Shifting more than the goal posts: developing classroom norms of inquiry-based learning in mathematics

The 3-year study described in this paper aims to create new knowledge about inquiry norms in primary mathematics classrooms. Mathematical inquiry addresses complex problems that contain ambiguities, yet classroom environments often do not adopt norms that promote curiosity, risk-taking and negotiation needed to productively engage with complex problems. Little is known about how teachers and students initiate, develop and maintain norms of mathematical inquiry in primary classrooms. The research question guiding this study is, “How do classroom norms develop that facilitate student learning in primary classrooms which practice mathematical inquiry?” The project will (1) analyse a video archive of inquiry lessons to identify signature practices that enhance productive classroom norms of mathematical inquiry and facilitate learning, (2) engage expert inquiry teachers to collaborate to identify and design strategies for assisting teachers to develop and sustain norms over time that are conducive to mathematical inquiry and (3) support and study teachers new to mathematical inquiry adopting these practices in their classrooms. Anticipated outcomes include identification and illustration of classroom norms of mathematical inquiry, signature practices linked to these norms and case studies of primary teachers’ progressive development of classroom norms of mathematical inquiry and how they facilitate learning

Don't just solve for x: letting kids explore real-world scenarios will keep them in maths class

In real life, ordering pizza for a group of people involves having a conversation about what people like, how much they can eat, how much they want to spend and whether pineapple really belongs on pizza.
 But in the context of a traditional maths class, the concept of ordering a pizza typically becomes a problem like this:
 If one pizza serves four children, how many pizzas do we need for a class of 28 children?
 An alarming number of Australian students don't choose mathematics in the senior school years. Figures from 2017 – the most recent available – show only 9.4% of Australian students in years 11 and 12 were enrolled in extended mathematics. This is the lowest percentage in more than 20 years

Inferring to a model: using inquiry-based argumentation to challenge young children's expectations of equally likely outcomes

Children’s informal reasoning about uncertainty can be considered a product of their beliefs, language, and experiences, much of which is formed outside of formal schooling. As a result, students can adopt informal intuitions that are incompatible with formal reasoning. Although the creation of cognitive conflict has been considered as one means of challenging students’ understandings, prior research in probability suggests that students may simultaneously hold multiple, incompatible understandings without conflict arising. Design-based methodology was adopted to investigate young (7–8 years old) students’ inferential reasoning under uncertainty, using an inquiry-based unit developed around addition bingo. This paper selectively reports on students’ inferences that initially suggested they were tacitly working from a uniform distribution (equiprobability bias), but shifted as students collected empirical data (from a discrete symmetric triangular distribution). Their inferences were challenged using an argumentation framework, with particular emphasis on the need for defensible evidence. Initial findings suggest potential for argumentation and inferential approaches that make students’ conceptions explicit through ‘visibilizing’ their knowledge

Using expectancy-value theory to explore aspects of motivation in inquiry based learning in primary mathematics

Inquiry-based learning (IBL) is a pedagogical approach in which students address complex, ill-structured problems set in authentic contexts. While IBL is gaining ground in Australia as an instructional practice, there has been little research that considers implications for student motivation and engagement. Expectancy-value theory (Eccles and Wigfield 2002) provides a framework through which children’s beliefs about their mathematical competency and their expectation of success are able to be examined and interpreted, alongside students’ perceptions of task value. In this paper, Eccles and Wigfield’s expectancy-value model has been adopted as a lens to examine a complete unit of mathematical inquiry as undertaken with a class of 9–10-year-old students. Data were sourced from a unit (∼10 lessons) based on geometry and geometrical reasoning. The units were videotaped in full, transcribed, and along with field notes and student work samples, subjected to theoretical coding using the dimensions of Eccles and Wigfield’s model. The findings provide insight into aspects of IBL that may impact student motivation and engagement. The study is limited to a single unit; however, the results provide a depth of insight into IBL in practice while identifying features of IBL that may be instrumental in bringing about increased motivation and engagement of students in mathematics. Identifying potentially motivating aspects of IBL enable these to be integrated and more closely studied in IBL practises

Aspire high: impacting student aspirations in a regional community

This paper provides initial evidence of the effectiveness of an educational program in a Tasmanian regional community that has experienced ongoing industrial restructuring. In response to these changes, community and civic leaders adopted a multifaceted strategic plan to address employment needs and opportunities. Part of this plan involved targeting school children to help them explore a broader range of educational and career options. The program, Aspire High, involves Year 5 children visiting workplaces, the local Year 11 and 12 college, the local technical college, and a local university campus. This paper reports results from student interviews and surveys. While it is difficult to attribute changes in students’ attitudes and aspirations solely to Aspire High, it is evident that they were enthusiastic about the program. Secondary findings showed that students become less positive towards school by Year 8, and that boys are less likely to be positive towards school and more likely to choose a traditionally gendered occupation

Aspire High: Impacting Student Aspirations In A Regional Community

This paper provides initial evidence of the effectiveness of an educational program in a Tasmanian regional community that has experienced ongoing industrial restructuring. In response to these changes, community and civic leaders adopted a multifaceted strategic plan to address employment needs and opportunities. Part of this plan involved targeting school children to help them explore a broader range of educational and career options. The program, Aspire High, involves Year 5 children visiting workplaces, the local Year 11 and 12 college, the local technical college, and a local university campus. This paper reports results from student interviews and surveys. While it is difficult to attribute changes in students’ attitudes and aspirations solely to Aspire High, it is evident that they were enthusiastic about the program. Secondary findings showed that students become less positive towards school by Year 8, and that boys are less likely to be positive towards school and more likely to choose a traditionally gendered occupation

Duration of androgen deprivation therapy with postoperative radiotherapy for prostate cancer: a comparison of long-course versus short-course androgen deprivation therapy in the RADICALS-HD randomised trial

Background Previous evidence supports androgen deprivation therapy (ADT) with primary radiotherapy as initial treatment for intermediate-risk and high-risk localised prostate cancer. However, the use and optimal duration of ADT with postoperative radiotherapy after radical prostatectomy remains uncertain. Methods RADICALS-HD was a randomised controlled trial of ADT duration within the RADICALS protocol. Here, we report on the comparison of short-course versus long-course ADT. Key eligibility criteria were indication for radiotherapy after previous radical prostatectomy for prostate cancer, prostate-specific antigen less than 5 ng/mL, absence of metastatic disease, and written consent. Participants were randomly assigned (1:1) to add 6 months of ADT (short-course ADT) or 24 months of ADT (long-course ADT) to radiotherapy, using subcutaneous gonadotrophin-releasing hormone analogue (monthly in the short-course ADT group and 3-monthly in the long-course ADT group), daily oral bicalutamide monotherapy 150 mg, or monthly subcutaneous degarelix. Randomisation was done centrally through minimisation with a random element, stratified by Gleason score, positive margins, radiotherapy timing, planned radiotherapy schedule, and planned type of ADT, in a computerised system. The allocated treatment was not masked. The primary outcome measure was metastasis-free survival, defined as metastasis arising from prostate cancer or death from any cause. The comparison had more than 80% power with two-sided α of 5% to detect an absolute increase in 10-year metastasis-free survival from 75% to 81% (hazard ratio [HR] 0·72). Standard time-to-event analyses were used. Analyses followed intention-to-treat principle. The trial is registered with the ISRCTN registry, ISRCTN40814031, and ClinicalTrials.gov , NCT00541047 . Findings Between Jan 30, 2008, and July 7, 2015, 1523 patients (median age 65 years, IQR 60–69) were randomly assigned to receive short-course ADT (n=761) or long-course ADT (n=762) in addition to postoperative radiotherapy at 138 centres in Canada, Denmark, Ireland, and the UK. With a median follow-up of 8·9 years (7·0–10·0), 313 metastasis-free survival events were reported overall (174 in the short-course ADT group and 139 in the long-course ADT group; HR 0·773 [95% CI 0·612–0·975]; p=0·029). 10-year metastasis-free survival was 71·9% (95% CI 67·6–75·7) in the short-course ADT group and 78·1% (74·2–81·5) in the long-course ADT group. Toxicity of grade 3 or higher was reported for 105 (14%) of 753 participants in the short-course ADT group and 142 (19%) of 757 participants in the long-course ADT group (p=0·025), with no treatment-related deaths. Interpretation Compared with adding 6 months of ADT, adding 24 months of ADT improved metastasis-free survival in people receiving postoperative radiotherapy. For individuals who can accept the additional duration of adverse effects, long-course ADT should be offered with postoperative radiotherapy. Funding Cancer Research UK, UK Research and Innovation (formerly Medical Research Council), and Canadian Cancer Society

Adding 6 months of androgen deprivation therapy to postoperative radiotherapy for prostate cancer: a comparison of short-course versus no androgen deprivation therapy in the RADICALS-HD randomised controlled trial

Background Previous evidence indicates that adjuvant, short-course androgen deprivation therapy (ADT) improves metastasis-free survival when given with primary radiotherapy for intermediate-risk and high-risk localised prostate cancer. However, the value of ADT with postoperative radiotherapy after radical prostatectomy is unclear. Methods RADICALS-HD was an international randomised controlled trial to test the efficacy of ADT used in combination with postoperative radiotherapy for prostate cancer. Key eligibility criteria were indication for radiotherapy after radical prostatectomy for prostate cancer, prostate-specific antigen less than 5 ng/mL, absence of metastatic disease, and written consent. Participants were randomly assigned (1:1) to radiotherapy alone (no ADT) or radiotherapy with 6 months of ADT (short-course ADT), using monthly subcutaneous gonadotropin-releasing hormone analogue injections, daily oral bicalutamide monotherapy 150 mg, or monthly subcutaneous degarelix. Randomisation was done centrally through minimisation with a random element, stratified by Gleason score, positive margins, radiotherapy timing, planned radiotherapy schedule, and planned type of ADT, in a computerised system. The allocated treatment was not masked. The primary outcome measure was metastasis-free survival, defined as distant metastasis arising from prostate cancer or death from any cause. Standard survival analysis methods were used, accounting for randomisation stratification factors. The trial had 80% power with two-sided α of 5% to detect an absolute increase in 10-year metastasis-free survival from 80% to 86% (hazard ratio [HR] 0·67). Analyses followed the intention-to-treat principle. The trial is registered with the ISRCTN registry, ISRCTN40814031, and ClinicalTrials.gov, NCT00541047. Findings Between Nov 22, 2007, and June 29, 2015, 1480 patients (median age 66 years [IQR 61–69]) were randomly assigned to receive no ADT (n=737) or short-course ADT (n=743) in addition to postoperative radiotherapy at 121 centres in Canada, Denmark, Ireland, and the UK. With a median follow-up of 9·0 years (IQR 7·1–10·1), metastasis-free survival events were reported for 268 participants (142 in the no ADT group and 126 in the short-course ADT group; HR 0·886 [95% CI 0·688–1·140], p=0·35). 10-year metastasis-free survival was 79·2% (95% CI 75·4–82·5) in the no ADT group and 80·4% (76·6–83·6) in the short-course ADT group. Toxicity of grade 3 or higher was reported for 121 (17%) of 737 participants in the no ADT group and 100 (14%) of 743 in the short-course ADT group (p=0·15), with no treatment-related deaths. Interpretation Metastatic disease is uncommon following postoperative bed radiotherapy after radical prostatectomy. Adding 6 months of ADT to this radiotherapy did not improve metastasis-free survival compared with no ADT. These findings do not support the use of short-course ADT with postoperative radiotherapy in this patient population

Scaffolding Statistical Inquiries for Young Children

Statistics in the early years is often limited to the construction and ‘reading’ of simple data representations as distinct from employing statistical inquiries that engage students with data in more authentic and meaningful contexts. One of the challenges of engaging with data inquiries is the extent to which students struggle with the lack of structure and direction, thus requiring additional support, or scaffolding. This chapter details the framework used for introducing statistical inquiry to young students and then provides insights that emerged from observation and analysis of a class of 5–6 year olds engaged in their own data investigation to illustrate. The findings suggest that considerable teacher scaffolding is required to progress students through inquiries and this was largely achieved through questioning employed to focus students on both the inquiry process and the statistical content to be addressed

Dot plots and hat plots: Supporting young students emerging understandings of distribution, center and variability through modeling

An important use of statistical models and modeling in education stems from the potential to involve students more deeply with conceptions of distribution, variation and center. As models are key to statistical thinking, introducing students to modeling early in their schooling will likely support the statistical thinking that underpins later, more advanced work with increasingly sophisticated statistical models. In this case study, a class of 10–11 year-old students are engaged in an authentic task designed to elicit modeling. Multiple data sources were used to develop insights into student learning: lesson videotape, work samples and field notes. Through the use of dot plots and hat plots as data models, students made comparisons of the data sets, articulated the sources of variability in the data, sought to minimize the variability, and then used their models to both address the initial problem and to justify the effectiveness of their attempts to reduce induced variation. This research has implications for statistics curriculum in the early formal years of schooling