Current Mathematics Education Research Articles

Geometric Thinking of Prospective Mathematics Teachers: Assessing the Foundation Built by University Undergraduate Education in Ghana

This study investigates the geometric thinking levels of final year prospective mathematics teachers in Ghana, utilizing the van Hiele model to evaluate their proficiency. The main purpose was to assess whether university undergraduate mathematics education provides a sufficiently strong foundation for teaching senior high school geometry. A descriptive survey design was employed, involving 1,255 prospective mathematics teachers from three universities: University of Education Winneba (UEW), University of Cape Coast (UCC), and Akenten Appiah-Menka University of Skills Training and Entrepreneurial Development (AAMUSTED). The van Hiele Geometry Test (VHGT) was administered to measure participants’ levels of geometric thinking. The results revealed that 8.8% of participants attained van Hiele Level 1 (visualization), 30.0% reached Level 2 (analysis), and 32.4% achieved Level 3 (abstraction). However, only 15.9% and 12.9% of prospective teachers reached Levels 4 (deduction) and 5 (rigor), respectively. These findings indicate a significant gap between the current geometric thinking skills of prospective teachers and the expectations of the Ghanaian mathematics curriculum, which anticipates higher-order thinking skills. The study concludes that the current undergraduate mathematics education programs in Ghanaian universities may not be adequately preparing future teachers to teach senior high school geometry effectively. It is recommended that these programs be revised to include more focus on developing higher-order geometric thinking skills, with an emphasis on deductive reasoning, formal proof-based learning and rigor in geometry thinking. Enhancing the curriculum and teaching methods could narrow this gap and improve the overall quality of geometry education in Ghana.

Developing reflective practice among teachers of mathematics

This qualitative case study of four middle school and secondary school mathematics teachers examines how teachers’ reflective practice supported their selection of strategies that align with the needs of current mathematics education according to the 10 dimensions of mathematics education. The findings suggest that teachers’ reflection practice, through collaboration with other teachers and creating a positive safe environment within their classroom for students’ feedback, impacts their design of classroom practices. They prioritize planning and preparing for the dimensions that are being discussed in the meetings with other teachers. Another major finding is that high level reflective teachers’ attitudes toward teaching mathematics is consistent with the needs of current mathematics education. Lastly, meeting individual needs of students is the dimension that all teachers in this study, regardless of their level of reflection, were struggling to reflect on and plan for. Overall, each teacher reported reflective practices that appeared to align with the attitudes and practices for teaching mathematics survey.

Exploring the "Teaching and Learning" of Calculus Course from the Perspective of Teaching Connection

In the current Mathematics education system, there is an obvious disconnection between college mathematics (taking calculus as an example) and middle school mathematics. If the connection is not smooth, it will directly affect the teaching effect of college mathematics. This article analyzes the causes of poor connection from the perspectives of differences in teaching objectives and methods, disconnection and overlap in teaching content, differences in learning methods, external environmental influences, and individual differences in student sources. We have proposed bridging strategies from the perspectives of teachers' "teaching" and students' "learning", providing teaching references for improving the effectiveness of university mathematics teaching and cultivating high-quality mathematics talents.

PEMBELAJARAN COOPERATIVE INTEGRATED READING AND COMPOSITION (CIRC) TERHADAP KEMAMPUAN NUMERASI DALAM MENYELESAIKAN SOAL PEMECAHAN MASALAH

Current mathematics education should meet requirements that involve critical thinking skills, real-world relevance, the use of technology, and communication and collaboration abilities. In this regard, students need to have good numeracy skills, which involve the ability to use numbers and mathematical symbols in everyday problem-solving, such as calculations and data interpretation. Numeracy skills are important in shaping responsible and competent individuals. Additionally, problem-solving strategies are also at the core of mathematics teaching. Research has shown that the use of the Cooperative Integrated Reading and Composition (CIRC) instructional model has positive consequences for mathematical problem-solving proficiency. With the CIRC model, students can effectively improve their numeracy skills and mathematical problem-solving strategies. This research was conducted using a quantitative method, t-test, and paired sample test. The research subjects consisted of 50 eighth-grade students at SMP Negeri 7 Tungkal Jaya. Data was collected through documents, observations, and tests. Data analysis was done by conducting a paired sample t-test to assess the significance of the influence of CIRC learning on students' problem-solving competence. It is important to conduct further research involving larger samples and considering factors that may potentially affect learning outcomes.

An analysis of the policy on early childhood mathematics education in China

Early childhood mathematics education plays an important role in pre-school education, and it has a varied role in the development of many aspects of young children's abilities and self-confidence. Research has found that the mathematical sensitivity of the early years determines to a large extent the extent to which young children will enjoy mathematics as adults. At the same time, mathematics encourages children to think about things in a hierarchical way, thus further developing their ability to think and solve problems from all dimensions. As society continues to develop and progress, and as China places more and more emphasis on early childhood education, there are many common issues that need to be addressed, and education policy is particularly important as a document that provides direction for these issues. Official policy on mathematics education and its direction will not only influence the publication of mathematics-related picture books, but also the development of kindergarten curricula, changes in teachers' teaching methods, and even the development of young children's abilities in various areas, which, if properly formulated, will lay a good foundation for the future development of young children and gradually strengthen the country's educational advantage. This paper will provide some insights into mathematics education in kindergartens, teachers and families to fill some of the academic gaps by classifying, analysing and interpreting current mathematics education policies for young children in China.

A framework to characterize young school children's individual mathematical creativity—an integrative review

Both educational policies and current mathematics education research highlight that all students should be given the opportunity to be creative in mathematics class. However, if creativity is of such significance to mathematics learning, how can we describe the mathematical creativity of school children? Conducting an integrative literature review, this article aims to answer this question by synthesizing conceptual aspects and research results on the mathematical creativity of young school children working on mathematical open tasks. Here, concepts of creativity in mathematics education based on a divergent production approach are emphasized in detail. This leads to the introduction of the term “individual mathematical creativity” and to the suggestion of a framework to qualitatively characterize the individual mathematical creativity of school children working on open tasks. Its relevance and application as a scientific and/or educational tool to analyze and foster the creativity of students are explained exemplarily using the creative task processing of the 6-year-old student Jessica.

Pre-service High School Mathematics Teachers' Cognition of the Implementation of Mathematical Operation Literacy

After the reform of mathematics in the new curriculum, the educational issue of mathematical operation literacy has attracted increasing attention from all walks of life. The core goal of current mathematics education is the cultivation of mathematical operations literacy for middle school students. The measures to implement mathematical operation literacy have become a research hotspot. This paper hopes to provide theoretical basis and learning suggestions for teachers to further develop logical reasoning literacy in learning by analyzing the research findings of pre-service high school mathematics teachers' understanding of logical reasoning literacy. 51 postgraduates majoring in education in a university were taken as the survey object and an open-ended interview method was used to investigate their cognition of the implementation of mathematical operation literacy. It is found that the current pre-service high school mathematics teachers: 1. The cognition on the implementation of mathematical operation literacy focuses on "skills and repeated practice"; 2. The cognition of the implementation of mathematical operation literacy is not comprehensive. The degree of realization of cognitive aspects in the implementation of mathematical operation literacy has not reached half of the implementation measures proposed by predecessors; 3. The cognition of the implementation of mathematical operation literacy is not very consistent with the implementation measures proposed by predecessors. Although there is a certain degree of overlap between the two, the coincidence ratio is low. The suggestions put forward by pre-service high school mathematics teachers are narrow in scope and need to be further explored and considered.

Based on the necessity of mathematical life social investigation research

From the perspective of education and teaching, this paper takes mathematics education as an example. According to the questionnaire statistics of middle school students and college students on the application of mathematics in life, it leads to the necessity of mathematics in life. Applying the advantages of education and teaching methods at home and abroad, and combining the current mathematics education and teaching in our country, this paper expounds the theoretical value and practical application value of mathematics in life, aiming to make students realize the true meaning of mathematics and integrate mathematics into our daily life.

Notions of Creativity in Mathematics Education Research: a Systematic Literature Review

Interest in creativity in mathematics education research is increasing, and the field of research is growing. Yet, research on creativity and the notions (we use this wording to accumulate understandings, beliefs, and ideas about the construct) of creativity that are addressed in empirical research are diverse and difficult to organize in an overview, with different theoretical backgrounds and theoretical assumptions underlying them. The aim of this article is therefore to provide a systematic overview of notions of creativity addressed in recent empirical research on mathematical education. We conducted a systematic literature review, guided by the question, What notions of creativity are addressed in current mathematics education research and what theoretical foundations do they rely on? The article gives an overview of the five predominant notions of creativity that were identified in current empirical research in mathematics education from 2006 to 2019. We describe and evaluate these notions and identify trends that will help to structure this diverse field of research.

Sense making in middle grades

In this paper, we will see how an eleven-year-old girl discusses and presents her solution to a problem involving fractions and rates. The readers will be able to watch a video of the girl’s presentation of a middle school problem. An analysis of the solution and the presentation is discussed in the context of current mathematics education research.

Problem-solving teacher training, the effect of the ProyectaMates Programme in Tenerife

ABSTRACT This study reflects on the importance of problem solving and the need to be aware of different methods and strategies to respond to the challenges posed by current mathematics education. The experience was carried out on the island of Tenerife and aimed to assess the training of primary education teachers in problem solving strategies. For this purpose a questionnaire was administered to a total of 121 teachers (91 in training and 30 in practice) and interviewed a total of 8 participants. Part of the participating teachers received specific problem-solving training through a training project called ProyectaMates which made it possible to assess the effect of training. The data obtained revealed the deficiencies in initial teacher training and the need to train teachers in a specific way to solve problems, thus corroborating the effectiveness of the ProyectaMates Programme.

Let us rethink how to teach mathematics using gaming principles

ABSTRACT This study explored the gaming principles that fitted well in the theory of learning in good computer games and attempted to incorporate those principles into mathematics education. A qualitative dominant mixed methods approach was employed, in which qualitative interviews [eight students, six teachers and eight parents] and quantitative surveys [students, n = 174] were administered concurrently to explore the participants’ thoughts and beliefs about mathematics education and computer games. Initially, gaming principles were identified and compared with the existing mathematics classroom setting. Then, a gamified approach was proposed. Data collected has indicated that the current mathematics education tends to be exam-oriented, predominantly product-focused, emphasizes drill-and-practice, without instant feedback, where mistakes are not welcomed and there is an absence of story. On the other hand, students learn differently when playing computer games. Gameplay is process-focused and involves problem-based learning, where instant feedback is provided. Computer games work on the principle of failing forward and often include stories. By applying the gaming principles into mathematics education, the authors propose mathematics education to be process-focused, problem-based, and promote an attitude of learning from mistakes, and suggest an introduction of storytelling into classroom activities.

Use and Abuse of Calculators: Implications for Mathematics Education

Fostering mathematical understanding and sense for numbers is an objective for current mathematics education. This paper presents a historical vision of the use of numbers and of calculation processes and reflects about the current need of electronic calculators. The coexistence of two different mathematical systems, one based on the Greek axiomatic mathematics and another, the floating point system, used in electronic calculators, can lead to some confusions that which affects the teaching of mathematics, especially in the numerical sense development. The paper also presents common mistakes caused by the missing verification of the results from calculations or lack of awareness about the limitations of calculators. Finally, the implications those elements have on the mathematical education are presented together with some conclusions.

Trend Paradigma dalam Pendidikan Matematika

The current mathematics education is the fruit of past educational debates. First, we examine the past attempts to change the way mathematics is being taught and argue that education is always based on a traditional paradigm. Next try to explain the emergence of a new paradigm that grew out of a combination of theories from cognitive psychology, awareness of the importance of culture for learning, and the belief that students must get meaningful learning. This article discusses theories about paradigms that underlie the learning theory in general education, especially mathematics education. These paradigms include behaviourism, constructivism, critical theory, cognition theory. We discuss some of the implications of this reform related to how mathematics educators might work with math teachers.

Dutch sixth graders\u2019 use of shortcut strategies in solving multidigit arithmetic problems

Strategy flexibility, adaptivity, and the use of clever shortcut strategies are of major importance in current primary school mathematics education worldwide. However, empirical results show that primary school students use such shortcut strategies rather infrequently. The aims of the present study were to analyze the extent to which Dutch sixth graders (12-year-olds) use shortcut strategies in solving multidigit addition, subtraction, multiplication, and division problems, to what extent student factors and task instructions affected this frequency of shortcut strategy use, and to what extent the strategies differed in performance. A sample of 648 sixth graders from 23 Dutch primary schools completed a paper-and-pencil task of 12 multidigit arithmetic problems, designed to elicit specific shortcut strategies such as compensation. Based on the students’ written work, strategies were classified into whether a shortcut strategy was used or not. Results showed that the frequency of shortcut strategies ranged between 6 and 21% across problem types, and that boys and high mathematics achievers were more inclined to use shortcut strategies. An explicit instruction to look for a shortcut strategy increased the frequency of these strategies in the addition and multiplication problems, but not in the subtraction and division problems. Finally, the use of shortcut strategies did not yield higher performance than using standard strategies. All in all, spontaneous as well as stimulated use of shortcut strategies by Dutch sixth graders was not very common.

Flint, Michigan, Water Crisis: Connecting to Local Issues in Mathematics Classrooms

This department publishes brief news articles, announcements, and guest editorials on current mathematics education issues that stimulate the interest of TCM readers and cause them to think about an issue or consider a specific viewpoint about some aspect of mathematics education.

Supporting Opportunities for Productive Struggle: Implications for Planning Mathematics Lessons

This department publishes brief news articles, announcements, and guest editorials on current mathematics education issues that stimulate the interest of TCM readers and cause them to think about an issue or consider a specific viewpoint about some aspect of mathematics education.

Latest tool kit supports teachers' math instruction

This department publishes brief news articles, announcements, and guest editorials on current mathematics education issues that stimulate the interest of TCM readers and cause them to think about an issue or consider a specific viewpoint about some aspect of mathematics education.

Connecting Children's Mathematical Thinking with Family and Community Knowledge in Mathematics Instruction

This department publishes brief news articles, announcements, and guest editorials on current mathematics education issues that stimulate the interest of TCM readers and cause them to think about an issue or consider a specific viewpoint about some aspect of mathematics education.

An Appropriate Prompts System Based on the Polya Method for Mathematical Problem-Solving

Current mathematics education emphasizes techniques, formulas, and procedures, neglecting the importance of understanding, presentation, and reasoning. This turns students into passive listeners that are well-practiced only in using formulas that they do not understand. We therefore adopted the Polya problem-solving method to provide students with a diversified foundation for problem-solving. Furthermore, giving students immediate feedback in the form of prompts can help them to find the answers on their own them, thereby helping them learn more effectively. The primary objective of this study was to investigate the influences of a teaching activity incorporating Polya’s method and an appropriate prompt mechanism on the learning effectiveness of students. Research Subjects were two classes selected from an elementary school in Taiwan; one as the experimental group were taught with the providing appropriate prompts based on the Polya strategy of mathematical problems solving, the other one as the control group were treated by the conventional instructions. The results showed that: (1) there were significant differences between the experimental group and the control group in the learning effectiveness; (2) most of the students in the experimental group were satisfied by the proposed prompts system.