Inquiry pedagogy to promote emerging proportional reasoning in primary students

Fielding-Wells, Jill; Dole, Shelley; Makar, Katie

doi:10.1007/s13394-013-0111-6

Cited by 36 publications

(22 citation statements)

References 40 publications

(37 reference statements)

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“…Furthermore, Sawatzki (2014a) argued that an effective approach to teaching financial literacy is to incorporate age-appropriate financial dilemmas that involve social, ethical and mathematical problem solving, and this was illustrated in the case we presented. Thus, we found that through group-based learning in inquiry-based mathematics lessons (see Fielding-Wells et al 2014), it was possible for students to experience age-appropriate financial dilemmas (Sawatzki 2014a) and to consider, through discussion, how their financial decisions affected others (Lucey et al 2015).…”

Section: Concluding Remarks and Implications For Future Researchmentioning

confidence: 99%

Exploring the classroom practices that may enable a compassionate approach to financial literacy education

2017

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From an early age, children are faced with financial dilemmas and are expected to make effective financial decisions about money. In this paper, we explore the classroom practices that may enable a compassionate approach to financial literacy education. We observed an inquiry-based mathematics lesson in a Year 4 primary school classroom. The financial maths task asked students to decide on the best fundraising option for the school. We used the theory of practice architectures to analyse the interactions in the classroom in order to understand what may have enabled and constrained classroom practices. We found that classroom practices such as engaging with peers through positive and collaborative learning opportunities, making ethical, social and mathematical connections of the task, and considering the impact of financial decisions on others may enable a compassionate approach to financial literacy education.

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Section: Concluding Remarks and Implications For Future Researchmentioning

confidence: 99%

Exploring the classroom practices that may enable a compassionate approach to financial literacy education

2017

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“…The teacher was able to use this discussion to encourage students with accurate conceptions and more articulately formed ideas to share with the class and thus refine their own understandings. Responses the students offered were challenged and a deeper focus on proportion, as distinct from an absolute length, was achieved (for greater discussion on the development of students' proportional reasoning in this unit, refer to Fielding-Wells, Dole, & Makar, 2014). The students determined in discussion that they would need a range of adult human proportions to contrast against Barbie and consideration was given to which measures would be appropriate for the purpose.…”

Section: Devise Phase: 2 Hoursmentioning

confidence: 99%

Developing argumentation in mathematics: The role of evidence and context

Wells¹

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Multiple potential benefits to the introduction of argumentation into classroom environments have been identified and documented, including the potential to extend teaching goals to emphasise cognitive and metacognitive processes, epistemic criteria and reasoning, as well as the enculturation of students into the practices and discourses of a subject. Argumentation structures and practices offer the means to focus students on the need for quality evidence, potentially encouraging students to focus deeply on mathematical content. Much of the work with argumentation that has already occurred in mathematics is associated with justification of procedural choices to arrive at a correct answer. By contrast, mathematical inquiry offers the opportunity for students to engage in ill-structured, ambiguous problems that have neither a defined solution path nor a single correct answer. Thus there is great potential for argumentation to be effective in inquirybased learning environments. However, very little research has focused on argumentation practices of students undertaking inquiry of this nature.The study presented is thus exploratory; designed to both develop deeper understanding of Inquiry-Based Argument practices and possibilities, and to identify how students' developing use of evidence in argumentation could be understood and supported.Specifically, the study sought to address the following research questions: A design research methodology approach was utilised, with iterative cycles of inquiry and argumentation implemented in a single inquiry classroom of Year 4-5 students (n=27, aged 8-10). These cycles introduced the role of evidence, the structure of argument, and evidence and argument quality, to a class environment that embraced a knowledge building culture (Bereiter & Scardamalia, 1996). Berland and Reiser's (2009) Goals of Argument and McNeill and Martin's (2011)Conclusion-Evidence-Reasoning Framework were used to guide the instructional approach which was modified progressively to meet the developing needs of the students. 3Data were generated through videos of emerging classroom practices, interviews with students, student work artefacts, teaching notes, and observations over the course of ten months. A Grounded Theory Approach (Corbin & Strauss, 2008) was utilised for data analysis. The analysis identified several significant results of introducing Inquiry-Based Argument into the classroom:1. Introducing argument practices enabled the ‗visibilising' of student thinking, increasing opportunities to develop and utilise cognitive conflict.2. An increased focus by students on the need for quality evidence enables them to be able to put forth and negotiate arguments.In turn, these factors appear to enable students to:1. Develop complex appreciation for argument structure, progressing from intuitive responses to development of qualified arguments.2. Demonstrate understanding and appreciation of the critical role of evidence and evidence quality in the development of deepened mathematical understanding...

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“…How mathematics is learnt in an inquiry setting will differ to learning mathematics in other settings. Students are required to make many decisions throughout the inquiry process involving how to proceed to solve the problem being explored (Fielding-Wells, Dole & Makar, 2014;Fielding-Wells & Makar, 2012;Makar, 2008;. The social norms and expectations established in the classroom which make the community of inquiry (Goos, 2004;Makar, 2012) will also influence how students think about mathematics as they: contemplate the ideas of others, approach tasks with a focus on creation and finding-out rather than on taught rules and procedures, respond to set-backs they encounter and analyse their own thinking to clearly communicate their ideas to others.…”

Section: Learning Mathematics In An Inquiry Classroommentioning

confidence: 99%

Measuring Messy Mathematics: Assessing learning in a mathematical inquiry context

Fry¹

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The pedagogy of inquiry to teach mathematics presents a seemingly messy yet busy classroom, where children are engaged in using purposeful mathematics to collaboratively generate effective and creative solutions to open-ended, ambiguous questions. Problems arise when describing student learning in inquiry settings, when assessment practices are chosen that do not align with or are not designed to capture learning in this context. This study will present an inquiry into mathematics inquiry classrooms, to analyse and interpret the relationships between three classroom elements of assessment, teaching and learning. Distinctive to this study, the researcher was also the classroom teacher which offers the reader close insight into school practices in these classrooms. The researcher aimed to understand if an alignment between these classroom elements could support teaching and learning in inquiry settings. Using design research as a methodology (Cobb et al., 2003), two primary, inquiry classrooms (Years three and six) are presented as three iterative phases of study, each using particular theoretical lenses and analytical tools. In the first phase of study, theoretical analysis of formative assessment practices was based on Dewey's (1891) conception of thinking as a process involving abstraction, comparison and synthesis. Vygotsky's (1978) zone of proximal development was the analytical tool in the second phase of study and was used to analyse how the classroom teacher adjusted her teaching based on feedback she received through formative assessment. The third and final phase looked closer at the mathematical learning revealed through formative assessment using the DNR framework (Harel & Koichu, 2010): a Piagetian-influenced framework. Duckworth's (2006) belief framework was also used to consider an interrelated synthesis of findings from this study, to assist in the development and refinement of assessment practices that align with using the inquiry pedagogy to teaching mathematics.Findings from three phases in this study revealed the inadequacy of summative assessment practices in capturing and describing student learning and thinking, fostered at higher levels through inquiry.In the first phase of study, analysis of assessment completed by students as part of their everyday, classroom curriculum reflected how such assessment only requires students to perform lower-level, reproductive thinking. In contrast, formative assessment opportunities encouraged students through inquiry to conceptualise their mathematical thinking in connected and abstract ways. The second phase of study focused on teaching in one inquiry classroom and characterised the difficulties classroom teachers face as they implement inquiry into their mathematics curriculum. Analysis of inquiry teaching and learning in this phase characterised how the teacher needed to be an engineer: able to interweave student ideas as potentialities, into the scaffolding of particular learning goals.ii Interweaving by the teacher, of students' connections t...

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Inquiry pedagogy to promote emerging proportional reasoning in primary students

Cited by 36 publications

References 40 publications

Exploring the classroom practices that may enable a compassionate approach to financial literacy education

Exploring the classroom practices that may enable a compassionate approach to financial literacy education

Developing argumentation in mathematics: The role of evidence and context

Measuring Messy Mathematics: Assessing learning in a mathematical inquiry context

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