Visualising mathematical knowledge and understanding

Contemporary mathematics education attempts to instil within learners the conceptualization of mathematics as a highly organized and inter-connected set of ideas. To support this, a means to graphically represent this organization of ideas is presented which reflects the cognitive mechanisms that shape a learner’s understanding. This organisation of information may then be analysed, with the view to informing the design of mathematics instruction in face-to-face and/or computer-mediated learning environments. However, this analysis requires significant work to develop both theory and practice.

A novel cyclization product from the polyphosphoric acid catalyzed addition of propanal to limonene

The polyphosphoric acid catalyzed addition of propanal to limonene yielded a novel bicyclic ether 2,2,6-trimethyl-4-ethyl-3-oxabicyclo[3.3.1]non-6-ene (I). The yield of (I) was significantly increased by carrying out the reaction under nitrogen rather than in air.

Practical considerations for integrating alternate reality gaming into science education

In this article, I present my experience with integrating an alternate reality gaming (ARG) framework into a pre-service science teacher education course. My goal is to provide an account of my experiences that can inform other science education practitioners at the tertiary and secondary levels that wish to adopt a similar approach in their classes. A game was designed to engage pre-service teachers with issues surrounding the declining enrolments in science, technology, engineering and mathematics disciplines (i.e., the STEM crisis; Tytler, 2007) and ways of re-engaging learners with STEM subjects. The use of ARG in science education is highly innovative. Literature on the use of ARG for educational purposes is scarce so in the article I have drawn on a range of available literature on gaming and ARG to define what it is and to suggest how it can be included in school science classrooms.

Greek or not : the use of symbols and abbreviations in mathematics

The use of symbols and abbreviations adds uniqueness and complexity to the mathematical language register. In this article, the reader’s attention is drawn to the multitude of symbols and abbreviations which are used in mathematics. The conventions which underpin the use of the symbols and abbreviations and the linguistic difficulties which learners of mathematics may encounter due to the inclusion of the symbolic language are discussed. 2010 NAPLAN numeracy tests are used to illustrate examples of the complexities of the symbolic language of mathematics.

Australian shows

This book is a reader for primary school students, stage 27-30 (fluent), incorporating mathematics themes. There is a fictional narrative, entitled "A Day at the Show", that describes the activities of Tess and Alex when visiting their local show. A non-fiction exposition, entitled "Supporting Australian Shows", explains more about Australian shows and why we should support them. Accompanying the book is a "building comprehension card" to assist teachers in their classroom use of the reader.

The flying doctors

This book is a reader for primary school students, stage 24-26 (fluent), incorporating mathematics themes. There is a fictional narrative, entitled "A Flying Visit", that describes Tess' and Alex's encounter with the Flying Doctor. A non-fiction recount, entitled "Fundraising for the Flying Doctors", describes the activities of a class group in raising money for the Flying Doctors. Accompanying the book is a "building comprehension card" to assist teachers in their classroom use of the reader.

Teaching Teachers for the Future (TTF) project TPACK Survey : summary of the key findings

This paper presents a summary of the key findings of the TTF TPACK Survey developed and administered for the Teaching the Teachers for the Future (TTF) Project implemented in 2011. The TTF Project, funded by an Australian Government ICT Innovation Fund grant, involved all 39 Australian Higher Education Institutions which provide initial teacher education. TTF data collections were undertaken at the end of Semester 1 (T1) and at the end of Semester 2 (T2) in 2011. A total of 12881 participants completed the first survey (T1) and 5809 participants completed the second survey (T2). Groups of like-named items from the T1 survey were subject to a battery of complementary data analysis techniques. The psychometric properties of the four scales: Confidence - teacher items; Usefulness - teacher items; Confidence - student items; Usefulness- student items, were confirmed both at T1 and T2. Among the key findings summarised, at the national level, the scale: Confidence to use ICT as a teacher showed measurable growth across the whole scale from T1 to T2, and the scale: Confidence to facilitate student use of ICT also showed measurable growth across the whole scale from T1 to T2. Additional key TTF TPACK Survey findings are summarised.

She who can, teaches

The following are real statements from real women taken from two surveys (2001, 2008). While they were all pre-service teachers training to teach specialist secondary IT or computer science subjects, some were straight from school while others were mature-age or career-change students. Some were questioning whether they should follow careers in the IT industry or should they continue into IT teaching. This is a poetic transcription of their voices.

Tell me what you see : Pre-service teachers' recognition of exemplary digital pedagogy

How do you identify "good" teaching practice in the complexity of a real classroom? How do you know that beginning teachers can recognise effective digital pedagogy when they see it? How can teacher educators see through their students’ eyes? The study in this paper has arisen from our interest in what pre-service teachers “see” when observing effective classroom practice and how this might reveal their own technological, pedagogical and content knowledge. We asked 104 pre-service teachers from Early Years, Primary and Secondary cohorts to watch and comment upon selected exemplary videos of teachers using ICT (information and communication technologies) in Science. The pre-service teachers recorded their observations using a simple PMI (plus, minus, interesting) matrix which were then coded using the SOLO Taxonomy to look for evidence of their familiarity with and judgements of digital pedagogies. From this, we determined that the majority of preservice teachers we surveyed were using a descriptive rather than a reflective strategy, that is, not extending beyond what was demonstrated in the teaching exemplar or differentiating between action and purpose. We also determined that this method warrants wider trialling as a means of evaluating students’ understandings of the complexity of the digital classroom.

Hybridized writing for scientific literacy : pedagogy and evidence

Disengagement of students in science and the scientific literacy of young adults are interrelated international concerns. One way to address these concerns is to engage students imaginatively in activities designed to improve their scientific literacy. Our ongoing program of research has focused on the effects of a sequence of activities that require students to transform scientific information on important issues for their communities from government websites into narrative text suitable for a lay reader. These hybridized stories we call BioStories. Students upload their stories for peer review to a dedicated website. Peer reviews are intended to help students refine their stories. Reviewing BioStories also gives students access to a wider range of scientific topics and writing styles. We have conducted separate studies with students from Grade 6, Grade 9 and Grade 12, involving case study and quasi-experimental designs. The results from the 6th grade study support the argument that writing the sequence of stories helped the students become more familiar with the scientific issue, develop a deeper understanding of related biological concepts, and improve their interest in science. Unlike the Grade 6 study, it was not possible to include a control group for the study conducted across eight 9th grade classes. Nevertheless, these results suggest that hybridized writing developed more positive attitudes toward science and science learning, particularly in terms of the students’ interest and enjoyment. In the most recent case study with Grade 12 students, we found that pride, strength, determination, interest and alertness were among the positive emotions most strongly elicited by the writing project. Furthermore, the students expressed enhanced feelings of self-efficacy in successfully writing hybridized scientific narratives in science. In this chapter, we describe the pedagogy of hybridized writing in science, overview the evidence to support this approach, and identify future developments.

Analysing children’s drawings : applied imagination

This article centres on a research project in which freehand drawings provided a richly creative and colourful data source of children’s imagined, ideal learning environments. Issues concerning the analysis of the visual data are discussed, in particular how imaginative content was analysed and how the analytical process was dependent on an accompanying, secondary data source comprising brief, explanatory written texts.

Identities and transformational experiences for quantitative problem solving : gender comparisons of first-year university science students

Women are underrepresented in science, technology, engineering and mathematics (STEM) areas in university settings; however this may be the result of attitude rather than aptitude. There is widespread agreement that quantitative problem-solving is essential for graduate competence and preparedness in science and other STEM subjects. The research question addresses the identities and transformative experiences (experiential, perception, & motivation) of both male and female university science students in quantitative problem solving. This study used surveys to investigate first-year university students’ (231 females and 198 males) perceptions of their quantitative problem solving. Stata (statistical analysis package version 11) analysed gender differences in quantitative problem solving using descriptive and inferential statistics. Males perceived themselves with a higher mathematics identity than females. Results showed that there was statistical significance (p<0.05) between the genders on 21 of the 30 survey items associated with transformative experiences. Males appeared to have a willingness to be involved in quantitative problem solving outside their science coursework requirements. Positive attitudes towards STEM-type subjects may need to be nurtured in females before arriving in the university setting (e.g., high school or earlier). Females also need equitable STEM education opportunities such as conversations or activities outside school with family and friends to develop more positive attitudes in these fields.

Examining preservice teachers’ applied learning experiences in the Teacher Education Done Differently (TEDD) project

Reviews have criticised universities for not embedding sufficient praxis for preparing preservice teachers for the profession. The Teacher Education Done Differently (TEDD) project explored praxis development for preservice teachers within existing university coursework. This mixed-method investigation involved an analysis of multiple case studies with preservice teacher involvement in university programs, namely: Ed Start for practicum I (n=26), III (n=23), and IV (n=12); Move It Use It (Health and Physical Education program; n=38), Studies of Society and its Environment (SOSE, n=24), and Science in Schools (n=38). The project included preservice teachers teaching primary students at the campus site in gifted education (the B-GR8 program, n=22). The percentage range for preservice teacher agreement of their praxis development leading up to practicum I, III, and IV was between 91-100% with a high mean score range (4.26-5.00). Other university units had similar findings except for SOSE (i.e., percentage range: 10-86%; M range: 2.33-4.00; SD range: 0.55-1.32). Qualitative data presented an understanding of the praxis development leading to the conclusion that additional applied learning experiences as lead-up days for field experiences and as avenues for exploring the teaching of specific subject areas presented opportunities for enhancing praxis.

Identifying leadership practices for mentoring preservice teachers

There are many forms of leadership and concepts of school leadership have evolved significantly over the last few decades. Mentoring is a form of leadership, where the classroom teacher (mentor) leads and guides the preservice teacher towards advancing teaching practices. What do school executives identify as their leadership practices and what leadership practices have inspired them? This study uses a five-part Likert scale survey with extended written responses that were coded into themes. These participants indicated they had leadership potential, which they associated with being organised, passionate and knowledgeable about education, interpersonally-skilled to build relationships, and visionary with action plans for improving education. These practices were also identified by participants as inspiring practices from leaders they knew. Generally, these participants perceived themselves as transformational leaders. Transformational practices associated with individualized consideration, intellectual stimulation, inspirational motivation, and idealized influences were agreed upon by 80% or more of the participants. Mentors need to understand inspiring leadership practices and identify their own leadership practices that may lead towards reflection on practice and, hence, a way to make educationally-sound changes in leadership behaviour.

How can Australia sustain middle-schooling education?

Middle schooling is a crucial area of education where adolescents experiencing physiological and psychological hanges require expert guidance. As more research evidence is provided about adolescent learning, teachers are considered pivotal to adolescents’ educational development. The two levels of implementing reform measures need to be targeted, that is, at the inservice and preservice teacher levels. This quantitative study employs a 40-item, five-part Likert scale survey to understand preservice teachers’ (n=142) perceptions of their confidence to teach in the middle school at the conclusion of their tertiary education. The survey instrument was developed from the literature with connections to the Queensland College of Teachers professional standards. Results indicated that they perceived themselves as capable of creating a positive classroom environment with seven items greater than 80%, except with behaviour management (<80% for two items) and they considered their pedagogical knowledge to be adequate (i.e., 7 out of 8 items >84%). Items associated with implementing middle schooling curriculum had varied responses (e.g., implementing literacy and numeracy were 74% while implementing learning with real-world connections was 91%). This information may assist coursework designers. For example, if significant percentages of preservice teachers indicate they believe they were not well prepared for assessment and reporting in the middle school then course designers can target these areas more effectively.