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Shelley Dole - One of the best experts on this subject based on the ideXlab platform.
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USING DIGITAL PHOTOGRAPHY TO SUPPORT TEACHING AND LEARNING OF Proportional Reasoning CONCEPTS
2020Co-Authors: Geoff Hilton, Shelley Dole, Annette Hilton, Merrilyn GoosAbstract:Abstract Proportional Reasoning entails multiplicative relationships in situations of comparison. Successful Proportional reasoners can recognise a Proportional situation as distinct from a non-Proportional one; they have a sense of co-variation and they have a range of strategies for solving Proportional problems. As educators we realise that teaching Proportional Reasoning cannot solely rely on asking students to complete symbolic and mechanical methods, such as the cross-product algorithm. To develop Proportional Reasoning, students must have regular opportunities to experience the underlying concepts. These concepts include foundational aspects of Proportional Reasoning, such as fractional thinking, multiplicative thinking (as opposed to additive), relative thinking (as opposed to absolute), as well as concepts of rate and scale. As part of a large multi-state project in Australia to enhance middle years students' numeracy through a focus on Proportional Reasoning, 120 teachers participated in a series of professional learning workshops. These teachers generally reported feeling confident teaching the algorithmic aspects of Proportional Reasoning but a number of them specifically asked for assistance with the conceptual development of their students' Proportional Reasoning. In response, the researchers developed a series of activities with the teachers, where digital cameras were used in the school environs to capture images that represented examples of Proportional Reasoning concepts. In small groups, the teachers moved around the school taking their photos and then reported back to the workshop, showing their images through a data projector while they explained the concepts they felt their images captured. This presentation articulates the ways that the digital cameras were used by the teachers to capture and report on the Proportional Reasoning concepts, and their thoughts and aspirations as to how they would use the cameras to develop the Proportional Reasoning of their students
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Promoting middle school students’ Proportional Reasoning skills through an ongoing professional development programme for teachers
Educational Studies in Mathematics, 2016Co-Authors: Annette Hilton, Geoff Hilton, Shelley Dole, Merrilyn GoosAbstract:Proportional Reasoning, the ability to use ratios in situations involving comparison of quantities, is essential for mathematical competence, especially in the middle school years, and is an important determinant of success beyond school. Research shows students find Proportional Reasoning and its foundational concepts difficult. Proportional Reasoning does not always develop naturally, however some research suggests that with targeted teaching, its development can be promoted. This paper reports on a large Australian study involving over 130 teachers and their students. A major goal of the study was to investigate the efficacy of ongoing teacher professional development for promoting middle years students’ Proportional Reasoning. A series of professional development workshops was designed to enhance the teachers’ understanding of Proportional Reasoning and to extend their repertoire of teaching strategies to promote their students’ Proportional Reasoning skills. The workshop design was informed by research literature on Proportional Reasoning teaching and learning as well as the results of a diagnostic instrument administered to over 2500 middle years students prior to the professional development. Between workshops, the teachers implemented a variety of targeted teaching activities. This paper reports on pre- and post- instrument student data collected at the beginning and end of the first year of the project (i.e., after completion of half of the workshops). The findings suggest that targeted professional development and explicit teaching can make a difference to students’ Proportional Reasoning.
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Inquiry pedagogy to promote emerging Proportional Reasoning in primary students
Mathematics Education Research Journal, 2014Co-Authors: Jill Fielding-wells, Shelley Dole, Katie MakarAbstract:Proportional Reasoning as the capacity to compare situations in relative (multiplicative) rather than absolute (additive) terms is an important outcome of primary school mathematics. Research suggests that students tend to see comparative situations in additive rather than multiplicative terms and this thinking can influence their capacity for Proportional Reasoning in later years. In this paper, excerpts from a classroom case study of a fourth-grade classroom (students aged 9) are presented as they address an inquiry problem that required Proportional Reasoning. As the inquiry unfolded, students' additive strategies were progressively seen to shift to Proportional thinking to enable them to answer the question that guided their inquiry. In wrestling with the challenges they encountered, their emerging Proportional Reasoning was supported by the inquiry model used to provide a structure, a classroom culture of inquiry and argumentation, and the Proportionality embedded in the problem context.
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Development and application of a two-tier diagnostic instrument to assess middle-years students’ Proportional Reasoning
Mathematics Education Research Journal, 2013Co-Authors: Annette Hilton, Geoff Hilton, Shelley Dole, Merrilyn GoosAbstract:Proportional Reasoning involves the use of ratios in the comparison of quantities. While it is a key aspect of numeracy, particularly in the middle years of schooling, students do not always develop Proportional Reasoning naturally. Research suggests that many students do not apply Proportional methods appropriately and that they often erroneously apply both multiplicative and additive thinking. Further, students cannot always distinguish non-Proportional situations from those that are Proportional. Understanding the situations in which students mistakenly use additive or multiplicative thinking and the nature of the Proportional Reasoning that students apply to different problem types is important for teachers seeking to support their students to develop Proportional Reasoning in the classroom. This paper describes the development and use of a two-tier diagnostic instrument to identify situations in which students could and could not apply Proportional Reasoning and the types of Reasoning they used. It presents data from an Australian study involving over 2000 middle-years students (Years 5 to 9) as a means of illustrating the use of the instrument for diagnosing students’ Reasoning in different situations. The findings showed that the instrument was useful for identifying problem types in which students of different ages were able to apply correct Reasoning. It also allowed identification of the types of incorrect Reasoning used by students. The paper also describes useful applications of the instrument, including its use as a diagnostic instrument by classroom teachers and its use in the design of classroom activities included in teacher professional learning workshops.
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kitchen gardens contexts for developing Proportional Reasoning
Australian primary mathematics classroom, 2013Co-Authors: Annette Hilton, Geoff Hilton, Shelley Dole, Merrilyn Goos, Mia ObrienAbstract:It is great to see how the sharing of ideas sparks new ideas. In 2011 Lyon and Bragg wrote an APMC article on the mathematics of kitchen gardens. In this article the authors show how the kitchen garden may be used as a starting point for Proportional Reasoning. The authors highlight different types of proportion problems and how the authentic context of a kitchen garden may be used to spark interest in Reasoning.
Geoff Hilton - One of the best experts on this subject based on the ideXlab platform.
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USING DIGITAL PHOTOGRAPHY TO SUPPORT TEACHING AND LEARNING OF Proportional Reasoning CONCEPTS
2020Co-Authors: Geoff Hilton, Shelley Dole, Annette Hilton, Merrilyn GoosAbstract:Abstract Proportional Reasoning entails multiplicative relationships in situations of comparison. Successful Proportional reasoners can recognise a Proportional situation as distinct from a non-Proportional one; they have a sense of co-variation and they have a range of strategies for solving Proportional problems. As educators we realise that teaching Proportional Reasoning cannot solely rely on asking students to complete symbolic and mechanical methods, such as the cross-product algorithm. To develop Proportional Reasoning, students must have regular opportunities to experience the underlying concepts. These concepts include foundational aspects of Proportional Reasoning, such as fractional thinking, multiplicative thinking (as opposed to additive), relative thinking (as opposed to absolute), as well as concepts of rate and scale. As part of a large multi-state project in Australia to enhance middle years students' numeracy through a focus on Proportional Reasoning, 120 teachers participated in a series of professional learning workshops. These teachers generally reported feeling confident teaching the algorithmic aspects of Proportional Reasoning but a number of them specifically asked for assistance with the conceptual development of their students' Proportional Reasoning. In response, the researchers developed a series of activities with the teachers, where digital cameras were used in the school environs to capture images that represented examples of Proportional Reasoning concepts. In small groups, the teachers moved around the school taking their photos and then reported back to the workshop, showing their images through a data projector while they explained the concepts they felt their images captured. This presentation articulates the ways that the digital cameras were used by the teachers to capture and report on the Proportional Reasoning concepts, and their thoughts and aspirations as to how they would use the cameras to develop the Proportional Reasoning of their students
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Primary school teachers implementing structured mathematics interventions to promote their mathematics knowledge for teaching Proportional Reasoning
Journal of Mathematics Teacher Education, 2019Co-Authors: Annette Hilton, Geoff HiltonAbstract:Proportional Reasoning is the ability to use multiplicative thinking and make multiple comparisons. It is known to be challenging for many students and at the same time, many teachers require support to develop sufficient subject matter knowledge and pedagogical content knowledge to teach the diverse concepts that underpin Proportional Reasoning. The data reported in this paper are drawn from the first year of a broader study aiming to promote the teaching and learning of elements of Proportional Reasoning across the curriculum by engaging primary school teachers in ongoing professional development that includes the implementation of a series of mathematics interventions, each of which included a research component. This paper focuses on the impact of implementing the interventions on the teachers’ mathematical knowledge for teaching. Three structured interventions were implemented by eight teachers (Years 3, 4, 5) during each of three school terms. Data collected showed that engaging in this scaffolded type of practitioner research, the structured nature of the interventions, and reflection on the outcomes of each intervention promoted teachers’ subject matter knowledge and pedagogical content knowledge.
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Promoting middle school students’ Proportional Reasoning skills through an ongoing professional development programme for teachers
Educational Studies in Mathematics, 2016Co-Authors: Annette Hilton, Geoff Hilton, Shelley Dole, Merrilyn GoosAbstract:Proportional Reasoning, the ability to use ratios in situations involving comparison of quantities, is essential for mathematical competence, especially in the middle school years, and is an important determinant of success beyond school. Research shows students find Proportional Reasoning and its foundational concepts difficult. Proportional Reasoning does not always develop naturally, however some research suggests that with targeted teaching, its development can be promoted. This paper reports on a large Australian study involving over 130 teachers and their students. A major goal of the study was to investigate the efficacy of ongoing teacher professional development for promoting middle years students’ Proportional Reasoning. A series of professional development workshops was designed to enhance the teachers’ understanding of Proportional Reasoning and to extend their repertoire of teaching strategies to promote their students’ Proportional Reasoning skills. The workshop design was informed by research literature on Proportional Reasoning teaching and learning as well as the results of a diagnostic instrument administered to over 2500 middle years students prior to the professional development. Between workshops, the teachers implemented a variety of targeted teaching activities. This paper reports on pre- and post- instrument student data collected at the beginning and end of the first year of the project (i.e., after completion of half of the workshops). The findings suggest that targeted professional development and explicit teaching can make a difference to students’ Proportional Reasoning.
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Development and application of a two-tier diagnostic instrument to assess middle-years students’ Proportional Reasoning
Mathematics Education Research Journal, 2013Co-Authors: Annette Hilton, Geoff Hilton, Shelley Dole, Merrilyn GoosAbstract:Proportional Reasoning involves the use of ratios in the comparison of quantities. While it is a key aspect of numeracy, particularly in the middle years of schooling, students do not always develop Proportional Reasoning naturally. Research suggests that many students do not apply Proportional methods appropriately and that they often erroneously apply both multiplicative and additive thinking. Further, students cannot always distinguish non-Proportional situations from those that are Proportional. Understanding the situations in which students mistakenly use additive or multiplicative thinking and the nature of the Proportional Reasoning that students apply to different problem types is important for teachers seeking to support their students to develop Proportional Reasoning in the classroom. This paper describes the development and use of a two-tier diagnostic instrument to identify situations in which students could and could not apply Proportional Reasoning and the types of Reasoning they used. It presents data from an Australian study involving over 2000 middle-years students (Years 5 to 9) as a means of illustrating the use of the instrument for diagnosing students’ Reasoning in different situations. The findings showed that the instrument was useful for identifying problem types in which students of different ages were able to apply correct Reasoning. It also allowed identification of the types of incorrect Reasoning used by students. The paper also describes useful applications of the instrument, including its use as a diagnostic instrument by classroom teachers and its use in the design of classroom activities included in teacher professional learning workshops.
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kitchen gardens contexts for developing Proportional Reasoning
Australian primary mathematics classroom, 2013Co-Authors: Annette Hilton, Geoff Hilton, Shelley Dole, Merrilyn Goos, Mia ObrienAbstract:It is great to see how the sharing of ideas sparks new ideas. In 2011 Lyon and Bragg wrote an APMC article on the mathematics of kitchen gardens. In this article the authors show how the kitchen garden may be used as a starting point for Proportional Reasoning. The authors highlight different types of proportion problems and how the authentic context of a kitchen garden may be used to spark interest in Reasoning.
Annette Hilton - One of the best experts on this subject based on the ideXlab platform.
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USING DIGITAL PHOTOGRAPHY TO SUPPORT TEACHING AND LEARNING OF Proportional Reasoning CONCEPTS
2020Co-Authors: Geoff Hilton, Shelley Dole, Annette Hilton, Merrilyn GoosAbstract:Abstract Proportional Reasoning entails multiplicative relationships in situations of comparison. Successful Proportional reasoners can recognise a Proportional situation as distinct from a non-Proportional one; they have a sense of co-variation and they have a range of strategies for solving Proportional problems. As educators we realise that teaching Proportional Reasoning cannot solely rely on asking students to complete symbolic and mechanical methods, such as the cross-product algorithm. To develop Proportional Reasoning, students must have regular opportunities to experience the underlying concepts. These concepts include foundational aspects of Proportional Reasoning, such as fractional thinking, multiplicative thinking (as opposed to additive), relative thinking (as opposed to absolute), as well as concepts of rate and scale. As part of a large multi-state project in Australia to enhance middle years students' numeracy through a focus on Proportional Reasoning, 120 teachers participated in a series of professional learning workshops. These teachers generally reported feeling confident teaching the algorithmic aspects of Proportional Reasoning but a number of them specifically asked for assistance with the conceptual development of their students' Proportional Reasoning. In response, the researchers developed a series of activities with the teachers, where digital cameras were used in the school environs to capture images that represented examples of Proportional Reasoning concepts. In small groups, the teachers moved around the school taking their photos and then reported back to the workshop, showing their images through a data projector while they explained the concepts they felt their images captured. This presentation articulates the ways that the digital cameras were used by the teachers to capture and report on the Proportional Reasoning concepts, and their thoughts and aspirations as to how they would use the cameras to develop the Proportional Reasoning of their students
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Primary school teachers implementing structured mathematics interventions to promote their mathematics knowledge for teaching Proportional Reasoning
Journal of Mathematics Teacher Education, 2019Co-Authors: Annette Hilton, Geoff HiltonAbstract:Proportional Reasoning is the ability to use multiplicative thinking and make multiple comparisons. It is known to be challenging for many students and at the same time, many teachers require support to develop sufficient subject matter knowledge and pedagogical content knowledge to teach the diverse concepts that underpin Proportional Reasoning. The data reported in this paper are drawn from the first year of a broader study aiming to promote the teaching and learning of elements of Proportional Reasoning across the curriculum by engaging primary school teachers in ongoing professional development that includes the implementation of a series of mathematics interventions, each of which included a research component. This paper focuses on the impact of implementing the interventions on the teachers’ mathematical knowledge for teaching. Three structured interventions were implemented by eight teachers (Years 3, 4, 5) during each of three school terms. Data collected showed that engaging in this scaffolded type of practitioner research, the structured nature of the interventions, and reflection on the outcomes of each intervention promoted teachers’ subject matter knowledge and pedagogical content knowledge.
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Promoting middle school students’ Proportional Reasoning skills through an ongoing professional development programme for teachers
Educational Studies in Mathematics, 2016Co-Authors: Annette Hilton, Geoff Hilton, Shelley Dole, Merrilyn GoosAbstract:Proportional Reasoning, the ability to use ratios in situations involving comparison of quantities, is essential for mathematical competence, especially in the middle school years, and is an important determinant of success beyond school. Research shows students find Proportional Reasoning and its foundational concepts difficult. Proportional Reasoning does not always develop naturally, however some research suggests that with targeted teaching, its development can be promoted. This paper reports on a large Australian study involving over 130 teachers and their students. A major goal of the study was to investigate the efficacy of ongoing teacher professional development for promoting middle years students’ Proportional Reasoning. A series of professional development workshops was designed to enhance the teachers’ understanding of Proportional Reasoning and to extend their repertoire of teaching strategies to promote their students’ Proportional Reasoning skills. The workshop design was informed by research literature on Proportional Reasoning teaching and learning as well as the results of a diagnostic instrument administered to over 2500 middle years students prior to the professional development. Between workshops, the teachers implemented a variety of targeted teaching activities. This paper reports on pre- and post- instrument student data collected at the beginning and end of the first year of the project (i.e., after completion of half of the workshops). The findings suggest that targeted professional development and explicit teaching can make a difference to students’ Proportional Reasoning.
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Development and application of a two-tier diagnostic instrument to assess middle-years students’ Proportional Reasoning
Mathematics Education Research Journal, 2013Co-Authors: Annette Hilton, Geoff Hilton, Shelley Dole, Merrilyn GoosAbstract:Proportional Reasoning involves the use of ratios in the comparison of quantities. While it is a key aspect of numeracy, particularly in the middle years of schooling, students do not always develop Proportional Reasoning naturally. Research suggests that many students do not apply Proportional methods appropriately and that they often erroneously apply both multiplicative and additive thinking. Further, students cannot always distinguish non-Proportional situations from those that are Proportional. Understanding the situations in which students mistakenly use additive or multiplicative thinking and the nature of the Proportional Reasoning that students apply to different problem types is important for teachers seeking to support their students to develop Proportional Reasoning in the classroom. This paper describes the development and use of a two-tier diagnostic instrument to identify situations in which students could and could not apply Proportional Reasoning and the types of Reasoning they used. It presents data from an Australian study involving over 2000 middle-years students (Years 5 to 9) as a means of illustrating the use of the instrument for diagnosing students’ Reasoning in different situations. The findings showed that the instrument was useful for identifying problem types in which students of different ages were able to apply correct Reasoning. It also allowed identification of the types of incorrect Reasoning used by students. The paper also describes useful applications of the instrument, including its use as a diagnostic instrument by classroom teachers and its use in the design of classroom activities included in teacher professional learning workshops.
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kitchen gardens contexts for developing Proportional Reasoning
Australian primary mathematics classroom, 2013Co-Authors: Annette Hilton, Geoff Hilton, Shelley Dole, Merrilyn Goos, Mia ObrienAbstract:It is great to see how the sharing of ideas sparks new ideas. In 2011 Lyon and Bragg wrote an APMC article on the mathematics of kitchen gardens. In this article the authors show how the kitchen garden may be used as a starting point for Proportional Reasoning. The authors highlight different types of proportion problems and how the authentic context of a kitchen garden may be used to spark interest in Reasoning.
Merrilyn Goos - One of the best experts on this subject based on the ideXlab platform.
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USING DIGITAL PHOTOGRAPHY TO SUPPORT TEACHING AND LEARNING OF Proportional Reasoning CONCEPTS
2020Co-Authors: Geoff Hilton, Shelley Dole, Annette Hilton, Merrilyn GoosAbstract:Abstract Proportional Reasoning entails multiplicative relationships in situations of comparison. Successful Proportional reasoners can recognise a Proportional situation as distinct from a non-Proportional one; they have a sense of co-variation and they have a range of strategies for solving Proportional problems. As educators we realise that teaching Proportional Reasoning cannot solely rely on asking students to complete symbolic and mechanical methods, such as the cross-product algorithm. To develop Proportional Reasoning, students must have regular opportunities to experience the underlying concepts. These concepts include foundational aspects of Proportional Reasoning, such as fractional thinking, multiplicative thinking (as opposed to additive), relative thinking (as opposed to absolute), as well as concepts of rate and scale. As part of a large multi-state project in Australia to enhance middle years students' numeracy through a focus on Proportional Reasoning, 120 teachers participated in a series of professional learning workshops. These teachers generally reported feeling confident teaching the algorithmic aspects of Proportional Reasoning but a number of them specifically asked for assistance with the conceptual development of their students' Proportional Reasoning. In response, the researchers developed a series of activities with the teachers, where digital cameras were used in the school environs to capture images that represented examples of Proportional Reasoning concepts. In small groups, the teachers moved around the school taking their photos and then reported back to the workshop, showing their images through a data projector while they explained the concepts they felt their images captured. This presentation articulates the ways that the digital cameras were used by the teachers to capture and report on the Proportional Reasoning concepts, and their thoughts and aspirations as to how they would use the cameras to develop the Proportional Reasoning of their students
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Promoting middle school students’ Proportional Reasoning skills through an ongoing professional development programme for teachers
Educational Studies in Mathematics, 2016Co-Authors: Annette Hilton, Geoff Hilton, Shelley Dole, Merrilyn GoosAbstract:Proportional Reasoning, the ability to use ratios in situations involving comparison of quantities, is essential for mathematical competence, especially in the middle school years, and is an important determinant of success beyond school. Research shows students find Proportional Reasoning and its foundational concepts difficult. Proportional Reasoning does not always develop naturally, however some research suggests that with targeted teaching, its development can be promoted. This paper reports on a large Australian study involving over 130 teachers and their students. A major goal of the study was to investigate the efficacy of ongoing teacher professional development for promoting middle years students’ Proportional Reasoning. A series of professional development workshops was designed to enhance the teachers’ understanding of Proportional Reasoning and to extend their repertoire of teaching strategies to promote their students’ Proportional Reasoning skills. The workshop design was informed by research literature on Proportional Reasoning teaching and learning as well as the results of a diagnostic instrument administered to over 2500 middle years students prior to the professional development. Between workshops, the teachers implemented a variety of targeted teaching activities. This paper reports on pre- and post- instrument student data collected at the beginning and end of the first year of the project (i.e., after completion of half of the workshops). The findings suggest that targeted professional development and explicit teaching can make a difference to students’ Proportional Reasoning.
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Development and application of a two-tier diagnostic instrument to assess middle-years students’ Proportional Reasoning
Mathematics Education Research Journal, 2013Co-Authors: Annette Hilton, Geoff Hilton, Shelley Dole, Merrilyn GoosAbstract:Proportional Reasoning involves the use of ratios in the comparison of quantities. While it is a key aspect of numeracy, particularly in the middle years of schooling, students do not always develop Proportional Reasoning naturally. Research suggests that many students do not apply Proportional methods appropriately and that they often erroneously apply both multiplicative and additive thinking. Further, students cannot always distinguish non-Proportional situations from those that are Proportional. Understanding the situations in which students mistakenly use additive or multiplicative thinking and the nature of the Proportional Reasoning that students apply to different problem types is important for teachers seeking to support their students to develop Proportional Reasoning in the classroom. This paper describes the development and use of a two-tier diagnostic instrument to identify situations in which students could and could not apply Proportional Reasoning and the types of Reasoning they used. It presents data from an Australian study involving over 2000 middle-years students (Years 5 to 9) as a means of illustrating the use of the instrument for diagnosing students’ Reasoning in different situations. The findings showed that the instrument was useful for identifying problem types in which students of different ages were able to apply correct Reasoning. It also allowed identification of the types of incorrect Reasoning used by students. The paper also describes useful applications of the instrument, including its use as a diagnostic instrument by classroom teachers and its use in the design of classroom activities included in teacher professional learning workshops.
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kitchen gardens contexts for developing Proportional Reasoning
Australian primary mathematics classroom, 2013Co-Authors: Annette Hilton, Geoff Hilton, Shelley Dole, Merrilyn Goos, Mia ObrienAbstract:It is great to see how the sharing of ideas sparks new ideas. In 2011 Lyon and Bragg wrote an APMC article on the mathematics of kitchen gardens. In this article the authors show how the kitchen garden may be used as a starting point for Proportional Reasoning. The authors highlight different types of proportion problems and how the authentic context of a kitchen garden may be used to spark interest in Reasoning.
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evaluating middle years students Proportional Reasoning
Mathematics Education Research Group of Australasia, 2012Co-Authors: Annettte Hilton, Geoff Hilton, Shelley Dole, Merrilyn Goos, Mia ObrienAbstract:Proportional Reasoning is a key aspect of numeracy that is not always developed naturally by students. Understanding the types of Proportional Reasoning that students apply to different problem types is a useful first step to identifying ways to support teachers and students to develop Proportional Reasoning in the classroom. This paper describes the development of a diagnostic instrument that aims to identify situations in which students can apply Proportional Reasoning and the types of Reasoning they use.
Chandra Hawley Orrill - One of the best experts on this subject based on the ideXlab platform.
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Framing a robust understanding of Proportional Reasoning for teachers
Journal of Mathematics Teacher Education, 2021Co-Authors: Travis Weiland, Chandra Hawley Orrill, Gili Gal Nagar, Rachael Eriksen Brown, James BurkeAbstract:Proportional Reasoning is foundational in school mathematics. Despite the importance of Proportional Reasoning, little has been written about the knowledge needed for teachers to teach Proportional Reasoning relative to its importance. In this paper, we present an initial definition for a robust understanding of Proportional Reasoning for teaching based on synthesizing past scholarship in conjunction with an empirical study of the knowledge resources practicing teachers use to make sense of Proportional Reasoning tasks. As a result of this effort, we present here an initial framing of operationalized knowledge resources based upon our definition for a robust understanding that could be used as an analytic tool. We also describe how such a framework of knowledge resources is useful in the context of teacher education, and we provide an example of how the framework was used to analyze the knowledge resources a teacher employed to make sense of a Proportional Reasoning task. We end by discussing possible implications our framework has for designing teacher education experiences and further research that is needed.
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Mathematics Teachers’ Use of Knowledge Resources When Identifying Proportional Reasoning Situations
International Journal of Science and Mathematics Education, 2019Co-Authors: Rachael Eriksen Brown, Travis Weiland, Chandra Hawley OrrillAbstract:In this qualitative study, we investigated teachers’ use of Proportional knowledge resources while being asked to appropriately identify if a given situation was Proportional or not using clinical interview data from a large grant funded project. We found that knowledge resources related to the mathematical structure of the situation were most useful in correctly identifying the situation. Interestingly, teachers were often able to identify a mathematical expression for the situations; however, these rules did not support the correct identification of the situation as Proportional or not. We discuss suggested knowledge resources for the creation of a coordination class for identifying situations that are Proportional from those that are not as well as implications for teacher education and professional development around Proportional Reasoning.
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mathematics teachers ability to identify situations appropriate for Proportional Reasoning
Research in Mathematics Education, 2019Co-Authors: Travis Weiland, Chandra Hawley Orrill, Rachael Eriksen Brown, Gili Gal NagarAbstract:ABSTRACTIn this study, we investigated teachers’ abilities correctly to identify situations that are appropriate for Proportional Reasoning and factors that might influence their ability using data...
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middle school teachers use of mathematics to make sense of student solutions to Proportional Reasoning problems
International Journal of Science and Mathematics Education, 2018Co-Authors: Erik Jacobson, Joanne Lobato, Chandra Hawley OrrillAbstract:Mathematics teacher education aims to improve teachers’ use of mathematical knowledge to support teaching and learning, an aspect of pedagogical content knowledge (PCK). In this study, we interviewed teachers to understand how they used mathematics to make sense of student solutions to Proportional Reasoning problems. The larger purpose was to find accurate ways of categorizing teachers’ ability to do this vital aspect of teaching and thereby to inform assessment, teacher education, and professional development. We conjectured that teachers’ PCK for Proportional Reasoning could be reliably described in terms of attention to quantitative meanings in story problem contexts and in terms of understanding naive forms of Proportional Reasoning. Instead, our findings reveal that individual teachers used a variety of means to make sense of (1) cognitively similar student solutions to different tasks and (2) mathematically related steps of a student solution within a single task. These findings illustrate the complexity of PCK for the topic of Proportional Reasoning and suggest the limits of what can be inferred about teacher knowledge from teachers’ evaluations of student solutions. We discuss implications for teacher education and assessment.
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middle school teachers knowledge of Proportional Reasoning for teaching
2011Co-Authors: Joanne Lobato, Chandra Hawley OrrillAbstract:Proportional Reasoning comprises a network of understandings and relationships, and it represents a milestone in students' cognitive development (Lamon, 2007; Vergnaud, 1983). Furthermore, Proportional Reasoning is foundational to students’ later development of concepts related to functions, graphing, algebraic equations, and measurement (Karplus, Pulos, & Stage, 1983; Lobato & Ellis, 2010; Thompson & Saldanha, 2003). Because Proportional Reasoning is complex, helping students develop the associated big ideas and essential understandings is not easy. This pedagogical task involves deepening one’s own understanding as a teacher and being sensitive to the types of Reasoning that are most accessible as entry points for students while pushing them to develop more sophisticated forms of Reasoning.
