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Interest in Science, Technology, Engineering and Mathematics (STEM) has gained momentum due to increasing calls for a more STEM-literate society. As teaching integrated STEM poses curricular and pedagogical challenges for most generalist primary teachers, professional development (PD) is essential to support them to develop appropriate knowledge and efficacy to teach STEM. This paper presents a qualitative study of 17 primary teachers, 2 school principals and the PD facilitator. It explores the perceived impact of a customised three-phase STEM PD program on teacher efficacy in STEM education using Bandura's (1977) sources of efficacy as an analytic lens. The findings illustrate how particular features of the PD model were identified as contributing to the development of participating teachers' performance accomplishment, emotional arousal, vicarious experiences and verbal persuasion. In particular, there was consensus that the developmental structure of the STEM PD program, in terms of teachers' assuming increasing ownership for their STEM learning, incrementally enhanced teacher efficacy in STEM education. Implications of this study for STEM education and in particular STEM PD are discussed fully.

Prospective teachers' mathematics efficacy beliefs affect school placement experiences and influence later teacher behaviour and subsequent student outcomes. These efficacy beliefs are open to change during initial teacher education and become more resistant to change once the teacher enters the workforce. Therefore, it is important to measure mathematics teacher efficacy early in initial teacher education and identify low efficacy beliefs. This study measured the mathematics teaching efficacy beliefs of 402 prospective primary teachers. Arising from Rasch analysis of the efficacy scores of these teachers, 22 participants who displayed a range of mathematics teaching efficacy beliefs were interviewed to gain insights into factors affecting these beliefs. Participants communicated greater confidence in tasks requiring procedural (tell-items) than conceptual knowledge (explain-items). Both low and high efficacy participants reported traditional experiences of mathematics teaching and learning as students. However, high efficacy participants reported mastery of mathematics within these traditional contexts, whereas their low efficacy peers did not report mastery. Furthermore, all participants reported how memories of their school mathematics experiences informed their level of efficacy when thinking about teaching mathematics, thus revealing the powerful influence of mastery experiences.

Concern that stereotypical perceptions of scientists may influence attitudes towards science and willingness to pursue STEM-related careers has motivated interest in children's perceptions of scientists. This study investigated primary children's drawings of scientists at work based on Chambers' 'Draw-A-Scientist Test' (DAST) and explored the influence of living during the COVID-19 pandemic on perceptions of scientists. One hundred and ninety-four children participated in the study; school closures interrupted the study resulting in fifty-one participating during the COVID-19 pandemic. Stereotypic views of scientists that increased with age were revealed; differences between age groups were statistically significant. Drawings frequently depicted smiling lab-coated males working indoors using chemistry equipment. Boys incorporated significantly more stereotypic views in their drawings than girls. Same-sex preference for drawings of scientists was evident with female scientists drawn only by girls; however, this same sex preference weakened for girls, and they drew more male scientists as they got older. The absence of many traditional stereotypical indicators and presence of positive dispositions towards scientists and their work were welcome findings. There was greater awareness of the work of scientists amongst younger participants and a shift to broader conceptions of this work, both associated with living during the COVID-19 pandemic.

An essential task for mathematics teachers is posing problems. Selecting mathematics problems that develop mathematical proficiency and engage students in desirable mathematical practices is a critical decision-making process. We present the Framework for Posing Elementary Mathematics Problems (F-PosE) developed to focus prospective teacher noticing on desirable features of mathematics problems and inform decision-making processes around the selection of problems for use in elementary classrooms. Development of the framework was informed by a three-phase design research process consisting of an extensive review of the literature, document content analysis and successive testing of mathematics problems in elementary classrooms in partnership with teachers and children. Consequently, it draws from emergent practice informed by the collective endeavour of a community of educators. The framework consists of eight indicators: use of a motivating and engaging context, clarity in language and cultural context, curriculum coherence, attention to cognitive demand, an appropriate number of solution steps to support reasoning, a variety of solution strategies, facilitating multiple solutions and opportunity for success. This F-PosE provides a critical focusing lens for prospective teachers when creating and selecting mathematics problems specifically for use in elementary classrooms.

Responding to mathematical problems is a core activity in classrooms. The problems that teachers select determine the mathematical content, processes and nature of mathematical inquiry occurring in classrooms and thereby contribute to the development of mathematical skills and dispositions. Selecting, designing or reformulating mathematical problems is a critical skill, then, for prospective and practising teachers. This study explores the influence of a mathematical letter writing initiative in developing the problem posing skills of 28 prospective primary teachers. We examine the characteristics of mathematical problems designed by prospective teachers, and their understandings of what constitutes a good mathematical problem, prior to and following completion of a 12-week letter writing initiative with 10-11-year-old children. Analysis of the data reveals the benefits of engaging in the initiative as evidenced in improvements in several problem characteristics. There was an increase in the number of multiple approach and multiple solution problems and in the level of cognitive demand of problems posed. The challenge of posing non-traditional problems, alongside the competing demands of building in opportunities for success, may have diminished participants' ability to evaluate and attend to the cognitive demand of problems.

This paper explores Year 3 Irish students' problem-solving strategies when responding to a skyscraper growing pattern problem. Students' strategies reveal their understandings of multiplicative thinking, pattern, and algebraic reasoning. The version of the growing pattern lesson was that a 'teaching through problem solving' approach was taken, where no explicit strategies were modelled by the teacher at the start of the problem-solving process (Hourigan & Leavy 2022). Instead, once the teacher introduced the problem, these Year 3 students solved a range of mini-challenges using their own invented strategies. During the planning phase, the teachers had predicted various ways students may see and understand the characteristics of the growing pattern (Friel & Markworth 2009; Markworth 2012). This paper explores the modifications made to the problem context to promote engagement, the range of approaches adopted by two different classes of Year 3 students in response to the problem challenges, as well as the role of the teacher in guiding students to understand the problem and in orchestrating the sharing of student strategies.

The authors use finding the area of irregular shapes as the context for developing flexible strategies for measuring area. This article builds on their paper, "Setting a Design Challenge: Promoting the Discovery of the Relationship between Area and Perimeter" (EJ1272407). As part of Lesson Study research within an initial teacher education programme, a group of five preservice elementary teachers worked alongside two mathematics teacher educators to develop a sequence of instruction that would introduce two classes of Year 5 students (age 10-12) to realistic problems to support them in developing their area understandings. Previously, students explored the relationship between area and perimeter. This paper presents the classroom practices within the second implementation of the sequence of instruction, having refined various aspects of the lesson in light of observations and reflections after the first implementation e.g., groups size, modelling.

The association or relationship between two variables, also known as covariation, has been identified as one of the fundamental statistical concepts. This article details a statistical investigation that was used to informally introduce Grade 6 students to this concept.

This paper explores the experiences and professional learning of a group of in-service primary school teachers, participating in a STEM education programme in Ireland. Four primary teachers from the same case school engaged in a two-year project to explore STEM teaching and learning. This STEM project was structured as a multi-tiered partnership involving these four in-service teachers collaborating with six STEM teacher educators and a group of pre-service primary teachers, working together to develop an effective school-university STEM collaboration. The project focused on developing and facilitating meaningful classroom-based STEM learning experiences for primary aged children in the school. This paper specifically explores the professional learning and experiences of the in-service teacher participants. The teachers engaged in co-creating and co-facilitating a series of STEM lessons over two years in partnership with, and supported by the university STEM Education faculty. The paper provides insight into the participating teachers' professional learning in STEM education, as well as implications for school-university partnerships.

With increasing focus on primary curricular reform in Ireland, there is a growing recognition of the significance of early childhood education. As a result, professional development organisations are now examining the effectiveness of science, technology, engineering and mathematics (STEM) education for young children. This study investigates how teachers in a multi-grade primary school initially approached teaching integrated STEM lessons to children aged 4–7 years. Over the course of one school year, three teachers engaged in four cycles of lesson study. Through an action research approach, the researchers collected qualitative data from interviews, lesson plans, collaborative weekly meetings and observation sheets. The study identified difficulties associated with the teachers' limited comprehension of integrated STEM education and demonstrated how the Engineering Design Process helped to mitigate these challenges. The findings offer valuable insights into the knowledge requirements involved in developing children's 21st century skills. The research concluded that teachers enhanced children's STEM learning by providing opportunities for them to explore their curiosity, make predictions and experiment through open-ended play experiences. [ABSTRACT FROM AUTHOR]

Problem solving is a key priority in school mathematics. Central to the valuable role played by problem solving is the quality of the problems posed. While we recognize the features of good problems and how to support learners in solving problems, less is known about the ways in which prospective teachers' (PTs) conceptions of what constitutes a 'good' problem develop within the confines of an Initial Teacher Education program. This study explored the effect of engagement in a mathematics education course on the problem-posing skills of 415 prospective primary teachers. A 3-week instructional unit consisting of a series of lectures and tutorials on problem solving and problem posing was implemented. A questionnaire examining participants' understandings of and ability to pose problems was administered prior to and following instruction. Results reveal that participation brought improvements in conceptions of what constituted a good problem and in the ability to pose good problems (targeted at grades 1-4). Initial problems generally were arithmetic, required one step to solve and had only one correct solution. Following the instructional unit, attention was paid to designing problems that had the potential of multiple strategy use, multiple possible correct solutions, multiple modes of representation and the incorporation of extraneous information. Despite these improvements, the complexities of problem posing and the challenges that persist for PTs in posing good problems are evidenced. Recommendations are made for the enhancement of problem-posing experiences, most notably developing skills in identifying mathematically worthwhile problems from a selection of problems or in reformulating given problems to make them better, that support PTs in developing the knowledge and understandings required to pose mathematically worthwhile problems.

This paper presents insights from classroom practice where mathematical thinking, and in particular statistical literacy, are central to solving a STEM problem. We demonstrate that when an investigation sparks student interest and requires active participation, there are opportunities to experience the functionality of statistics.

The authors describe activities designed to teach the concept of weight to five and six year old children, using the imaginary 'Measureland' and its brand-new ride 'The Zipline Balancer'. They explore how they addressed misconceptions and insights are provided into the evolving measurement understandings of young children.

Probability education has fast become a contested area, with curriculum authorities in some countries recently suspending its introduction until the post-primary years. In other countries, children as young as 7 years are introduced to informal probability concepts. These recent international shifts in practice have contributed to a paucity of attention to the understandings of probability among pre-service and practising teachers. This presents implications for teacher educators who seek to provide opportunities for pre-service teachers (PSTs) to develop appropriate knowledge for teaching. This paper reports on the probabilistic understandings of a sample of 104 elementary PSTs. It focuses on one particular aspect of this knowledge -- understanding of probabilistic fairness. The study examines the approaches taken by PSTs when designing fair and unfair activities for use in the primary classroom. We place particular attention on the variety of random generators selected and the features of the activities designed by PSTs to illustrate fairness. Almost half of participants successfully designed fair and unfair activities for three different random generators. Particular random generators, namely playing cards, dice and coins presented more challenge and less successful outcomes. The findings provide an initial step in unravelling the complexities of understanding probabilistic fairness and serve to inform the design of curriculum experiences in probability instruction in initial teacher education (ITE) contexts.

As part of Lesson Study research within an initial teacher education programme two mathematics teacher educators worked alongside a group of five pre-service elementary teachers to create a motivating and meaningful problem-based lesson. The lesson promoted Year 5 students' understandings of the relationship between area and perimeter. The results showed that problem-based lessons provide a motivating and meaningful content for student learning in mathematics.

While there is abundant research reporting the impact of Lesson Study as a professional development framework for qualified teachers, its potential within initial teacher education remains relatively unexplored. We present a particular model of formal Lesson Study which has been experienced annually for a decade by Irish pre-service primary teachers. This study examines the perceived effects on learning of this Lesson Study model on a large sample of pre-service primary teachers (N = 225) who worked in 45 different lesson study groups over a 10 year period (2008-2017). Data analysis reveals that participants' perceptions of learning fell within two distinct themes namely 'An awakening regarding teacher content knowledge' and 'Cornerstones of learner-centred practice', each of which consisted of rich inter-connected sub-themes. As a result of engaging in Lesson Study, participants report an increased awareness of the importance of deep content knowledge in addition to adopting a learner-centred approach to their practice. Participants also believed that Lesson Study enhanced their professional knowledge and skills in the curricular area of focus (mathematics, in this case). While this study focuses on self-report data, these opinions are fundamental given research which proposes that interventions will fail if participants judge them to be ineffective.

Research examining the characteristics of both qualified and pre-service teachers focuses on traits including gender, socio-economic and socio-demographic background, knowledge and a variety of relevant affective constructs. Studies also investigate such traits among entrants to initial teacher education (ITE). The desire for more diversity within the teaching profession has led to alternative entry routes to the teaching profession (consecutive model for post-graduates) for those who may be unable to gain entry via the traditional concurrent (undergraduate) route. Internationally, there are divergent viewpoints and practices in relation to the value and use of the respective routes. This paper presents a comparative study within the Irish context, examining whether the consecutive model route to ITE promotes diversity in terms of entrants' attitudes to mathematics. The study examines the entry-level mathematics attitudes of two distinctive groups of ITE entrants, namely 419 concurrent and 59 consecutive elementary pre-service teachers, in one Irish ITE institution prior to engagement with their ITE mathematics education programme. It compares their enjoyment of mathematics as well as their beliefs regarding the value of mathematics and examines the extent to which any distinguishing differences are apparent among the respective cohorts using the Aiken's Revised Mathematics Attitude Scale. Analyses indicate generally positive attitudes among both cohorts; however, differences are evident between the cohorts with the consecutive route cohort demonstrating particularly apposite attitudes. The findings support the belief that the consecutive ITE route holds merit and prompts further investigation regarding the unique dispositions that these entrants possess.

We are pleased to bring you this follow-up to Mairéad Hourigan and Aisling Leavy's article [EJ1289314] that was published in issue 1 this year. In this contribution, they demonstrate that embedding mathematics within a rich context and learning sequence assists with the consolidation of student understanding and makes more effective use of teacher planning time.

Changes in society demand constantly evolving education systems. Teachers' practice is crucial to the successful implementation of educational reforms. A major obstacle for practicing teachers in implementing reform mathematics is that they have not experienced it themselves as learners. Consequently, teachers require extended, practice-based professional development to support them in the implementation phase of reform endeavours. Japanese Lesson Study has increased in popularity internationally as a professional development model due to its potential to facilitate teachers to learn in and from the practice of teaching. This self-study examines two mathematics teacher educators' first experience of facilitating Lesson Study with Irish primary in-service teachers. Reflection on the Lesson Study carried out with in-service teachers in 8 urban schools revealed three critical incidents that promoted deeper understanding of the context. The findings provide insights into the realities of managing and leading Lesson Study with in-service teachers, in particular the various barriers affecting teacher engagement. Alternative approaches to practice to address these challenges are also identified. [ABSTRACT FROM AUTHOR]

Teacher knowledge is a critical focus of educational research in light of the potential impact of teacher knowledge on student learning. The dearth of research exploring entry-level preservice teachers' geometric knowledge poses an onerous challenge for mathematics educators in initial teacher education (ITE) when designing experiences that develop preservice teachers' geometric knowledge to support the task of teaching. This study examines the geometric thinking levels of entry-level Irish preservice primary teachers (N = 381). Participants' geometric thinking levels were determined through a multiple-choice geometry test (van Hiele Geometry Test) prior to commencing a Geometry course within their ITE program. The findings reveal limited geometric thinking among half of the cohort and question the extent to which pre-tertiary experiences develop appropriate foundations to facilitate a smooth transition into ITE mathematics programs. The study also examines the nature of misconceptions among those with limited geometric thinking and presents suggestions to enhance the geometric understandings of preservice teachers.

Background: The relationship between attitudes and behaviour has led to a focus on the role played by attitudes in the teaching and learning of mathematics. Purpose: This paper reports on an investigation into studentteachers' self-reported attitudes towards mathematics in the context of a mathematics education programme. The programme had been developed by the authors in response to a new, reformed four-year undergraduate initial teacher education (ITE) for primary teachers in Ireland. The authors aimed to use the feedback to evaluate and develop the course further. Sample: We report on the attitudes of 345 pre-service primary teachers enrolled in a four-year undergraduate ITE programme. 281 of these participants had matched survey data before and after participating in the mathematics education programme. Method and Design: Four evaluation criteria were used as a conceptual framework for the evaluation of the mathematics education programme. A multi-method approach was taken in investigating the students' attitudes to mathematics by using a scale as a quantitative measure of attitude alongside open-ended survey items that provided qualitative insights into changes in attitudes. Results and conclusions: Results from the survey data suggested overall that the participants' attitudes towards mathematics were more positive after they had experienced the mathematics education programme. Overall, the written responses suggested that according to self-reportage, participants perceived that participation in the mathematics education programme had affected their attitudes towards mathematics positively. Comments indicated that the 'small group' tutorial structure was particularly well received and was associated with opportunities to actively engage, explore, interact and reflect. Suggestions offered by the participants will be used to inform planning and development of the mathematics programme.

As part of Japanese Lesson study research focusing on "comparing and describing likelihoods", fifth grade elementary students used real-world data in decision-making. Sporting statistics facilitated opportunities for informal inference, where data were used to make and justify predictions.

In this article the authors describe an instructional unit designed and taught in two classes of kindergarten children. The goals of the unit were to present a "driving question" to motivate the process of statistical investigation, to genuinely engage children in the stages of statistical investigation, and to facilitate them in experiencing an alternative data collection method. In an elementary school classroom, data are usually collected through surveys (asking people their favorite ice-cream flavor) or observing events (counting the colors of cars in the parking lot). A survey is a popular and effective data collection method (compare Cook 2008); nevertheless, for this unit the teachers wanted the children to experience an alternative method of data collection, namely "observation." They also wanted the students to experience statistics as a tool to investigate everyday problems. So, they presented the children with an ordinary problem: What puppet should a teacher buy for her class? To solve the problem, they would have to collect data to identify the character that appeared most frequently in a piece of children's literature. The teachers used the PPDAC (problem, plan, data, analysis, conclusion) cycle (Wild and Pfannkuch 1999) as a guiding framework for the unit. A bibliography is included.

We describe how the use of a games environment combined with technology supports upper primary children in engaging with a concept traditionally considered too advanced for the primary classes: "The Law of Large Numbers."

There is international dissatisfaction regarding the standard of mathematics subject matter knowledge (MSMK) evident among both qualified and prospective elementary teachers. Ireland is no exception. Following increasing anecdotal evidence of prospective elementary teachers in one Irish College of Education (provider of initial teacher education programme) demonstrating weaknesses in this regard, this study sought to examine and address the issue through two cycles of action research. The examination of the nature of prospective teachers' MSMK (as well as related beliefs in the main study) informed the design and implementation of an intervention to address the issue. A mixed method approach was taken throughout. In both cycles, Shapiro's criteria were used as a conceptual framework for the evaluation of the initiative. This paper focuses on the perceived and actual effects of the intervention on participants' MSMK. As well as its contribution at a local and national level, the study provides an Irish perspective on approaches taken to address the phenomenon internationally.

While within a geometric repeating pattern, there is an identifiable core which is made up of objects that repeat in a predictable manner, a geometric growing pattern (also called visual or pictorial growing patterns in other curricula) "is a pattern that is made from a sequence of figures [or objects] that change from one term to the next in a predictable way" (Billings, Tiedt & Slater, 2007, p. 303). In this article, the authors explore several examples of ways to use geometrical growing patterns to develop students' algebraic thinking. Examples are situated within interesting contexts to elicit algebraic generalisations by working through a five-phase analysis process.

The context of students as architects is used to examine the similarities and differences between prisms and pyramids. Leavy and Hourigan use the Van Hiele Model as a tool to support teachers to develop expectations for differentiating geometry in the classroom using practical examples.

Quite a bit of the arithmetic in elementary school contains elements of algebraic reasoning. After researching and testing a number of instructional strategies with Irish third graders, these authors found effective methods for cultivating a relational concept of equality in third-grade students. Understanding equality is fundamental to algebraic understanding. Although we introduce the equals sign to children as young as five or six, equality is not simple. The notion of equal is "complex and difficult for students to comprehend" (RAND Mathematics Study Panel 2003, p. 53). Overcoming such difficulty is essential because an understanding of equality supports the transition from arithmetic to algebra and forms the basis for comprehension of equations and inequalities. The huge impact that understanding equality has on later algebraic understanding draws attention to the importance of identifying and tackling misconceptions that are related to equality when they arise in elementary school classrooms. This article describes ways the authors worked with school children in Ireland to refine nine approaches to developing notions of equality.