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Identifying cognitive processes important to mathematics learning but often overlooked Six competencies that are fundamental to the development of ‘mathematical literacy’, or a person’s ability to apply their mathematical knowledge to practical situations, were presented at the ACER Research Conference in Melbourne on 16 August. The competencies are communication, mathematising, representation, reasoning, devising strategies, and using symbolic, formal and technical language and operations. “These competencies can be thought of as a set of individual characteristics or qualities possessed to a greater or lesser extent by individuals,” said Ross Turner, Principal Research Fellow at ACER. “The more you possess these competencies, the better able you will be to make effective use of your mathematical knowledge to solve contextualised problems.” Using examples from the 2003 OECD Programme for International Student Assessment (PISA) Mr Turner demonstrated that different mathematical problems call for the activation of the six competencies, to a differing extent. Mr Turner said that currently not enough time and effort is devoted to fostering the development of these fundamental competencies and proposes that the competencies should be directly targeted and advanced in our mathematics classes. “Current curriculum structures do not provide sufficient incentive for teachers to focus on these competencies as crucial outcomes,” Mr Turner said. “Students need to be given opportunities to articulate their thinking about mathematics tasks and about mathematical concepts.” He argued that developing mathematical literacy at school is important because students will need to apply their mathematical knowledge to handle real world challenges such as those encountered in the workplace, during leisure and in life as a citizen. “The mathematical capabilities students demonstrate by the time they are nearing school leaving age foreshadow the approach those individuals will take to using mathematics later in life.” He said that the problem is the opportunities to use mathematics that we come across in life are not packaged in the same way they were in school. “At school you knew when you were going to mathematics class and you knew the mathematics teacher would show you new mathematical ideas or skills, give you some examples and then point you to a set of exercises more or less like those used to demonstrate the idea or skill you were learning.” “In the real world, that’s not normally how opportunities to use mathematics come to us. We have to make the judgments and decisions about what mathematical knowledge might be relevant, and how to apply that knowledge.” Ross Turner manages ACER’s International PISA project, coordinating the ACER team and international consortium partners to meet the requirements of ACER’s contract with the OECD. He has filled this role as a Principal Research Fellow since 2007, and before that provided general leadership and management to the PISA project and to other ACER projects as a Senior Research Fellow since 2000. Ross also provides leadership in the mathematics area, having led PISA mathematics framework and test development and being responsible for PISA mathematics implementation throughout his time at ACER. Ross Turner's presentation, Identifying cognitive processes important to mathematics learning but often overlooked, and presentation slides are available from the ACER research repository. « Back to eNews
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Six competencies that are fundamental to the development of ‘mathematical literacy’, or a person’s ability to apply their mathematical knowledge to practical situations, were presented at the ACER Research Conference in Melbourne on 16 August.

The competencies are communication, mathematising, representation, reasoning, devising strategies, and using symbolic, formal and technical language and operations.

“These competencies can be thought of as a set of individual characteristics or qualities possessed to a greater or lesser extent by individuals,” said Ross Turner, Principal Research Fellow at ACER.

“The more you possess these competencies, the better able you will be to make effective use of your mathematical knowledge to solve contextualised problems.”

Using examples from the 2003 OECD Programme for International Student Assessment (PISA) Mr Turner demonstrated that different mathematical problems call for the activation of the six competencies, to a differing extent.

Mr Turner said that currently not enough time and effort is devoted to fostering the development of these fundamental competencies and proposes that the competencies should be directly targeted and advanced in our mathematics classes.

“Current curriculum structures do not provide sufficient incentive for teachers to focus on these competencies as crucial outcomes,” Mr Turner said.

“Students need to be given opportunities to articulate their thinking about mathematics tasks and about mathematical concepts.”

He argued that developing mathematical literacy at school is important because students will need to apply their mathematical knowledge to handle real world challenges such as those encountered in the workplace, during leisure and in life as a citizen.

“The mathematical capabilities students demonstrate by the time they are nearing school leaving age foreshadow the approach those individuals will take to using mathematics later in life.”

He said that the problem is the opportunities to use mathematics that we come across in life are not packaged in the same way they were in school.

“At school you knew when you were going to mathematics class and you knew the mathematics teacher would show you new mathematical ideas or skills, give you some examples and then point you to a set of exercises more or less like those used to demonstrate the idea or skill you were learning.”

“In the real world, that’s not normally how opportunities to use mathematics come to us. We have to make the judgments and decisions about what mathematical knowledge might be relevant, and how to apply that knowledge.”

Ross Turner manages ACER’s International PISA project, coordinating the ACER team and international consortium partners to meet the requirements of ACER’s contract with the OECD. He has filled this role as a Principal Research Fellow since 2007, and before that provided general leadership and management to the PISA project and to other ACER projects as a Senior Research Fellow since 2000. Ross also provides leadership in the mathematics area, having led PISA mathematics framework and test development and being responsible for PISA mathematics implementation throughout his time at ACER.

Ross Turner's presentation, Identifying cognitive processes important to mathematics learning but often overlooked, and presentation slides are available from the ACER research repository.