Pub Date : 2021-11-01DOI: 10.1177/00049441211041855
H. McMaster, C. Preston, Hailan Wang, Mersini Perivolarellis
Australia has a National Numeracy Learning Progression (NNLP) that is strongly aligned with the Australian Curriculum: Mathematics. This article examines how a sub-element within this progression could be impacting students’ learning of Science. This sub-element is firmly based on Mathematics education research as to how students build their understanding of geometric measurement (the structure of length, area and volume). Mathematics educators subsequently researched children’s measurement of mass and included it within the same sub-element of the NNLP. The contexts in which mass and volume are measured in Mathematics are different to those used in teaching Science. This article presents two studies that used variation theory and task-based interviews of children in Years 5 and 6, to explore their thinking about mass and volume in a Science context. The findings suggest that mathematical constructs in geometric measurement could be constraining the development of scientific ideas about matter. This research has implications for furthering the development of the NNLP to encompass scientific aspects of measuring matter.
{"title":"The case for a sub-element ‘measuring matter’ within the Australian national numeracy learning progression","authors":"H. McMaster, C. Preston, Hailan Wang, Mersini Perivolarellis","doi":"10.1177/00049441211041855","DOIUrl":"https://doi.org/10.1177/00049441211041855","url":null,"abstract":"Australia has a National Numeracy Learning Progression (NNLP) that is strongly aligned with the Australian Curriculum: Mathematics. This article examines how a sub-element within this progression could be impacting students’ learning of Science. This sub-element is firmly based on Mathematics education research as to how students build their understanding of geometric measurement (the structure of length, area and volume). Mathematics educators subsequently researched children’s measurement of mass and included it within the same sub-element of the NNLP. The contexts in which mass and volume are measured in Mathematics are different to those used in teaching Science. This article presents two studies that used variation theory and task-based interviews of children in Years 5 and 6, to explore their thinking about mass and volume in a Science context. The findings suggest that mathematical constructs in geometric measurement could be constraining the development of scientific ideas about matter. This research has implications for furthering the development of the NNLP to encompass scientific aspects of measuring matter.","PeriodicalId":46741,"journal":{"name":"Australian Journal of Education","volume":null,"pages":null},"PeriodicalIF":1.3,"publicationDate":"2021-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44474468","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"教育学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-11-01DOI: 10.1177/00049441211055521
G. Oates, R. Seah
{"title":"Learning progressions/trajectories in mathematics and science education: A case for evidence-based curricula reform? Guest editorial","authors":"G. Oates, R. Seah","doi":"10.1177/00049441211055521","DOIUrl":"https://doi.org/10.1177/00049441211055521","url":null,"abstract":"","PeriodicalId":46741,"journal":{"name":"Australian Journal of Education","volume":null,"pages":null},"PeriodicalIF":1.3,"publicationDate":"2021-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43775320","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"教育学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-09-30DOI: 10.1177/00049441211044798
M. Stephens, L. Day, Marj Horne
Generalisation is a key feature of learning algebra, requiring all four proficiency strands of the Australian Curriculum: Mathematics (AC:M): Understanding, Fluency, Problem Solving and Reasoning. From a review of the literature, we propose a learning progression for algebraic generalisation consisting of five levels. Our learning progression is then elaborated and validated by reference to a large range of assessment tasks acquired from a previous project Reframing Mathematical Futures II (RMFII). In the RMFII project, Rasch modelling of the responses of over 5000 high school students (Years 7–10) to algebra tasks led to the development of a Learning Progression for Algebraic Reasoning (LPAR). Our learning progression in generalisation is more specific than the LPAR, more coherent regarding algebraic generalisation, and enabling teachers to locate students’ performances within the progression and to target their teaching. In addition, a selection of appropriate teaching resources and marking rubrics used in the RMFII project is provided for each level of the learning progression.
{"title":"An empirically based practical learning progression for generalisation, an essential element of algebraic reasoning","authors":"M. Stephens, L. Day, Marj Horne","doi":"10.1177/00049441211044798","DOIUrl":"https://doi.org/10.1177/00049441211044798","url":null,"abstract":"Generalisation is a key feature of learning algebra, requiring all four proficiency strands of the Australian Curriculum: Mathematics (AC:M): Understanding, Fluency, Problem Solving and Reasoning. From a review of the literature, we propose a learning progression for algebraic generalisation consisting of five levels. Our learning progression is then elaborated and validated by reference to a large range of assessment tasks acquired from a previous project Reframing Mathematical Futures II (RMFII). In the RMFII project, Rasch modelling of the responses of over 5000 high school students (Years 7–10) to algebra tasks led to the development of a Learning Progression for Algebraic Reasoning (LPAR). Our learning progression in generalisation is more specific than the LPAR, more coherent regarding algebraic generalisation, and enabling teachers to locate students’ performances within the progression and to target their teaching. In addition, a selection of appropriate teaching resources and marking rubrics used in the RMFII project is provided for each level of the learning progression.","PeriodicalId":46741,"journal":{"name":"Australian Journal of Education","volume":null,"pages":null},"PeriodicalIF":1.3,"publicationDate":"2021-09-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43259336","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"教育学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-08-12DOI: 10.1177/00049441211036518
D. Panizzon, J. Pegg, D. Arthur, G. McCloughan
Few would argue the value of learning progressions in providing useful structures for selecting and sequencing in a developmental manner the key components of an ‘intended curriculum’. Yet, there are pervading issues around what is meant by a developmental sequence, along with how they are used to assess what learners know, understand and can do. One key oversight in Science is recognising the role of technical and non-technical language in student conceptual development. This article reports on the construction of a hypothesised learning progression that identifies students’ progress in understanding essential concepts in the Chemical Sciences from Foundation to Year 6. It is based upon an extensive analysis of the technical and non-technical language of the Australian Curriculum: Science. The progression was constructed by focusing upon learner-appropriate language and scientific understanding with the Structure of the Observed Learning Outcome model (Pegg, 2018) providing the theoretical basis for ensuring systematic and objective rigour in the resultant developmental progression.
{"title":"Designing a developmental progression to assess students’ conceptual understandings by focusing on the language demands in Science","authors":"D. Panizzon, J. Pegg, D. Arthur, G. McCloughan","doi":"10.1177/00049441211036518","DOIUrl":"https://doi.org/10.1177/00049441211036518","url":null,"abstract":"Few would argue the value of learning progressions in providing useful structures for selecting and sequencing in a developmental manner the key components of an ‘intended curriculum’. Yet, there are pervading issues around what is meant by a developmental sequence, along with how they are used to assess what learners know, understand and can do. One key oversight in Science is recognising the role of technical and non-technical language in student conceptual development. This article reports on the construction of a hypothesised learning progression that identifies students’ progress in understanding essential concepts in the Chemical Sciences from Foundation to Year 6. It is based upon an extensive analysis of the technical and non-technical language of the Australian Curriculum: Science. The progression was constructed by focusing upon learner-appropriate language and scientific understanding with the Structure of the Observed Learning Outcome model (Pegg, 2018) providing the theoretical basis for ensuring systematic and objective rigour in the resultant developmental progression.","PeriodicalId":46741,"journal":{"name":"Australian Journal of Education","volume":null,"pages":null},"PeriodicalIF":1.3,"publicationDate":"2021-08-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42883693","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"教育学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-08-09DOI: 10.1177/00049441211036521
Rosemary Callingham, Jane Watson, G. Oates
Mathematics curricula have traditionally focused on content knowledge, often in the form of a scope and sequence of increasingly difficult mathematics. The importance of using and applying mathematics is recognised in the current Australian Curriculum Mathematics (AC: M) as ‘proficiencies’ that are intended to be integrated with the content. There is little support for teachers to develop these proficiencies – reasoning, understanding, problem solving and fluency. Learning progressions are sequences of learning that focus on cognitive processes, and thus provide a useful basis for curriculum development. Using an empirical Statistical Reasoning Learning Progression as an exemplar, a new approach to curriculum development is suggested that links content knowledge with the proficiencies. The outcome is a zone-based, rather than year level based, curriculum that allows teachers to target their teaching, so that students develop increasingly sophisticated understanding of statistics and probability.
{"title":"Learning progressions and the Australian curriculum mathematics: The case of statistics and probability","authors":"Rosemary Callingham, Jane Watson, G. Oates","doi":"10.1177/00049441211036521","DOIUrl":"https://doi.org/10.1177/00049441211036521","url":null,"abstract":"Mathematics curricula have traditionally focused on content knowledge, often in the form of a scope and sequence of increasingly difficult mathematics. The importance of using and applying mathematics is recognised in the current Australian Curriculum Mathematics (AC: M) as ‘proficiencies’ that are intended to be integrated with the content. There is little support for teachers to develop these proficiencies – reasoning, understanding, problem solving and fluency. Learning progressions are sequences of learning that focus on cognitive processes, and thus provide a useful basis for curriculum development. Using an empirical Statistical Reasoning Learning Progression as an exemplar, a new approach to curriculum development is suggested that links content knowledge with the proficiencies. The outcome is a zone-based, rather than year level based, curriculum that allows teachers to target their teaching, so that students develop increasingly sophisticated understanding of statistics and probability.","PeriodicalId":46741,"journal":{"name":"Australian Journal of Education","volume":null,"pages":null},"PeriodicalIF":1.3,"publicationDate":"2021-08-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45211248","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"教育学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-08-05DOI: 10.1177/00049441211037409
Joan Burfitt
The aim of this study was to show that some of the errors made by students when responding to mathematics assessment items can indicate progress in the development of conceptual understanding. By granting partial credit for specific incorrect responses by early secondary students, estimates of the difficulty of demonstrating full and partial knowledge of skills associated with the development of proportional reasoning were determined using Rasch analysis. The errors were confirmed as indicators of progress, and hence partial knowledge, when the thresholds of achievement followed a logical order: The greater the proficiency of the students, the more likely they were to receive a higher score. Consideration of this partial knowledge can enhance the descriptions of the likely behaviours of students at the various levels of learning progressions and this can be informative for teachers in their planning of learning activities.
{"title":"Using partial knowledge to inform the creation of learning progressions","authors":"Joan Burfitt","doi":"10.1177/00049441211037409","DOIUrl":"https://doi.org/10.1177/00049441211037409","url":null,"abstract":"The aim of this study was to show that some of the errors made by students when responding to mathematics assessment items can indicate progress in the development of conceptual understanding. By granting partial credit for specific incorrect responses by early secondary students, estimates of the difficulty of demonstrating full and partial knowledge of skills associated with the development of proportional reasoning were determined using Rasch analysis. The errors were confirmed as indicators of progress, and hence partial knowledge, when the thresholds of achievement followed a logical order: The greater the proficiency of the students, the more likely they were to receive a higher score. Consideration of this partial knowledge can enhance the descriptions of the likely behaviours of students at the various levels of learning progressions and this can be informative for teachers in their planning of learning activities.","PeriodicalId":46741,"journal":{"name":"Australian Journal of Education","volume":null,"pages":null},"PeriodicalIF":1.3,"publicationDate":"2021-08-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1177/00049441211037409","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47689292","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"教育学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-08-05DOI: 10.1177/00049441211036532
R. Seah, Marj Horne
Promoting reasoning is the goal of mathematics education. While reasoning behaviours can be observed, how to characterise them and nurture their growth remains ambiguous. In this article, we report our effort in drafting a learning progression and geometric thinking model and using them to investigate Australian students’ geometric reasoning abilities. The data were taken from a large-scale study into the development of mathematical reasoning. Rasch analysis resulted in eight thinking zones being charted. Using a mixed method, we analysed 446 Year 7 to 10 students’ responses on a task that requires them to enlarge a logo, state its coordinates and calculate the enlarged area. In-depth, fine-grained analysis of students’ explanations revealed the range of skills and techniques students used to reason about the situation. The findings suggest that higher level reasoning was characterised by evidence of increased visualisation skills and proficient use of mixed mediums to communicate intent. The implications of the findings for curriculum and classroom practice are discussed.
{"title":"Developing reasoning within a geometric learning progression: Implications for curriculum development and classroom practices","authors":"R. Seah, Marj Horne","doi":"10.1177/00049441211036532","DOIUrl":"https://doi.org/10.1177/00049441211036532","url":null,"abstract":"Promoting reasoning is the goal of mathematics education. While reasoning behaviours can be observed, how to characterise them and nurture their growth remains ambiguous. In this article, we report our effort in drafting a learning progression and geometric thinking model and using them to investigate Australian students’ geometric reasoning abilities. The data were taken from a large-scale study into the development of mathematical reasoning. Rasch analysis resulted in eight thinking zones being charted. Using a mixed method, we analysed 446 Year 7 to 10 students’ responses on a task that requires them to enlarge a logo, state its coordinates and calculate the enlarged area. In-depth, fine-grained analysis of students’ explanations revealed the range of skills and techniques students used to reason about the situation. The findings suggest that higher level reasoning was characterised by evidence of increased visualisation skills and proficient use of mixed mediums to communicate intent. The implications of the findings for curriculum and classroom practice are discussed.","PeriodicalId":46741,"journal":{"name":"Australian Journal of Education","volume":null,"pages":null},"PeriodicalIF":1.3,"publicationDate":"2021-08-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1177/00049441211036532","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41309831","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"教育学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-08-01DOI: 10.1177/00049441211031014
J. Page
{"title":"Kilderry A and Raban B (eds), Strong foundations. Evidence informing practice in early childhood education and care","authors":"J. Page","doi":"10.1177/00049441211031014","DOIUrl":"https://doi.org/10.1177/00049441211031014","url":null,"abstract":"","PeriodicalId":46741,"journal":{"name":"Australian Journal of Education","volume":null,"pages":null},"PeriodicalIF":1.3,"publicationDate":"2021-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1177/00049441211031014","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43979525","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"教育学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-08-01DOI: 10.1177/00049441211030728
J. Bowd, T. Bowles, V. McKenzie
Homework has been associated with a range of academic and cognitive benefits for secondary students. Research has also revealed that students’ homework behaviours can vary with demographic traits. An important factor that may account for some of this variation is the role played by teachers and schools in homework allocation. It is hypothesised that some of the demographic variables that have been found to predict individual students’ homework practices are also related to teachers’ practices in terms of the frequency and volume of homework allocated at the classroom level. To test this hypothesis, Australian data from the 2015 Trends in International Mathematics and Science Study are analysed in the current study. Results show that the frequency of mathematics homework allocated by teachers is related to some variables that have commonly predicted the differences in student achievement such as socioeconomic status, valuing of and confidence in mathematics, teaching experience and school location. The implications of these findings for schools and education systems are explored as suggestions for ensuring that homework policies and practices do not exacerbate demographic differences in school outcomes.
{"title":"The effects of demography, expectations and student attitudes on Australian secondary school teachers’ homework practices","authors":"J. Bowd, T. Bowles, V. McKenzie","doi":"10.1177/00049441211030728","DOIUrl":"https://doi.org/10.1177/00049441211030728","url":null,"abstract":"Homework has been associated with a range of academic and cognitive benefits for secondary students. Research has also revealed that students’ homework behaviours can vary with demographic traits. An important factor that may account for some of this variation is the role played by teachers and schools in homework allocation. It is hypothesised that some of the demographic variables that have been found to predict individual students’ homework practices are also related to teachers’ practices in terms of the frequency and volume of homework allocated at the classroom level. To test this hypothesis, Australian data from the 2015 Trends in International Mathematics and Science Study are analysed in the current study. Results show that the frequency of mathematics homework allocated by teachers is related to some variables that have commonly predicted the differences in student achievement such as socioeconomic status, valuing of and confidence in mathematics, teaching experience and school location. The implications of these findings for schools and education systems are explored as suggestions for ensuring that homework policies and practices do not exacerbate demographic differences in school outcomes.","PeriodicalId":46741,"journal":{"name":"Australian Journal of Education","volume":null,"pages":null},"PeriodicalIF":1.3,"publicationDate":"2021-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47956312","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"教育学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-08-01DOI: 10.1177/00049441211031674
S. Alagumalai, N. Buchdahl
Recent studies reiterate the importance of mathematical literacy and the identification of skills, knowledge and cognitive processes which contribute to composite test scores to facilitate targeted remediation and extension activities. To this end, the current article examines data from the 2012 cycle of the Programme for International Student Assessment (PISA), using multilevel modelling techniques to explore the relationship between selected student-level and teacher/school-level factors and the three processes of interpret, employ and formulate which were measured as the skills underlying mathematical literacy in that assessment. Results of the analyses indicate that boys outperform girls significantly (p < 0.001) in all three processes whereby formulate invokes relatively more inter- and intra-level influences compared with interpret. Apart from the relatively higher item-difficulties of formulate, an increase in the complexity of contextual effects at the student and the teacher/school-level emerges as mathematical processes move from interpret to employ to formulate. Findings also reveal that students taught by teachers who had mathematics as a major in their undergraduate studies and who work in relatively smaller classes or groups show higher performance in all three mathematical literacy processes. Use of ICT in mathematics lessons is negatively associated with the three mathematical literacy processes. The additional negative effect of mathematical extracurricular activities at school on the processes highlights the need to rethink how technology and extracurricular lessons are to be used, designed/structured and delivered to optimise the learning of mathematical processes, and ultimately improve mathematical literacy.
{"title":"PISA 2012: Examining the influence of prior knowledge, time-on-task, school-level effects on achievements in mathematical literacy processes – Interpret, employ and formulate","authors":"S. Alagumalai, N. Buchdahl","doi":"10.1177/00049441211031674","DOIUrl":"https://doi.org/10.1177/00049441211031674","url":null,"abstract":"Recent studies reiterate the importance of mathematical literacy and the identification of skills, knowledge and cognitive processes which contribute to composite test scores to facilitate targeted remediation and extension activities. To this end, the current article examines data from the 2012 cycle of the Programme for International Student Assessment (PISA), using multilevel modelling techniques to explore the relationship between selected student-level and teacher/school-level factors and the three processes of interpret, employ and formulate which were measured as the skills underlying mathematical literacy in that assessment. Results of the analyses indicate that boys outperform girls significantly (p < 0.001) in all three processes whereby formulate invokes relatively more inter- and intra-level influences compared with interpret. Apart from the relatively higher item-difficulties of formulate, an increase in the complexity of contextual effects at the student and the teacher/school-level emerges as mathematical processes move from interpret to employ to formulate. Findings also reveal that students taught by teachers who had mathematics as a major in their undergraduate studies and who work in relatively smaller classes or groups show higher performance in all three mathematical literacy processes. Use of ICT in mathematics lessons is negatively associated with the three mathematical literacy processes. The additional negative effect of mathematical extracurricular activities at school on the processes highlights the need to rethink how technology and extracurricular lessons are to be used, designed/structured and delivered to optimise the learning of mathematical processes, and ultimately improve mathematical literacy.","PeriodicalId":46741,"journal":{"name":"Australian Journal of Education","volume":null,"pages":null},"PeriodicalIF":1.3,"publicationDate":"2021-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44130563","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"教育学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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