• Deepa Sobha