Conference Agenda

Motivation and research question

Mathematical problem posing, the process of interpreting concrete or abstract situations and formulating them as meaningful mathematical problems (Stoyanova & Ellerton, 1996), is a form of authentic mathematical inquiry and creation recognised as important for students’ learning by educators and curriculum frameworks internationally (e.g., Chinese Ministry of Education, 2022; National Council of Teachers of Mathematics [NCTM], 2000). Further to being important in its own right, problem posing has been associated with improved competence in mathematical creative thinking, a key transferrable skill for life and work, and mathematical problem solving, which is problem posing’s twin activity central to virtually all mathematics curricula internationally (Shriki, 2013; Wang et al., 2022).

Recognising problem posing’s importance, researchers designed and implemented problem-posing interventions, albeit with mixed results. In a systematic review of 39 problem-posing intervention studies and a meta-analysis of 26 of them (Zhang et al., under review a&b), we synthesised key intervention components and measured their relative or combined effect on students’ problem-posing competence. Thus, we gained insights into what works best, for whom, and under what conditions. Yet, those promising components were not all integrated into the same intervention, nor was the impact of such an intervention explored on all of the following: problem posing, problem solving, and creative thinking.

Based on best knowledge in the literature about problem posing interventions (Zhang et al., under review a&b), we designed a new problem posing intervention aiming to enhance secondary students’ mathematical problem-posing and problem-solving competences and creative thinking, incorporating the components with the most evidence of impact in the literature. In this paper, we report findings about the effectiveness of the intervention to achieve its intended learning outcomes, by addressing the following research question:

To what extent does the developed problem-posing intervention, implemented in secondary school classrooms, enhance students’ mathematical problem-posing competence, problem-solving competence, and creative thinking?

The problem-posing intervention

We developed the problem-posing intervention using our findings from a systematic review and a meta-analysis of interventions published between 1990 and 2021 that aimed at fostering participants’ mathematical problem-posing competence (Zhang et al., under review a&b). We identified three categories of intervention components from the review (ibid): activity-based practice that engaged participants in experiencing problem posing (e.g., overview of what problem posing is–WPP, discussion of what “good” problems are–WGP), method-based assistance that helped participants pose problems (e.g., use of strategies involved in problem posing–SPP, use of problem posing examples–PPE), and environment-based support that guided interaction among participants and the teacher (e.g., interactive learning environment–ILE). The results of our meta-analysis showed that the problem-posing interventions had a significant and positive impact on participants’ mathematical problem-posing competence (g=0.72, p<.001). Particularly, the effect sizes of interventions that incorporated method-based assistance or environment-based support were on average 84% or 83% higher than those of interventions without such kinds of intervention components, respectively.

Based on these findings, our designed intervention, in the form of annotated lesson plans for delivery by the teachers, incorporated all three categories of intervention components, including the following five specific components that we found to be particularly promising: WPP, WGP, SPP, PPE, and ILE. The intervention duration was 220 minutes and is aimed for 13-to-15-year-olds who tend not to be occupied by high-stakes assessments. Also, these students tend to be at a critical juncture in their schooling when the intervention can better equip them for further mathematical studies. Finally, the intervention is not meant to be treated as extracurricular due to its intended impact on the recognised, key learning goals of mathematical problem solving and creativity.

The pedagogical landscape of elementary mathematics education is significantly influenced by the type and quality of problems presented in the classroom. Traditional methodologies, which often emphasize rote learning and procedural mastery, fall short of fostering critical thinking and inquiry, essential components for cultivating mathematical proficiency (Henningsen & Stein, 1997). Recognizing this, the literature advocates a paradigm shift toward integrating problem solving and reasoning as fundamental aspects of mathematics education, thereby enriching students' learning experiences and enhancing their conceptual understanding (e.g., Miranda & Mamede, 2022; National Council of Teachers of Mathematics (NCTM), 2000; Van de Walle et al., 2010).

Problem solving, as described by the NCTM (2000), should not be an isolated segment of the curriculum but an integral part of mathematics learning, integrated into the core of education. NCTM (2000) further notes that problem solving highlights mathematical engagement. In addition, the cognitive and metacognitive dimensions of problem solving underscore the importance of engaging with problems in ways that go beyond mere computation. Jonassen (2000) articulates that the significance of a problem derives from its potential to contribute to “societal, cultural, or intellectual” domains, which requires a solver's engagement in mental representation and manipulation of the problem space (p. 65). This perspective is complemented by Lester and Kehle's definition, which emphasizes problem solving as an active engagement process “using prior knowledge and experience” (cf. Santos-Trigo, 2007, p. 525).

Problem-posing, similar to problem-solving, is an integral part of this pedagogical development. It is recognized as a sophisticated mathematical activity that promotes creativity, flexibility, and deeper understanding (Silver, 1994). It is defined as the ability to formulate, reformulate, and explore problems based on existing mathematical situations or concepts. It could be described as “one of the highest forms of mathematical knowing and a sure path to gain status in the world of mathematics” (Crespo, 2015, p. 494). NCTM (2000) also points out that students need “to create engaging problems by drawing inspiration from various scenarios encompassing mathematical and non-mathematical contexts” (p. 258). In light of these considerations, this study explores the interplay between problem solving and problem posing in the context of mathematics education for preservice elementary teachers. Specifically, it seeks to examine the nature and quality of problems posed by preservice teachers, the challenges they face in the problem-posing process, and how their problem-solving skills influence their ability to generate meaningful mathematical problems. Through a comprehensive analysis of pre-service teachers' engagement with problem solving and problem posing, this research aims to contribute to how to support the pre-service teachers' skills and the interplay between them to create better learning environments for their students by improving their teaching strategies.

Introduction:

In contemporary education, considerable emphasis is placed on the implementation of pedagogical techniques that promote effective teaching through active engagement of students with educational content. Among these approaches, problem-based learning (PBL) stands out as a method that fosters the development of creative thinking, autonomy, and problem-solving abilities among students, while also facilitating the application of acquired knowledge in practical contexts. This study aims to investigate the influence of employing problem-based learning methods in preparing 10th grade students for an external summative assessment in the domain of mathematics.

Theoretical Basis of the Study

Summative assessment serves as a means of evaluating the educational accomplishments of students upon completion of specific sections or cross-cutting topics within the curriculum. It also encompasses the assessment conducted over a designated educational period, such as a quarter, as well as external assessments. These assessments entail the allocation of points and grades, while providing valuable insights on student progress to teachers, parents, and students themselves.

External summative assessments are carried out upon the culmination of particular levels of education, encompassing primary, basic, and secondary education. The benchmarks utilized in these exams adhere to international standards, such as the Cambridge Primary (grade 5), IGCSE (grade 10), AS-level, and A-level (grades 11-12). External summative assessment exams feature multiple components, including closed and open-ended questions that require both concise and detailed responses.

Upon the completion of external summative assessments, students in 12th grade receive an NIS Grade 12 Certificate. This certificate holds recognition by esteemed universities in Kazakhstan, as well as by leading international organizations. [1]

The issue we encountered revolved around our school's performance in mathematics during external summative assessments, as we ranked last within the Nazarbayev Intellectual School network. Notably, there existed a disparity between internal assessments and external assessments. The aim of this action research was to enhance the quality of mathematics outcome measures among 10th grade students. The study pursued the following research question: How does the integration of problem-based learning impact students' effective preparation for external summative assessments in mathematics?

Problem-Based Learning (PBL) technology has been utilized in higher education since the mid-20th century, serving as an interactive learning method. Initially employed by universities in the United States and Canada during the 1950s, PBL later proliferated across European universities during the 1960s. The introduction of this technique initially occurred in the Faculty of Medicine at Case Western Reserve University. Recognizing the contemporary context characterized by an information and technological "explosion," which entails rapidly evolving requirements for future professionals, PBL emerged as the training model best aligned with this situation. [2]

The traditional approach to higher education emphasizes the passive transfer and rote memorization of existing knowledge. Students grapple with the monotonous task of memorizing vast amounts of information that, in their estimation, may not always directly pertain to their forthcoming professional endeavors. Consequently, apathy, detachment, and occasionally disillusionment arise. Frequently, students tend to forget a substantial portion of the material they have learned once an assessment has been completed. Moreover, the retained information often proves challenging to apply when attempting to solve problems across related subject areas, especially within the realm of real-world professional application. [3]

The foundation of PBL rests upon a constructivist approach, which has garnered opposition from critics of this teaching method. In line with the constructivist trend, which emphasizes student participation in the construction of new knowledge through the reevaluation of experiences, PBL brings about significant changes in the learning process itself. It assumes an active and socially-oriented character, thereby embracing a more interactive format.[4]

In its recent Education Blueprint, the Malaysian Ministry of Education has emphasised the imperative to enhance national critical thinking skills. This call-to-action stems from the alarming low rankings in the PISA Problem-Solving Test, and mathematics test and reports from employers highlighting pervasive skill gaps. This research aims to explore a potential tool for developing problem-solving skills: Strategy Video Games (SVGs).
The integration of play in education systems is a growing trend in various nations, including China, the USA, and Denmark, recognising its significance in pedagogy (Mardell, Solis & Bray, 2019). Play, as highlighted by Prince (2017), is instrumental in children's learning and the development of problem-solving skills and fluid reasoning. Given the acknowledged benefits of play and the recognition of video games as a manifestation of play, thus, proposing the use of SVGs is not an outrageous idea to improve cognition. Digital games, specifically SVGs, not only enrich the learning experience but also foster skill development, enhance memorisation, and deepen understanding in STEM fields (Ishak, Din & Hasran, 2021). This approach aligns with the current digital landscape where today's youth spend significant time in the digital world, and SVG skills inherently mirror those demanded by the problem-solving process. However, despite this potential, there is limited empirical evidence linking SVGs to problem-solving skill improvement.
Most research to date on gaming and PS focuses exclusively on self-reported measures. For example, Adachi and Willoughby's (2013) previous study sought to investigate the correlation between strategy video gameplay frequency and adolescents' self-reported problem-solving skills. Their findings suggested a positive relationship: a higher video gameplay frequency was associated with higher self-reported problem-solving skills. The only study that has searched for such links using non-self-reports struggled to find an effect. In this project, Emihovich (2017) explored the impact of two distinct types of video gameplay, namely strategy role-playing video games (World of WarCraft) and brain-training video games (CogniFit), on undergraduates' problem-solving skills. However, the study found no significant effects on problem-solving. Nonetheless, Emihovic, Rogue and Mason (2020) noted that results could be different by prompting participants to actively recognise the strategies during gaming sessions. Therefore, by adding reflection sessions as a medium to transfer learnt problem-solving skills from SVGs to real-life situations could yield different outcomes. Research on metacognition and mindset suggests that combining SVGs with student reflection could further enhance skill development.
The utilisation of reflection sessions in problem-solving proves to be a valuable tool in education. Reflection, as defined by Bjuland (2004), involves the conscious consideration of personal experiences, aligning with Dewey (1933), Inhelder and Piaget (1958), Hiebert (1992), and Wistedt (1994) in the context of forming interactions between ideas and action. In education, reflection is the process of thoughtful examination and evaluation of one's experiences, thoughts, and actions to gain insight and make informed decisions for future practice (Chang, 2019). It plays a pivotal role in transforming experiences into the development of new skills, attitudes, knowledge, and capabilities (Gribbin, Aftab, Young, & Park, 2016).
Thus, this study hypothesises that strategy video gaming may affect both (1) externally assessed and (2) self-reported problem-solving skills when reflection sessions are employed. In response, this study investigated the relationship between SVG and two dependent variables: (1) externally assessed problem-solving skills (2) self-reported problem-solving skills. To test the power of student reflection on problem-solving development, it further assessed whether changes in these variables differed with or without engagement in reflection sessions.
RQ 1: Does playing SVGs affect (1) externally-assessed problem-solving skill assessment scores?
RQ1a: Do these effects change with the inclusion of reflection sessions?
RQ 2: Does playing SVGs affect the (2) self-reported problem-solving skill assessment scores?
RQ2a: Do these effects change with the inclusion of reflection sessions?

The flipped classroom is a teaching technique that has gained worldwide currency during recent years. In a flipped approach, the information-transmission element of students’ learning is moved out of the classroom; instead, students view recorded lectures in their own study time ahead of the live session. This frees the class time for activities (such as discussion and problem-solving) in which students can apply their knowledge and potentially gives the teacher a better opportunity to detect their misconceptions.

According to the State Education Policy (Republic of Kazakhstan), mathematics is one of the fundamental subjects that all students must study up to higher education. Mathematics receives a lot of attention in the school curriculum from primary to secondary school, reflecting the importance of the subject in modern society. It is particularly disappointing that students consistently perform poorly in mathematics in internal and external examinations, despite the relative importance of the subject.

The purpose of this study, which was conducted at the Nazarbayev Intellectual School of Physics and Mathematics in the city of Aktobe, was to determine the effect of the “flipped classroom” approach on mathematics achievement and interest of students. Given this, a quasi-experimental design was used, specifically non-equivalent pretest-posttest control group design. The study’s participants were a sample of 56 learners selected from two classes purposively. Each two SS 1 classes, divided into experimental and control groups via balloting.

The following research questions guided the study.

1. What are the mean achievement scores of students who received mathematics instruction using flipped classroom approach and their peers in the control group?

2. What are the mean achievement scores of male and female students who received flipped classroom approaches?

3. What are the mean interest scores of students who received mathematics instruction using flipped classroom approach and their peers in the control group?

4. What are the mean interest scores of male and female students who received flipped classroom approach?

The following hypotheses guided the study.

1. Difference exists between the mean achievement scores of students who received mathematics instruction using flipped classroom approach and their peers in the control group.

2. Difference exists between the mean achievement scores of male and female stu­dents who received mathematics instruction using flipped classroom approach.

3. Difference exists between the mean interest scores of students who received mathematics instruction using flipped classroom approach and their peers in the control group.

4. Difference exists between the mean interest scores of male and female students who received mathematics instruction using flipped classroom approach.

Data were gathered through the instrumentality of the Mathematics Achievement Test (MAT) and Mathematics Interest Inventory (MII), which have reliability scores of 0.88 and 0.79, respectively. Prior to and following a six-week course of treatment, each group completed a pretest and posttest. SPSS, a statistical tool for social sciences, was applied to analyse the acquired data. The mean and standard deviation were utilised to report the study’s questions, and analysis of covariance (ANCOVA) was utilised to evaluate the hypotheses at a 0.05 significance level. Results established that learners taught mathematics utilising flipped classroom approach had higher mathematics achievement and interest scores than their peers taught using the conventional approach. Results also revealed that the achievement and interest scores of male and female learners who received mathematics instruction using flipped classroom approach were the same. Considering the findings, recommendations were given, among others, that mathematics teachers should use the flipped classroom approach to assist learners in boosting their achievement and interest in mathematics, especially in geometry.

Issues in mathematics education are wide-ranging, with the subject often perceived as hard, formulaic, and consisting of a series of unrelated abstract concepts, with a strong focus on assessment (Bray & Tangney, 2017). Historically an over-reliance on skills and procedures has led to a lack of mathematical fluency and conceptual understanding, with problem solving viewed as little more than worded calculations (Schoenfeld, 2016). The main drivers of reforms in mathematics curriculum internationally focus on efforts to address these issues by, at least in part, giving greater considerations to the student at the centre of the learning. Maths students should be supported to develop a positive disposition towards the subject, by highlighting connections between the different mathematical strands (NCCA, 2017) and teaching for robust understanding (Schoenfeld, 2017) to ensure maths becomes more relevant for school and society in general.

Recent iterations of maths education reforms continue to show that changing how we teach mathematics is difficult, teachers struggle to find time to engage with reform or create new resources and as a result tend to rely heavily on textbooks (O’Meara & Milinkovic, 2023). Although various technological advances have been heralded as a “silver bullet” that will solve the issues with student engagement with mathematics, take-up and implementation of such resources by teachers has often remained at the periphery (Bennison & Goos, 2010). Many reasons have been cited as barriers to teacher uptake of new technological developments, including systemic issues such as class-size, timetabling and cost (Bray & Tangney, 2017), as well as access and logistical problems. However, another pressing issue, is a need for professional development (PD) for teachers (OECD, 2015).

There is consistent evidence indicating that a sustained and experiential approach to PD is essential to support teacher change (Desimone, 2011). It is essential that practitioners are provided with opportunities to develop their own understanding of the value and relevance of any proposed change, as well as to recognise the impact that it might have on their practice and on student outcomes (Kärkkäinen, 2012).

The latest technological advancement that is predicted to have a significant impact on our societies and futures is generative AI (GenAI). Many questions have arisen about its potential impact on education, which are speculated to be both positive and negative (Giannini, 2023). While there are ethical concerns about the black box nature around the understanding of the AI processes, and the veracity of the information which it provides (Kaplan-Rakowski et al., 2023), there are also significant fears around cheating and plagiarism. However, when used appropriately, GenAI offers many opportunities, with UNESCO suggesting it can be used for activities ranging from idea generation to a reflection aid (Sabzalieva & Valentini, 2023). Of relevance to this work is the potential for GenAI to support teachers in the generation of, and reflection upon, lesson plans and resources that address the issues in mathematics education highlighted above. Hence the “two birds” reference in title – teachers are learning how to engage with GenAI while creating lessons which aim to meet the goals of curriculum reform. However, in order to support this, appropriate PD must be provided.

Constructivism and constructionism are the theoretical frameworks that underpins this research, acknowledging an approach in which both the technology and the user are constructing knowledge (Ackermann E., 2001). As part of a wider PD engagement with schools experiential GenAI workshops are being designed and delivered. The workshops support teachers through an immersive, iterative experience, to create and reflect upon lesson ideas, lesson plans and rich learning experiences, that give context and purpose to their lessons.

The generation and use of digital data and analyses in education comes with promises and opportunities, especially where digital materials allow use of Learning Analytics (LA) as a tool in Data-Based Decision-Making (DBDM). LA implies, analysing educational data to understand and optimise learning and learning environments (Siemens & Baker, 2012). In this paper we discuss LA as “a sophisticated form of data driven decision making” (Mandinach & Abrams, 2022, p. 196) as we explore how LA is used to support mathematics teaching and learning with digital materials in classroom practice. Data driven decision making or DBDM has been defined by Schildkamp and Kuiper (2010) as “systematically analyzing existing data sources within the school, applying outcomes of analyses to innovate teaching, curricula, and school performance, and, implementing (e.g., genuine improvement actions) and evaluating these innovations” (p. 482). DBDM is a key for the interpretation of LA, and can use any form of data, but in this review, the term DBDM is restricted to digital data. Using LA as a tool for DBDM could streamline data, making it more readily interpretable. However, questions remain about how usage can translate into practice (Mandinach & Abrams, 2022).

Quality of technology integration is not merely about technology use, but also about pedagogical use (Ottestad & Guðmundsdottir, 2018), about transformation and amplification of teaching as well as learning through use of technology (Consoli, Desiron & Cattaneo, 2023). LA within Digital Learning Material (DLM) can offer learners adaptive functions seamlessly embedded in DLMs or, provide learners (and teachers) compiled student assessments in relation to learning goals extracted from learning activities (Wise, Zhao & Hausknecht, 2014). The role of the teacher in student learning is clearly of central importance (Hattie & Yates, 2013; Yackel & Cobb, 1996), and teachers have a key responsibility to make digital technology a recourse in teaching to support student learning (Scherer, Siddiq & Tondeur, 2019).

This paper present findings from an exploratory systematic scoping review which was conducted regarding the use and impact of LA and DBDM in classroom practice to outline aspects related to Digital Learning Material (DLM), teacher usage, and student learning in the context of K-12 mathematics education.

A scoping review was deemed most appropriate since it can be performed even if there is limited number of published primary research (Gough, Oliver & Thomas, 2017), fitting new research areas such as LA, as it provides “a technique to ‘map’ relevant literature in the field of interest” (Arksey & O’Malley, 2005, p. 20), as well as combine different kinds of evidence (Gough, et al., 2017).

Networks hold a meeting during ECER. All interested are welcome.

There are disparities in achievement and opportunity across the board in areas of socio-economic disadvantage. The gaps in mathematics are particularly stark and this has significant negative implications for student choice in post-secondary education and subsequent access to further education and occupations, particularly within STEM-fields. This study uses Bronfenbrenner and Morris’s (2007) Process-Person-Context-Time (PPCT) as a theoretical framework to present a snapshot of some of the influential factors at play, and then to examine the initial results of a systematic literature review (SLR) that explores empirical attempts that have been made to address these issues.

The importance of education in relation to future earnings, health and wellbeing is well understood, and, according to the Salamanca Statement and Framework outlined by UNESCO (1994), it behoves governments and other stakeholders around the world to implement strategies that will improve the educational opportunities for disadvantaged children. However, in order to do so, it is essential to firstly ask what factors might influence these outcomes, and secondly, how can we best address them. In this introductory section the PPCT theoretical framework is used to present some of the myriad factors at play specifically within the field of mathematics education, providing a holistic base upon with to consider any strategies to address them. Using PPCT as a lens, the following key points have emerged:

Process: According to Ekmekci, Corkin, and Fan (2019), while students from socio-economically disadvantaged backgrounds are particularly in need of effective pedagogy, they are more likely to “receive less effective instruction on average compared to their higher income peers” p. 58. Within such contexts, teacher’s pedagogic approaches tend to focus more on controlling behaviours (Megowan-Romanowicz, Middleton, Ganesh, & Joanou, 2013). These are examples of intrinsic didactical exclusion which reproduce structural disadvantage in societies, through mathematics.

Person: As noted by Ní Shuilleabhain, Cronin, and Prendergast (2020), students’ attitudes towards mathematics tend to be more negative in schools in areas of low Socio-Economic Status (SES), and pupils in such schools tend to have higher levels of mathematical anxiety and lower self-concept in mathematics.

Context: Low SES Neighbourhoods are often recognised as being less conducive to educational achievement, with less access to social capital via mentors or role models, and fewer resources (Dietrichson, Bøg, Filges, & Klint Jørgensen, 2017). Dotson and Foley (2016) highlight the challenges in hiring and retaining high quality mathematics teachers to schools in low SES areas, citing the “inherent difficulty” of working in such contexts. This can lead to a cycle of low expectations for students, and, given that “the development of student motivation flows at least partially through teacher motivations and motivation related behaviors” (Megowan-Romanowicz et al., 2013, p. 53), the influence of such low expectations can be damaging.

Time: The initial years in post-primary are understood as crucial for a student’s mathematical journey, with performance at this stage acting as a gatekeeper to higher-level mathematics courses and beyond that to STEM courses and careers. Unfortunately, it is precisely at this juncture that achievement gaps tend to widen for students from lower SES backgrounds (McKenna, Muething, Flower, Bryant, & Bryant, 2015).

This section has highlighted a few of the many reasons why achievement in mathematics is stratified along socio-economic lines. This study uses a SLR methodology to attempt to address the following research questions:

1. What types of empirical research have been undertaken aiming to address the mathematical achievement gap between low SES students and their more affluent peers?
2. What ‘best practices’ or ‘guidelines’ can be extrapolated from these studies to inform future work?

Despite attempts to address the well-documented issues in mathematics education with curriculum reform and associated professional development (PD) programmes, significant challenges remain in relation to the teaching and learning of mathematics in schools, particularly in areas of low socio-economic status (SES). In relation to recent curriculum reform in Ireland, research has highlighted teachers’ frustration with the new curriculum specification, a lack of faith in the teaching methodologies being promoted, and a demand for additional PD and support (Byrne & Prendergast, 2020). This lack of faith can mean that teachers often select, a la carte, the approaches they feel address their own concerns or align most with their own beliefs, leading to at best a hybridized version of practice (Cavanagh, 2006).

A wealth of research highlights the prevalence of what Corkin et al. (2015) refer to as “pedagogy of poverty”, noting that students from low SES backgrounds are at an increased risk of rigid, teacher-centric, formulaic pedagogical approaches, focusing on punctuality, and maintaining control. Factors influencing the approaches used include low teacher perception of student ability, which can often be related to, low teacher self-efficacy, out-of-field or inexperienced teachers, or lack of buy-in to reform practices, (Byrne & Prendergast, 2020; Ni Shuilleabhain et al., 2021; Yanisko, 2016). Given the domain-specific challenges of mathematics, and the additional challenge associated with educational disadvantage, there is a need for targeted intervention with schools that serve underrepresented cohorts.

PD is obviously central to such an intervention, but for it to be effective, the literature suggests that it must be a sustained, long running programme that acknowledges the iterative and reflective nature of development of teaching practices, and is deeply rooted in the context of the school (Desimone, 2011; Lieberman, 1995). It should jointly focus on a hands-on element and a co-creative, collaborative planning element within a community of practice. These separate but complimentary factors facilitate the iterative shift between knowledge building and practice through the reflective process (Valerio, 2021).

This paper describes a project that involves working with mathematics teachers in low SES schools in an effort to support them to make the most of curriculum reform and to ultimately help improve student engagement and attainment in the subject at lower secondary (ages ~12 – 15).

The theoretical framework underpinning this is expectancy-value theory (EVT), which posits that both one’s expectation for success (expectancy) and how one values a task (a combined measure of intrinsic, attainment, utility values and cost) directly influence the decision to undertake, and the level of persistence towards, the task (Wigfield & Eccles, 2000). The “task” in the context of this research, is conceptualised as faithful engagement with the new curriculum specification.

Based on the principals of EVT and the features of effective PD described by Desimone (2011) a series of PD interventions were co-planned and co-created, by the research team and participating teachers, with the aim of increasing task value and supporting growth in expectancy beliefs of the teachers. This was achieved by:

• Creating bespoke PD sessions in direct response to feedback of perceived needs and barriers of participants in relation to their practice and implementation of the intended revised curriculum, thus increasing perceived utility.
• Co-creative lesson planning, combined with in-school support in terms of planning time and co-teaching to reduce perceived cost of engagement.
• Focusing on best-practice informed strategies of context-rich problems and inquiry-based learning to increase student engagement, which in turn increases teacher attainment value.
• Giving teachers low-risk opportunities to experience reform practices, through observations, co-teaching and targeted workshops, scaffolds growth in expectancy and ability values.

In the past few years, the interest in the mathematical development of preschool children has increased. An important reason for this is the evidence provided by research that children’s competence levels in numeracy before or at the beginning of school are significant predictors of their achievement over the school years (e.g., Watts et al., 2014). Considering also that mathematical literacy is a key component of STEM education, which contributes to the knowledge and skills individuals need to develop to live and grow in our modern societies of information and technology, (early) mathematics education should be regarded as one of the most important constituents of the educational system. Early years mathematics education aims to offer children mathematical experiences and learning opportunities through which the children shall strengthen their mental abilities, to be able to structure mathematical concepts and develop mathematical skills both in the present and in the future.

In recent years several researchers have studied preschool children’s number sense and number-related abilities, including quantitative reasoning, that is, additive reasoning, which refers to addition and subtraction (e.g., Purpura & Lonigan, 2013) and multiplicative reasoning, which refers to multiplication and division (e.g., Nunes et al., 2015; Van den Heuvel-Panhuizen & Elia, 2020). Multiplicative reasoning, which is more complex than additive reasoning (Urlich, 2015), has received less research attention.

The present study focuses on the mathematical concept of division. Specifically, the research objective of the study is to gain an in-depth insight into kindergartners’ thinking in division. The research questions that are addressed in the present study are the following: (a) How do kindergartners make sense of division?, (b) What strategies do kindergartners use to solve division problems?, (c) What difficulties do kindergartners encounter in division? A further concern of the study was to identify possible differences in making sense of division by kindergartners of different ages.

Division is the process of dividing a quantity or a set into equal parts. Partitive division and quotative division are two major types of division problems (Nunes et al., 2015). In partitive division a group of objects is divided into equal subgroups and the solver has to find the size of each subgroup. In the quotative division, the size of the whole group and the size of each equal subgroup are known and the solver must find out how many equivalent subgroups there are (Van de Walle et al., 2014).

From the two types of division, partitive division is the type of division that children develop first (Clements et al., 2004). An informal strategy that is often used by children in partitive division with concrete objects is the distribution of the objects one by one (one-by-one strategy) or two by two (two-by-two strategy) to the recipients (subgroups). The difficulties encountered by the children in division are often caused by the increase of the quantity children are asked to divide among a certain number of recipients and also by the increase of the number of recipients to whom the certain quantity must be divided in partitive division or by the increase of the number of items of each equal subgroup in quotative division (Clements et al., 2004).

In recent years, there is a growing interest in early childhood mathematics education research at an international level (Elia et al., 2023). This interest is attributed to a large extent to the increasing emphasis given on preschool education in many countries (e.g., Kagan & Roth, 2017) and to the findings of various studies which provide evidence for the significant role of young children’s early mathematical competences in their mathematics learning and performance later at school (Watts et al., 2014). Based on the above, the need of high-quality mathematics learning experiences from the beginning of children’s education is stressed.

A major pedagogical tool that is systematically used in early childhood education is picture books. Picture books are books that convey information either through a combination of images - text, or only through a series of images (Kümmerling – Meibauer et al., 2015). Picture books are used to nurture children’s emotional, social, and intellectual development as well as to develop children in content areas such as mathematics (Cooper et al., 2020). Particularly, picture books can provide a meaningful framework for learning mathematics and provide an informal base of experience with mathematical ideas that can be a starting point for more formal levels of understanding (Van den Heuvel-Panhuizen et al., 2009). Based on the findings of van den Heuvel-Panhuizen et al.’s study (2016), reading picture books should have an important place in the kindergarten curriculum to support children’s mathematical development.

Picture book reading in preschool can be done as an informal and spontaneous activity in which children are involved during free play and also as an activity that is organized and guided by the teacher (Van den Heuvel-Panhuizen & Elia, 2013). Considering the latter case, picture books can be used in all phases of the learning process, such as introducing new mathematical concepts, assessing children’s prior knowledge, deepening understanding and revising topics (Van den Heuvel-Panhuizen & Elia, 2012). Educators can make use of picture books by asking questions, posing problems to children, offering opportunities to discuss mathematical ideas and by adding relevant activities to provoke further exploration of the mathematics included in picture books.

In previous studies, different types of picture books were used to stimulate children’s mathematical development. With respect to the mathematical content included in the picture books, based on Marston’s (2014) work, a distinction can be made between (a) picture books with explicit mathematical content, which are written with the purpose to teach children mathematics, (b) picture books with embedded mathematical content, which are written primarily to entertain but the mathematics is intentional, and (c) picture books with perceived mathematical content, which tell an appealing story and in which mathematics is unintentional and implicit in the story.

According to the recent review on picture book reading in early years mathematics by Op ‘t Eynde et al. (2023), research studies that investigate the interplay between the picture books characteristics and the quality of picture book reading in early mathematics, based on the children’s and/or readers’ utterances, are rare. The present study could be considered as a step towards this research dimension, as it aims to explore the potential of the use of picture books with different characteristics in prompting children’s mathematical thinking.

Considering that, even if picture books are not written to teach mathematics, they may offer many opportunities for the exploration of mathematical ideas by young children (e.g., Dunphy, 2020), our study addresses the following research question: What are the possibilities offered by the use of picture books with embedded mathematical content and picture books with perceived mathematical content for inducing mathematical thinking in early childhood?

In primary education, geometrical drawing abilities hold pivotal importance. The ability to visually represent geometric shapes is a foundational skill that not only introduces students to the world of mathematics but also serves as a precursor to advanced spatial reasoning capabilities (Clements & Battista, 1992). This research aims to assess primary school students' geometrical drawing abilities comprehensively. By employing paper-pencil tests utilizing grid and isometric paper, the objective is to gauge the student's proficiency in visually representing two- and three-dimensional geometric shapes. This endeavor seeks to understand primary school students' current geometrical drawing skills.
The second objective involves an evaluation of the geometrical drawing abilities of pre-service primary school teachers. Through similar paper-pencil tests, the aim is to gauge the aptitude of prospective teachers to represent geometric shapes in various dimensions. This assessment is crucial for identifying potential areas of improvement in teacher training programs to ensure that future educators are equipped to impart geometric concepts effectively. The third objective
involves a comparative analysis of primary school students and pre-service teachers' performance in two- and three-dimensional geometric drawing tasks. By discerning potential differences in their abilities, this research seeks
to contribute valuable insights into the relationship between educational background and geometrical drawing proficiency. For these purposes, the three research questions are as follows: (a) What are the geometrical drawing abilities of primary school students? (b) What are the geometrical drawings? What are the abilities of pre-service primary school teachers? (c) What are the similarities and differences in drawing abilities for 4th graders and prospective teachers?

Formation of a model of an inquisitive, intelligent, thoughtful, sociable, consistent, fair, caring, risky, harmonious, reflective student through the organization of research work in mathematics lessons. To show students the importance of organizing research work in mathematics lessons in educating a person with comprehensively developed high moral values, who is ready to apply the acquired knowledge in the process of continuing education in unfamiliar situations.
The article discusses how students can develop their research skills through small research activities. The work of various scientists is analyzed, the results of jointly planned classes on the development of students ' motivation for learning and research skills are analyzed. In the course of organizing research work in action, effective points of joint planning of teachers were identified and outlined. As a result of the study, it was found that the compilation of problems related to real life in a practical direction develops the ability of thinking to synthesize, analyze.

Conducting meaningful research work in mathematics lessons is the basis for developing students ' deeper understanding of the subject and the ability to apply it in real life. The fact that students learn, Act and reflect in a repeated cycle can lead them from academic knowledge to practical insight and the development of its positive attitude to learning, as well as personal and social responsibility.

The purpose of the study: to study the logical abilities of students through a problematic learning approach

to increase interest in their work, to teach students to work consciously on themselves, as well as to achieve solid knowledge, high learning outcomes through this method of teaching.
Research objectives:
Definition of the theoretical, basis of problem-based learning in the scientific and methodological literature;
- Consider ways to solve problems in the development of students ' thinking;
- Pedagogical and psychological description of the level of development of students;
Scientific forecast of the study: if the organized work is organized systematically, purposefully, it will be possible to develop students ' thinking through problem-based learning approaches.

A mathematical study is a long-term, open-ended study consisting of a set of questions, the answers of which are interconnected and mutually contribute to obtaining a solution. The problems are open-ended, unfinished, because students always come up with new questions based on their observations. Additional characteristics of student research include the following:
Students use the same methods used in mathematical research. They work through data acquisition, visualization, abstractions, and proof cycles.
Students communicate with each other through mathematical language: they describe their thoughts, write their judgments and predictions, use symbols, prove their conclusions, and study mathematics.
If the study consists of class or group work, then students become a community of mathematicians, exchanging experience and complementing each other with questions, assumptions, theorems.

Influence of mathematical research work on the subject
The student has a high memory and ability to concentrate, develops the ability to quickly complete a task in unfamiliar situations, and develops the skills of logical thinking, effective use of information.
It is clearly seen that the student is more motivated in the learning process, the ability to identify and find an effective solution to the problem is improved, and he gets pleasure in solving it.
The student has a high ability to think creatively, is able to identify complex patterns using mathematical approaches, such as mathematical language, developed creative thinking, and the ability to visualize tasks in space.
Every research work shows that students can think critically, analyze and present something new, new ideas with energy, whether on their own or in a group. When we find mathematical patterns, we feel that real pleasure is experienced through emotion.

The gendered choice and role of mathematics in pre-tertiary education is maybe one of the most pertinent research topics in education literature (e.g., Ellison & Swanson, 2023; Else-Quest et al., 2010; Uerz et al, 2004; Van der Werfhorst et al., 2003). While Finnish girls outperform boys in mathematics in the comprehensive school, it seems that once they have a possibility to make educational choices after the comprehensive school, the interplay of the internal versus external frame of reference for academic self-concept (Marsh & Shavelson, 1985) sets in motion and leads girls away from math (see also Marsh, 1990; Marsh et al., 2015). In Finland, this has been reported in students’ choice both between the two tracks of the Finnish dual model of upper secondary education (academic vs. vocational), among the different vocational programs, and within the relatively open syllabus of academic upper secondary education (Kupiainen & Hotulainen, 2019). In the current presentation, we set to explore the interplay of students’ gender and math choice in the academic upper secondary education, and its relation to students’ later educational choices.

In the dual model of Finnish upper secondary education (academic and vocational tracks, 56 % vs. 44 % of the age cohort, respectively), ninth grade students have a right to choose among all programs across the country but entrance to academic track schools is based on students’ ninth grade GPA (grade point average). Reflecting girls’ better achievement, they form a majority among academic track students (56 %). Yet, reflecting a longstanding gender-imbalance in students’ attitude toward mathematics and despite Finnish girls outperforming boys in the OECD PISA study (e.g., Hiltunen et al., 2023) and their better grades in math in the comprehensive school (Kupiainen & Hotulainen, 2022, p. 140), there is a clear gender difference in students’ choice between the Basic and Advanced syllabi in mathematics at the upper secondary level after the comprehensive school where all students follow the same syllabus for all subjects (Kupiainen et al., 2018).

The context of the presentation is a recent study of the impact of the Finnish higher education student selection reform of 2018 on academic upper secondary students’ study choices and wellbeing. Despite the long tradition of the Finnish matriculation examination with separate exams for each subject, Finnish tertiary education student admission has traditionally relied on a combination of field-specific entrance examinations and matriculation examination results. In 2018, a reform decreed that half of students in all fields of study shall be accepted based solely on their matriculation examination results and the other half solely on an entrance examination. The main goal of the reform was to speed Finnish students’ slow transit from secondary to tertiary education as due to a backlog of older matriculates vying for a place, two thirds of new matriculates have been yearly left without a place in higher education. The reform was backed by research on the drawbacks of the earlier entrance examination-based student selection (Pekkarinen & Sarvimäki, 2016) and tied the credit awarded for each subject-specific exam to the number of courses covered by the exam. The reform raised vocal criticism, mainly for Advanced Mathematics bringing most credit with its biggest course-load even in fields where it might appear of less value. Yet, the only earlier study on students’ relative success in the matriculation examination showed that on average, students of Advanced Mathematics fared in all exams they included in their examination (average 5,6 exams) better than students sitting for the exam in Basic Mathematics or with no mathematics exam, also allowed in the Finnish system (Kupiainen et al. 2018).