The Relationship of Mathematics Anxiety, Mathematical Beliefs, and Instructional Practices of Elementary School Teachers

Since the early 1960s, mathematics education researchers have considered the affective domain (attitudes, beliefs, opinions, motivation) as an important aspect of teaching and learning mathematics (Goldin, 2002; Mcleod, 1992). It is suggested that the affective characteristics may be the missing variable that links teachers’ instructional practices to students’ learning (Ernest, 1989a). Two affective variables strongly related to teachers’ instructional practices are mathematics anxiety and mathematical beliefs (see, e.g., Beswick, 2006; Jong & Hodges, 2013; Philipp, 2007; Wilkins, 2008). The purpose of this quantitative survey study was to explore the relationships among mathematics anxiety, mathematical beliefs, and instructional practices of practicing elementary teachers as they relate to the mathematics reform efforts promoted by the National Council of Teachers of Mathematics (see, e.g., 1989, 1991, 1995, 2000, 2014). The study was grounded, theoretically, in Ernest’s social constructivism as a philosophy of mathematics and mathematics teaching and learning (1998) and in his model of relating teachers’ content knowledge, attitudes, instructional beliefs, and instructional practice (1989). The study included 153 practicing elementary teachers who teach mathematics to students in Pre-K–5. These teachers completed the following online surveys: Mathematics Anxiety Scale, the Teaching Beliefs Survey and the Self-Report: Elementary Teachers Commitment to Mathematics Education Reform Survey. Quantitative data analysis methods included descriptive statistics, correlational analyses, and multiple regression analysis. Results indicated statistically significant correlational relationships between mathematics anxiety, mathematical beliefs, and instructional practices. Regression analyses were conducted to identify mathematics anxiety and mathematical beliefs as predictors of instructional practices. Results were significant for mathematical beliefs as a predictor, but not significant for mathematics anxiety as a predictor of instructional practices. Implications and recommendations for further study are discussed

Spatial Reasoning Construction: The Way to Use It to Solve Geometric Problems

The aim of this research was to determine the spatial reasoning constructs employed by pre-service elementary school teachers when solving geometry problems. A total of 36 participants were invited to complete an online test, after which two selected individuals were engaged in solving the problems. Interviews were then conducted to accurately describe the process of solving geometric problems. The results showed the existence of two types of spatial reasoning constructions, namely series and parallel. Both construction types revealed the interrelationship between spatial reasoning and the problem-solving process. This research highlighted the significance of spatial reasoning as an integral component in solving geometric problems, emphasizing the need for further investigation into its distinctiveness. This could be achieved by incorporating advanced geometric concepts and materials into future research

Mathematical Justification Research in Mathematics Education Across Grades: A Systematic Literature Review

Justification is a set of responses or responses that a person gives when asked to provide mathematical reasons for the results he makes. Justification can be used as a social process in which mathematical knowledge is explained, and systematically verified based on ideas, definitions, and properties that apply in mathematics such as representations used to display concepts. Research on justification in mathematics education has been carried out for a long time. This study aims to evaluate mathematics justification studies from articles published after 2016 and before April 2022 from ERIC and Google Scholar Databases. The key questions in this study are how these articles are distributed based on year publication, country, participant, mathematics subject, method, and how to support mathematical justification. This study used a Systematic Literature Review (SLR) by Preferred Reporting Items for Systematic Reviews and Meta-Analysis (PRISMA) guidelines including inclusion and exclusion criteria and then the data were extracted, resulting in 30 studies to be reviewed. The result shows that by year of publication the articles fluctuation distributed, based on country no data from Africa and Australia was found in the databases, the participant is mostly preservice mathematics teachers, whereas only one publication studied in high school students, geometry is the most mathematics subject used in research since every grade contain this material, the method is frequently given by qualitative research with various approach, how to supporting mathematical justification is also discussed

Peningkatan Kemampuan Pemecahan Masalah Geometri dan Self-Efficacy Matematis Siswa SMA Melalui Pembelajaran Investigasi

Pencapaian geometri siswa mendapat poin rendah pada hasil survey dan penilaian dari tahun ke tahun berdampak pada peningkatan kemampuan pemecahan masalah geometri (PMG) dan self-efficacy matematis (SEM). Kemampuan PMG adalah kemampuan siswa memecahkan masalah jarak pada bangun ruang yang dirancang menurut level van Hiele. SEM adalah derajat keyakinan siswa terhadap kemampuan dirinya untuk benar memecahkan suatu masalah geometri. Kemampuan PMG dan SEM dapat didorong melalui kegiatan yang melibatkan proses investigasi. Proses investigasi melibatkan tahap entry, attack, review, dan extension. Penelitian ini mengkaji peningkatan kemampuan PMG dan SEM melalui pembelajaran investigasi pada siswa kelas XII-IPS tahun pelajaran 2018/2019 di satu SMA Tanjungpandan, Bangka Belitung. Penelitian ini menerapkan kuasi eksperimen dengan desain pretes-postes kelompok kontrol. Data dianalisis berdasarkan perbedaan pembelajaran, gender, dan tingkat kemampuan dasar geometri (KDG). Hasil analisis menyimpulkan bahwa terdapat perbedaan kemampuan PMG siswa signifikan berdasarkan gender dan tingkat KDG, namun tidak berdasarkan pembelajaran. Sedangkan pencapaian SEM siswa, hanya berbeda signifikan berdasarkan tingkat KDG tetapi tidak berdasarkan pembelajaran maupun gender. Pengaruh interaksi pembelajaran dan gender adalah signifikan terhadap kemampuan PMG, tetapi tidak pada pengaruh interaksi pembelajaran dan tingkat KDG. Sementara terhadap SEM siswa, hanya signifikan pada pengaruh interaksi pembelajaran dan tingkat KDG. Secara bersama-sama bahwa KDG dan kedua model SEM, yaitu mathematics test-taking dan mathematics skill, berpengaruh terhadap kemampuan PMG siswa, baik dimoderasi pembelajaran maupun gender. Students’ achievements in geometry were low on surveys and assessments results from year to year have an impact on enhancing geometry problem solving (GPS) ability and mathematical self-efficacy (MSE). GPS ability is the students’ ability to solve the problem of the distance in solid that was designed based on van Hiele's level. SEM is the degree of students’ confidence in their ability to solve a geometry problem correctly. GPS ability and MSE can be encouraged through activities involving an investigative process. The investigation process involves entry, attack, review, and extension phase. This research is to study an enhancement students’ GPS ability and mathematical self-efficacy (MSE) through investigative learning for 12th social program students in the academic year 2018/2019 at the one high school at Tanjungpandan Bangka Belitung. This research applied quasi-experiment by the pretest-postest control group design. Data were analyzed based on differences in the learning approach, gender, and the geometry ability (BGA) of basic level. The analysis result concluded that there is significant difference of students’ GPS ability based on gender and BGA level category, but not for the learning approach. At the same time, a students’ MSE achievement just significant different based on the BGA level but it is not for both of learning approach and gender. An interaction effect between learning approach and gender is significant toward GPS ability, but not for interaction between learning approach and BGA level. While the students’ MSE, just significantly at the interaction effect between learning approach and BGA level. Parallely that BGA and two MSE models, that is mathematics test-taking and mathematics skill, affected to students’ GPS ability, as well moderated by learning approach and gender

Images of abstraction in mathematics education: Contradictions, controversies, and convergences

In this paper we offer a critical reflection of the mathematics education literature on abstraction. We explore several explicit or implicit basic orientations, or what we call images, about abstraction in knowing and learning mathematics. Our reflection is intended to provide readers with an organized way to discern the contradictions, controversies, and convergences concerning the many images of abstraction. Given the complexity and multidimensionality of the notion of abstraction, we argue that seemingly conflicting views become alternatives to be explored rather than competitors to be eliminated. We suggest considering abstraction as a constructive process that characterizes the development of mathematical thinking and learning and accounts for the contextuality of students’ ideas by acknowledging knowledge as a complex system