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Learning essential knowledge by design: promoting and connecting mathematics and science in the middle years of schooling

Shelley Dole
Tony Wright
Doug M. Clarke

Dr Shelley Dole is a Senior Lecturer and Dr Tony Wright is a Lecturer at the University of Queensland. Doug Clarke is Professor of Mathematics Education at Australian Catholic University, Melbourne.

Quality mathematics and science education is vital for all students, providing essential knowledge for future citizenship. However, it is well documented that many students in the middle years encounter difficulties with the study of these two subjects, a situation which has led to repeated calls for new approaches to curriculum, pedagogy and assessment (eg, Kilpatrick, Swafford & Findell, 2001; Committee on Science, Engineering and Public Policy, 2005). It is in the middle years of schooling that essential ideas must be made explicit in the mathematics and science curriculum to either crystallise learning or lay the foundations for advanced secondary study. All students should exit compulsory schooling with rich, connected conceptualisations in these domains.

Mathematics and science educators from universities in Queensland and Victoria are currently addressing this issue, through a research project with middle years' teachers. The three-year project, involving seven state and private schools in Queensland, is focused on one of the common core themes of mathematics and science: proportional reasoning.

Proportional reasoning

According to the American Association for the Advancement of Science (AAAS), two components underpin proportional reasoning: (1) ratios and proportionality (part/whole knowledge, relationships, computation) and (2) describing change (knowledge of related changes, kinds of change and invariance). Proportional reasoning is therefore fundamental to both mathematics and science (Lamon, 1994).  It underpins many topics in the middle years mathematics curriculum, such as scale drawing, surface area/volume ratio, probability, molarity, force and motion, algebra, and fractions. Proportional reasoning is also used to represent change graphically and symbolically, with relevance to science topics such as Atoms and Molecules, Laws of Motion, Systems, and Natural Selection.

Proportional reasoning enables students to understand the relationships in proportional situations and to work meaningfully with them. It is used, for example, to determine the best value out of 200 grams for $3 and 250 grams for $4. Research has continually revealed that many students in the middle years struggle with proportion-related topics (eg, Behr, Harel, Post & Lesh, 1992; Ben-Chaim, Fey, Fitzgerald, Benedetto & Miller, 1998; Lo & Watanabe, 1997). Such underdeveloped proportional reasoning potentially impacts real-world situations, sometimes with disastrous consequences.

Implications for curriculum

Proportional reasoning clearly permeates both the mathematics and science curriculum, yet typically, these two subjects are taught separately in Australian schools, and, in the secondary school context in particular, they are often taken by different teachers. The AAAS has stated that scientific literacy is promoted through linking mathematics, science and technology curriculum. It has argued that curriculum should not comprise isolated bits of information, but a ‘rich fabric of mutually supporting ideas and skills that develops over time’. One of Bell’s (1993) principles of effective mathematics teaching is assisting students to make connections between isolated pieces of knowledge. This principle is equally valid for all curriculum areas and is one of the principles to be applied in this project. (AAAS, 2001 p 3). With a more interconnected view of curriculum, teachers are in a much stronger position to create learning environments that assist students to link knowledge and develop rich conceptual bases of understanding.

Current organisation of the Australian school curriculum around eight key learning areas ensures a broad and balanced curriculum but also can contribute to knowledge compartmentalisation, overlap and redundancy. Partly in response to an overcrowded curriculum, an essential learnings approach has been taken in several Australian states. The criticism of such approaches is the potential lack of rigour and content-specific knowledge, particularly in science and mathematics. The solution to these criticisms lies in the careful design of the integrated curriculum.

The current project

The current project will support the advancement of curriculum reform at the grass-roots level, as well as providing evidence-based research to validate components of proportional reasoning through teaching mathematics and science. Our proposal is to take a ‘conscious, systematic and explicit … structured and goal-oriented’ approach (Kalantzis & Cope, 2004, p 39), involving learning by design, working with teachers to plan learning experiences that meet the challenge of engaging learners in authentic ways. This approach will ensure that the rigour and content levels of an integrated mathematics/science curriculum can be maintained in a student-focused framework for the middle years.

The researchers and teachers will develop, implement and document innovative, relevant and connected learning in mathematics and science. The project aims to answer the following questions:

  1. What is the impact of researcher- and teacher-developed materials on students’ knowledge of proportion and related topics and teachers’ knowledge for teaching?
  2. What forms of assessment are most revealing of students’ proportional reasoning skills and their understandings of related key ideas and the connections between them?
  3. In what ways does the information collected about individuals and groups of students inform curriculum, lesson planning and classroom interactions?
  4. What implications for middle years curriculum reform emerge from this study in terms of curriculum development, collaboration of mathematics and science teachers, and the nature of essential knowledge in mathematics and science?

The project, funded through an ARC Linkage grant, will involve Redeemer Lutheran College, Rochedale, Bundamba State Secondary College, Bremer State High School, All Hallows School, Brisbane, Faith Lutheran College, Redlands, St Peter’s Catholic Primary School, Rochedale and Kenmore State High School. The research team includes the current authors.

In summary, the project brings teachers and educators together to explore the synergies between mathematics and science curriculum through proportional reasoning, to create and implement innovative and engaging learning experiences and assessment strategies across mathematics and science topics, and to reflect upon their classroom practice and the learning outcomes of their students. This exciting research project will contribute to the development of a curriculum framework that connects key concepts between mathematics and science.



American Association for the Advancement of Science (AAAS) 2001, Atlas of Science Literacy: Project 2061, AAAS.

Behr, M, Harel, G, Post, T & Lesh, R, 1992, 'Rational number, ratio and proportion' in D Grouws (Ed), Handbook on Research of Teaching and Learning (pp 296–333), McMillan, New York.

Bell, A 1993, 'Principles for the design of teaching', Educational Studies in Mathematics, vol 24, no 1, 5–34.

Ben-Chaim, D, Fey, J, Fitzgerald, W, Benedetto, C & Miller, J 1998, 'Proportional reasoning among 7th grade students with different curricular experiences', Educational Studies in Mathematics, 36, 247–273.

Committee on Science, Engineering and Public Policy 2005, 10,000 teachers, 10 million minds and K–12 science and mathematics education, rising above the gathering storm: Energizing and employing America for a brighter economic future, The National Academy Press, Washington, DC.

Kalantzis, M. & Cope, B 2004, Designs for learning. eLearning, 1 (1), pp 38–93.

Kilpatrick, J, Swafford, J & Findell, B 2001, Adding It Up: Helping children learn mathematics, National Academy Press, Washington, DC.

Lamon, S 1994, 'Ratio and proportion: Cognitive foundations in unitizing and norming' in H Guershon & J Confrey (Eds), The Development of Multiplicative Reasoning in the Learning of Mathematics (pp 89–120), State University of New York Press, Albany, New York.

Lo, J-J & Watanabe, T 1997, 'Developing ratio and proportion schemes: A story of a fifth grader', Journal for Research in Mathematics Education, 28 (2), 216–236.

Key Learning Areas


Subject Headings

Educational evaluation
Curriculum planning
Science teaching
Middle schooling
Mathematics teaching