Prospective Primary Teachers’ Professional Noticing in Non-formal Learning Environments: The Case of a Mathematics Fair

Research around mathematics teachers’ professional noticing has been largely contextualised by the formal setting of the classroom. In addressing the lack of relevant studies in non-formal learning environments, this paper draws on student teachers’ observations within a Mathematics Fair, which was part of a mathematics methods module of a primary education undergraduate programme. Working in pairs, 64 student teachers designed interactive mathematical games which upper primary school pupils had the opportunity to play in an event having taken place at our university. In this study, we analyse student teachers’ individual reflective essays written after the Fair, where they discussed important, in their view, incidents and observations. Employing a thematic analysis approach, we identified four themes discussed by students: the task; learning; teaching; non-formal environment. We conclude with the implications for teacher education and suggestions for future research.

Methodology for Constructing and Using a Mathematical Model for Assessing Labor Costs for the Development of Distance Learning Courses

Distance learning plays a significant role in solving the problem of the sustainable development of society. Unfortunately, the development and implementation of distance courses are still carried out intuitively, which does not allow practical implementation of effective mathematics methods and slows down the introduction of breakthrough technologies. The aim of the research was to develop a new model and a methodology for assessing the labor costs of designing distance learning courses by university teachers based on a comprehensive assessment of the courses’ quality. The suggested model originally extends the constructive cost evaluation model already used in IT industry. The developed criteria make it possible to assess labor costs in relation to the quality of course development. The paper provides and analyzes such calculations on the example of courses in the theory of algorithms and programming.

Professional competence development when teaching computational informatics.

Bachelors and graduate students are offered in the course of teaching computational informatics, the ability to solve non-standard mathematical problems, which, as a rule, are not included in the content of teaching computational informatics. The article aimed to analyze the application effectiveness of non-standard mathematical problems in the course of teaching computational informatics, elaboration of constructive computational solution algorithms of inverse problems for differential equations, during which the bachelors and graduate students develop own professional competencies. The research conducted a review of previous literature on the topic. Formulation of the inverse problem for differential equations for the investigation of which the computational mathematics finite difference methods are applied, is presented. In the course of investigation, it was revealed that at elaborating the constructive computational algorithms of its solution, the bachelors and graduate students develop not only fundamental knowledge in the field of applied and computational mathematics, computational informatics methods, but also develop the professional competences, including computational thinking. Key words: professional competence; computational informatics; computational mathematics methods; non-standard.

How Elementary Teaching Candidates’ Learning Opportunities Are Associated with Their Knowledge, Self-Efficacy, and Beliefs

Background/Context Many elementary teacher education programs seek to prepare candidates to enact ambitious mathematics instruction that supports students in engaging in rigorous, conceptually rich mathematics tasks. Extant literature suggests that preparedness to engage in ambitious elementary mathematics instruction is multifaceted and includes teaching candidates’ mathematical knowledge for teaching (MKT), self-efficacy with regard to teaching mathematics, and pedagogical beliefs about mathematics. Prior research has produced findings that provide discrete, and at times conflicting, information about teacher preparation. Purpose/Objective/Research Question/Focus of Study This study examined how elementary candidates’ learning opportunities in mathematics content courses, mathematics methods courses, and student teaching were moderated by their reports about the quality of their experiences in courses and field placements to seem to affect their MKT, self-efficacy, and beliefs. Population/Participants/Subjects The study participants were 220 elementary teaching candidates who were in their final year of teacher preparation at four universities in three states. Research Design We employed multivariate path analysis, an approach that is purposefully designed to probe heterogeneity in teaching candidates’ experiences in courses and clinical placements. Data Collection and Analysis We administered two surveys to each study participant: an elementary teaching candidate survey, which included measures of mathematics teaching self-efficacy and pedagogical beliefs about mathematics, and an MKT survey. Findings/Results The number of mathematics content courses that elementary candidates took was positively associated with their MKT and mathematics teaching self-efficacy only when they also reported having positive experiences learning mathematics. When candidates reported increased opportunities to engage with representations, decompositions, and approximations of mathematics teaching practices in mathematics methods courses, this was associated with higher MKT scores and pedagogical beliefs about mathematics. When candidates reported that their cooperating teacher was a high-quality mentor, increased opportunities to observe, attempt, and receive feedback on mathematics teaching practices during their field experience were associated with mathematics teaching self-efficacy and pedagogical beliefs about mathematics. Conclusions/Recommendations The findings from this multivariate path analysis, which account for both the reported quantity and the perceived quality of elementary teaching candidate experiences, may shed light on conflicting findings in prior literature. There is little agreement in extant literature about associations between facets of teacher preparation and candidate knowledge, self-efficacy, or beliefs. Explaining the positive associations in some samples and lack of associations in others may have more to do with the quality of teaching candidate experiences than with whether a candidate was exposed to a particular opportunity to learn.

Learning to teach mathematics with robots: Developing the ‘T’ in technological pedagogical content knowledge

A multiple case study was conducted to investigate how Lego robotics instruction incorporated into a middle grades mathematics methods course could inform pre-service teachers’ (PSTs) TPACK through the lens of Social Constructivist Theory. The qualitative data analysis revealed that when instruction on Lego robotics technology is integrated into semester long mathematics methods courses, PSTs are able to improve their TPACK knowledge in regard to the robotics. Overall, the findings suggest instruction of educational technology tools should be incorporated into methods courses over a longer duration of time, and in depth, to better support the development of PSTs’ TPACK. To meet the demands of the teacher shortages while simultaneously supporting the needs of school districts, this research provides preliminary evidence of the need to incorporate content-specific technology into all methods courses.

Preparing Special Education Preservice Teachers to Teach Computational Thinking and Computer Science in Mathematics

Increasingly in K–12 schools, students are gaining access to computational thinking (CT) and computer science (CS). This access, however, is not always extended to students with disabilities. One way to increase CT and CS (CT/CS) exposure for students with disabilities is through preparing special education teachers to do so. In this study, researchers explore exposing special education preservice teachers to the ideas of CT/CS in the context of a mathematics methods course for students with disabilities or those at risk of disability. Through analyzing lesson plans and reflections from 31 preservice special education teachers, the researchers learned that overall emerging promise exists with regard to the limited exposure of preservice special education teachers to CT/CS in mathematics. Specifically, preservice teachers demonstrated the ability to include CT/CS in math lesson plans and showed understanding of how CT/CS might enhance instruction with students with disabilities via reflections on these lessons. The researchers, however, also found a need for increased experiences and opportunities for preservice special education teachers with CT/CS to more positively impact access for students with disabilities.

Supporting Preservice Secondary Mathematics Teachers’ Professional Judgment Around Digital Technology Use

The pervasiveness of digital technology creates an imperative for mathematics teacher educators to prepare preservice teachers (PSTs) to select technology to support students’ mathematical development. We report on research conducted on an assignment created for and implemented in secondary mathematics methods courses requiring PSTs to select and evaluate digital mathematics tools. We found that PSTs primarily focused on pedagogical fidelity (ease of use), did not consider mathematical fidelity (accuracy), and at times superficially attended to cognitive fidelity (how well the tool reflects students’ mathematical thinking processes) operationalized as the CCSS for Mathematical Practice and Five Strands of Mathematical Proficiency. We discuss implications for implementing the assignment and suggestions for addressing PSTs’ challenges with identifying the mathematical practices and five strands.

The Trend of Development and Functions of Mathematic Contemplation in Elementary School Boys

Here given the features, characteristic qualities of mathematic thinking and possibilities of increasing it during teaching mathematics in primary classes relatively to the formation of separate forms of mathematical thinking from the methods of teaching the mathematics, methods of scientific thinking.

IbM Workshop Metode Matematika Gasing Bagi Guru SD Muhammadiyah Se Jakarta Timur

AbstrakIbM pengabdian masyarakat melalui workshop metode matematika GASING bagi guru SD Muhammadiyah se Jakarta Timur. Tujuan dalam pengabdian ini adalah 1) peningkatan pemahaman tentang penjumlahan dan pengurangan; 2) peningkatan pemahaman tentang perkalian dan pembagian. Penerapan metode GASING dilaksanakan melalui empat tahapan. Tahap pertama adalah tahap persiapan, meliputi pembuatan buku modul, persiapan bahan ajar, workshett, persiapan strategi mengajar, dan koordinasi dengan pihak mitra terkait persiapan workshop. Tahap kedua adalah tahap pelaksanaan workshop, tahap ini diawali dengan pemberian pretest kepada para peserta, dilanjutkan dengan workshop metode matematika GASING, kemudian diakhiri dengan tahap posttest dan tahap pengisian angket kepuasan oleh peserta. Hasil yang dicapai dari kegiatan pengabdian masyarakat adalah pelatihan metode GASING dapat meningkatkan kemampuan guru-guru SD Muhammadiyah se Jakarta Timur dalam menghitung penjumlahan, pengurangan, perkalian. Kata kunci: Motede Matematika GASING, Workshop Matematika GASING SD. IbM Workshop on Gasing Mathematics Method for Teachers of Muhammadiyah Elementary Schools in East JakartaAbstractIbM community service through a workshop on GASING mathematics methods for Muhammadiyah elementary school teachers in East Jakarta. Aim in this service are 1) increasing understanding of addition and subtraction; 2) increasing understanding of multiplication and division. The application of the GASING method is carried out through four stages. The first stage is the preparation stage, which includes the making of a module book, preparation of teaching materials, worksheets, preparation of teaching strategies, and coordination with partners regarding preparation of workshops. The second stage is the implementation phase of the workshop, this stage begins with giving a pretest to the participants, followed by a workshop on mathematical methods GASING, then ends with the posttest stage and the stage of filling the satisfaction questionnaire by the participants. The result of community service activities is that the GASING method training can improve the ability of East Jakarta Muhammadiyah elementary school teachers to calculate addition, subtraction, multiplicatio. Keywords: GASING Mathematical Methods, GASING Elementary Mathematics Workshop.