Abstract: Abstract What could two people stand to gain from sharing a taxi ride' We aimed to explore the extent to which this challenging yet accessible financial context might stimulate students’ mathematical exploration of multiplicative thinking and proportional reasoning. Through teaching experiment methodology, data were collected from 37 Year 5 and 6 students (10–12 years of age) in suburban Melbourne. The findings reveal that the majority of the students had some intuitive understanding of how to solve a financial problem that involved rate, and at least half of them used either multiplicative thinking or proportional reasoning. While the study reported is small and cannot claim to be representative, the findings confirm that well-designed financial problems have the potential to unveil sophisticated mathematical understandings among primary school students. This research demonstrates what young adolescents can do prior to formal exposure to ratio and proportion as part of the curriculum. PubDate: 2019-03-19
Abstract: Abstract School leaders employ various school-based actions to influence students’ subject enrolments at senior secondary levels (Years 11 and 12), which in turn affect students’ entrance into tertiary courses and career choices. In the context of reported declines in the proportion of students opting to study higher-level mathematics, this qualitative study sought insights into seven Australian mathematics teacher leaders’ decision-making processes and actions in their particular school contexts. It aimed to relate their actions to particular attributions for enrolment declines and their goals for students’ learning and achievement. The leaders’ attributions included students’ lack of ability, changes in university courses’ pre-requisites, students’ lack of effort or persistence, and negative attitudes towards mathematics. The leaders described a variety of school-based actions; some school leaders had actually chosen opposing actions but expressed similar reasons for implementing them, and vice versa. Tensions among external pragmatic constraints, the actions of other school staff, and the teacher leaders’ own goals for student learning in mathematics framed the findings of this study. PubDate: 2019-03-13
Abstract: Abstract This article reports the findings of a study using tasks where a family orders and considers sharing the cost of a Fish n Chips meal. Purchasing take-away food is an example of an everyday situation where literacy and numeracy must be applied to make sense of tabulated price information. Originally developed for use in Australia, the tasks were modified so that they might be challenging yet accessible to 10–12-year-old Pāsifika students in New Zealand. Working collaboratively with two teachers in two different schools, we aimed to explore the ways and means by which Pāsifika students drew on social and cultural norms and practices as they applied mathematics to make financial decisions and interacted with each other in justifying solutions that offered what they deemed to be value for money and a fair approach to paying the bill. The students’ and teachers’ reactions to the lessons revealed that as students worked to reconcile social, cultural and mathematical funds of knowledge, their teachers gained meaningful insights into the values about money being learned within families and communities. PubDate: 2019-03-08
Abstract: Abstract The purpose of this study was to investigate the psychometric characteristics of the Math Anxiety Scale (MANX; Erol 1989, Unpublished master thesis, Bogazici University) with data collected from 952 middle school students in Turkey. The Rasch Rating Scale model was used to examine the MANX at the item level. The results revealed that although the MANX was sensitive to detect students with moderate levels of math anxiety and it was not targeted to identify those with very high and low math anxiety levels, it had high reliability and validity. Moreover, the majority of the MANX items were of good quality. The results of this study provide strong evidence for the validation of the MANX despite the need for deletion of eight misfit items and three items with the same item difficulties. Future research should consider possible revision or development of new items to capture gradations of challenges at the very high and low ends of the continuum. PubDate: 2019-03-01
Abstract: Abstract Despite the recognised importance of mathematical proof in secondary education, there is a limited but growing body of literature indicating how preservice secondary mathematics teachers (PSMTs) view proof and the teaching of proof. The purpose of this survey research was to investigate how PSMTs in Australia, the USA and Korea perceive of proof in the context of secondary mathematics teaching and learning. PSMTs were able to outline various mathematical and pedagogical aspects of proof, including purposes, characteristics, reasons for teaching and imposed constraints. In addition, PSMTs attended to differing, though overlapping, features of proof when asked to determine the extent to which proposed arguments constituted proofs or to decide which arguments they might present to students. PubDate: 2019-02-26
Abstract: Abstract In spite of the widely accepted need for language-responsive subject-matter teaching, few teachers are prepared for this challenge due to the lack of empirically founded subject-specific professional development (PD) programs for language-responsive classrooms. The design research study presented in this article pursues the dual aim of (a) promoting teachers’ expertise in language-responsive mathematics teaching using PD courses and (b) investigating teachers’ developing expertise in qualitative case studies. Both aims are pursued based on a conceptual framework for teacher expertise in language-responsive mathematics teaching, starting from typical situational demands that teachers face in language-responsive mathematics teaching and the orientations, categories, and pedagogical tools they need to cope with these situational demands, especially the demand to identify mathematically relevant language demands. For language-responsive teaching, the interplay of categories for mathematical goals and language goals turns out to be of high relevance. PubDate: 2019-02-13
Abstract: Abstract The purpose of the inquiry was to understand how children in primary grades (i.e., preschool, kindergarten, and second grade) engaged with affordances and constraints of features in a Base-10 Blocks virtual manipulative mathematics app designed to promote learning opportunities. Researchers conducted one-to-one interviews with 100 primary grade children as they interacted with the Montessori Number Base-10 Blocks iPad app. The video data were qualitatively analyzed using open descriptive, thematic, and structured coding. Results show that children’s actions when interacting with app features can affect their engagement with designed mathematics constraints and affordances. Results also identified three emergent themes around children’s engagement with the app’s simultaneous linking features: verification, self-correction, and making connections. Findings suggest the importance of helping children identify and reflect on affordances within virtual manipulative mathematics apps. These findings also indicate that as designers, educators and researchers design or select virtual manipulative mathematics apps for classroom use; they should to consider children’s prior achievement as well as in-app perceptions and engagement with design features in the apps. PubDate: 2019-01-26
Abstract: Abstract Differing research worldviews have typically resulted in interpretations at odds with one another. Yet, leveraging distinct perspectives can lead to novel interpretations and theoretical construction. Via an empirically grounded research commentary, we describe the value of such activity through the lens of previously reported findings. This synthesis of research from dissimilar scholarly traditions is one example of how paradigms in related but sometimes disconnected fields were used to provide a more comprehensive model of foundational numeracy development. While critique and skepticism may be valuable scholarly tools, we argue that such practices should be balanced with openness and belief towards ideas from worldviews different than our own. This balance can provide new and creative interpretations and extend our collective research power. PubDate: 2019-01-14
Abstract: The article Using multiple metaphors and multimodalities as a semiotic resource when teaching year 2 students computational strategies, written by Paula Mildenhall and Barbara Sherriff. PubDate: 2018-12-15
Abstract: Abstract Translating a mathematics lesson from curriculum materials into instruction is not straightforward, and launching, or beginning, a lesson such that students will become productively engaged in the target mathematics is nontrivial. The purpose of the study was to investigate preservice teachers’ curricular noticing as they draw upon curriculum materials to design instruction, with a focus on how to launch that lesson. We engaged preservice elementary licensure students at two universities in a four-part process of analyzing mathematics curriculum, planning a lesson, demonstrating their visualization of enactment through animating their lesson launch, and reflecting on the process. Findings indicate that the focal case study pair modified the curricular materials to model mathematical aspects of fractions, adapted the introduction of key academic vocabulary, and introduced materials not mentioned in the curriculum to draw children into the lesson. We discuss implications for preservice teachers’ planning of the lesson launch and their curricular noticing. PubDate: 2018-12-06
Abstract: Abstract This paper reports on a study of the process of professional development for mathematics teachers. The analysis connects two theoretical frameworks: the Meta-Didactical Transposition model developed by Arzarello et al. (2014), which describes the macro level, and, at the micro level, the idea of emergence, which has been around since at least the time of Aristotle and has been defined by Mill (1843), Lewes (1875), Blitz (1992), Huxley and Huxley (1947) and many others. The meta-didactical transposition model considers the evolution of teachers’ practices as part of a community process, while the notion of emergence helps us to gain better insights into the details of the practices of individual teachers. This paper focuses on secondary school teachers’ learning of new digital technologies to illuminate this theoretical framework. PubDate: 2018-12-01
Abstract: Recent research indicates that using multimodal learning experiences can be effective in teaching mathematics. Using a social semiotic lens within a participationist framework, this paper reports on a professional learning collaboration with a primary school teacher designed to explore the use of metaphors and modalities in mathematics instruction. This video case study was conducted in a year 2 classroom over two terms, with the focus on building children’s understanding of computational strategies. The findings revealed that the teacher was able to successfully plan both multimodal and multiple metaphor learning experiences that acted as semiotic resources to support the children’s understanding of abstract mathematics. The study also led to implications for teaching when using multiple metaphors and multimodalities. PubDate: 2018-12-01
Abstract: Abstract This paper seeks to theorise primary teachers’ degree of integration of digital technology in the mathematics classroom. In an age where digital technology use is ubiquitous, the issues surrounding teachers’ choice, and ultimately their uptake of digital technologies in the classroom, is an area that need to be further unpacked. Cross-case analysis of the two teachers’ uptake of digital technologies in their classroom, their pedagogical approaches and the reason for their choices provide insight into teachers’ technological, pedagogical and content knowledge (TPACK). Differences in the way the teachers use digital technology in their classroom seem to be connected to their TPACK developmental stage. PubDate: 2018-12-01
Abstract: Abstract Middle year students often do not see the mathematics in the real world whereas the Australian Curriculum: Mathematics aims for students to be “confident and creative users and communicators of mathematics” (Australian Curriculum Assessment and Reporting Authority [ACARA] 2012). Using authentic and real mathematics tasks can address this situation. This paper is an account of how, working within a Knowledge Producing Schools’ framework, a group of middle year students addressed a real community issue, the problem of the lack of a teenage safe space using mathematics and technology. Data were collected for this case study via journal observations and reflections, semi-structured interviews, samples of the students’ work and videos of students working. The data were analysed by identifying the mathematics the students used determining the function and location of the space and focused on problem negotiation, formulation and solving through the statistical investigation cycle. The paper will identify the mathematics and statistics these students used as they addressed a real problem in their local community. PubDate: 2018-12-01
Abstract: Abstract A foundational component of developing algebraic thinking for meaningful calculus learning is the idea of “function” that focuses on the relationship between varying quantities. Students have demonstrated widespread difficulties in learning calculus, particularly interpreting and modeling dynamic events, when they have a poor understanding of relationships between variables. Yet, there are differing views on how to develop students’ functional thinking over time. In the Australian curriculum context, linear relationships are introduced to lower secondary students with content that reflects a hybrid of traditional and reform algebra pedagogy. This article discusses an investigation into Australian secondary students’ understanding of linear functional relationships from Years 7 to 12 (approximately 12 to 18 years old; n = 215) in their approaches to three tasks (finding rate of change, pattern generalisation and interpretation of gradient) involving four different representations (table, geometric growing pattern, equation and graph). From the findings, it appears that these students’ knowledge of linear functions remains context-specific rather than becoming connected over time. PubDate: 2018-12-01
Authors:Erik Jacobson; Amber Simpson Abstract: Abstract Replication studies play a critical role in scientific accumulation of knowledge, yet replication studies in mathematics education are rare. In this study, the authors replicated Thanheiser’s (Educational Studies in Mathematics 75:241–251, 2010) study of prospective elementary teachers’ conceptions of multidigit number and examined the main claim that most elementary pre-service teachers think about digits incorrectly at least some of the time. Results indicated no statistically significant difference in the distribution of conceptions between the original and replication samples and, moreover, no statistically significant differences in the distribution of sub-conceptions among prospective teachers with the most common conception. These results suggest confidence is warranted both in the generality of the main claim and in the utility of the conceptions framework for describing prospective elementary teachers’ conceptions of multidigit number. The report further contributes a framework for replication of mathematics education research adapted from the field of psychology. PubDate: 2018-04-27 DOI: 10.1007/s13394-018-0242-x
Authors:Yew Hoong Leong; Lu Pien Cheng; Wei Yeng Karen Toh; Berinderjeet Kaur; Tin Lam Toh Abstract: Abstract The phrase ‘make it explicit’ is a common advice given to teachers. It is, however, not clear to us what this actually means when translated into classroom practice. Our review found that we are not alone: “explicit” is used in different ways in the education literature. This paper explores, through a case study of a teacher who stated “making things explicit” as an ostensible goal of his instructional practice, how the explicitation is realised in teaching mathematics. In particular, we examine how he used the instructional materials that he crafted to fulfil his goal of explicitation. We were able to uncover three strategies he used: explicit-from, explicit-within, and explicit-to. PubDate: 2018-04-02 DOI: 10.1007/s13394-018-0240-z
Authors:Lise Westaway; Mellony Graven Abstract: Abstract This article addresses the question: Why teachers of mathematics have yet to ‘take up’ progressive roles' Drawing on the philosophy of critical realism and its methodological equivalent, social realism, we analyse interview and observation data of four grade 3 teachers, with the view to identifying the mechanisms conditioning the expression of teachers’ identities. In so doing, we show how post-apartheid changes in systemic roles of teachers create contradictory tensions for teachers as these bring their own mathematical learning and teaching experiences into contradiction with the new post-apartheid roles they are mandated to enact. We examine how this contradiction, together with beliefs about mathematics, pedagogy and learners, is expressed in the teaching of grade 3 mathematics. We maintain that the complementarity between teachers’ beliefs and old systemic roles provides an explanation for why teachers of grade 3 mathematics have yet to ‘take-up’ progressive roles. The implications point to the need for teacher development that creates enablers that lead to changes in classroom practices that align with policy-designated, progressive roles in teaching mathematics. PubDate: 2018-03-01 DOI: 10.1007/s13394-018-0237-7
Authors:Colleen Vale; Wanty Widjaja; Brian Doig; Susie Groves Abstract: Abstract Structured problem-solving lessons are used to explore mathematical concepts such as pattern and relationships in early algebra, and regularly used in Japanese Lesson Study research lessons. However, enactment of structured problem-solving lessons which involves detailed planning, anticipation of student solutions and orchestration of whole-class discussion of solutions is an ongoing challenge for many teachers. Moreover, primary teachers have limited experience in teaching early algebra or mathematical reasoning actions such as generalising. In this study, the critical factors of enacting the structured problem-solving lessons used in Japanese Lesson Study to elicit and develop primary students’ capacity to generalise are explored. Teachers from three primary schools participated in two Japanese Lesson Study teams for this study. The lesson plans and video recordings of teaching and post-lesson discussion of the two research lessons along with students’ responses and learning are compared to identify critical factors. The anticipation of students’ reasoning together with preparation of supporting and challenging prompts was critical for scaffolding students’ capacity to grasp and communicate generality. PubDate: 2018-02-28 DOI: 10.1007/s13394-018-0239-5
Authors:Carly Sawatzki; Merrilyn Goos Abstract: Abstract This article examines some of the complexities associated with developing financially literate, enterprising young Australians through school education. We aimed to explore what seems to influence students in pricing goods for sale within their school community. Data were collected from more than 300 years 5 and 6 students (10–12 years of age) in four government primary schools in urban Darwin. Students were asked to respond to problem contexts involving fundraising as an example of an enterprise activity. The findings reveal that familiarity with fundraising initiatives, personal values, and language and literacy skills shaped the responses students gave. Students who gave loss-making and break-even responses were price conscious, but also tended to confuse terminology influencing mathematisation—i.e., “cost”, “price” and “profit”. Students who gave profit-making responses applied reasoning that was mathematical, financial and entrepreneurial, giving explanations that distinguished between these terms. We argue that these insights contribute to our understanding how upper primary school students interpret and respond to financial problems, with useful implications for schools and teachers. PubDate: 2018-02-19 DOI: 10.1007/s13394-018-0241-y
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