Inspiring mathematics and science in teacher education: project update

BACKGROUND Improving the quality of mathematics and science teaching and learning in schools is an issue high on the agendas of governments, universities, and the teaching profession itself. Demand for well-qualified teachers is an area of pressure at a time when teacher education in Australia is coming under increasing scrutiny due to the emergence of a national education policy environment. Inspiring Mathematics and Science in Teacher Education (IMSITE) is an Office of Learning and Teaching project funded under the three year Enhancing the Training of Mathematics and Science Teachers Programme. The project brings together a team of leading mathematicians, scientists, and educators from six universities representing diverse institutional, geographical, and socioeconomic contexts: The University of Queensland (lead), James Cook University, The University of Sydney, The University of Newcastle, University of Wollongong and The University of Tasmania. AIMS The aim of the project is to foster enduring collaborations between university-based education, mathematics, and science academics in order to prepare teachers who have a contemporary and dynamic view of the STEM disciplines. To this end, the project seeks to institutionalize new ways of integrating the content and pedagogical expertise of STEM academics and mathematics and science educators to enrich three key stages in the preparation of teachers: recruitment into teaching careers, participation in the pre-service program, and continuing professional learning following graduation. This project is designed to ensure deliberate and systematic engagement with universities beyond the lead and partner institutions, it will generate outcomes useful to all Australian institutions that offer pre-service teacher education programs. As well as producing resources that other universities can adapt to their own contexts, it seeks to identify models and principles for integrating content and pedagogy and for fostering collaboration that could be taken up by other disciplines involved in the pre-service preparation of teachers. DESCRIPTION The six participating universities are collaborating to develop, test, and evaluate the following approaches: (a) recruitment and retention strategies that promote teaching careers to undergraduate mathematics and science students; (b) innovative curriculum arrangements that combine authentic content and progressive pedagogy to construct powerful professional knowledge for teaching; (c) approaches by which universities can build long term relationships with teacher education graduates, enabling them to continually renew their professional and pedagogical knowledge of mathematics and science. Various workshops and roundtables designed to engage participants as critics, interpreters, and potential adopters of the products and processes of our project have been held in Australia and overseas. This presentation will share ideas raised at these workshops and summarize preliminary outcomes and activities at the participating universities. Additional feedback is welcomed

Distinct targeting of multiple mathematical proficiencies in first-year service teaching

Mathematics students need to develop several distinct proficiencies simultaneously. These include procedural fluency, strategic competence, adaptive reasoning, conceptual understanding and a productive disposition towards the subject. These distinctions can be made explicit to students and they are given differentiated learning outcomes, activities and assessments. Procedural fluency requires repetition and immediate and personalised feedback; this is provided through online formative assessment tasks. Valuable tutorial time can then be devoted to strategic competence and adaptive reasoning with extended problems drawn from different domains. Conceptual understanding is aided by drawing analogies between concrete examples from different disciplines and subsequently abstracting key concepts. A productive disposition is inculcated by embedding all activities in an authentic context and using contemporary and thought provoking applications

Using journal articles to build and assess communication skills in undergraduate mathematics

Communication is one of the threshold learning outcomes for undergraduate mathematics; in particular, the “appropriate interpretation of information communicated in mathematical and statistical form” and the “appropriate presentation of information, reasoning and conclusions in a variety of modes, to diverse audiences (expert and non-expert).” However, apart from honours or talented student projects or specific units on the logical structure of proofs, most undergraduate mathematics students do not get to think about or practice their communication skills. Before students attempt their own communication they review some mathematics written by more experienced peers. Journal articles written by other undergraduates were chosen as an authentic source to design an activity that requires students to analyse an article and connect it both to their own existing conceptual framework and the content of the unit they are currently studying. About 700 students in a first year life-science service unit on mathematical modelling were asked to choose a topic they felt was interesting or relevant to them from a list of about 20 undergraduate journal articles. They were required to identify how the methods used matched the topics in the unit they were studying and to choose one result, graph or table from the article and explain it in their own words. This assignment was submitted close to the end of the semester. The majority of students engaged appropriately with the task, though a small proportion copied content from the article without showing any understanding. About 120 students in a third year normal level mathematical modelling unit were given a journal article to read at the start of the semester. They were asked to identify all the concepts and techniques that were familiar to them but were also asked to identify what was unfamiliar and what they expected to become accessible as they completed the unit. Two subsequent assignments in the unit revisited the same journal article as more of its content and concepts could be grasped. A consequence was that students developed a global image of this unit and so asked me more in-depth and interesting questions during semester. Feedback from the Mathematics Learning Centre revealed that even some struggling first year students really enjoyed the activity. Last year, tutors who marked the first year assignments were invited to complete and discuss the assignment with other tutors first; however, this was insufficient and compulsory and more explicit training on how to assess such an assignment will be used next time. Exemplars at different levels (pass, credit, etc.) will be provided to both students and tutors

Context, Connections and Communication: Using Journal Articles in Undergraduate Mathematics

Many undergraduate students fail to appreciate the deep connections between different areas of mathematics or the richness of links between mathematics and other disciplines. A compartmentalisation of mathematics into distinct and unrelated topics or a perceived lack of relevance to the real world or other university subjects can promote a surface approach to learning. These perceptions can be exacerbated by the different ways mathematics is communicated in different contexts or scientific fields. Units of study on mathematical modelling and applications provide opportunities to enhance transfer of mathematical concepts by showing students how mathematics is used in a variety of contexts and shared by different communities of scientists. Activities based around appropriately chosen journal articles can provide students authentic examples of context, connections and communication

Mixed Methods Research on the Nexus Between Mathematics and Science

The importance of maths within STEM education is uncontested and yet there remains a paucity of studies examining the relationship, or nexus, between maths and science at university level. In Australia, recent concern over levels of participation and standards in maths and science education makes such research an imperative. In this paper we present the methodology for a multi-phase mixed methods study of the relationship between maths and science at one Australian university, including: (i) correlation between mathematics and other disciplinary attainments, (ii) measurement of the transferability of undergraduates’ learning, (iii) exploring factors associated with the transfer; and (iv) both students’ and experts’ views on the relationship between mathematics and science and the teaching and learning factors that facilitate or hinder transfer. Importantly, this naturalistic study draws on secondary data and interviews to explore this relationship as it occurs within normal university activity; transfer, for example, is observed in students’ performance in university exams. We report on findings from phase one of the study, by outlining student participation in first year mathematics study in relation to various factors and highlight gender and socioeconomic gaps, and we examine the high school maths preparation in relation to students’ pass rates in STEM degrees

Resource use and study habits in a first-year mathematics service unit

We analysed students’ actual and intended use of a variety of study resources in a first year mathematics service course. We combined online tracking with self-report via survey and interviews. Our major finding was that students desire and intend to use a variety of resources but in actuality focus on traditional modes of engagement. We also found evidence that these students adopted different study habits and a different learning approach in their service maths units as compared to their discipline units

Participation & transfer of learning between tertiary mathematics, science, and engineering education

Transfer of mathematical learning is critically important in science education and learning as mathematical knowledge and skills are applied into diverse disciplines. However, little research on transfer of tertiary mathematical learning has been conducted despite its importance. This study conducts mixed methods naturalistic inquiry to investigate transferability of mathematics from various angles using a range of research methodologies (secondary data analysis, case studies and a Delphi study) and variables within natural settings and processes of university education. The study will further extensively examine the relationship between students’ educational, socio-economic, demographic and cultural backgrounds and the transferability of mathematics from first year service courses. Preliminary findings on background information of undergraduate students studying these courses are reported

Transfer of first year mathematical learning in stem disciplinary university assessment

KEYWORDS: transfer of learning, mathematics, science, higher education Background University academics in STEM disciplines are concerned about their first year students’ poor mathematical skills and knowledge applied in their disciplines. Mathematics is of critical importance for their success in subsequent learning and transfer of mathematics learning is seen as important. However, little research has investigated this issue in a naturalistic way, beyond experimental assessments. Aims We quantitatively measure the transfer of mathematical learning in the natural context of first year mathematics service courses in university, using a Transfer Index (Roberts, Sharma, Britton & New, 2007) and an ATAR Adjusted Transfer Index. In addition, we explain how transferability of mathematics, mathematics attainment and ATAR can predict attainments in science/engineering. Research strategy An important feature of our study is a naturalistic inquiry into transfer of mathematical learning. In other words, we examined transfer, using existing university assessment, including final exams and tests. Secondary data analysis is the research strategy employed. Population and sample The population is undergraduate university students in STEM disciplines in Australia. We employed cluster sampling. A single university in Sydney was chosen as a cluster due to considering costs and time. Our sample consisted of students studying first year mathematics service courses (N=1,186). Data collection and analysis There were two types of data. First, attainments, such as ATAR, and demographic information, such as age, gender and SES, was obtained from university databases. Second, we also produced primary data by calculating transfer indexes. Exploratory data analysis, correlational analysis and path analysis were conducted to examine the relationship between these variables. Results We found transfer of mathematical learning in regular and advanced physics courses and in an engineering course. Unexpectedly, there were no questions which required knowledge and skills learned from mathematics service courses in final exams in biology and molecular bioscience courses. Conclusions ATAR and transfer indexes had significant effects on subsequent learning in physics and engineering with effect sizes (standardised beta) from 0.18 to 0.41 of a standard deviation. However there were limited opportunities to measure transfer because many of the courses examined did not assess mathematical knowledge or skills. This is surprising given the investment in mathematics service courses for students in these courses. We suggest better communication, between these disciplines and mathematics, could lead to better curricular and assessment planning that promotes mathematical learning within STEM degrees. References Roberts, A.L., Sharma, M.D., Britton, S. & New, P.B. (2007). An index to measure the ability of first year science students to transfer mathematics. International Journal of Mathematical Education in Science and Technology, 38(4), 429-448. Proceedings of the Australian Conference on Science and Mathematics Education, Curtin University, Sept 30th to Oct 1st, 2015, page X, ISBN Number 978-0-9871834-4-6

Oral assessment in science and mathematics: how, what, and why?

Science educators seek to teach diverse skills, including effective communication and problem-solving skills, many of which cannot easily be assessed in written form or are well suited to non-written assessment forms. This workshop will explore some innovative uses of oral assessment to develop and assess key skills such as communication and problem-solving, aiming to use participants’ experiences to inspire further innovation in assessment practice. It will explore what forms of oral assessment are used by science academics, how it is implemented, and why particular skills or attributes are being assessed or developed. In this “flipped classroom” style workshop, participants will be invited to watch a video beforehand outlining some current practices of oral assessment, including its use to develop and assess problem-solving skills. Participants are encouraged to come to the workshop prepared to discuss the process, marking criteria, and broader purpose for oral assessments