Developing young students’ meta-representational competence through integrated mathematics and science investigations

This paper describes students’ developing meta-representational competence, drawn from the second phase of a longitudinal study, Transforming Children’s Mathematical and Scientific Development. A group of 21 highly able Grade 1 students was engaged in mathematics/science investigations as part of a data modelling program. A pedagogical approach focused on students’ interpretation of categorical and continuous data was implemented through researcher-directed weekly sessions over a 2-year period. Fine-grained analysis of the developmental features and explanations of their graphs showed that explicit pedagogical attention to conceptual differences between categorical and continuous data was critical to development of inferential reasoning.

Assessment in tertiary mathematics

There is a growing consensus among many educators that the goals of teaching and learning mathematics are to help students solve real-life problems, participate intelligently in daily affairs, and prepare them for jobs (Gardiner, 1994; Roeber, 1995). These goals suggest that the role of routine procedural skills should be diminished while more emphasis ought to be placed on learners gaining conceptual insights and analytical skills that appear essential in real-life mathematical problem solving (Schoenfeld, 1993; Stenmark, 1989).

The role of fluency in a mathematics item with an embedded graphic: Interpreting a pie chart.

The purpose of this study was to identify the pedagogical knowledge relevant to the successful completion of a pie chart item. This purpose was achieved through the identification of the essential fluencies that 12–13-year-olds required for the successful solution of a pie chart item. Fluency relates to ease of solution and is particularly important in mathematics because it impacts on performance. Although the majority of students were successful on this multiple choice item, there was considerable divergence in the strategies they employed. Approximately two-thirds of the students employed efficient multiplicative strategies, which recognised and capitalised on the pie chart as a proportional representation. In contrast, the remaining one-third of students used a less efficient additive strategy that failed to capitalise on the representation of the pie chart. The results of our investigation of students’ performance on the pie chart item during individual interviews revealed that five distinct fluencies were involved in the solution process: conceptual (understanding the question), linguistic (keywords), retrieval (strategy selection), perceptual (orientation of a segment of the pie chart) and graphical (recognising the pie chart as a proportional representation). In addition, some students exhibited mild disfluencies corresponding to the five fluencies identified above. Three major outcomes emerged from the study. First, a model of knowledge of content and students for pie charts was developed. This model can be used to inform instruction about the pie chart and guide strategic support for students. Second, perceptual and graphical fluency were identified as two aspects of the curriculum, which should receive a greater emphasis in the primary years, due to their importance in interpreting pie charts. Finally, a working definition of fluency in mathematics was derived from students’ responses to the pie chart item.

Middle school students' perceptions of engineering

This paper focuses on implementing engineering education in middle school classrooms (grade levels 7-9). One of the aims of the study was to foster students’ and teachers’ knowledge and understanding of engineering in society. Given the increasing importance of engineering in shaping our daily lives, it is imperative that we foster in students an interest and drive to participate in engineering education, increase their awareness of engineering as a career path, and inform them of the links between engineering and the enabling subjects, mathematics, science, and technology. Data for the study are drawn from five classes across three schools. Grade 7 students’ responded to initial whole class discussions on what is an engineer, what is engineering, what characteristics engineers require, engineers (family/friends) that they know, and subjects that may facilitate an engineering career. Students generally viewed engineers as creative, future-oriented, and artistic problem finders and solvers; planners and designers; “seekers” and inventors; and builders of constructions. Students also viewed engineers as adventurous, decisive, community-minded, reliable, and “smart.” In addition to a range of mathematics and science topics, students identified business studies, ICT, graphics, art, and history as facilitating careers in engineering. Although students displayed a broadened awareness of engineering than the existing research suggests, there was limited knowledge of various engineering fields and a strong perception of engineering as large construction.

Year 7 students’ approaches to understanding and solving NAPLAN numeracy problems

This study investigated how the interpretation of mathematical problems by Year 7 students impacted on their ability to demonstrate what they can do in NAPLAN numeracy testing. In the study, mathematics is viewed as a culturally and socially determined system of signs and signifiers that establish the meaning, origins and importance of mathematics. The study hypothesises that students are unable to succeed in NAPLAN numeracy tests because they cannot interpret the questions, even though they may be able to perform the necessary calculations. To investigate this, the study applied contemporary theories of literacy to the context of mathematical problem solving. A case study design with multiple methods was used. The study used a correlation design to explore the connections between NAPLAN literacy and numeracy outcomes of 198 Year 7 students in a Queensland school. Additionally, qualitative methods provided a rich description of the effect of the various forms of NAPLAN numeracy questions on the success of ten Year 7 students in the same school. The study argues that there is a quantitative link between reading and numeracy. It illustrates that interpretation (literacy) errors are the most common error type in the selected NAPLAN questions, made by students of all abilities. In contrast, conceptual (mathematical) errors are less frequent amongst more capable students. This has important implications in preparing students for NAPLAN numeracy tests. The study concluded by recommending that increased focus on the literacies of mathematics would be effective in improving NAPLAN results.

Reading students’ representations

Students’ text, symbols, and graphics give teachers a glimpse into mathematical thinking associated with investigating the Peas problem.

Does 'habitus' count in Chinese Australians' mathematics achievement?

Large-scale international comparative studies and cross-ethnic studies have revealed that Chinese students, whether living in China or overseas, consistently outperform their counterparts in mathematics achievement. These studies tended to explain this result from psychological, educational, or cultural perspectives. However, there is scant sociological investigation addressing Chinese students’ better mathematics achievement. Drawing on Bourdieu’s sociological theory, this study conceptualises Chinese Australians’ “Chineseness” by the notion of ‘habitus’ and considers this “Chineseness” generating but not determinating mechanism that underpins Chinese Australians’ mathematics learning. Two hundred and thirty complete responses from Chinese Australian participants were collected by an online questionnaire. Simple regression model statistically significantly well predicted mathematics achievement by “Chineseness” (F = 141.90, R = .62, t = 11.91, p < .001). Taking account of “Chineseness” as a sociological mechanism for Chinese Australians’ mathematics learning, this study complements psychological and educational impacts on better mathematics achievement of Chinese students revealed by previous studies. This study also challenges the cultural superiority discourse that attributes better mathematics achievement of Chinese students to cultural factors.

Chinese Australians’ Chineseness and their mathematics achievement : the role of habitus

Large-scale international comparative studies and cross-ethnic studies have revealed that Chinese students, living either in China or overseas, consistently outperform their counterparts in mathematics. Empirical research has discussed psychological, educational, and cultural reasons behind Chinese students’ better mathematics performance. However, there is scant sociological investigation of this phenomenon. The current mixed methods study aims to make a contribution in this regard. The study conceptualises Chineseness through Bourdieu’s sociological notion of habitus and considers this habitus of Chineseness generating, but not determining, mechanism that underpins commitment to mathematics learning. The study firstly analyses the responses of 230 Chinese Australian participants to a set of questionnaire items. Results indicate that the habitus of Chineseness significantly mediates the relationship between participants’ commitment to mathematics learning and their mathematics achievement. The study then reports on the interviews with five participants to add nuances and dynamics to the mediating role of habitus of Chineseness. The study complements the existing literature by providing sociological insight into the better mathematics achievement of Chinese students.

Preparing engineering graduates for the knowledge economy through blended delivery of mathematics

Contemporary higher education institutions are making significant efforts to develop cohesive, meaningful and effective learning experiences for Science, Technology, Engineering and Mathematics (STEM) curricula to prepare graduates for challenges in the modern knowledge economy, thus enhancing their employability (Carnevale et al, 2011). This can inspire innovative redesign of learning experiences embedded in technology-enhanced educational environments and the development of research-informed, pedagogically reliable strategies fostering interactions between various agents of the learning-teaching process. This paper reports on the results of a project aimed at enhancing students’ learning experiences by redesigning a large, first year mathematics unit for Engineering students at a large metropolitan public university. Within the project, the current study investigates the effectiveness of selected, technology-mediated pedagogical approaches used over three semesters. Grounded in user-centred instructional design, the pedagogical approaches explored the opportunities for learning created by designing an environment containing technological, social and educational affordances. A qualitative analysis of mixed-type questionnaires distributed to students indicated important inter-relations between participants’ frames of references of the learning-teaching process and stressed the importance (and difficulty) of creating appropriate functional context. Conclusions drawn from this study may inform instructional design for blended delivery of STEM-focused programs that endeavor to enhance students’ employability by educating work-ready graduates.

The enactment of the New Basics Project in a special school

This study investigates the impact of the New Basics Project on teachers at a special school for students with intellectual impairments. The study is aimed at exploring the complex nature of the work of special educators as they enact the New Basics curriculum with a particular focus on the teachers’ opinions about challenges that arose for their curriculum, pedagogy and assessment practices. Attention is also paid to how the principal’s leadership supported the enactment of the New Basics in respect to what he did and why he used particular strategies. The nine teachers and their principal were involved in a series of in-depth, semi-structured interviews from one of only three special schools in phase one of the New Basics trial in Queensland, Australia. These interviews produced data from the special educators as they were confronted with a new curriculum that challenged their previous teaching practices. The enactment of the New Basics curriculum occurred within the context of a state-sanctioned mandate to provide alternative programs to those offered in mainstream schools, for students with special needs. This thesis explores these teachers' experiences using critical theory as a basis for analyzing their opinions on issues such as the role of the special educator, tensions between old and new curricula, pedagogical and assessment practices, and connections between the at-school learning experiences for intellectually impaired students and the realities of post-school life. The investigation also examines the leadership conduct of the principal in changing times at the school. The findings suggest that the New Basics has played a significant role in providing structures for developing communities of practice amongst teachers; in supporting special educators to focus more on the educational needs of the students (e.g., literacy, numeracy, financial planning) and less on their medical needs (e.g., toileting, feeding, personal hygiene); and supporting school leadership that empowers and listens critically to teachers as essential components of the successful enactment of curriculum reforms like the New Basics.

Integrating engineering model eliciting activities in elementary school curricula

This paper argues for a future-oriented, inclusion of Engineering Model Eliciting Activities (EngMEAs) in elementary mathematics curricula. In EngMEAs students work with meaningful engineering problems that capitalise on and extend their existing mathematics and science learning, to develop, revise and document powerful models, while working in groups. The models developed by six groups of 12-year students in solving the Natural Gas activity are presented. Results showed that student models adequately solved the problem, although student models did not take into account all the data provided. Student solutions varied to the extent students employed the engineering context in their models and to their understanding of the mathematical concepts involved in the problem. Finally, recommendations for implementing EngMEAs and for further research are discussed.

Shadowlands (Directed by Caroline Heim)

The controversial love affair of CS Lewis, Oxford scholar and writer of the Narnia Chronicles, is set in a constellation of music, sculpture and mime. CS Lewis’s intriguing relationship with poet Joy Davidman moves, inspires and confronts us with the big questions. Beauty contrasts with the ephemeral land of the shadows. Crossbow’s adaption of William Nicholson’s soulful and witty play explores the joy and the grief of “experience: that most brutal of teachers.” Showcasing the abilities of Brisbane and Sydney actors, the company that brought you The Miracle Worker and Anne of the Thousand Days, will quicken your senses and stir your heart with Shadowlands. All performances have a tactile tour of the stage 20 minutes before the start time of the show. Special signed performance for hearing impaired patrons Thur 5 Aug 2pm

The miracle worker

Helen Keller’s fight to speak, to understand, to love aided by her teacher Annie Sullivan was nothing short of a miracle. This is her story. Crossbow Productions staged six performances of The Miracle Worker at the Brisbane Powerhouse in June 2009 to raise awareness of people living with disabilities. The play was shadow signed for the hearing impaired and tactile tours of the set were held before each performance for the vision impaired. Over 200 hearing and vision impaired attended and 70 of these had never been to the theatre before. I’m deaf and we should be able to go to anything, and you’ve done that for us. As a blind person, I got a great deal from it. I found it extremely moving. There should be a thousand or so in the audience rather than a hundred so that everyone can experience it.

‘Wanna do more math’: engaging underachieving Indigenous learners the YuMi Deadly way.

The Accelerating Indigenous Mathematics (AIM) Program offered by the YuMi Deadly Centre from QUT accelerates the mathematics learning of underperforming students in Years 8 - 10 by a) apportioning Years 2-10 Australian Curriculum: Mathematics content into three years, and b) provides a teaching approach that accelerates the mathematical learning. The philosophy of the YuMi Deadly teaching approach for mathematics is one that requires a ‘body’, ‘hand’, ‘mind’ pedagogy. This presentation will provide examples of the “‘body’, ‘hand’, ‘mind’” mathematics pedagogy. In AIM classrooms, mathematics is presented this approach is having a positive impact. Students are willing ‘to have a go’ without shame; and they develop the desire to learn and improve their numeracy.