Content Focuses Chinese and US Preservice Teachers Developed in Mathematics Instructions on Whole Number

• In Event: Reimagining Pedagogical Tools and Practices

Proposal

Purposes and Rationales

Artificial intelligence increasingly shapes our lives, healthcare, finance, education deliveries, and jobs as machine learning engineers, data scientists, and robotic scientists (Rawat & Mishra, 2022). Mathematics ideas, such as linear algebra, probability theory, mathematical statistics, and mathematical modeling, constitute the theoretical foundation for artificial intelligence and its development (Jiang, 2022). Consequently, it is important to help students learn mathematics effectively by living, learning, and working with artificial intelligence.

Chinese students demonstrated stronger mathematics performance than U.S. students (Wang & Lin, 2009, 2013). Chinese teachers also developed a stronger mathematics understanding, shaping their instruction quality and students’ learning than their U.S. peers (Ma, 1999; Zhou et al., 1999). Thus, it is important to examine how Chinese teachers demonstrate their understanding of mathematics in teaching differently from U.S. teachers (Cheng, 2014). A careful examination of such differences between Chinese and U.S. preservice teachers is useful to verify whether Chinese teachers developed more effective ways to represent their content understanding than U.S. teachers due to their preparation programs (Yang et al., 2020).

The whole-number topics are foundational in the elementary curriculum (Thanheiser, 2012) and are central to developing their understanding of linear algebra necessary for working with and developing artificial intelligence (Jiang, 2022). Thus, it is worth examining how Chinese and U.S. preservice teachers demonstrate their whole-number understanding in teaching differently using three questions. Whether and to what extent did Chinese and U.S. elementary preservice teachers develop different whole-number focuses in their lessons? How much did they focus on conceptual understanding in teaching whole numbers differently? How much did they focus on procedure operations in teaching whole numbers differently?

Theoretical Framework

Mathematics common content knowledge is one of three strands of mathematics content knowledge for teaching with specialized mathematics content and horizon content knowledge strands as the other two (Ball et al., 2008). Such a knowledge strand includes mathematics concepts and procedures that all educated adults are expected to understand and use in solving various problems. The whole number is important for elementary mathematics instruction (Carpenter et al., 1998). Common mathematics content knowledge shapes the quality of mathematics instruction and, thus, student learning (Hill et al., 2005). This conception guided coding systems development to capture whole-number ideas that Chinese and U.S. preservice teachers develop in their mathematics lessons. It also included coding the conceptual or procedural focuses when whole-number ideas were presented.

Methodology

Participants and Context
This study included 10 Chinese and 10 U.S. preservice teachers as its participants. They were purposefully chosen from various sections of a mathematics methods course in a Chinese and a U.S. university elementary program based on whether they taught a whole number of topics in their practicum classrooms.

Data Sources and Analysis
This study collected the whole-number lessons taught by five Chinese and five U.S. preservice teachers. These lessons were taught in their practicum classrooms during student teaching after they completed their mathematics methods courses.

The following analyses were conducted to address the study’s questions. First, we transcribed all the lessons and translated the Chinese lesson transcripts into English. Second, we coded each lesson for specific whole-number ideas shown in the lessons, and conceptual understanding or procedural operation focuses on demonstrating the ideas. Third, we calculated the frequencies of the above coding results and conducted independent t-tests for conceptual understanding and procedural operation focuses for Chinese and U.S. teachers, respectively.

Findings

Whole-Number Topics Focusing on Conceptual Understanding
Chinese participants developed fewer whole-number ideas focusing on conceptual understanding in their lessons than U.S. participants. The t-test showed slightly significant differences for demonstrating whole-number ideas focusing on conceptual understanding t(8)=1.89, p=.05, between Chinese participants (M=23.00, SD=9.38) and U.S. peer (M=55.2, SD=36.95).

Chinese participants developed fewer cardinal numbers, additions, and multiplication ideas focusing on conceptual understanding than their U.S. peers. As shown in the t-test results, significant differences for cardinal number ideas, t(8)=1.37, p<.05, between Chinese participants (M=10.00, SD=2.00) and U.S. peers (M=16.20, SD=9.96), for addition, t(8)=1.28, p<01, between Chinese (M=3.20, SD=4.66) and U.S. (M=14.00, SD=19.11) and for multiplication, t(8)=.70, p<.05 between Chinese (M=2.20, SD=2.77) and U.S. (M=4.20, SD=5.76).

Chinese and U.S. participants developed division and subtraction ideas focusing on conceptual understanding. The t-test results show no significant differences for division ideas t(8)=-.764, p>.05 between Chinese (M=5.80, SD=2.59) and US (M=3.20, SD=7.16) and for subtraction, t(8)=2.39, p>.05 between Chinese (M=1.40, SD=2.61) and U.S. (M=16.40, SD=13.81).

Whole-Number Topics Focusing Procedure Operation
Chinese and U.S. participants developed whole-number ideas focusing on procedure operations similarly. The t-test showed no significant differences (t(8)=2.92, p>.05) in whole-number ideas focusing on procedure operations between Chinese (M=22.40, SD=10.16) and U.S. participants (M=57.60, SD=25.00).

However, Chinese participants developed more addition and counting ideas focusing on procedure operations than U.S. peers. Significant differences exist for addition, t(8)=1.67, p<.05, between Chinese (M=3.00, SD=4.58) and U.S. (M=16.00, SD=16.76) and for counting, t(8)=2.00, p<.05, between Chinese (M=1.20, SD=1.79) and U.S. (M=6.00, SD=5.05).

Chinese and U.S. participants developed cardinal number, subtraction, multiplication, and division ideas focusing on procedure operations similarly. The t-test results show no significant differences for cardinal numbers, t(8)=-4.83, p>.05, between Chinese (M=8.80, SD=1.17) and U.S. (M=3.00, SD=1.58), for subtraction, t(8)=3.01, p>.05 between Chinese M=18.80, SD=12.50 and U.S. M=1.60, SD=2.61, for multiplication, t(8)=-.21, p>.05, between Chinese (M=5.80, SD=9.18) and U.S. (M=2.00, SD=2.83), and for division, t(8)=.89, p>.05, between Chinese (M=4.60, SD=10.29) and U.S. (M=5.60, SD=2.30).

Discussions and Implications

The findings of this study contribute to the empirical understanding that Chinese and U.S. preservice teachers could develop ideas focusing on conceptual understanding differently, which challenges that Chinese teachers focused on conceptual understanding (Perry et al., 1993) with a whole-number counter-example at the preservice level. They contribute to the empirical understanding that Chinese and U.S. preservice teachers could develop whole-number ideas focusing on procedure operations, which resonate with U.S. teachers focused on procedure operations in teaching (Cai, 2005). It further contributes to the knowledge base for a content-based approach to develop preservice teachers’ knowledge and practices for mathematics teaching and for developing relevant policies and programs (Ball et al., 2008).

Authors

• Jian Wang, Texas Tech University

• Hyunjin Shim

• Xuan He, texas tech University

• Raymond Flores, Texas Tech University