Developing noticing of reasoning through demonstration lessons

Observation of fellow educators conducting demonstration lessons is one avenue for teachers to develop sensitivity to noticing students’ reasoning. We examined teachers’ noticing of children’s learning behaviours in one demonstration lesson of the Mathematical Reasoning Professional Learning Research Program (MRPLRP). The observations of teachers evident in the audio-taped post-lesson group interviews conducted at one school are reported in this paper. The teachers noticed that the children struggled to employ mathematical language to communicate their reasoning and expressed concern about gaps in children’s understanding of key mathematical concepts. The teachers viewed limitations in language and mathematical conceptual understandings as a barrier to effective reasoning.

Year 3/4 children's forms of justification

Engaging children in justifying, forming conjectures and generalising is critical to develop their mathematical reasoning. Previous studies have revealed limited opportunities for primary school children to justify their thinking, form conjectures and generalise in mathematics lessons. Forms of justification of Year3/4 children from three schools in Victoria, Australia will be examined. Evidence from children's written explanations and their verbal explanations captured in video recordings revealed that some children employed sophisticated mathamatical ideas in their justifications. The value of making children's reasoning explicit through written explanations and verbal communications is highlighted.

The teaching contest as a professional development activity to promote classroom instruction excellence in China

Teaching contests might be alien to many readers outside of China mainland, but as one of professional development activities, it is well known by most of Chinese school teachers. This chapter, based on the data collected by mail surveys to the contest organizers, evaluation panel members, contest winners, and ordinary participating teachers, and detailed notes taken from various meetings of the evaluation committee, as well as a lesson video of one of the three contest winners, we aimed to the 2011 national high school teachers' teaching contests carefully, to examine the aims and processes of teaching contests, their possible merits or weaknesses for teachers’ professional development, and features of exemplary lessons demonstrated during the national teaching contest. It was found that the aim of the teaching contest was totally not the competition per se., to promote curriculum development and teachers' professional development, to provide a big platform for those teachers who pursue excellence in teaching to display, discuss, explore, and share with others about mathematics instruction were real intentions of the organizers.

The Use of Videos and Classroom Artefacts in Professional Development of Teachers and Teacher Educators in Indonesia

This study is grounded on adaptations of Realistic Mathematics Education, Lesson Study and design-based research in Indonesian classroom contexts. Design-based research has gained currency in educational research over the past decade due to its strength to bridge the divide between theoretical research and educational practice in naturalistic settings. Design-based approaches involve a process of designing mathematical tasks, observing the enacted design in classrooms and reflecting on the process from analysing the classroom artefacts. Video plays a central role in supporting teachers and teacher educators to study and reflect on students’ mathematical thinking and in capturing the dynamic of classroom teaching and learning process. This chapter will examine and analyse practitioners’ lenses in capturing the dynamic and complexity of classroom mathematical learning using video vignettes and classroom artefacts including digital photos of classroom moments and students’ work. Practitioners’ lenses are taken as a window to capture key teaching and learning moments from the lessons. Analysis of this selection of these video vignettes along with other classroom artefacts based on practitioners’lenses provides insights into practitioners’ views on key teaching and learning moments in mathematics lessons.

Modelling of the stiffness evolution of truss core structures damaged by plastic buckling

A finite element study based on 1D beam element model is performed in order to investigate the mechanical behavior of an elasto-plastic beam loaded in axial compression over its buckling limit. The mode of loading is related to the damage of truss-cored beams in truss-cored laminates. The analysis takes into account the effects of geometry and material properties. The results of the FEM analysis are used for developing a simple mechanical model based on the basic Euler-Bernoulli beam theory and accounts for the beam compressibility. The model uses phenomenological functions containing parameters related to the basic material and geometrical properties. The presented model is developed in the form of closed solution which does not require complex numerical methods or extensive parametric studies. Predictions of the compressive stiffness degradation of truss-cored composites are made with the proposed model and compared with the results of FEM simulations. The error of the stiffness prediction with respect to the FEM results is within 10% over a 5 fold range of stiffness.

Improving laboratory learning through self and peer assessment of laboratory reports

The laboratory provides an opportunity for students to achieve many learning outcomes including to critically evaluate information, interpret and draw conclusions from scientific data, and communicate scientific results, information, or arguments. This paper describes a laboratory-writing task that involves self and peer evaluation. After discussion of the expectations of laboratory report writing during class, students self and peer evaluate reports. In a process similar to double-blind journal refereeing, students practise critically evaluating the quality of academic writing using a rubric. The summative assessment is based on how consistent their evaluations are with the evaluations of the same reports performed by their peers. The formative assessment is that students receive peer evaluations and feedback via a rubric on reports that they have written. The skill of critically evaluating their own reports is used to improve the laboratory reports in subsequent assessment tasks.