Anxiety characterises the experience of many preservice educators who feel unprepared to teach mathematics (Adler & Davis, 2006) and many teachers, especially females, experience anxiety when teaching mathematics (Beilock, Gunderson, Ramirez, & Levine, 2010). Given that there is a strong correlation between a teacher’s content knowledge and overall student achievement (Hill, Rowan, & Ball, 2005), the anxiety and lack of preparation of preservice teachers presents a problem for teacher educators.

The research project is based on an intervention in which  final-year elementary pre-service teachers tutored first-year tertiary (nursing) students in mathematics. This is not a boutique program; it could operate with psychology, veterinary science, dentistry, architecture, science or engineering students, for example. The careers such students aim for provide an authentic context for the teaching and learning of mathematics.

This is evidenced in nursing. Numeracy is an important skill for nurses, yet it is often taught by nurse educators who do not have qualifications in either mathematics or teaching. Current literature continues to draw attention to the difficulty undergraduate nurses encounter with basic maths principles (Bagnasco,et al, 2016).The problem extends even to countries that provide high quality, high-equity education;  even Norwegian students tend to have poor mathematics skills ((Røykenes & Larsen, 2010). Drug calculations are described as a one of eleven competency areas of medication competency in nurses (Sulosaari, Suhonen,& Leino‐Kilpi, 2011) yet a Canadian study found 77.4% of drug errors by student nurses resulted from incorrect drug calculations (Gorgich, Barfroshan, Ghoreishi, & Yaghoobi, 2016).

The underlying problem for nursing students is lack of comprehension or lack of insight into the mathematics of the problem (Eley, Sinnot, Steinle, Trenning, Boyd & Dimeski, 2014). The most common areas of maths that nurses need support with are ratios, percentages, fractions and place value (Wright, 2005). These are topics in the Australian school curriculum.  In the final year of their degree, elementary preservice teachers can be expected to understand this mathematics and know how to teach it.

The research-based educational design project program comprised 100 final-year Australian pre-service primary teachers tutoring 153 first-year nursing students in fractions, decimals, measurement conversions, place value, ratio, proportion and rates. The design is founded on three areas of literature: authentic learning, communities of practice and mathematical visualisation.

Authentic Learning : authentic is used in a Freirean (1970/1993)  sense to refer to activity “that takes as its starting point the interests, perspectives, desires, and needs of the students,” (Gutierrez, Simic-Muller and Diez Palomar, 2009) This program was designed to familiarise  preservice teachers with the  clinical experience of nurses undertaking drug calculations, demonstrating the benefits of mathematics to the social world.

Communities of Practice: In order to provide support to preservice teachers, small groups of five students worked cooperatively. These CoPs were structured on the model of  Complex Instruction (CI) (Boaler, 2008), of which two beliefs were emphasised: (1) uncooperative students are a responsibility for other students, not a burden on them and (2) knowing maths as an individual has the purpose of ‘helping others’ rather than dominating others.

Mathematical Visualisation:   A visual representation of a mathematics problem can present the essential concrete elements of the problem in an iconic (visual) form mapped to the symbols (words and numbers) that represent them (Weeks et al, 2013).  This is an unusual approach in nursing education, however. In a study of 72 nursing programs in the USA, 48 different styles of ‘formula’ were used to solve same dosage problem (Worrell and Hudson, 1989).  Such ‘formulas’ can lead to computation errors if the nursing student doesn’t understand fractions, proportions, multiplication and division, as was so with many of the lowest-scoring students in this program.

The purpose of educational design research (or research-based design) is to develop research-based solutions for complex problems in educational practice (McKenney & Reeves, 2018). In Design Based Research, “design research”, “formative research” or “design experiments” are analogous terms to design and develop an intervention (such as programs, teaching-learning strategies and materials, products and systems) as a solution to a complex educational problem as well as to advance our knowledge about the characteristics of these interventions and the processes to design and develop them. The researcher is careful to document the time, commitment, and contingencies that are involved in the creation and implementation of the intervention (Anderson & Shattuck, 2012). These details are given here. Authentic learning: Preservice teachers were given copies of tests on drug calculations that are typically taken by nursing students, in order to familiarise them with the level of mathematics nurses require. They were also given a set of Clinical Practice questions, supplied by nurse educators, which they solved weekly in their CoP groups as part of their regular fourth-year course in mathematics education. Lastly, they were encouraged to develop a friendship with their nursing student, and to discuss her nursing studies and practical experience, in order to acquaint themselves with the realities of the need for proficient mathematics in nursing – especially decimals, measurement conversions and rates, with which many primary preservice teachers are not confident. Each Community of Practice (comprising 5 -6 preservice teachers) tutored 5-7 nursing students for one hour weekly for 9 weeks, with preservice teachers often working one-on-one with one or two nursing students within the CoP. The CoP allowed preservice teachers to plan for and to reflect on their teaching together. They also shared their weekly plans within their own CoP so that in case of an unexpected absence, other members of their CoP could tutor their nursing student. Mathematical Visualisation: Clinical Practice questions were solved by preservice teachers (in the hour before the tutoring program) using visual images weekly. After each session, the ‘visual’ solutions (diagrams and photographs of models) were placed on a website that was accessible by all preservice teachers. During the tutoring sessions, a mathematics educator was available on request to help with modelling visual solutions.

Student achievement: Scores of the lowest achieving quartile increased from 52% to 86% after 9 weeks. Test scores were maintained 3 months later. The higher three quartiles also showed significant growth in their scores. If the competence of teachers is reflected in student outcomes, this shows a correspondingly high level of mathematical and pedagogical competence in preservice teachers. Authentic learning: Nursing students' feelings about being inadequately prepared to calculate drug dosages accurately, attended by their anxiety about the consequences , had powerful effects on the preservice teachers. This was perhaps the most potent of the three strategies used in the program to establish an authentic context. Preservice teachers' realisation that their professional knowledge in mathematics made a genuine difference to the nursing student was also a powerful motivator. Communities of Practice: The CoP enhanced pre-service teachers’ confidence through the provision of mutual support and assistance. The emphasis on learning within a culture of inclusion and respect as in the Complex Instruction model (Boaler, 2008) meant that some students continued the tutoring program afterwards out of friendship. This may be partly responsible for the continued high outcomes of the students three months after the program finished. Mathematical Visualisation: Visualisation was a focus in the three previous years of mathematics instruction. Consequently, most preservice teachers used visualisations and models when solving Clinical Practice problems with nursing students. A small minority reverted to formulas. The visual teaching approach generated greater understanding of mathematics by nursing students than the customary formula-based approach. Visualisation was used especially at times when the English language obscured mathematical meaning, as it does in place value, measurement conversions and fractions. This is a question of current interest to the researchers, to be investigated further.

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