Conference Agenda

The 21^st century will bring challenges that call for individuals who can problem-solve, persevere, and innovate (Geisinger, 2016). As educators prepare students for addressing society’s trials, they must focus on helping students develop critical thinking skills. To accomplish this, mathematics education is crucial in expanding students’ abilities to analyse, synthesise, and predict information (Shakirova, 2007). Countries worldwide recognise the need for students to learn these skills and consequently revamped curriculums, teacher education programs, and policies (ACARA, 2022; NCCA, 2016). Although progress in students’ academic achievements in mathematics is evident worldwide, deficits remain (Mullis et al., 2011; Gilleece et al., 2020), signalling a need to investigate how mathematics education can ensure the development of students’ higher-level thinking skills.

This research project investigates how to support teachers in asking higher-level thinking questions in mathematics lessons. Asking students questions requiring higher-level thinking skills can increase their success in mathematics (Davoudi & Sadeghi, 2015) and aid them in developing critical thinking skills that are essential beyond mathematics classrooms (Nappi, 2017). Research indicates that teachers mainly ask lower-level thinking questions which require students to recall or restate information (Boaler & Brodie, 2004; Desli & Galanopoulou, 2015). As a result, this project aims to develop an electronic toolset that guides primary teachers through effectively including dialogue and higher-level questioning in mathematics lessons, named the e-DAQ. In addition to this teacher resource, the e-DAQ aims to be a form of continued professional development (CPD) for teachers, educating them on the importance of these questions and encouraging teachers to reflect on how to increase the use of higher-level questions. Theories on teaching and learning, which guide this research, will be expanded upon by completing this project. The following questions guide the research:

1. Can we collaboratively develop an electronic toolkit for primary teachers on effectively incorporating questioning in mathematics lessons?
2. Will the e-DAQ positively impact teachers’ instruction, and to what degree? Furthermore, will it act as a form of CPD for teachers, expanding their knowledge of mathematics? If so, what makes it an effective form of CPD?
3. How can this research contribute to educational design research theories?

An emerging theoretical framework is being used to guide this research, influenced by pedagogical considerations, constructivism, and cognitively guided instruction. In addition, theories relating to mathematics education, particularly questioning in mathematics education, are essential to the project. As this research also aims to investigate the role the e-DAQ plays in assisting teachers in developing professionally, theories relating to CPD helped to form the evolving conceptual framework. Several themes emerged as critical to developing the proposed framework, including Autonomy, Community, Efficacy, Motivation, and Identity, and therefore was appropriately named the ACMIE Theoretical Framework. The ACMIE Theoretical Framework guided the development of the e-DAQ, its implementation, and future analysis.

Although this research is being conducted in Ireland, the expected outcomes apply to countries worldwide. Countries are reexamining their mathematics curriculums and teacher education programs to meet the demands of the 21^st century that students will face. In addition, the themes generated to develop the ACMIE Theoretical Framework were synthesised from worldwide data on mathematics instruction, student achievement results, and professional development programs. As a result, the e-DAQ has the potential to aid teachers and students outside Ireland. In addition, the valuable perspectives gained on how teachers experience CPD and their values relating to professional learning will benefit international education systems.

Based on the updated Lithuanian Programs of Primary Education, one of the emphasized areas of achievement is problem-solving skills. Problem-solving abilities are an essential part of cognitive domain assessments in international educational research. In such surveys as TIMSS or PISA, part of the tasks requires students to apply mathematical concepts and thinking to make decisions, and thus justify and argue their answers. Therefore, problem-solving and mathematical thinking are important aspects when evaluating educational success (National Council of Teachers of Mathematics, 2000). The transfer of knowledge and the development of skills are part of the learning process, the combination of which is the ability to apply the acquired knowledge and skills in unfamiliar new situations, i.e. problem-solving tasks.

Reading and problem-solving in mathematics are two of the main skills taught in the early years of early formal education (Durand et al., 2005). Achievement in mathematics depends on the ability to understand and solve complex problems based on inherent logic (Lipnevich et al., 2016). A major source of difficulty in problem-solving is students' inability to actively monitor, control, and regulate their cognitive processes (Artzt et al., 1992).

To understand the problem-solving strategies, used by students and to determine which difficulties are caused by the insufficient level of knowledge and abilities relevant to the subject of mathematics and which are caused by the improper management of the learning process, complementary methods are used in the study. Mathematics learning difficulties are studied by focusing on the process of solving mathematical problems (Rosiyanti et al., 2021; Nurkaeti, 2018), for a deeper analysis the eye tracking method is applied (Stohmair et al., 2020; Schindler et al., 2019). To reveal a more detailed process of problem-solving, the think aloud method is applied (Rosenzweig et al., 2011; Ericsson, 2006).

The problem is expressed in the following questions: what difficulties do the students have in solving the problem; what are the diagnostic possibilities of eye-tracking technology in the process of problem-solving; what problem-solving strategies are used by students without mathematics learning difficulties; can these strategies be developed as a coping mechanism for students with mathematics learning difficulties?

The object of the research is students' problem-solving strategies as a mechanism for overcoming mathematics difficulties.

Hypotheses

1. When solving problematic tasks, students with a high level of achievement use self-created decision strategies, that are not acquired during the educational process.

2. The eye tracking system determines the cognitive and metacognitive strategies chosen by elementary school students and applied in problem-solving.

The aim is to determine the coping strategies of elementary school students with educational difficulties in learning mathematics.

Piaget's theory of cognitive development will be used in this research. Piaget suggested that children's cognitive development occurs in stages (Papalia & Feldman, 2011). Children themselves are active and motivated to learn, they learn through their own experience, structure, and organized schemes and patterns.

According to Polya, the steps in problem-solving are: understanding the problem, making a plan, executing the plan, and checking the answer (Polya, 1988). Several studies have shown that difficulties in solving mathematics problems can occur at any stage of the action (i.e., planning, doing, and evaluating (Zimmerman, 2000), but most problems occur during the planning and evaluation stages. In this regard, students often show difficulties when planning how to respond to a task, and they are inadequate or lack sufficient strategy concentration to perform all-effort calculations (Garcia et al., 2019).

Metacognitive theory. Metacognitive theories are broadly defined as systematic frameworks used to explain and guide cognition, metacognitive knowledge, and regulatory skills. (Schraw, 1995). Specifically, it refers to the processes used to plan, monitor, and evaluate one's understanding and performance.

The rapid changes in the times we live have led to an increase in the importance of scientific skills in our lives. To overcome the challenges of the twenty-first century in the science and technology sector, students need to be equipped with 21st-century skills to ensure their competitiveness in the globalization era (Turiman et al., 2013).

Among the 21st-century skills, the most important ones are numeracy and scientific literacy (Word Economic Forum, 2015; OECD, 2013). Scientific literacy is the ability to engage with science-related issues, and with the ideas of science, as a reflective citizen (OECD, 2017). It emphasizes the importance of being able to apply scientific knowledge in the context of real-life situations. Numeracy represents the ability to use numbers and other symbols to understand and express quantitative relationships (World Economic Forum, 2015).

TIMSS is the most advanced study that can provide an overview of the results of Romanian eighth-grade students in mathematics and sciences (physics, chemistry, biology, and geography). In 2019, Romanian students obtained a score of 479 points in mathematics (intermediate international benchmark) and 470 points in science (intermediate international benchmark). Analyzing Romania's participation (2007 - 2019) in the TIMSS study, it can be seen that the mathematics scores situate within the range of 458-479, and the science scores situate within the range of 462 - 470.

Unfortunately, the results obtained by the Romanian students within TIMSS 2019 remain below the average of the European countries and far below the regional average, being observed a significant variation in the quality of the national education system: the percentage of students who obtained "advanced" results is only 6% in mathematics and 4% in physics, while the percentage of students with "low" results or below the average-functional level is 70%. Romania recorded a much higher rate than other countries in terms of numerical or scientific illiteracy: 22% of students were not able to use mathematics or physics even in the simplest contexts.

The proposed research investigates the factors that affect the learning process in mathematics and sciences for 8th-grade students. Among the learning factors we will take into consideration, we mention: (1) carrying out experiments during science classes, (2) the way of working in the classroom (teamwork, individual work), (3) frequency of homework, (4) allocated time for homework, (5) self-efficacy towards math and science, (6) positive affect towards math and sciences, (7) teaching methods, (8) private lessons and also demographic characteristics as (9) gender and (10) residence.

The data analysis procedure will be conducted in two steps: (1) Analysis of each predictor’s (1-10) contribution to the total variance of TIMSS results of participants; (2) Comparison between high and advanced benchmark students (highest 25% of scores) and low and intermediated benchmark students (lowest 25% of scores) taking into consideration all the predictors, to see which of them contributes most to the results of high and advanced benchmark students.

Metacognition demonstrates great potential to equip children to become successful learners. Metacognition’s significance for mathematical competence is especially proven (Siagian et al., 2019). Therefore, attention should be paid to metacognition throughout students’ school path.

The most prominent definition of metacognition comes from the psychologist Flavell (1979); it refers to individuals’ knowledge of their own cognitive processes and their ability to regulate these processes. Most theoretical definitions distinguish between metacognition into metacognitive knowledge (later in this paper McKnow) and metacognitive skills (later McSkil) (Desoete & De Craene, 2019). McKnow refers to individuals’ knowledge of how people learn and process information, and it is categorised into strategy, task, and person knowledge (Flavell, 1979). Instead, Conrady (2015) distinguishes knowledge to declarative, procedural, and conditional knowledge. McSkil indicates the ability to consider one's actions and, when necessary, correct them (Schraw et al., 2006). Scholars (Schraw et al., 2006) define McSkil into evaluation, debriefing, planning, information management, and monitoring.

Several studies about metacognition in mathematics learning are conducted. Studies have highlighted the significant role of metacognition in performance and supporting the selection of learning strategies and fostering the development of self-regulatory (Desoete & De Craene, 2019). In this study, metacognition is explored more detailed subcomponents of metacognition. The research questions are as follows: what subcomponents of metacognition are recognisable from students’ answers about a problem-solving task, math, and its learning? How do subcomponents differ among different age students?