MATLAB toolboxes : robotics and vision for students and teachers

In this column, Dr. Peter Corke of CSIRO, Australia, gives us a description of MATLAB Toolboxes he has developed. He has been passionately developing tools to enable students and teachers to better understand the theoretical concepts behind classical robotics and computer vision through easy and intuitive simulation and visualization. The results of this labor of love have been packaged as MATLAB Toolboxes: the Robotics Toolbox and the Vision Toolbox. –Daniela Rus, RAS Education Cochair

Students as decoders of graphics in mathematics

This paper reports on students’ ability to decode mathematical graphics. The findings were: (a) some items showed an insignificant improvement over time; (b) success involves identifying critical perceptual elements in the graphic and incorporating these elements into a solution strategy; and (c) the optimal strategy capitalises on how information is encoded in the graphic. Implications include a need for teachers to be proactive in supporting students’ to develop their graphical knowledge and an awareness that knowledge varies substantially across students.

Implementing a Pattern and Structure Mathematics Awareness Program (PASMAP) in kindergarten

This paper provides an interim report of a large empirical evaluation study in progress. An intervention was implemented to evaluate the effectiveness of the Pattern and Structure Mathematical Awareness Program (PASMAP) on Kindergarten students’ mathematical development. Four large schools (two from Sydney and two from Brisbane), 16 teachers and their 316 students participated in the first phase of a 2-year longitudinal study. Eight of 16 classes implemented the PASMAP program over three school terms. This paper provides an overview of key aspects of the intervention, and preliminary analysis of the impact of PASMAP on students’ representation, abstraction and generalisation of mathematical ideas.

Culture-fair assessment : challenging Indigenous students through effortful mathematics teaching

This paper reports on a mathematics education research project centred on teachers’ pedagogical practices and capacity to assess Indigenous Australian students in a culture-fair manner. The project has been funded by the Australian Research Council Linkage program and is being conducted in seven Catholic and Independent primary schools in north Queensland. Our Industry Partners are Catholic Education and the Association of Independent Schools, Queensland. The study aims to provide greater understanding about how to build more equitable assessment practices to address the issue of underperforming Aboriginal and Torres Strait Islander (ATSI) students in regional and remote Australia. The goal is to identify ways forward by attending to culture-fair assessment practice. The research is exploring the attitudes, beliefs and responses of Indigenous students to assessment in the context of mathematics learning with particular focus on teacher knowledge in these educational settings in relation to the design of assessment tasks that are authentic and engaging for these students in an accountability context. This approach highlights how teachers need to distinguish the ‘funds of knowledge’ (González, Moll, Floyd Tenery, Rivera, Rendón, Gonzales & Amanti, 2008) that Indigenous students draw on and how teachers need to be culturally responsive in their pedagogy to open up curriculum and assessment practice to allow for different ways of knowing and being

Teaching and learning mathematics with robotics in middle-years of schooling

Engaging and motivating students in mathematics lessons can be challenging. The traditional approach of chalk and talk can sometimes be problematic. The new generation of educational robotics has the potential to not only motivate students but also enable teachers to demonstrate concepts in mathematics by connecting concepts with the real world. Robotics hardware and the software are becoming increasing more user-friendly and as a consequence they can be blended in with classroom activities with greater ease. Using robotics in suitably designed activities promotes a constructivist learning environment and enables students to engage in higher order thinking through hands-on problem solving. Teamwork and collaborative learning are also enhanced through the use of this technology. This paper discusses a model for teaching concepts in mathematics in middle year classrooms. It will also highlight some of the benefits and challenges of using robotics in the learning environment.

Comparing mentors’ reports on their own mentoring of primary preservice teachers

Implementing the Australian Curriculum will require targeting both teachers and preservice teachers as enactors of reform. Classroom teachers in their roles as mentors have a significant role to play for developing preservice teachers. What mentors do in their mentoring practices and what mentors think about mentoring will impact on the mentoring processes and ultimately reform outcomes. What are mentors’ reports on their mentoring of preservice teachers for teaching science and mathematics? This quantitative study presents mentors’ reports on their mentoring of primary preservice teachers (mentees) in mathematics (n=43) and science (n=29). Drawing upon a previously validated instrument (Hudson, 2007), this instrument was amended to allow mentors to report on their perceptions of their mentoring. Mentors claimed they mentored teaching mathematics more than science. However, 20% or more indicated they did not provide mentoring practices for 25 out of 34 survey items in the science and 9 out of 34 items in the mathematics. Educational reform will necessity mentors to be educated on effective mentoring practices for mathematics and science so the mentoring process can be more purposeful. Indeed, mentors who have knowledge of such practices may address the potential issues of more than 20% of mentees not receiving these practices. To ensure the greatest success for an Australian Curriculum mentors may need professional development in order to assist mentees’ development into the profession.

School-based experiences : developing primary science preservice teachers' practice

Reviews into teacher education emphasise the need for preservice teachers to have more school-based experiences. In this study, a school-based experience was organised within a nine-week science curriculum university unit that allowed preservice teachers’ repeated experiences in teaching primary science. This research uses a survey, questionnaire with extended written responses, and researcher observations to investigate preservice teachers’ (n=38) learning experiences in two school settings. Survey results indicated that the majority of these preservice teachers either agreed or strongly agreed that school-based experiences developed their: personal-professional skill development (100%); system requirements (range: 81-100%); teaching practices (81-100%); student behaviour management (range: 94-100%); providing student feedback (89-94%); and reflection on practice (92-100%). Qualitative data provided insights into their development particularly for science content knowledge and receiving positive reinforcement on effective teaching behaviours. According to these preservice teachers, the school-based experiences facilitated “teachable moments – having the knowledge or skills to run with students’ questions or ideas” and allowed preservice teachers to “critically reflect between groups to make the task flow better”. Embedding school-based experiences needs to be part of each and every preservice teacher education unit so preservice teachers can develop confidence, knowledge and skills within authentic school contexts.

Early childhood teachers' mathematical content knowledge

The process of becoming numerate begins in the early years. According to Vygotskian theory (1978), teachers are More Knowledgeable Others who provide and support learning experiences that influence children’s mathematical learning. This paper reports on research that investigates three early childhood teachers mathematics content knowledge. An exploratory, single case study utilised data collected from interviews, and email correspondence to investigate the teachers’ mathematics content knowledge. The data was reviewed according to three analytical strategies: content analysis, pattern matching, and comparative analysis. Findings indicated there was variation in teachers’ content knowledge across the five mathematical strands and that teachers might not demonstrate the depth of content knowledge that is expected of four year specially trained early years’ teachers. A significant factor that appeared to influence these teachers’ content knowledge was their teaching experience. Therefore, an avenue for future research is the investigation of factors that influence teachers’ content numeracy knowledge.

Re-engaging adolescent students in science : an experienced teachers' classroom

Adolescents are both aware of and have the impetuous to exploit aspects of Science, Technology, Engineering and Mathematics (STEM) within their personal lives. Whether they are surfing, cycling, skateboarding or shopping, STEM concepts impact their lives. However science, mathematics, engineering and technology are still treated in the classroom as separate fragmented entities in the educational environment where most classroom talk is seemingly incomprehensible to the adolescent senses. The aim of this study was to examine the experiences of young adolescents with the aim of transforming school learning at least of science into meaningful experiences that connected with their lives using a self-study approach. Over a 12-month period, the researcher, an experienced secondary-science teacher, designed, implemented and documented a range of pedagogical practices with his Year-7 secondary science class. Data for this case study included video recordings, journals, interviews and surveys of students. By setting an environment empathetic to adolescent needs and understandings, students were able to actively explore phenomena collaboratively through developmentally appropriate experiences. Providing a more contextually relevant environment fostered meta-cognitive practices, encouraged new learning through open dialogue, multi-modal representations and assessments that contributed to building upon, re-affirming, or challenging both the students' prior learning and the teacher’s pedagogical content knowledge. A significant outcome of this study was the transformative experiences of an insider, the teacher as researcher, whose reflections provided an authentic model for reforming pedagogy in STEM classes.

Teacher change and professional development in mathematics education

It is generally agreed that if authentic teacher change is to occur then the tacit knowledge about how and why they act in certain ways in the classroom be accessed and reflected upon. While critical reflection can and often is an individual experience there is evidence to suggest that teachers are more likely to engage in the process when it is approached in a collegial manner; that is, when other teachers are involved in and engaged with the same process. Teachers do not enact their profession in isolation but rather exist within a wider community of teachers. An outside facilitator can also play an active and important role in achieving lasting teacher change. According to Stein and Brown (1997) “an important ingredient in socially based learning is that graduations of expertise and experience exist when teachers collaborate with each other or outside experts” (p. 155). To assist in the effective professional development of teachers, outside facilitators, when used, need to provide “a dynamic energy producing interactive experience in which participants examine and explore the complex components of teaching” (Bolster, 1995, p. 193). They also need to establish rapport with the participating teachers that is built on trust and competence (Hyde, Ormiston, & Hyde, 1994). For this to occur, professional development involving teachers and outside facilitators or researchers should not be a one-off event but an ongoing process of engagement that enables both the energy and trust required to develop. Successful professional development activities are therefore collaborative, relevant and provide individual, specialised attention to the teachers concerned. The project reported here aimed to provide professional development to two Year 3 teachers to enhance their teaching of a new mathematics content area, mental computation. This was achieved through the teachers collaborating with a researcher to design an instructional program for mental computation that drew on theory and research in the field.

Career decision making among gifted students : the mediation of teachers

There is international concern about falling enrollments in higher education, particularly the sciences, by gifted students. In this mixed method study, the top performing 200 students (approximately 1%) within a particular education jurisdiction at the beginning of their first year at university were surveyed and 20 interviewed about their school experiences using a biographical interpretive design. This study focussed on identifying those characteristics of teachers which supported students’ interests. Participants identified seven characteristics of teachers that students identified as supportive of their potential career pathways. These included connecting pedagogical practices with student interests, being passionate about their subject matter, having good content knowledge, making learning experiences relevant, setting high expectations of students, being a good explainer of complex ideas, and being a good classroom manager. This study extends our knowledge of how teachers influence gifted students and has implications for both pre-service and in-service teacher education and career counselling.

Facilitating growth in prospective teachers’ knowledge : teaching geometry in primary schools

This paper reports on a study that focused on growth of understanding about teaching geometry by a group of prospective teachers engaged in lesson plan study within a computer-supported collaborative learning (CSCL) environment. Participation in the activity was found to facilitate considerable growth in the participants’ pedagogical-content knowledge (PCK). Factors that influenced growth in PCK included the nature of the lesson planning task, the cognitive scaffolds inserted into the CSCL virtual space, the meta-language scaffolds provided to the participants, and the provision of both private and public discourse spaces. The paper concludes with recommendations for enhancing effective knowledge-building discourse about mathematics PCK within prospective teacher education CSCL environments.

Understanding evaluation of learning support in mathematics and statistics

With rapid and continuing growth of learning support initiatives in mathematics and statistics found in many parts of the world, and with the likelihood that this trend will continue, there is a need to ensure that robust and coherent measures are in place to evaluate the effectiveness of these initiatives. The nature of learning support brings challenges for measurement and analysis of its effects. After briefly reviewing the purpose, rationale for, and extent of current provision, this article provides a framework for those working in learning support to think about how their efforts can be evaluated. It provides references and specific examples of how workers in this field are collecting, analysing and reporting their findings. The framework is used to structure evaluation in terms of usage of facilities, resources and services provided, and also in terms of improvements in performance of the students and staff who engage with them. Very recent developments have started to address the effects of learning support on the development of deeper approaches to learning, the affective domain and the development of communities of practice of both learners and teachers. This article intends to be a stimulus to those who work in mathematics and statistics support to gather even richer, more valuable, forms of data. It provides a 'toolkit' for those interested in evaluation of learning support and closes by referring to an on-line resource being developed to archive the growing body of evidence. © 2011 Taylor & Francis.