Friday - 11.35: session 20 – Mathew Toll & Shi Chunxu is back on, in B48, replacing Sha Xie.

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A conceptual framework for understanding the complexities of mathematical proficiency

As many as ninety percent of the prospective students for tertiary education institutions in South Africa have no more than an intermediate level of mathematical proficiency. This has been identified as a key obstacle to student success and emphasizes the need for specialized support programmes for developing mathematical proficiency.

In this study the Epistemic Plane of the Specialization dimension of Legitimation Code Theory is proposed as a conceptual framework for illuminating the complexities of developing mathematical proficiency and for designing differentiated support in first year mathematics. This framework is orthogonal with the vertical axis, or ontic relations (OR) axis, translated as ‘what mathematical knowledge’ and the horizontal axis, or discursive relations (DR) axis, translated as ‘how one thinks/reasons mathematically’. The resulting four quadrants of this framework represent four strands of mathematical proficiencies.

A Doctrinal insight represents procedural fluency (‘how’ dominating ‘what’) in the sense of the knowledge of mathematical procedures of when and how to use them appropriately, and the skill in performing flexibly, accurately, and efficiently.

A Purist insight represents mathematical understanding in the sense of integrated and functional grasp of mathematical principles and mathematical thinking/reasoning.

A Situational insight represents strategic competence (‘what’ dominating ‘how’) in the sense of the ability to formulate/represent problems mathematically and to solve them using appropriate mathematical computations.

A Knower insight represents an intuitive approach using few mathematical principles and limited mathematical reasoning.

Navigating between these insights corresponds to integrating the four strands of mathematical proficiency and thereby developing a productive disposition towards mathematics, that is, the tendency to perceive mathematics as both useful and worthwhile, to be an effective doer of mathematics, and to believe that steady effort in understanding mathematics pays off.

This conceptual framework is shown to provide a systematic approach to thinking about the range of proficiencies identified by the National Benchmark Test (NBT) for Mathematics. A key observation is that mathematical proficiency presents differently in individual students and this may be understood in terms of gaps in mathematical knowledge and mathematical reasoning skills in five core areas assessed by the NBT: algebraic processing, functions, trigonometric functions, geometric concepts, number sense. This information is being used to guide individualized curriculum integrated differentiated support in first-year mathematics. Success of such support could then be evaluated in terms of how students navigate between the four insights and in terms of improvement in student success in STEM programmes.

As many as ninety percent of the prospective students for tertiary education institutions in South Africa have no more than an intermediate level of mathematical proficiency. This has been identified as a key obstacle to student success and emphasizes the need for specialized support programmes for developing mathematical proficiency.

In this study the Epistemic Plane of the Specialization dimension of Legitimation Code Theory is proposed as a conceptual framework for illuminating the complexities of developing mathematical proficiency and for designing differentiated support in first year mathematics. This framework is orthogonal with the vertical axis, or ontic relations (OR) axis, translated as ‘what mathematical knowledge’ and the horizontal axis, or discursive relations (DR) axis, translated as ‘how one thinks/reasons mathematically’. The resulting four quadrants of this framework represent four strands of mathematical proficiencies.

A Doctrinal insight represents procedural fluency (‘how’ dominating ‘what’) in the sense of the knowledge of mathematical procedures of when and how to use them appropriately, and the skill in performing flexibly, accurately, and efficiently.

A Purist insight represents mathematical understanding in the sense of integrated and functional grasp of mathematical principles and mathematical thinking/reasoning.

A Situational insight represents strategic competence (‘what’ dominating ‘how’) in the sense of the ability to formulate/represent problems mathematically and to solve them using appropriate mathematical computations.

A Knower insight represents an intuitive approach using few mathematical principles and limited mathematical reasoning.

Navigating between these insights corresponds to integrating the four strands of mathematical proficiency and thereby developing a productive disposition towards mathematics, that is, the tendency to perceive mathematics as both useful and worthwhile, to be an effective doer of mathematics, and to believe that steady effort in understanding mathematics pays off.

This conceptual framework is shown to provide a systematic approach to thinking about the range of proficiencies identified by the National Benchmark Test (NBT) for Mathematics. A key observation is that mathematical proficiency presents differently in individual students and this may be understood in terms of gaps in mathematical knowledge and mathematical reasoning skills in five core areas assessed by the NBT: algebraic processing, functions, trigonometric functions, geometric concepts, number sense. This information is being used to guide individualized curriculum integrated differentiated support in first-year mathematics. Success of such support could then be evaluated in terms of how students navigate between the four insights and in terms of improvement in

In this study the Epistemic Plane of the Specialization dimension of Legitimation Code Theory is proposed as a conceptual framework for illuminating the complexities of developing mathematical proficiency and for designing differentiated support in first year mathematics. This framework is orthogonal with the vertical axis, or ontic relations (OR) axis, translated as ‘what mathematical knowledge’ and the horizontal axis, or discursive relations (DR) axis, translated as ‘how one thinks/reasons mathematically’. The resulting four quadrants of this framework represent four strands of mathematical proficiencies.

A Doctrinal insight represents procedural fluency (‘how’ dominating ‘what’) in the sense of the knowledge of mathematical procedures of when and how to use them appropriately, and the skill in performing flexibly, accurately, and efficiently.

A Purist insight represents mathematical understanding in the sense of integrated and functional grasp of mathematical principles and mathematical thinking/reasoning.

A Situational insight represents strategic competence (‘what’ dominating ‘how’) in the sense of the ability to formulate/represent problems mathematically and to solve them using appropriate mathematical computations.

A Knower insight represents an intuitive approach using few mathematical principles and limited mathematical reasoning.

Navigating between these insights corresponds to integrating the four strands of mathematical proficiency and thereby developing a productive disposition towards mathematics, that is, the tendency to perceive mathematics as both useful and worthwhile, to be an effective doer of mathematics, and to believe that steady effort in understanding mathematics pays off.

This conceptual framework is shown to provide a systematic approach to thinking about the range of proficiencies identified by the National Benchmark Test (NBT) for Mathematics. A key observation is that mathematical proficiency presents differently in individual students and this may be understood in terms of gaps in mathematical knowledge and mathematical reasoning skills in five core areas assessed by the NBT: algebraic processing, functions, trigonometric functions, geometric concepts, number sense. This information is being used to guide individualized curriculum integrated differentiated support in first-year mathematics. Success of such support could then be evaluated in terms of how students navigate between the four insights and in terms of improvement in student success in STEM programmes.

As many as ninety percent of the prospective students for tertiary education institutions in South Africa have no more than an intermediate level of mathematical proficiency. This has been identified as a key obstacle to student success and emphasizes the need for specialized support programmes for developing mathematical proficiency.

In this study the Epistemic Plane of the Specialization dimension of Legitimation Code Theory is proposed as a conceptual framework for illuminating the complexities of developing mathematical proficiency and for designing differentiated support in first year mathematics. This framework is orthogonal with the vertical axis, or ontic relations (OR) axis, translated as ‘what mathematical knowledge’ and the horizontal axis, or discursive relations (DR) axis, translated as ‘how one thinks/reasons mathematically’. The resulting four quadrants of this framework represent four strands of mathematical proficiencies.

A Doctrinal insight represents procedural fluency (‘how’ dominating ‘what’) in the sense of the knowledge of mathematical procedures of when and how to use them appropriately, and the skill in performing flexibly, accurately, and efficiently.

A Purist insight represents mathematical understanding in the sense of integrated and functional grasp of mathematical principles and mathematical thinking/reasoning.

A Situational insight represents strategic competence (‘what’ dominating ‘how’) in the sense of the ability to formulate/represent problems mathematically and to solve them using appropriate mathematical computations.

A Knower insight represents an intuitive approach using few mathematical principles and limited mathematical reasoning.

Navigating between these insights corresponds to integrating the four strands of mathematical proficiency and thereby developing a productive disposition towards mathematics, that is, the tendency to perceive mathematics as both useful and worthwhile, to be an effective doer of mathematics, and to believe that steady effort in understanding mathematics pays off.

This conceptual framework is shown to provide a systematic approach to thinking about the range of proficiencies identified by the National Benchmark Test (NBT) for Mathematics. A key observation is that mathematical proficiency presents differently in individual students and this may be understood in terms of gaps in mathematical knowledge and mathematical reasoning skills in five core areas assessed by the NBT: algebraic processing, functions, trigonometric functions, geometric concepts, number sense. This information is being used to guide individualized curriculum integrated differentiated support in first-year mathematics. Success of such support could then be evaluated in terms of how students navigate between the four insights and in terms of improvement in

Tuesday July 2, 2019 11:00am - 11:40am

Room B46

Room B46