The examination-oriented assessment methods have been widely employed in Macau but the over-dependence on such methods may hinder students’ balanced development of mathematical proficiency (Morrison & Tang, 2002; Schoenfeld, 2007). Peer assessment may compensate the limitation of those methods by engaging students actively to assess. However, little research has focused on the implementation of peer assessment in Macau secondary school. This dissertation reports a study which implemented a five-step peer assessment in an eighth grade mathematics lesson in Macau based on Ploegh at al.’s (2009) and Tillema et al.’s (2011) frameworks, in which the quality criteria are taken into account for revising the procedures. 16 students participated in three action cycles and the action plan was modified to explore how the changes to the peer assessment may influence students’ learning and students’ views towards the implementation of peer assessment. The results show that it is effective to establish a formative peer assessment to promote students’ mathematical learning in Macau by adopting the frameworks. The students in general held positive attitude towards the implementation of the peer assessment. They regarded it as a fair assessment, appreciated the extra opportunity to discuss mathematics, and treated it as a way to collect more feedback on their strength and weakness. Peer assessment also served as a learning activity which helped them gain deeper understanding of mathematics. It was found that students’ involvement in the setting of the assessment criteria, making judgment and writing narrative feedback improved students’ use of mathematical language to express their ideas. Providing more opportunities to judge and discuss mathematical problems also fostered the development of their mathematical proficiency. This study also reveals that asking peers for feedback and discussion about the feedback is an efficient way to develop students’ adaptive reasoning. The students’ change of performance in the action cycles also suggests that peer assessment has the potential to help the students access higher level of development in their zone of proximal development (ZPD) and balance the role of authority in mathematics classroom. / published_or_final_version / Education / Master / Master of Education

Humans are born with a basic sense of number. This number sense, which is now called the Approximate Number System (ANS), allows us to represent numerosity without the use of symbols. There has been a debate on whether this nonsymbolic ANS contributes to our symbolic mathematics skills, and the recent findings are inclined to support the link between the two. However, what remains unclear is the mechanism underlying the relationship between the ANS and our mathematics skills, and whether children with Mathematics Learning Disabilities (MLD) suffer from a defective ANS. The present thesis aimed at addressing the above issues in two studies. Study 1 aimed at identifying the mechanism of how the ANS contributes to children’s mathematics skills. A group of 210 kindergarteners were tested on their ANS acuity, number-numerosity mapping skills (measured by counting and estimation tasks), and their arithmetic skills. They were then re-tested twice when they were in Grade 1.Using Structural Equation Modeling, it was found that children’s ANS acuity in kindergarten predicted their arithmetic skills one year later, and the relationship was mediated by their number-numerosity mapping skills. This suggested that ANS may contribute to mathematics learning by enabling more precise mapping between number symbols and the corresponding numerosity representation, hence making numbers meaningful. Studies 2A and 2B aimed at verifying whether children with MLD suffered from deficits in their ANS as well as their number-numerosity mapping skills. The same group of participants was followed one more time in Grade 2. Using the standard low-achievement method (Study 2A) and a more data-driven method known as the latent class growth analysis(Study 2B), two groups of children with MLD were identified. Both groups of children had deficits in both the ANS and their number-numerosity mapping skills as compared with their normally-achieving peers. Other groups of low-achieving children were also identified, and their difficulties seemed to be contributed by factors other than their ANS. While one of the low-achieving groups seemed to have deficit lying mainly on the number-numerosity mapping skills, the other low-achieving group did not show any cognitive deficits but had much lower SES compared to other groups. The relationship between the ANS and children’s mathematics achievement was supported and elaborated in the present study. The findings not only articulated a potential mechanism of how children learned about mathematics, but they also allowed educators to have better understanding of the cognitive profiles of children with MLD, thus facilitating early identification and intervention. The different profiles of the low-achieving groups also highlighted the need for differential intervention for different groups of low-achieving children. / published_or_final_version / Psychology / Doctoral / Doctor of Philosophy

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This study of student-to-student discussions focuses on a single inquiry-oriented transition to proof course. Mathematical proof is essential to a strong mathematics education but very often students complete their mathematics studies with limited abilities to construct and validate mathematical proofs (c.f. Harel & Sowder, 1998; Knuth, 2002; Almeida, 2000). The role of mathematical proof in education is to provide explanation and understanding. Both the research on mathematical discourse and the standards of the NCTM claim that participation in mathematical discourse provides opportunities for understanding. Although this link has been established, there is very little research on the role of students and the instructor during discussions on student generated proofs at the undergraduate level -- particularly in inquiry-oriented classes. This research analyzes the types of discussions that occurred in an inquiry-oriented undergraduate mathematics course in which proof was the main content. The discussions of interest involved at least two student participants and at least three separate utterances. These discussions fell along a continuum based on the level of student interaction. As a result of this research, the four main discussion types that were present in this course have been described in detail with a focus on the roles of the instructor and the students. The methodology for this research is qualitative in nature and is an exploratory case study. The data used for this research was video tapes of two to three class sessions per week of an Introduction to Number Theory course taught in the fall of 2005. / text

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published_or_final_version / abstract / Education / Master / Master of Education

published_or_final_version / abstract / Education / Master / Master of Education

No description available.