Assessment of primary 5 students' mathematical modelling competencies

 Mathematical modelling is increasingly becoming part of an instructional approach deemed to develop students with competencies to function as 21st century learners and problem solvers. As mathematical modelling is a relatively new domain in the Singapore primary school mathematics curriculum, many teachers may not be aware of the learning outcomes and competencies needed to develop in their students during mathematical modelling. This paper reports on the assessment of two groups of Primary 5 students’ (aged 11) mathematical modelling competencies in their first attempt in completing a modelling task. The students’ competencies are assessed to be at levels 1 and 2 of a researcher-designed rubric. Findings appear to suggest that students faced particular challenges in formulating a mathematical problem from the real-world problem through making assumptions. Implications on teacher education on the facilitation of problem formulation and mathematisation during mathematical modelling at the primary level are drawn.

Developing teacher competencies through videos for facilitation of mathematical modelling in Singapore primary schools

Mathematical modelling tasks which are situated in real-world contexts encourage students to draw connections between school-based mathematics and the real-world, enhancing their engagement in learning. Such tasks often require varied interpretations of the real-world problem context resulting in multiple pathways of solutions. Although mathematical modelling has been introduced in the Singapore mathematics curriculum since 2007, its incorporation in schools has been limited. One reason for this could be that teachers are challenged by how best to facilitate for rich student mathematisation processes during such tasks. This chapter reports how a multi-tiered teaching experiment using design research methodology was conducted to build teachers’ capacity in designing, facilitating, and evaluating student mathematisation during mathematical modelling tasks with an intact class of Primary 5 students (aged 10-11). The use of videos was critical because grounded images helped capture the dynamics and complexity of authentic classroom interactions. This chapter highlights how video recordings of teacher-student interactions during a modelling task were harnessed during design methodology cycles, particularly during the Retrospective Analysis phase, to activate critical moments of learning for the teacher towards developing her competencies in facilitating students’ mathematisation processes.

A framework for primary teachers’ perceptions of mathematical reasoning

Mathematical reasoning has been emphasised as one of the key proficiencies for mathematics in the Australian curriculum since 2011 and in the Canadian curriculum since 2007. This study explores primary teachers’ perceptions of mathematical reasoning at a time of further curriculum change. Twenty-four primary teachers from Canada and Australia were interviewed after engagement in the first stage of the Mathematical Reasoning Professional Learning Program incorporating demonstration lessons focused on reasoning conducted in their schools. Phenomenographic analysis of interview transcripts exploring variation in the perceptions of mathematical reasoning held by these teachers revealed seven categories of description based on four dimensions of variation. The categories delineate the different perceptions of mathematical reasoning expressed by the participants of this study. The resulting outcome space establishes a framework that facilitates tracking of growth in primary teachers’ awareness of aspects of mathematical reasoning.

Primary teachers notice the impact of language on children’s mathematical reasoning

Mathematical reasoning is now featured in the mathematics curriculum documents of many nations, but this necessitates changes to teaching practice and hence a need for professional learning. The development of children’s mathematical reasoning requires appropriate encouragement and feedback from their teacher who can only do this if they recognise mathematical reasoning in children’s actions and words. As part of a larger study, we explored whether observation of educators conducting mathematics lessons can develop teachers’ sensitivity in noticing children’s reasoning and consideration of how to support reasoning. In the Mathematical Reasoning Professional Learning Research Program, demonstration lessons were conducted in Australian and Canadian primary classrooms. Data sources included post-lesson group discussions. Observation of demonstration lessons and engagement in post-lesson discussions proved to be effective vehicles for developing a professional eye for noticing children’s individual and whole-class reasoning. In particular, the teachers noticed that children struggled to employ mathematical language to communicate their reasoning and viewed limitations in language as a major barrier to increasing the use of mathematical reasoning in their classrooms. Given the focus of teachers’ noticing of the limitations in some types of mathematical language, it seems that targeted support is required for teachers to facilitate classroom discourse for reasoning.

The positioning of mathematics in an environmental thematic curriculum

With a crowded curriculum, many primary schools attempt to integrate their key learning areas. One primary school in a large regional city has taken this a step further. Using the ’environment’ as the overarching theme, the key learning areas are interwoven into the teaching of the environment. This has presented some issues when attempting to teach English and Mathematics. These issues and the way the school and teachers solve them are documented in this case-study.

A curriculum innovation framework for science, technology and mathematics education

There is growing concern about falling levels of student engagement with school science, as evidenced by studies of student attitudes, and decreasing participation at the post compulsory level. One major response to this, the Australian School Innovation in Science, Technology and Mathematics (ASISTM) initiative, involves partnerships between schools and community and industry organisations in developing curriculum projects at the local level. This project fulfils many of the conditions advocated to engage students in learning in the sciences. ASISTM is underpinned by the notion of innovation. This paper describes the findings of case study research in which 16 ASISTM projects were selected as innovation exemplars. A definition of innovation and an innovation framework were developed, through which the case studies were analysed to make sense of the significance of the ideas and practices, participating actors, and outcomes of the projects. Through this analysis we argue that innovation is a powerful idea for framing curriculum development in the sciences at the local level that is generative for students and teachers, and that these ASISTM projects provide valuable models for engaging students, and for teacher professional learning.

Numeracy across the curriculum: recognising and responding to the demands and numeracy opportunities inherent in secondary teaching

The 1998 Report of the National Standards and Guidelines for Initial Teacher Education Project, 'Preparing a Profession' illustrates the emphasis being placed in Australia on the development of numeracy skills amongst not only primary but also secondary school pupils. This report demands that graduates of all initial teacher training courses should not only be numerate themselves, but should also understand the contribution of numeracy to education and daily life, and be able to identify and respond to pupils' numeracy learning needs. This report and its implementation in Victoria through the 'Guidelines for the Evaluation of Teacher Education Courses' led to the introduction in 1999 of a compulsory unit 'Numeracy across the curriculum' for all Deakin University students in the final year of their secondary teacher training course. This paper discusses the nature of the current emphasis on numeracy. It also describes the rationale, development and delivery of the first year of the 'Numeracy across the curriculum' unit, provides a brief evaluation from the perspective of staff and students, and discusses what impact such teacher education programs might have on secondary schools' approaches to numeracy.

Progressive discourse in mathematics classes - the task of the teacher

This paper uses data from two mathematics lessons to explore the nature of progressive discourse and examine critical features of teacher actions that contribute to mathematics classrooms functioning as communities of inquiry. Features found to promote progressive discourse include a focus on the conceptual elements of the curriculum and the use of complex, challenging tasks that problematised the curriculum; the orchestration of student reporting to allow all students to contribute to progress towards the community's solution to the problem; and a focus on seeking, recognizing, and drawing attention to mathematical reasoning and justification, and using this as a basis for learning.

What does mathematics understanding look like?

The concept of mathematical understanding is central to curriculum development, classroom interaction, and the training of mathematics teachers In this paper, some models of the growth of understanding that the literature presents are outlined Some results of a study that documented four primary teachers’ mental models of, and beliefs about, different forms of understanding are reported It is proposed that linear models may restrict ways that these teachers plan lessons Questions for further research are raised

Primary and secondary mathematics practice: how different is it?

This paper describes the practices of ninety-nine teachers at the beginning of their involvement in a large-scale project investigating the influence of subject cultures on school and teacher change. Data collected from these teachers, using the IMYMS. Components of effective teaching and Learning mapping procedure, were analysed to investigate similarities and differences in primary and secondary teachers’ perceptions of their practice in mathematics. Results of the analysis show different patterns across a range of components of effective teaching and learning.

A first priority when working with teachers is to help them become aware of and make problematic aspects of their current practice …. Only then would they have reason to attempt to reform their instructional practices when working with us. (Yackel, 1994, p. 386)