Rachel Thompson

Biglan (1973) divides academic disciplines into hard and soft, with subcategories of pure and applied, and life and non-life. We have conducted a study spanning these sub-categories in the 'hard' discipline of science, focused on looking for common factors that impede student learning. A survey of second year undergraduate courses in Thermal Physics, Quality of Medical Practice and Molecular Biology was conducted. A common theme identified was the students' struggle with numeracy skills. Our survey results suggest this has less to do with a real weakness in mathematics, the students in these courses generally have strong mathematical backgrounds, and is more related to two factors – lack of relevance, which reduces their willingness to engage with the challenging aspects of the mathematics, and difficulties in transforming their 'pure' mathematical training into a form that allows them to use it effectively in their chosen courses.

Suttle CM; Challinor KL; Thompson RE; Pesudovs K; Togher L; Chiavaroli N; Lee A; Junghans B; Stapleton F; Watt K; Jalbert I, 2015, 'Attitudes and barriers to evidence-based practice in optometry educators.', Optometry and Vision Science, vol. 92, no. 4, pp. 514 - 523

LeBard RJ, Thompson R, Quinnell R. Quantitative Skills and Complexity: How can we Combat these Challenges and Equip Undergraduate Students to Think and Practice as Biologists?International Journal of Innovation in Science and Mathematics Education. Special Issue: Biology Education Futures. In press October 2014.

Mapping the pedagogical process of learning in biology has shown that fieldwork and laboratory practicals require students to use quantitative skills in a high-level learning context. These tasks include creating graphical representations of data or performing statistical analysis and are major areas of disengagement and poor performance. Biology educators face a challenge: how to keep students engaged in mastering new techniques and methodology to develop the ‘thinking of a scientist’, while developing confidence using quantitative skills (the ‘maths’). Here we investigate how an online learning module on the regulation of gene expression was used in a molecular biology course to simplify this complex process of learning in science. The module emphasised the links between the concept (gene regulation), experiments (growing Escherichia coli in the presence of different effector molecules and substrates) and the data recorded. An audit of student assignments and surveys before and after the introduction of the module indicated that students improved their data presentation skills. Results highlight the complexity of the task students have to perform and the usefulness of consolidating information and providing extra time via a blended approach to laboratory practicals and are discussed in relation to the theoretical frameworks of threshold concepts, thinking dispositions and mindfulness.

Developing quantitative skills, or being academically numerate, is part of the curriculum  agenda in science teaching and learning. For many of our students, being asked to ‘do maths’ as part of ‘doing science’ leads to disengagement from learning. Notions of ‘I can’t do maths’ speak of a rigidity of mind, a ‘standoff ’, forming a barrier to learning in science that needs to be addressed if we, as science educators, are to offer solutions to the so-called ‘maths problem’ and to support students as they move from being novice to expert. Moving from novice to expert is complex and we lean on several theoretical frameworks (thinking dispositions, threshold concepts and mindfulness in learning) to characterize this pathway in science, with a focus on quantitative skills. Fluid thinking and application of numeracy skills are required to manipulate experimental data sets and are integral to our science practice; we need to stop students from seeing them as optional ‘maths’ or ‘statistics’ tasks within our discipline. Being explicit about the ways those in the discipline think, how quantitative data is processed, and allowing places for students to address their skills (including their confidence) offer some ways forward.

Connecting discipline scholars with the scholarship of teaching and learning (SoTL) is accepted as an essential part of professional academic practice across the higher education sector irrespective of discipline. To connect meaningfully with teaching practice, SoTL needs to be translated by the discipline scholar and narratives related to the discipline context constructed. Previous work on disciplinary diversity suggests that there is a need to take a more grounded approach to the development of discipline-based educational scholarship. How SoTL is defined is critical to how SoTL is interpreted within discipline contexts and some of the numerous models and definitions of SoTL transcend disciplinary boundaries, but there is no single agreed definition of what is meant by SoTL. This paper reviews some of the models of scholarly teaching and raises some questions about how the links between pedagogical theory and discipline teaching practice are made by discipline scholars. We advocate that by providing discipline scholars with ways to map and then collectively view their practices within disciplines that this is likely to provide information essential for exploring SoTL in each discipline and reconciling SoTL with academic disciplines.

Biglan (1973) divides academic disciplines into hard and soft, with subcategories of pure and applied, and life and non-life. We have conducted a study spanning these sub-categories in the ‘hard’ discipline of science, focused on looking for common factors that impede student learning. A survey of second year undergraduate courses in Thermal Physics, Quality of Medical Practice and Molecular Biology was conducted. A common theme identified was the students’ struggle with numeracy skills. Our survey results suggest this has less to do with a real weakness in mathematics, the students in these courses generally have strong mathematical backgrounds, and is more related to two factors – lack of relevance, which reduces their willingness to engage with the challenging aspects of the mathematics, and difficulties in transforming their ‘pure’ mathematical training into a form that allows them to use it effectively in their chosen courses.

Statistics is taught in undergraduate science and medicine courses as an essential research subject. For many science students there is a program requirement to include a first year mathematics and/or statistics course taught by mathematicians and/or statisticians with the topic revisited later within the discipline by academics who are not statisticians. Statistics are taught by a medically trained public health academic within evidence-based medicine in the undergraduate medicine program at University of NSW and taught as laboratory and field research skills by biology academics in the biology units of study at University of Sydney.

Seeing our students fail to comprehend the basics of the statistics taught using a more traditional ‘statistics-centric’ method we independently reviewed our courses. We detected particular areas of difficulty in our student’s learning, including numeracy skills as they are practiced in the discipline and threshold concepts1. We will argue that the unpicking of threshold concepts and focusing on the applied relevance of the concepts greatly assisted in improving our students’ understanding. Further, this paper explores how disciplinary factors may assist our students to cross the various thresholds that they encounter, be they generic or applied. This ‘tour-guide’ approach will be illustrated by showing how we use a network of three overarching threshold concepts delineated for medical statistics that link together multiple threshold concepts of generic and applied theory with other key concepts.

The intriguing finding of this re-developing of the statistics teaching for these courses was a recognition that as non-statisticians teaching statistics we have a unique view of how our students are learning statistics as we experienced this same process as non-statistician undergraduates. We were not very “statistically minded”, we found it hard to think in a statistical manner and we both struggled initially with statistical concepts. Although students of statistics and biology may both encounter similar obstacles when learning statistics, i.e. as they manipulate datasets, calculate probability and make statistical interferences, students of biology are required to extend beyond the statistical meaning of their analyses to the meaning that is coherent with the discipline, including critiquing experimental design. Notably, it is the application of statistics that distinguishes our students’ learning. Consequently, students of mathematics appear to find interest and relevance in the statistics themselves; whereas we see that those from life sciences find understanding and relevance in the biological and medical explanatory narratives used as well as the inferences that follow from their statistical findings. We have found stumbling points in learning both pure and applied statistical concepts which statisticians may not perceive for our students. As discipline experts teaching statistics to our students we are able to identify the threshold concepts and troublesome language that our students have difficulty with and have enhanced the teaching of applied elements to increase the relevance and clarify the key concepts. We view ourselves akin to “tour guides” assisting students as they traverse the statistics landscape on route to destination back in their home disciplines, thus making this troublesome subject more accessible, more acceptable and more easily understood by the discipline based student.
i Quinnell R. & Thompson R. 2010. Re-viewing academic numeracy in the tertiary education sector as a threshold concept. In Land, Meyer, & Baillie (Eds) Threshold Concepts within the Disciplines. Sense Publishers. Forthcoming.

We have been exploring the extent of 'the maths problem ' in science teaching and learning at tertiary level. It has been useful for us to refer to the discipline matrix of Biglan1 where science is defined as a "hard discipline", where "applied" disciplines (e.g. Medicine) are distinguished from "pure" (e.g. Physics and Biology) and where disciplines focused on "life" (e.g. Biology and Medicine) can be distinguished from "non-life" (Physics). Our investigations into the extent of 'the maths problem ' have crossed the pure and applied boundary and the 'life'-'non-life' boundary. It is of interest to us to see how closely correlated thresholds concepts are to discipline boundaries.
Regardless of subject, students saw numeracy as a problem in Physics, Medicine and Biology, with specific issues being: i) maths anxiety ii) difficulty with interpreting data iii) reconciling observations and experimental data with theory2. There are striking parallels in how students in each of the sub-disciplines have responded to question: "what was it about learning in this course did you find to be problematic?"  and the characteristics of practitioners on these same disciplines as described by Biglan1. For example, students of Medicine focused on how relevant the content of their statistics course was to their overall study, whereas students in Biology were grappling with the complexity of understanding a living system. The Higher Education sector has undergone changes over the past few decades3. There is now a greater number of vocational degrees being offered where 'relevance' is almost prerequisite to learning, and a more diverse student body with equally diverse experiences of mathematics prior to entry into university. These changes in the Higher Education sector highlight as concerns the issues of: i) 'relevance' in relation to how students in an applied discipline view numeracy, and ii) students using mathematics to understand concepts in sciences. One of the challenges we will need to address as we face this more diverse student body enrolled in vocationally-focused degree programs will be the increasing number of students for whom numeracy is a threshold.
By examining numeracy across science sub-disciplines we are identifying places where students are getting stuck as they begin to practice science. We have a view that by examining our practices within our discipline territories3, we will be able to map where the learning thresholds of our students are occurring. We think that our work may provide some necessary clues to devise teaching approaches to better connect students with the discipline by addressing issues with academic numeracy. References: 
1. Biglan, A. 1973. Relationships between subject matter characteristics and the structure & output of university departments.  Journal of Applied Psychology, 57: 204-213.
2. LeBard, R, Micolich, A, Thompson, R & Quinnell, R. 2009. Identifying common thresholds in learning for students working in the ‘hard’ discipline of Science.  Proceedings of the 2009 Uniserve Science conference Motivating Science Undergraduates: Ideas and Interventions : 72 - 77. http://science.uniserve.edu.au/ images/content/2009_papers/LeBard.pdf 
3. Becher, T and Trowler, P. (2001). Academic Tribes and Territories: intellectual enquiry and the cultures of disciplines (2nd edition). Buckingham: Open University Press/SRHE.
Justification:  our work addresses the theme of ‘exploring transformative dimensions’ by focusing on how students begin to learn our discipline practices in Science. We will offer some examples of changes to teaching and assessment practices to improve student engagement with understanding how to operate within our discipline.

"*Rosanne Quinnell (University of Sydney); Rebecca LeBard (BABS UNSW) and Rachel Thompson (Medicine UNSW)
*presenting author"
Quinnell R, Lebard R, Thompson R. 2012. Academic Numeracy: Challenging Thinking Dispositions to Enable Students to Enter and Cross the Liminal Space. Special interest seminar: Connections - Threshold concepts.  UNSW 2012 Nov, 12.

We have been exploring the extent of 'the maths problem' in science teaching and learning at tertiary level. It has been useful for us to refer to the discipline matrix of Biglan1 where science is defined as a "hard discipline", where "applied" disciplines (e.g. Medicine) are distinguished from "pure" (e.g. Physics and Biology) and where disciplines focused on "life" (e.g. Biology and Medicine) can be distinguished from "non-life" (Physics). Our investigations into the extent of 'the maths problem' have crossed the pure and applied boundary and the 'life'-'non-life' boundary. It is of interest to us to see how closely correlated thresholds concepts are to discipline boundaries.
Regardless of subject, students saw numeracy as a problem in Physics, Medicine and Biology, with specific issues being: i) maths anxiety ii) difficulty with interpreting data iii) reconciling observations and experimental data with theory2. There are striking parallels in how students in each of the sub-disciplines have responded to question: "what was it about learning in this course did you find to be problematic?" and the characteristics of practitioners on these same disciplines as described by Biglan1. For example, students of Medicine focused on how relevant the content of their statistics course was to their overall study, whereas students in Biology were grappling with the complexity of understanding a living system.The Higher Education sector has undergone changes over the past few decades3. There is now a greater number of vocational degrees being offered where 'relevance' is almost pre-requisite to learning, and a more diverse student body with equally diverse experiences of mathematics prior to entry into university. These changes in the Higher Education sector highlight as concerns the issues of: i) 'relevance' in relation to how students in an applied discipline view numeracy, and ii) students using mathematics to understand concepts in sciences. One of the challenges we will need to address as we face this more diverse student body enrolled in vocationally-focused degree programs will be the increasing number of students for whom numeracy is a threshold.
By examining numeracy across science sub-disciplines we are identifying places where students are getting stuck as they begin to practice science. We have a view that by examining our practices within our discipline territories3, we will be able to map where the learning thresholds of our students are occurring. We think that our work may provide some necessary clues to devise teaching approaches to better connect students with the discipline by addressing issues with academic numeracy.
References:
1. Biglan, A. 1973. Relationships between subject matter characteristics and the structure & output of university departments. Journal of Applied Psychology, 57: 204-213.
2. LeBard, R, Micolich, A, Thompson, R & Quinnell, R. 2009. Identifying common thresholds in learning for students working in the ‘hard’ discipline of Science. Proceedings of the 2009 Uniserve Science conference Motivating Science Undergraduates: Ideas and Interventions: 72 - 77. http://science.uniserve.edu.au/images/content/2009_papers/LeBard.pdf
3. Becher, T and Trowler, P. (2001). Academic Tribes and Territories: intellectual enquiry and the cultures of disciplines (2nd edition). Buckingham: Open University Press/SRHE.

The thresholds concepts framework was used to identify the underlying dysfunctional attitudes and stances students may adopt that can preclude them from engaging in our discipline practices. In the sciences numeracy skills are integral to the professional practice of data handling, data presentation and interpretation. We have found that students lacking in numerical confidence are more hesitant to engage in these activities, which impacts of their learning of the discipline by directly inhibiting how well the students tackle threshold concepts with numeracy elements.

While mathematics can be enabling, we postulate that the transfer of numeracy skills can be inhibited by a transfer in “maths anxiety”, a “transferable anxiety”, that doesn’t appear unique to a particular discipline. In the classroom, this often translates to a hierarchical standoff: “I can’t do maths” versus “they can’t do maths”. Students who default to this position are at risk of not engaging in our practice as they have adopted a thinking disposition where a lack of depth in understanding has been previously legitimised i.e. if they retain the static position long enough, the educator will eventually offer a worked solution.

We have identified and compared inclinations and assessed students’ abilities across three disciplines within science. We have been able to map these onto the Perkins et al. (1993) framework of “triadic thinking dispositions” and offer descriptions of the sensitivities, inclinations and abilities that place students “at risk” of not engaging in numeric activities. We have designed a diagnostic tool to help students understand and self-challenge their level of confidence in numeracy. We postulate from the tool’s evaluation, on the success of this learning activity in helping students cross the liminal space and also posit how this might improve our students’ ability to transfer their numeracy skills and confidence more readily across disciplines.

Quinnell R.**, Thompson R., Markovina N., LeBard R*.  Curtin University, Sept 30th to Oct 1st, 2015, page X, ISBN Number 978-0-9871834-4-6. *presenting author **author for correspondence.

BACKGROUND: WHAT THE PAPERS SAY.
In recent years there have been concerning headlines in the media that speak to the pervasiveness of the maths problem through Australian science, technology and mathematics (STEM) education from primary to tertiary. The Australian Financial Review referred to ‘Australia’s maths crisis’ (Mather, 2015) in reference to the 15-year trend of Australian school students' continuing poor performance in international testing. This 15-year trend aligns with the ‘20-year decline in science and maths education’ (Phillips, 2015). The Conversation tells us ‘Aspiring teachers [are] abandoning HSC maths’ (Smith, 2015) so that those intending to teach at school are not gaining the basics during their own school education and so are likely to struggle with gaining adequate maths expertise to be able to teach it and there appears to be no incentive to study maths when ‘HSC maths: students studying advanced maths [are] stung with lower marks in ATAR’ (Bagshaw, 2015). This headline ‘Science graduates are not that hot at maths – but why?’ (Matthews, 2014) refers to the lack of sound numeracy skills our science graduates demonstrate. If nothing else, these headlines tell us that the maths problem as it manifests in tertiary life science teaching and learning is both complex and of concern to the public at large.

MATHS IN CONTEXT: WHERE BIOLOGY MEETS MATHS
So where does that leave teachers in the higher education sector who rely on schools to provide the mathematics foundations for non-maths STEM disciplines, particularly in the Life Sciences, were the synergies between Mathematics and Biology seem less obvious students than the between, say, Mathematics and Physics? In Biology we require students to confidently transfer their numeracy skills, rather than their maths anxiety, to our discipline area and we require students to develop the discipline-specific numeric sensitivities.

Given the complexity of both the Maths Problem and numeracy skills transfer, solutions to address these will need be complexity and to be as pervasive as the problem itself. Our work to date (e.g. Quinnell, Thompson & LeBard, 2013) has been largely theoretical and focussed on characterising learning and teaching thresholds and discipline sensitivities in academic numeracy for biology students. Sensitivities are interesting and in the context of numeracy include: 1) the use of engineering notation rather strict scientific notation in some Life Science disciplines such as physiology; and 2) the use of unit of measure prefixes in molecular biology and biochemistry so students in general biology must be, or become, proficient in switching between engineering notation and unit of measure prefixes. We need to not only provide numeracy support that has been contextualised for the discipline with the aim to develop sensitivities but the support materials ought to address issues such as maths anxiety and/or poor numeric confidence.

FUTURE DIRECTIONS: SHARABLE AND ADAPTABLE SOLUTIONS
We have now begun to storyboard an online diagnostic and learning analytics feedback system that can be repurposed, or "reinvented", by others. Learning analytics in systems such as SmartSparrow [https://www.smartsparrow.com/] or Numbas [http://www.numbas.org.uk/] will allow easy identification of threshold learning areas, or learning obstacles which are where most students stuck. Critical to this initiative will be allow for students to access a level of learning analytics to track their progress with development of numeracy skills, discipline sensitivities and confidence.

REFERENCES
Bagshaw, E. (2015, May 19). HSC maths: students studying advanced maths stung with lower marks in ATAR. The Sydney Morning Herald. Retrieved June 10, 2015, from http://www.smh.com.au/national/education/hsc-maths-students-studying-advanced-maths-stung-with-lower-marks-in-atar-20150519-gh45ox.html
Mather, J., & Tadros, E. (2014, June 7). Australia’s maths crisis. The Australian Financial Review. Retrieved June 10, 2015, from http://www.afr.com/news/policy/education/australias-maths-crWoSs-20140606-iwfn1
Matthews, K. (2014, September 29). Science graduates are not that hot at maths – but why? The Conversation. Retrieved June 10, 2015, from http://theconversation.com/science-graduates-are-not-that-hot-at-maths-but-why-32021
Phillips, N. (2014, October 6). 20-year decline in year 12 science and maths participation. The Sydney Morning Herald. Retrieved June 10, 2015, from http://www.smh.com.au/technology/sci-tech/20year-decline-in-year-12-science-and-maths-participation-study-finds-20141006-10qvq2.html
Quinnell, R., Thompson, R., & LeBard, R. (2013). It's not maths; it's science: exploring thinking dispositions, learning thresholds and mindfulness in science learning. International Journal of Mathematical Education in Science and Technology, 44(6), 808-816. doi: http://dx.doi.org/10.1080/0020739X.2013.800598
Smith, A. (2015). Aspiring teachers abandoning HSC maths. The Sydney Morning Herald. Retrieved June 10, 2015, from http://www.smh.com.au/nsw/aspiring-teachers-abandoning-hsc-maths-20150213-13drr7.html

In order to reinforce key concepts, undergraduate life science students (e.g. biology and medicine) are given opportunities to link the descriptions of phenomena presented in lectures to their own in-class or field observations. However, in our classes a proportion of our students disengage when the focus shifts to calculating biological parameters or to population studies (statistics). Our work to date has focused on characterising the underlying dysfunctional attitudes and stances our students adopt when faced with calculations that can preclude them from engaging in our discipline practices. Not all students see the relevance of developing numeracy skills to their studies in science and medicine and need to be extrinsically motivated. Although there may be some elements in common (e.g. maths anxiety), the 'maths problem' as it manifests in science teaching and learning is different to the 'maths problem' as it is seen in maths teaching and learning. For biology and medical students learning science, encountering ‘maths’ can lead to disengagement; in these instances ‘maths’ is more akin to a “transferable anxiety" than a “transferable skill”. In biology and medicine, being able to conceptually move between the phenomena and the abstracted figures or equations derived from experimental data requires the application (transference) of sound academic numeracy skills; developing and applying numeracy skills is the implicit learning objective, or hidden curriculum objective, of the undergraduate life science curriculum. Other implicit learning objectives are that our students are to be numerically competent and confident (or at the very least to develop competence and confidence) when 1. gathering, manipulating and presenting their own quantitative data sets and 2. critically appraising published data. There are a raft of expectations and assumptions associated with student learning objectives that include the expectations that our students have reasonably well-developed numeracy skills from their previous studies in mathematics at secondary school, and that transferring and applying their numeracy skills into their science studies in other discipline contexts, such as the life sciences, will be relatively unproblematic. However, for a novice, there is a high degree of complexity of thought and critical thinking required to complete a single experiment and write it up as a report. Shifting from ‘novice’ to ‘expert’, developing skills and discipline sensitivities and building confidence requires students to be afforded opportunities to practice and to get feedback. There are insufficient opportunities for students to practice their skills (including numeracy and abstraction) particularly given the reduction in the number of assessment tasks our students now do, which is probably about a tenth of the assignments we were doing even a decade ago. Having a clearer understanding of when and how our biology and medical students disengage from learning when they encounter 'maths' when learning science will inform the best ways to offer them support.