Faculty of Education - Research Publications
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ItemAlgebraic reasoning in years 5 and 6: classifying its emergence and progression using reverse fraction tasks(SPRINGER HEIDELBERG, 2022-11)Abstract This paper builds on our previous research and investigates how students’ fractional competence and reasoning can provide clear evidence of non-symbolic algebraic thinking and its progressive transition towards fully generalised algebraic thinking. In a large-scale study, 470 primary students completed a written paper and pencil test. This included three reverse fraction tasks which required students to find an unknown whole when presented with a quantity representing a fraction of that whole. Seventeen students from one participating primary school undertook a semi-structured interview which included reverse fraction tasks, similar to those on the written test, but with progressive levels of abstraction, starting with particular instances and becoming more generalised. Two important products of the study are the Classification Framework for Reverse Fraction Tasks and the Emerging Algebraic Reasoning Framework. The interview results highlight two critical transition points for the emergence of students’ algebraic reasoning. The first is the ability to transition from additive strategies to multiplicative strategies to solve reverse fraction problems. Students reliant on diagrams and additive strategies struggled to solve more generalised tasks that required multiplicative rather than additive strategies. The second transition is the shift from multiplicative thinking to algebraic reasoning where students could generalise their multiplicative knowledge to deal with any quantity represented in a reverse fraction task.
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ItemNo Preview AvailableSymbols in physics: difficulties experienced by first-year undergraduate students(National Science Teachers Association, 2021-05-01)Symbols are a cornerstone of the written language of physics and mathematics but inconsistencies in their use pose a challenge to students. This article reports on interviews held with first-year undergraduate physics students, focused on their early experiences with symbols in university physics. Students reported being confused by the symbolic aspects of their studies in physics over and above the concepts being taught. Many students commented on experiencing difficulties, as the symbolic notation used in high school mathematics and physics differed to their tertiary experiences. Additionally, the extent of the multiple uses of a single symbol, and the multiple symbols used for a single concept were at times problematic for students. These experiences highlight the need for greater attention to be focused on early undergraduate students’ prior symbolic knowledge, and the formation of explicit connections between the varied nomenclature both within physics, and between physics and mathematics.
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ItemTeaching with new technology: four 'early majority' teachers(SPRINGER, 2013-10)
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ItemRevealing educationally critical aspects of rate(Springer, 2012-09-01)Rate (of change) is an important but complicated mathematical concept describing a ratio comparing two different numeric, measurable quantities. Research referring to students' difficulties with this concept spans more than 20 years. It suggests that problems experienced by some calculus students are likely a result of pre-existing limited or incorrect conceptions of rate. This study investigated 20 Australian Year 10 students' understanding of rate as revealed by phenomenographic analysis of interviews. Eight conceptions of rate emerged, leading to the identification of four educationally critical aspects of the concept which address gaps in students' thinking. In addition, the employment of phenomenography, to reveal conceptions of rate, is described in detail.
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ItemHelping Teachers to Make Effective Use of Real-World Examples in Statistics(International Statistical Institute, 2010)
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ItemLESSON STUDY WITH A TWIST: RESEARCHING LESSON DESIGN BY STUDYING CLASSROOM IMPLEMENTATION(INT GRP PSYCHOL MATH EDUC, 2009)
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ItemInvestigating Students' Numerical Misconceptions in Algebra(Mathematics Education Research Group of Australasia, 2009)
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ItemExamining the didactic contract when handheld technology is permitted in the mathematics classroom(SPRINGER HEIDELBERG, 2010-11)
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