Introducing the multi-faceted teaching experiment

A mathematics classroom is comprised of many mathematicians with varying understanding of mathematics knowledge, including the teacher, students and sometimes researchers. To align with this conceptualisation of knowledge and understanding, the multi-faceted teaching experiment will be introduced as an approach to study all classroom participants’ interactions with the shared knowledge of mathematics. Drawing on the experiences of a large curriculum project, it is claimed that, unlike a multi-tiered teaching experiment, the multi-faceted teaching experiment provides a research framework that allows for the study of mathematicians’ building of knowledge in a classroom without privileging the experience of any one participant.

Investigating functional thinking in the elementary classroom : foundations of early algebraic reasoning

This paper examines the development of student functional thinking during a teaching experiment that was conducted in two classrooms with a total of 45 children whose average age was nine years and six months. The teaching comprised four lessons taught by a researcher, with a second researcher and classroom teacher acting as participant observers. These lessons were designed to enable students to build mental representations in order to explore the use of function tables by focusing on the relationship between input and output numbers with the intention of extracting the algebraic nature of the arithmetic involved. All lessons were videotaped. The results indicate that elementary students are not only capable of developing functional thinking but also of communicating their thinking both verbally and symbolically.

A problem-posing intervention in the development of problem-solving competence of underachieving, middle-year students

This study reported on the issues surrounding the acquisition of problem-solving competence of middle-year students who had been ascertained as above average in intelligence, but underachieving in problem-solving competence. In particular, it looked at the possible links between problem-posing skills development and improvements in problem-solving competence. A cohort of Year 7 students at a private, non-denominational, co-educational school was chosen as participants for the study, as they undertook a series of problem-posing sessions each week throughout a school term. The lessons were facilitated by the researcher in the students’ school setting. Two criteria were chosen to identify participants for this study. Firstly, each participant scored above the 60th percentile in the standardized Middle Years Ability Test (MYAT) (Australian Council for Educational Research, 2005) and secondly, the participants all scored below the cohort average for Criterion B (Problem-solving Criterion) in their school mathematics tests during the first semester of Year 7. Two mutually exclusive groups of participants were investigated with one constituting the Comparison Group and the other constituting the Intervention Group. The Comparison Group was chosen from a Year 7 cohort for whom no problem-posing intervention had occurred, while the Intervention Group was chosen from the Year 7 cohort of the following year. This second group received the problem-posing intervention in the form of a teaching experiment. That is, the Comparison Group were only pre-tested and post-tested, while the Intervention Group was involved in the teaching experiment and received the pre-testing and post-testing at the same time of the year, but in the following year, when the Comparison Group have moved on to the secondary part of the school. The groups were chosen from consecutive Year 7 cohorts to avoid cross-contamination of the data. A constructionist framework was adopted for this study that allowed the researcher to gain an “authentic understanding” of the changes that occurred in the development of problem-solving competence of the participants in the context of a classroom setting (Richardson, 1999). Qualitative and quantitative data were collected through a combination of methods including researcher observation and journal writing, video taping, student workbooks, informal student interviews, student surveys, and pre-testing and post-testing. This combination of methods was required to increase the validity of the study’s findings through triangulation of the data. The study findings showed that participation in problem-posing activities can facilitate the re-engagement of disengaged, middle-year mathematics students. In addition, participation in these activities can result in improved problem-solving competence and associated developmental learning changes. Some of the changes that were evident as a result of this study included improvements in self-regulation, increased integration of prior knowledge with new knowledge and increased and contextualised socialisation.

Young children's understandings about "square" in 3D virtual reality microworlds

This paper reports an investigation of primary school children’s understandings about "square". 12 students participated in a small group teaching experiment session, where they were interviewed and guided to construct a square in a 3D virtual reality learning environment (VRLE). Main findings include mixed levels of "quasi" geometrical understandings, misconceptions about length and angles, and ambiguous uses of geometrical language for location, direction, and movement. These have implications for future teaching and learning about 2D shapes with particular reference to VRLE.

Re-imagining STEM : peer scaffolding ICT in initial teacher education

In this paper, we report on how peer scaffolding was used to effect change in tertiary teaching practice and academic disposition in the use of Information and Communication Technology (ICT) in Science teaching and learning. We present a small-scale case study investigating the practice of one of this paper’s authors. It is told through two salient episodes which narratively describe the scaffolding used to support a teaching experiment. This was made possible through the national Teaching Teachers for the Future Project (2011-2012) which aimed to enhance the technological pedagogical capability of pre-service teachers across Australia. The outcome was a demonstrable shift in the academic’s disposition towards the use and benefits of ICT in teaching science and an increase in skills and confidence for both the academic and his students. This study and its outcomes fit within the contemporary push to “re-imagine” the teaching of Science, and more broadly of STEM, in schools.

Re-imagining STEM : peer scaffolding ICT in Initial Teacher Education

In this paper, we report on how peer scaffolding was used to effect change in tertiary teaching practice and academic disposition in the use of Information and Communication Technology (ICT) in Science teaching and learning. We present a small-scale case study investigating the practice of one of this paper’s authors. It is told through two salient episodes which narratively describe the scaffolding used to support a teaching experiment. This was made possible through the national Teaching Teachers for the Future Project (2011-2012) which aimed to enhance the technological pedagogical capability of pre-service teachers across Australia. The outcome was a demonstrable shift in the academic’s disposition towards the use and benefits of ICT in teaching science and an increase in skills and confidence for both the academic and his students. This study and its outcomes fit within the contemporary push to “re-imagine” the teaching of Science, and more broadly of STEM, in schools.

Indigenous students transitioning to school : responses to pre-foundational mathematics

Australian Indigenous students' mathematics performance continues to be below that of non-Indigenous students. This occurs from the early years of school, due largely to knowledge and social differences on entry to formal schooling. This paper reports on a mathematics research project conducted in one Aboriginal community school in New South Wales, Australia. The project aimed to identify and explain the ways that young Australian Indigenous students (age 2-4 years) learn number language and processes, specifically attribute language, sorting, 1-1 correspondence and, counting. The project adopted a mixed methods approach. That is, the methodology was decolonising (Smith 1999) in that it collaborated with and gave benefit back to the Indigenous community and school being researched. It was qualitative and interpretative (Burns 2000) and incorporated an action-research teaching-experiment approach where and teachers collaborated with the researchers to try new teaching methods. This paper draws on data pertaining to students' response to diagnostic interview questions, the pre- and post-test results of the interview and photographic evidence as observations during mathematics learning time. Participants referred to in this paper include one female principal (N = 1), and the transition class of students' pre- (N = 6) and post-test (N = 3) results of the pre-foundational processes (also referred to as attributes). The results were encouraging with improvements in colour (34%), patterns (33%); capacity (38%). As a result of this project, our epistemology regarding the importance of finding out about students' pre-foundational knowledge and understandings and providing a culturally appropriate learning environment with resources has been built upon.

Structuring representations of continuous data through investigations in grade 1

The study of data modelling with elementary students involves the analysis of a developmental process beginning with children’s investigations of meaningful contexts: visualising, structuring, and representing data and displaying data in simple graphs (English, 2012; Lehrer & Schauble, 2005; Makar, Bakker, & Ben-Zvi, 2011). A 3-year longitudinal study investigated young children’s data modelling, integrating mathematical and scientific investigations. One aspect of this study involved a researcher-led teaching experiment with 21 mathematically able Grade 1 students. The study aimed to describe explicit developmental features of students’ representations of continuous data...

Mathematics, programming, and STEM

Learning mathematics is a complex and dynamic process. In this paper, the authors adopt a semiotic framework (Yeh & Nason, 2004) and highlight programming as one of the main aspects of the semiosis or meaning-making for the learning of mathematics. During a 10-week teaching experiment, mathematical meaning-making was enriched when primary students wrote Logo programs to create 3D virtual worlds. The analysis of results found deep learning in mathematics, as well as in technology and engineering areas. This prompted a rethinking about the nature of learning mathematics and a need to employ and examine a more holistic learning approach for the learning in science, technology, engineering, and mathematics (STEM) areas.

Teaching and Learning Entrepreneurship for Micro and Small Businesses in the Cultural Industries Sector

Reports on an ESRC-funded, in-depth qualitative research project into 50 micro and small enterprises (MSEs) in the cultural industries. Our evidence sheds light on the extent to which the teaching and learning strategies adopted by higher education, further education and other VET providers are effective in providing entrepreneurship education and training for this innovative, high skill sector. Our findings suggest that entrepreneurs in this sector learn best by being able to experiment with ideas, by “doing” and networking with others and by working with more experienced mentors in their sector. The article concludes by suggesting a more “naturalistic” approach to teaching and learning entrepreneurship for micro and small businesses in the cultural industries sector.

Fostering cultural awareness in pre-service teacher education : an experiment in Asia literacy capacity building in an Australian university

This paper presents the findings of a small pilot study conducted with a group of final year pre-service teachers studying a secondary social science curriculum method unit in an Australian university. One of the study’s research objectives aimed at identifying how students responded to efforts to embed intercultural understanding through Studies of Asia in their final curriculum method unit. The unit was designed and taught by the researcher on the assumption that beginning social science teachers need to be empowered with pedagogical skills and new dispositions to deal with value laden emerging regional and global concerns in their Australian secondary school classrooms. This pilot study’s research methodology was located within the qualitative framework of a participatory action research model whereby the lecturer who designed, coordinated and taught the unit was also the researcher. Its scope was limited to one semester with volunteer students. The pilot study sought to investigate responses to several issues, and this paper reports on pre-service teacher reflections on the content, pedagogy and learning they experienced in their weekly sessions with specific reference to cultural understanding, Studies of Asia and the development of Asia literacy. It also reports on pre-service teacher reflections about their own evolving capacity as beginning teachers. The findings indicate that pre-service teachers valued the opportunity to engage with learning experiences which enhanced their conceptual understandings about culture whilst also extending their pedagogical and content knowledge.

Teaching parallel computing concepts with a desktop computer

Parallel computing is currently used in many engineering problems. However, because of limitations in curriculum design, it is not always possible to offer students specific formal teaching in this topic. Furthermore, parallel machines are still too expensive for many institutions. The latest microprocessors, such as Intel’s Pentium III and IV, embody single instruction multiple-data (SIMD) type parallel features, which makes them a viable solution for introducing parallel computing concepts to students. Final year projects have been initiated utilizing SSE (streaming SIMD extensions) features and it has been observed that students can easily learn parallel programming concepts after going through some programming exercises. They can now experiment with parallel algorithms on their own PCs at home. Keywords

Investigating sea level rise due to global warming in the teaching laboratory using Archimedes’ principle

A teaching laboratory experiment is described that uses Archimedes’ principle to precisely investigate the effect of global warming on the oceans. A large component of sea level rise is due to the increase in the volume of water due to the decrease in water density with increasing temperature. Water close to 0 °C is placed in a beaker and a glass marble hung from an electronic balance immersed in the water. As the water warms, the weight of the marble increases as the water is less buoyant due to the decrease in density. In the experiment performed in this paper a balance with a precision of 0.1 mg was used with a marble 40.0 cm3 and mass of 99.3 g, yielding water density measurements with an average error of -0.008 ± 0.011%.