A series of three new books from ACER helps teachers to develop a problem-based approach to learning mathematics as a powerful alternative to drill-and-practice or skills-based learning, as Cath Pearn explains.
Among the many reforms to the Australian Curriculum has been a sharpening of the focus for mathematics on a problem-based approach to learning. According to the Rationale for the Australian Curriculum: Mathematics, the current mathematics curriculum focuses on ‘developing increasingly sophisticated and refined mathematical understanding, fluency, reasoning, and problem-solving skills. These proficiencies enable students to respond to familiar and unfamiliar situations by employing mathematical strategies to make informed decisions and solve problems efficiently.’
While few would debate the development of these proficiencies, the question is what constitutes a problem-based approach to mathematics learning. Research about what is or what is not problem solving has been a focus for decades. Richard Lesh and Judith Zawojewski in their 2007 work ‘Problem solving and modeling’ suggested that a task, or goal-directed activity ‘becomes a problem (or problematic) when the “problem solver” (which may be a collaborating group of specialists) needs to develop a more productive way of thinking about the given situation.’
Likewise, Frank Lester and Paul Kehle in ‘From problem solving to modeling’ suggest that successful problem solving involves ‘coordinating previous experiences, knowledge, familiar representations and patterns of inference, and intuition in an effort to generate new representations and related patterns of inference that resolve some tension or ambiguity…that prompted the original problem-solving activity.’
These definitions of problem solving approaches to mathematics have informed the development of the Creative Activities in Mathematics series, which explores ways to use a wealth of investigations and open-ended active learning activities in classrooms to engage students with mathematics and develop their problem-solving, collaboration and mathematical skills.
Activities presented in the series are underpinned by a survey of the pedagogical and theoretical basis of mathematical problem solving and inquiry in general. The series addresses important principles identified by Frank Lester, following an extensive review of the research literature about problem solving. These include that:
- students must engage with problem-solving tasks regularly for an extended period of time
- students must have the opportunity to solve a variety of types of problems, and
- students' problem-solving abilities are best developed when problems are provided in the context of learning important mathematical concepts.
The Creative Activities in Mathematics series offer a variety of real-life activities so that students can learn how to recognise and solve a variety of different problems in different mathematical contexts. ■
To find more about the Creative Activities in Mathematics series, visit www.acer.edu.au/cam
To find more about occasional professional learning to support teachers in using the Creative Activities in Mathematics series in their classrooms, visit www.acer.edu.au/professional-learning