Leong, Yew Hoong

Driven by the IT Master Plan implemented by the local education authority, schools in Singapore have over the recent few years incorporated the use of computers in the classroom, including the integration of relevant software for the teaching and learning of mathematics. Educators extol the huge potential in computers being superior over conventional teaching aids and in the suitability of computer software in encouraging students' exploration as a way of learning Mathematics.

This study investigated how the use of a common construction programme in different pedagogical settings impacted spatial ability and achievement scores of students within concepts in transformation geometry.

The subjects were Secondary Two Express stream students from a school with above-average ranking among National schools. Three classes participated in the study. All the classes were taught an instructional module on transformation geometry with the use of the Geometer's Sketchpad. The software was however employed differently in the three classes: In Class A (n = 41), the approach adopted by the teacher was that of guided-inquiry, and the technological use was supportive of the pedagogy - students have hands-on experience with the software to explore and make conjectures; in class C(n - 38), the teachers' predominant role was that of an expositor and the students' role that of knowledge-recipients, and the software was used as a teacher's tool to demonstrate dynamically the properties of motions; Class B (n = 42) was the 'in-between' of Class A and Class C - adopting the pedagogy of guided-inquiry in whole-class discourses with the teacher manipulating objects on the displays on the projected screen what students would for themselves like to do on the computers.

Pre- and Post-treatment tests were conducted using the Wheatley Spatial Ability Test (WSAT), which is a widely-used instrument in testing students' ability in mental manipulations of planimetric objects. Paired-sample t-tests show highly significant increases between pre- and posttest scores in all the classes. There was no significant difference in the posttest scores between the classes after factoring in differences in the pre-test scores, as analysed using ANCOVA.

A Motion Geometry Test (MGT) was constructed to test the subjects' level of attainment of National curricula objectives within the topic of 'Motion Geometry' in the syllabus at the end of the intervention period. An F-test indicated that scores from students in Class C were significantly lower than those from the other two classes. There was no significant difference in MGT scores between Class A and Class B.

One-to-one teacher-student interview sessions were conducted with five selected students from each class to further investigate the strength of concepts learnt during the treatment period. Each student was presented with four on-screen object-image figures and his/her task was to fully describe the possible single transformation for each task; the teacher provided prompts when the student encountered difficulties in proceeding further. Analysis of the teacher-student responses points to higher level concept abstraction found in students from Class A.

Although there is an acknowledged need to attend to the learning needs of low achievers in mathematics, there is relatively scant research in this area locally. This proposed project aims to contribute to this sub-field within mathematics education. In particular, this study will focus on helping Normal Academic (NA) students make improvements in their learning of Mathematics.

In designing a set of instructional materials to use in his classroom, a teacher heavily offloaded items (e.g., worked examples, practice questions, exercises) from school-based materials and textbooks. At a cursory level, one may easily dismiss this as a thoughtless lifting of curricular materials. But upon careful analysis – as is detailed in this paper – a different picture emerges. In this paper, we describe and analyse how this teacher adapted one of many worked examples, beyond its typical use, during instruction to develop students’ conceptual understanding of proportionality. We argue that he noticed and harnessed multiple affordances in a single item that most teachers may overlook, without the need to modify the example, and propose a notion of “affordance space” as a lens to view teachers’ design of instructional materials.

We recognize that though teachers may participate in various forms of professional development (PD) programmes, learning that they may have gained in the PD may not always lead to corresponding perceivable changes in their classroom teaching. We offer a theoretical re-orientation towards this issue by introducing a construct we term “concretisation”. Concretisations are resources developed in PD settings which can be converted into tangible tools for classroom use. In theorising such resources, we contribute in informing the design process of teacher professional development for better impact into actual classroom practice. We purport principles of design which render concretisations effective. Subsequently, we test these principles by presenting a specific case of teaching mathematical problem solving.

In the field of education, research projects that involve both the researcher and teacher being the same person are common today, as attested by the significant number of teacher-researcher studies. One issue confronting the dual role of teacher-researcher is the nature of interaction between the underlying goals that come with each of these roles. There are some researchers who express concern that the combination of these goals within the teacher-researcher may compromise either or both of the work of teaching and research in an unproductive way. This paper is an account of my' adventure in attempting to fulfil both teaching and research goals in my work as teacher-researcher in a year 7 (Secondary One)geometry class in Singapore. My experience is then re-interpreted in the context of the ongoing conflicting-versus-complementary talk on the interaction between teacher/researcher'selves'. A model is proposed to account for the seemingly opposite sides of the camp as reported in the literature on this issue.

In this symposium, we discuss some preliminary data collected from our problem solving project which uses a design experiment approach. Our approach to problem solving in the school Curriculum is in tandem with what Schoenfeld (2007) claimed: “Crafting instruction that would make a wide range of problem-solving strategies accessible to students would be a very valuable contribution … This is an engineering task rather than a conceptual one” (p. 541). In the first paper, we look at how two teachers on this project taught problem solving. As good problems are key to the successful implementation of our project, in the second paper, we focus on some of the problems that were used in the project and discuss the views of the participating students on these problems. The third paper shows how an initially selected problem led to a substitute problem to meet our design criteria.

This study delves into the dynamics between diverse learning behaviors among K-12 students and their learning gains using a dataset of 508 students learning three math skills in ASSISTments. Employing K-means clustering based on students’ initial and final skill mastery alongside their engagement level, three distinct clusters emerged for each skill, revealing varying degrees of learning from ASSISTments. By analyzing decision tree classification models for each skill using affective labels such as boredom and frustration, we hypothesize that students within the same cluster of a skill may exhibit heterogeneous learning patterns that affect their subsequent learning of new skills. Further exploration demonstrates that students who transit between clusters when learning new skills differ significantly in their initial and final mastery of previously learned skills and their affective labels associated with those skills. Regression analysis underscores that students’ initial and final mastery of antecedent skills have some influence on their subsequent mastery of new skills. Unraveling the intricate relationship between student learning behaviors and the effectiveness of ASSISTments offers valuable insights into tailoring AI-enhanced educational tools, not only for learning the current skill but also for preparing for the future learning of new skills.