The Mathematics and Science Nexus and the Transfer of Mathematical Learning at University

Abstract

Mathematics and science education are critical for further development of economies and the sustainability of modern societies. Mathematics is widely recognised as an important foundation of science. However, internationally academics in STEM disciplines face challenges, such as declining student participation rates, poor mathematical preparedness and low academic performance. Despite the importance of the mathematics and science nexus and challenges therein, there is a paucity of literature examining this relationship, especially in higher education. This research investigates the relationship between mathematics and science within the university context. In particular, the study explores the relationship between students’ learning in first year undergraduate mathematics services courses and later learning in the STEM disciplines of biology, biochemistry, engineering and physics. Several methods are used to explore this: 1) secondary data analysis examining association between attainment in mathematics and science; 2) the creation of an index for measurement of transfer of learning using university examinations; 3) the modeling of transfer’s relationship with other factors in learning; 4) think-aloud accounts of the processes in transfer tasks; and finally 5) interviews with both students and academics exploring the nexus between mathematics and science and issues relating to the transfer of learning between them. Initial analyses showed how high school preparation in mathematics, or a lack of it, was strongly related to university mathematics and science failure rates; and multiple regression analyses confirmed strong relationships between university mathematics and science attainment (R2 from .43 to .87; n from 57 to 308). For example, 84% of the variance in second semester biology scores can be explained by first semester biology and mathematics scores. This relationship may be explained, in part, by the shared general abilities assessed in these disciplines and also by transfer of learning. A Transfer Index (Roberts, Sharma, Britton & New, 2007) was calculated from content-matched questions in university mathematics and science exams. This identified transfer of mathematics learning to physics and engineering (n from 27 to 382), but the biology and biochemistry exams provided no opportunity to demonstrate transfer. Path analyses demonstrated the complex relationships between various factors and the Transfer Index, including its strong association with overall mathematics performance and also general educational ability – as reflected in university entrance scores. Students’ thinking processes in transfer were then examined using think-aloud accounts (n=10) of how they solved physics questions requiring mathematical knowledge and skills covered in their mathematics service course curriculum. The degree of transfer observed varied considerably and obstacles to transfer were identified. Students used thinking processes (interpretation, integration, planning, and execution) recursively, in tandem with a range of metacognitive strategies. Follow up interviews with students and academics showed disparities in their respective views of transfer and also their perceptions of the mathematics and science nexus. While constrained by the focus on a single institution in Australia, this study makes a contribution to our understanding of transfer of mathematical learning and demonstrates an innovative, naturalistic mixed methodology approach. Future research is needed to further develop more naturalistic accounts of transfer, examine long-term effects and explore the diverse contexts in which transfer of learning may occur. Important implications for teaching, learning and assessment are discussed.