Teaching Approaches and Student Algebra Achievement: A Comparison of Hong Kong and US

• In Event: School reform processes and student outcomes: cross-national perspectives

Proposal

In mathematics teaching, there has always been a debate between conceptual based teaching and procedural based teaching (Hoff, 2003). To improve student mathematics learning, policy makers developed various reform documents to improve mathematics teaching with focuses on conceptual understanding. As shown in international comparative studies, students in Hong Kong usually demonstrated better performance than US students (Kastberg, Chan, & Murray, 2016; Kelly, Nord, Jenkins, Chan, & Kastberg, 2013). The international survey reports led us to consider what mathematics teaching that teachers in Hong Kong practice as different from US in producing better student learning results? This study examines three research questions: What are the patterns of mathematics teaching that teachers develop in algebra classrooms in Hong Kong and US? To what extent do these patterns reflect conceptual or procedural mathematics teaching as conceptualized? What are the relationships between mathematics teaching approaches and student algebra performance comparing Hong Kong and US?
Theoretical Framework
Two theories frame the design of the study. The first is the conception of the role of conceptual based and procedural based instruction in shaping student mathematics learning outcomes (Hiebert & Wearne, 1992; Hiebert & Grouws, 2007). It is widely assumed that conceptual teaching would be more likely to help students develop a deep mathematics understanding and problem-solving skills (Blöte, Van der Burg, & Klein, 2001). This conception is used in this study to select and group specific teaching items to construct teaching approach variables.
Another assumption is the perspective of culturally relative pedagogy. This theory emphasizes that students who have different cultural backgrounds usually have different learning methods and thoughts, therefore, effective teachers should incorporate student various cultural norms and behaviors into their instruction in mathematics classrooms (Ladson-Billings, 1995, 1997). Based on this theory, teaching is considered closely related with culture (Gay, 2010). It helps to interpret the results about the relationship between teaching approaches and student performance in different countries.
Methodology
Data used in this study was selected from eighth-grade Hong Kong and US from the Trends in International Mathematics and Science Study (TIMSS) 2015, which is developed to survey fourth-grade and eighth-grade student achievement in mathematics and science every four years (Martin, Mullis, & Hooper, 2016). This data offered a representative sample of eighth-grade teachers and students in various classrooms in Hong Kong and US. The specific sample size includes 172 teachers and 4155 students in Hong Kong, and 367 teachers and 10221 students in US. In TIMSS 2015, the teacher questionnaire contains various items related with mathematics teachers’ instructional approaches, and the student questionnaire provides specific items related with two controlled variables, student SES and self-confidence. Student mathematics achievement in algebra is also available in this database, and student algebra scores are used as the dependent variable in this study.
Exploratory factor analysis (EFA) was first used to identity the categories of instructional approaches that mathematics teachers developed in Hong Kong and US. Then, descriptive analysis and t-test were used to indicate the frequency mean and popularity of each instructional approach. To explore the influence of instructional approaches on student algebra performance, Hierarchical Linear Modeling (HLM) was used because it is suitable for the sampling data which involves two-stage in this study.
Results and Discussion
Our analysis led to several results. First, it suggested that conceptual based teaching and procedural teaching approach were used in both Hong Kong and US eighth-grade algebra classrooms as conceptualized (Hiebert & Wearne, 1992; Hiebert & Grouws, 2007). However, the results showed that procedural based instruction was more popular in Hong Kong as the procedural mean is significantly higher than conceptual in algebra (Mp=3.006, Mc=2.731), while conceptual based instruction was more popularly used in US (Mp=3.090, Mc=3.392). This confirms the finding of prior study in Hong Kong (Mok, 2009), but challenges the finding that procedural based approach was more popularly practiced in US (McKinney & Frazier, 2008).
Second, this study indicated that the frequency of conceptual based teaching contributed importantly to students’ algebra performance in Hong Kong (p < .001), while exerted no significant influence in US (p > .05). This challenges the assumption that conceptual teaching approach is generally instrumental to improve students’ mathematics learning (Blöte et al., 2001). The reason about why conceptual based instruction had such a limited role in helping shape eighth-grade student algebra performance in US worth a further and careful examination.
Third, procedural based instruction contributed importantly to students’ algebra achievement in Hong Kong (p < .001). However, in the US classroom contexts, the more often teachers used procedural based teaching, the more likely their students performed poorly in algebra. This supports the assumption that the effectiveness of a teaching approach, to the extent, depends on the kinds of student cultural backgrounds (Ladson-Billings, 1995, 1997).
Finally, in comparison with instructional approaches, student SES and self-confidence indicated significant impacts on student algebra performance in both Hong Kong and US (p< .05). This is consistent with findings that student SES and self-confidence are strongly associated with their achievement (Alvidrez & Weinstein, 1999; Byrnes & Miller, 2007; Colbeck, Cabrera, & Terenzini, 2001; Valentine, DuBois, & Cooper, 2004).
Significance
This study contributes to the large data based empirically evidence about mathematics teaching approaches popularly used in eighth-grade algebra classrooms, and the influence of instructional approaches on student algebra achievement comparing Hong Kong and US. The study poses a question about the popular assumption about the positive effects of conceptual based teaching on student mathematics learning. For researchers, this implicates that they need to further explore why conceptual based instruction is not related to student algebra achievement in US as expected. For teachers, the implication is that they need to be careful when using conceptual and procedural based instruction in their classrooms to improve student learning. For policy makers, this study suggests that when developing mathematics teaching reform initiatives to improve student mathematics performance through transforming instructional approaches, it should be cautious in implementing those theoretically assumed teaching approaches developed in other countries as effective teaching approaches are culturally relevant (Gay 2010; Sleeter 2008).

Authors

• Nan Wu, Texas Tech University

• Jian Wang, Texas Tech University