Conference Agenda

Historically, school mathematics has been viewed as a complex and abstract subject with little relevance to daily life (Ernest, 2016). Eccles (1983) found that student negativity towards mathematics increases over time, mirroring a decline in self-belief and motivation. Eccles et al. (1993) subsequently investigated the causes of declining motivation, and found that getting older was not the primary driver; rather the decline was influenced by teachers exhibiting more control over students as they advanced through grades, restricting student decision-making and conveying lower expectations in students’ ability.

In their seminal report, Kilpatrick et al. (2001) identified five interconnected components that are necessary to learn mathematics successfully. One of these components is productive disposition, essentially a combination of self-efficacy and perceived usefulness for mathematics (Kilpatrick et al., 2001). Both self-efficacy and seeing that mathematics demonstrates utility (useful for future goals) are considered vital for motivation (Gafoor & Kurukkan, 2015).

For this study, Eccles & Wigfield’s (2020) Situated Expectancy-Value Theory will be used as a theoretical framework. The framework indicates primarily that expectancies and values drive future performance. Eccles (1983) found that motivation is boosted when students value the tasks that they are engaging with. Task values are a function of attainment values (Importance of succeeding), intrinsic values (Enjoyment), utility values (help with forthcoming goals) and cost(Eccles & Wigfield, 2020). In their framework, Eccles & Wigfield (2020) indicate that utility value is the most ‘malleable’ of task values. Utility value interventions have shown promise in improving student effort generally (Hulleman et al., 2008), but also specifically within mathematics (Liebendörfer & Schukajlow, 2020). However, despite evidence that utility value interventions positively impact student motivation, many teachers are unaware of its relevance (Hulleman & Barron, 2013).

While utility value interventions may improve motivation, what one person might see as useful another may not; it is important to remain cognisant of the fact that utility values are individual, and can be influenced by cultural differences. It is therefore worthwhile considering the potential of culturally responsive teaching as a method of enhancing students’ perceived utility values towards mathematics. Hunter et al. (2016) noted student reactions to culturally relevant interventions, citing comments such as “When the problems are about us you can see that maths is real and it’s useful……not just something random you do at school”. This demonstrates that relating mathematics to familiar contexts can impact utility value. Lowrie (2004) also highlights the benefits of using artefacts to make mathematical tasks more realistic, which may lead to students seeing increased utility value in mathematics.

Another approach that has been noted as supporting students to understand the relevance of more abstract mathematical concepts is mathematical modelling (Liebendörfer & Schukajlow, 2020). With mathematical modelling there is no definite answer; students take real-life scenarios, mathematise them, identify variables, make assumptions, generate initial solutions before iteratively reviewing the process (Sahin et al., 2019). By engaging with the process of modelling, students can reflect and generate further examples themselves. Regular Mathematical modelling tasks can enable students to encounter numerous concepts routinely in a variety of contexts, benefitting productive disposition and indeed all five components of mathematical proficiency (Kilpatrick et al., 2001).

The goal of this research is to draw together mathematical modelling and culturally responsive teaching in an approach to mathematics teaching that aims increase students’ perceived utility values, productive disposition and motivation, ultimately contributing to successful learning of mathematics. The overarching research question is: What impact does incorporating culturally relevant mathematical modelling tasks have on students’ utility value for mathematics?

Educational assessment studies show that students have difficulties in mathematics, particularly in problem solving. This could be a difficulty in at least one of the four phases (Polya, 1945), namely: understanding the problem, making a plan, carrying out the plan, and looking back. Other studies have also examined the different ways in which students cope with such difficulties. Problem solving is a fundamental skill, both now and in the future. Researchers have long been concerned with its development, and its relevance remains undiminished. The academic study of problem solving emerged in the second half of the 20th century. In the 1970s and 1980s, it focused primarily on elucidating the nature of mathematical problems, students' approaches to solving them, and the salient aspects of problem solving that warrant investigation (Schoenfeld, 1985). More recently, scholarly attention has shifted to educators' perspectives on problem solving and strategies for its improvement (Boaler, 2002; Schoenfeld, 2010, 2014; Stein et al., 2008).

In this study, we have investigated the multifaceted domain of problem solving, with a particular focus on the strategies employed in solving mathematical word problems. Van der Schoot et al. (2009) investigated the factors that differentiate successful and less successful problem solvers in their approach to word problems, highlighting in particular the impact of consistency and markedness. Recognised as a fundamental tool for assessing students' practical application of mathematical knowledge, mathematical word problems are often presented in text form rather than using purely mathematical symbols (Daroczy et al., 2015). In solving these problems, as highlighted by Verschaffel et al. (2000), the solver is required to use mathematical operations on known or inferred numerical values from the problem statement to arrive at a solution. This process, according to Kang et al. (2023), can serve as an indicator of the problem solver's abstract reasoning ability. Recently, the scholarly focus has shifted to exploring educators' perspectives on problem solving and coping strategies to improve it (Boaler, 2002; Schoenfeld, 2010, 2014; Stein et al., 2008). Significantly, not every mathematical word problem is sufficiently challenging for students, highlighting the need for exposure to truly complex tasks that promote mathematical sense making (Marcus & Fey, 2003; NCTM, 1991; van de Walle, 2003). Word problems are a particularly difficult type of problem for mathematics students (Verschaffel et al., 2020). Jacobson (2023) defines dyscalculia as a term for specific learning disabilities that affect a child's ability to do arithmetic and number. The estimated prevalence is 5-7% in primary school children. Mathematics covers a wide range of areas: arithmetic, problem solving, geometry, algebra, probability and statistics. Solving mathematical problems requires students to mobilise a range of skills related to number sense, symbol decoding, memory, visuospatial skills, logic, etc., and may lead to difficulties in any one or a combination of these skills (Karagiannakis et al., 2014). Even if these students have not been diagnosed with a mathematical disorder, they need systematic support to learn mathematics because, according to a study by Nelson and Powel (2017), they are likely to continue to experience mathematical difficulties in the future. This paper aims to construct a model for overcoming mathematics learning difficulties by taking into account the congruent abilities required for problem solving, based on Feuerstein's (2015) mediated learning method and Karagiannakis et al.'s (2014) mathematics learning difficulties.

How to develop skills and motivation to learn mathematics?

I speak from the perspective of Polish experiences in developing maths education. I refer to transmissive teaching in accordance with the curriculum culture. I do this with hope this might be interesting for an international audience as the beyond Polish specificity this case pertains to a more universal validity. The results my research show the importance of individualization of teaching and the role of building a sense of self-competence and mathematical self-confidence. At school, mathematics education is often based only on providing students with knowledge and implementing the core curriculum. According to Małgorzata Żytko (2013), the National Survey of Third-Grade Skills [Ogólnopolskie Badanie Umiejętności Trzecioklasistów, OBUT] suggested that the main aim of education is the implementation of the core curriculum, not the development of children and meeting their individual educational needs. Anna Brzezińska (1986) similarly stated that the teaching and communication style in the teaching-learning process should be "child-oriented" and not "core curriculum-oriented". She said that you should talk to the child and organize situations in which the student actively participates, investigates and tries to solve problems on his own. In turn, Edyta Gruszczyk-Kolczyńska (2011) proved that primary school reduces mathematical abilities. She showed that more than 50% preschoolers have mathematical abilities such as ease of learning mathematics, great cognitive curiosity, creativity, accuracy and independence in solving mathematical tasks. In the group of first-graders, only 12,5% students has outstanding talents. Gruszczyk-Kolczyńska noticed that after eight months of school, children are less creative, less courageous and have a lower sense of meaning in learning than in kindergarten. Therefore, the priority of my research was to focus on the developing the skills and motivation to learn mathematics of students with different levels of competence and meeting individual educational needs of each student. The basic questions that guided the research were: how to work on individualised strategies of teaching mathematics being a schoolteacher, so that each student makes progress in learning mathematics? What is the importance of strengthening a child's self-confidence and motivation in learning mathematics? What teaching methods and forms of work will be best for each student? I did the research among eight-grade primary school students. There were 21 students in this group. The research lasted from September 2022 to February 2023. The study group were students from Ukraine, students with dyslexia, selective auditory processing disorders and hyperactivity. I created an original program. It considered the individualization of teaching mathematics. I used a scaffolding strategy and various methods and forms of work (e.g. tutoring, project method, problem-based learning, using tasks with different levels of difficulty) and adapted the subject matter to the cognitive capacity of each student.

The shortage of mathematics teachers has raised several concerns in education systems around the world. One pressing issue involves addressing the vacancies in classrooms, often leading to the emergence of the out-of-field (OOF) teaching phenomenon. This phenomenon entails teaching a subject without a background in the subject or preparation for teaching it. Part of the literature have focused on the impact of teacher qualifications on students’ academic performance. There are studies that reveal disadvantages for students taught by OOF teachers (Porsch & Whannell, 2019). In subjects with cumulative content, such as mathematics, the complexity of which escalates across grade levels, the significance of teachers' qualifications becomes notably pronounced (Hobbs & Törner, 2019). Other strand of literature focus on the consequences for teachers. Challenges in competence and the additional workload associated with OOF teaching are often connected to job dissatisfaction and emotional challenges, including stress, anxiety, and burnout (Buenacosa & Petalla, 2022).

Consequently, different policies have emerged to address the issue of OOF mathematics teaching. Focusing on the English former Teacher Subject Specialism Training (TSST) programme and the Australian (NSW) Mathematics Retraining program, this study was guided by the question: how is the phenomenon of OOF mathematics teaching constructed in these two policies? Remembering that policies are designed by people makes us reflect on the assumptions that were made about the phenomenon, and which were left out

In 2023, the media has echoed the phenomenon, highlighting that 12% mathematics lessons are taught by someone without a mathematics degree in England, while in Australia 33% of secondary maths teachers were OOF (Carey & Caroll., 2023; Weale, 2023). England and Australia share historical ties, but they also exhibit distinctive educational systems shaped by unique cultural, policy, and contextual factors. This paper shedding light on the nuanced ways each case problematizes and therefore acts upon the same phenomenon. This paper has two objectives. On the one hand, to identify, through the analysis of two international cases, the assumptions regarding the phenomenon of OOF teaching. On the other hand, to compare the representations given to the phenomenon in England and NSW.

Traditionally in policy analysis, there has been a conventional belief that policy documents are rational and objective reactions to pre-established and fixed social problems (Bacchi, 2009; Ball, 1993). Therefore, analysts often inquire “what is this policy doing to fix the identified problem?” (Bacchi, 2009). Bacchi argues that these texts, by outlining necessary changes, incorporate implicit representations of the issue or problem they intend to address. Moreover, she contends that such policy documents may inadvertently contribute to defining and spreading the very issues they seek to solve.