Mathematical Thinking Research Articles

Problem Posing as a Way of Promoting Individual Mathematical Thinking in STEM Contexts – The Case of Climate Change

AbstractProblems encountered in Science, Technology, Engineering and Mathematics (STEM) contexts cannot be adequately described or solved with the knowledge of a single discipline. Instead, a high level of inter- and transdisciplinary knowledge and methods is required to overcome them. These help to pose problems about the complex challenges and solve them in a creative way. The better the knowledge within one and of different disciplines is interlinked, the more targeted questions can be formulated and answered. Mathematical concepts serve as the foundation for many of the pressing problems of our time. At the same time, these problems offer a wide range of opportunities for individualized exploration. They are equally suitable for students with different interests and levels of ability, as everyone can identify and work on an individual problem within the given context. However, numerous studies have shown that posing adequate mathematical problems must be learnt as well as knowledge from different disciplines is not automatically linked or transferred to other situations. The ability to grasp the formal structure of a problem, recognize problems, and find connecting problems are characteristics of mathematically gifted children and young people that need to be promoted. In our theory-based contribution, we use a concrete context to illustrate which possible mathematically rich problems can be posed by students of different ages and abilities. This approach facilitates the development of their individual abilities according to their interests and potential.

The cognitive gap in the mathematical thinking abilities of high school leavers for college: Are they ready?

After students spend approximately 12 years of formal math learning from high school, they bring a store of enormous “learned” mathematics factual knowledge to face the challenges and prepare for college/tertiary level learning. However, research has shown that early tertiary-level students struggle to learn college mathematics. The ability to think mathematically and use this learned factual knowledge (mathematical thinking) to solve higher-order thinking skills (HOTS) problems is essential to tertiary education. Thus, do these high school leavers have access to previously learned factual knowledge and use it effectively in solving these HOTS problems? This sequential research design study was conducted among 640 high school leavers who received an A in their national examination. In the first phase, the researchers investigated their mathematical thinking ability, followed by interviews with selected students on the difficulties and challenges they faced in solving the underlying problems. The findings showed that these students lack the ability to effectively use the previously learned factual knowledge from school mathematics to solve mathematical thinking problems. Secondly, they lack the habitual mind to check their answers after deriving a solution to a given problem. Thirdly, most rarely used heuristics to devise a strategy to solve fundamental math problems. Although the expectation of the school math curriculum over the last decade has been re-engineered towards “teaching students to think,” this expectation has yet to be fulfilled. Thus, university educators must do more to guarantee that high school leavers can deconstruct their mathematical knowledge and reconnect it with the underpinnings and linkages of college mathematics requirement.

Playful Activities to Develop Mathematical Thinking in High School Children

The research focused on analyzing how a program of playful activities influences the development of mathematical thinking in early childhood children who attend the preparatory education level, a process of transition between mathematical notions and the basic contents of this area of knowledge. The study used a quantitative methodology and quasi-experimental design based on the comparison of an experimental and a control group. The study population included 70 students aged 5 to 6 years. Initially, a diagnosis was applied based on the mathematical thinking questionnaire that obtained a reliability level of A=.855, through which shortcomings were evidenced in both groups. The final results showed a significant improvement in the experimental group, while the control group showed no significant changes.

Enhancing Students’ Abilities and Skills through Science Leaning Integrated STEM: A Systematic Literature Review

Integrated STEM learning is an appropriate approach to improve students' abilities and skills needed in the 21st century. Therefore, this literature study aims to discuss the effectiveness of integrated STEM implementation in science learning. The focus of this research includes integrated STEM implementation, effectiveness, and analysis of abilities and skills that can be improved through STEM integration. The method used in this literature study is a Systematic Literature Review, which includes several stages, namely Identification, Screening, and Included. The databases used include Springer, Taylor Francis, ERIC, and Google Scholar. This literature review article is limited to the last 8 years, from 2016 to 2023. After screening, 35 articles were obtained, which were used as literature material regarding the effectiveness of integrated STEM learning in science. The results of the study show that STEM implementation can be integrated with various learning models such as PjBL, PBL, Jigsaw, 5E-EDP, and 6E-Cycle. In addition, it can also be integrated with media, including interactive video, virtual labs, and mobile augmented reality. Integrated STEM has proven to be effective in improving students' abilities and skills. The student's abilities and skills include 4C skills, concept understanding and cognitive abilities, motivation, ICT and computational literacy, spatial and geographic thinking skills, and mathematical thinking skills.

The Effect of Book Genre in Eliciting Teacher Math Talk

ABSTRACTNumber books are an effective tool to increase math talk and promote children's mathematical thinking, but little is known about book genre effects. How do different types of number books impact mathematical input? This study examined whether book genre affects the amount and types of teachers' math talk. Using a within‐subjects design, we asked 31 teachers of 4‐ to 5‐year‐olds to read a narrative number book and a nonnarrative number book in a counterbalanced order. The books were matched in target numerical content. We found that the nonnarrative number book elicited more math talk than the narrative number book. In a qualitative analysis, we analyzed multiple conversational turns and found that both books allowed teachers to engage in simple math discussions, but there were differences in other types of math discussions. Together, these findings show that the quantity and quality of mathematical input differ as a function of genre.

Teaching Decimal Operations to Develop Mathematical Thinking and Reasoning Competency for Primary School Students in Vietnam

Vietnam is in the process of comprehensively reforming education. In 2018, the Vietnamese Ministry of Education and Training issued the General Education Program. In addition to general competencies, the 2018 General Education Program also aims to develop specific competencies for students, including mathematical competency. Mathematical competency includes 5 component competencies: mathematical thinking and reasoning; mathematical modeling competency; mathematical problem solving competency; mathematical communication competency; competency in using mathematical tools and means. This article presents some measures to develop mathematical thinking and reasoning competency for 5th grade students through teaching the content of calculations with decimals in primary school. These are also some suggestions for managers and teachers of primary schools in Vietnam to improve the quality of teaching Mathematics in general.

Mathematical Thinking and Learning in Early Childhood: A Consolidated Qualitative Synthesis of Cutting-Edge Research Literature

This study aims to synthesize current research on early childhood mathematical thinking and learning, focusing on cognitive development, instructional strategies, and environmental influences. The study provides a comprehensive qualitative analysis, integrating diverse theoretical frameworks and recent empirical findings for a nuanced understanding of early math education. Methodologically, it employs a thematic synthesis of qualitative studies, systematically reviewing literature from various academic databases to identify key patterns and themes. The research design involves coding text, developing descriptive themes, and generating analytical themes from peer-reviewed studies published between 2014 and 2024. The primary outcomes highlight the significant impact of play-based learning, interdisciplinary approaches, and parental involvement on early mathematical development. Additionally, the study underscores the role of technology and supportive learning environments in enhancing children's math skills. Conclusions emphasize the importance of holistic and culturally responsive educational practices. The practical implications provide valuable insights for educators, policymakers, researchers, and parents aiming to improve early childhood math education.

To promote the cultivation of mathematical thinking skills and strategies in games for the senior class of kindergarten children

With the advancement of quality education and an increase in research into preschool education, early childhood education is becoming more focused on individual physical and mental development, as well as the development of comprehensive quality education. Mathematical thinking ability represents a significant aspect of young children’s cognitive development. Given that young children’s brain development is not yet fixed, so their capacity for “plasticity” is considerable. The period between the ages of three and eight represents a critical phase in developing mathematical thinking ability in young children. Children undergo rapid growth in their mathematical understanding and reasoning abilities during this time. This paper will look at promoting the development of mathematical thinking and strategies in play for the senior class of kindergarten children, based on practice, in order to provide new strategies for preschool education. Through the research on the combination of games and mathematics education, we can provide better ideas and methods for the use of games in mathematics education, help the senior class of kindergarten children to develop their mathematical thinking skills, and help them to recognize, articulate, and generalize the quantitative relationships and spatial forms that exist in their daily lives so that they can be well-prepared for the next step of entering the primary school.

Quadratic equations with absolute values: an example of developing proof in mathematics students

Proof is the most important and fundamental aspect of mathematics. However, it is generally agreed by mathematics teachers at upper high school and first year university that students lack the ideas of proof. How to develop this in students is a common, difficult and perennial problem. In this paper, we develop some ideas of proof based on the number of solutions of an equation involving a quadratic polynomial and absolute values of linear functions. We begin with the simple idea of making more precise a question that is posed, investigating the problem through exploration, and arriving at some conjectures. We proceed to determine ways to prove the conjectures and thus convert them into theorems. The question discussed in this paper arose in a session for high school students held at the Department of Mathematics and Statistics of the University of Western Australia. The result is an excellent and interesting illustration of problem posing and solving in mathematics that underpins mathematical thinking. The paper is accessible to final year high school and first-year university mathematics students. We expect that it will serve as a resource for and inspire further ideas and examples for mathematics teachers, for teaching proof to students.

Learning obstacles in the generalization process: In case number pattern topic

Generalization plays an important role in mathematics because it is considered inherent in mathematical thinking in general. Where number pattern is a topic that is closely related to generalization. Problems are still found in generalizing number patterns so this can cause learning obstacles. This research aims to identify learning obstacles for Junior high school students in the generalization process with a focus on number pattern topics. This research is qualitative research with a case study method. The research subjects consisted of 30 grade 8 students in Jakarta who had studied number pattern. Subjects were given three test tasks, the results of which were used to figure out learning obstacles in the generalization process experienced by students and then continued with interviews with ten subjects. The findings show that learning obstacles in the pattern generalization process occur primarily at the expression and symbolic stages. Most students bypassed the generalization method, relying instead on formulas or manual calculations. Based on these results, it is recommended that educators implement didactic designs that offer targeted interventions during the expression and symbolic stages, such as using more interactive and symbolic reasoning activities to strengthen students' understanding and generalization skills in number patterns.

Parents' use of sustained shared thinking during joint mathematics activities with young children: Aninvestigation of its measurement, antecedents, and outcomes.

There is currently a dearth of tools to assess parents' use of effective interactive strategies for supporting early mathematics learning. One potential such strategy is sustained shared thinking. This study therefore constructed and validated a scale for measuring parents' use of sustained shared thinking during joint mathematics activities with young children, and examined its antecedents and outcomes. Four hundred and sixty-six parents completed a questionnaire about their conceptions of mathematics teaching and learning, home practices, as well as their kindergarten children's approach and avoidance motivation to learn mathematics. Additionally, the children were tested on numeration skills. Results showed that our new scale has three factors: exchanging ideas with children about mathematical problem-solving processes, creating a child-centred atmosphere for mathematics learning, and engaging children in mathematical thinking. Parents' uses of these three strategies were predicted by their constructivist conception of mathematics teaching and learning, and were differentially associated with the children's numeration skills, approach, and avoidance motivation to learn mathematics. Potential uses of our new scale in future home mathematics environment research are discussed.

Pemanfaatan Media Cetak dan Sosial untuk Meningkatkan Literasi dan Numerasi Siswa di Desa Namanjahe

This research aims to improve students' literacy and numeracy skills in Namanjahe Village through the utilization of print and social media. The approach used is participatory action research, where researchers are directly involved in activities to address the educational challenges faced by students. Based on interviews and observations, several issues were identified, such as low literacy rates, limited use of educational technology, and a pragmatic mindset that hinders mathematical thinking. The action plan includes introducing print media and social media in classroom activities, demonstrating how to use blogs, creating engaging learning environments, and participating in religious education activities at TPQ Al-Hidayah. The results of the program show that the use of diverse media can stimulate student interest and help improve their literacy and numeracy skills. However, consistent support and follow-up are still needed to ensure long-term impacts on student learning outcomes.

Nurturing prospective teachers noticing skills through argumentation: The case of fractions

This study aimed to investigate the extent to which prospective teachers’ noticing skills develop while they engage in argumentation on students' mathematical thinking regarding fractions. The study consisted of 10 third-year prospective teachers participating in online methods of teaching mathematics course. Classroom teaching experiment design was used where 8 sessions of teaching experiments were conducted. Data involved pre and post-tests, interviews, video recordings, daily reports, and post-discussion reflection papers. Findings revealed that prospective teachers' noticing skills of attending to students' strategies and making sense of their understanding were enhanced after their involvement in the classroom teaching experiment. Findings were discussed within the scope of the noticing literature.

Analyzing Student’s Mathematical Critical Thinking Ability of Concept Newman’s Error Analysis Review from Habits of Mind

This study aims to analyze and describe the mistakes made by students in completing mathematical critical thinking skills in terms of habits of mind (HOM) with three categories, namely limited, developing, and proficient. The review was also analyzed from the factors that led to the occurrence of errors based on error analysis according to Newman. This research uses qualitative research methods. The data collection techniques used are questionnaires, tests, and interviews. The instruments used are HOM questionnaires and mathematical critical thinking ability tests. The selection of the study subject was carried out purposively with the consideration that the subject had a HOM category. A total of 25 students who filled out the HOM scale and mathematical critical thinking ability test, 3 students were selected to be interviewed based on the HOM category classification. The data analysis techniques used in this study are data reduction, data presentation, and drawing conclusions. Based on the results of the study, students with limited HOM were only able to solve questions up to indicator 1 because they made mistakes in reading and process skills. Students with HOM develop, only able to solve problems up to indicator 2 due to Comprehension and transpormation errors. Students with proficient HOM, are able to solve questions up to indicator 3 because they make mistakes in the skill and encoding process.

Breaking Math Anxiety: A Success Story From an Indian Government School

Mathematics anxiety and fear among children pose significant educational challenges worldwide. This study examines the efficacy of a hybrid learning approach that combines digital game-based learning with hands-on activities to enhance mathematics engagement, reduce anxiety, and improve numeracy skills while fostering algebraic and mathematical thinking. The research was conducted at Government School, Ramagondanahalli, Bengaluru (RGHL), involving over 400 children aged 6-10 years from grades 1-5. Participants were primarily first-generation learners from economically disadvantaged backgrounds with limited access to educational resources. The intervention comprised weekly 70-minute sessions over six months, featuring the digital game "Magic Math Spell Caster" alongside modified traditional board games such as Snakes & Ladders, Bingo with Place Value Cards, and a custom Memory Card Game. The curriculum also incorporated activity worksheets with math manipulatives and practice sheets. The didactical approach underpinning the intervention was based on six key principles: Treating mathematics as a language to be spoken, promoting algebraic thinking; Structuring games into levels with well-defined learning objectives to scaffold mathematical thinking; Connecting concrete and abstract concepts to deepen understanding; Employing a hands-on approach to reinforce learning; Providing resources to every child to ensure equal access; Integrating assessments as digital interactive worksheets within gameplay. This approach allowed children to explore, make connections, and construct knowledge independently, fostering both algebraic and broader mathematical thinking skills. The program encouraged peer-to-peer learning by grouping children with different math proficiencies. Students progressed through game levels at their own pace, often exceeding curriculum expectations. This study contributes to the growing body of evidence supporting hybrid learning approaches in mathematics education for all children, emphasizing the development of robust mathematical and algebraic thinking skills.

Systematic Review on the Essentials of Creative Mathematical Thinking

Creative thinking skills can prepare students to be tangent, creative, and competent problem solvers in an ever-evolving world, so educators are required to understand patterns and factors that positively influence the development of creative thinking skills. The aim of this research is to identify patterns and factors that influence creative thinking skills in learning. The method used in this research is the exploration and conceptualization of mathematical creative thinking skills. The research explored 15 articles through Scopus databases, Google Scholar, Publish or Perish, and Google. Data analysis is conducted through CAQDAS ATLAS.ti, with coding objectives, methodology, and research conclusion. This research found that most of the articles highlighted task orientation, epistemological approaches, problem submission tasks, Multidimensional Creativity Assessment (MCA), tutor beliefs, problem solving, SCAMPER methods, valid instruments, social skills, confidence, belief and anxiety, and Practical Mathematical Talent Models. Overall, the contributions from this research have shown the importance of building creative thinking skills in mathematics and science education, along with various approaches and factors that contribute to the development of such skills.

Computational Thinking Readiness Level of First-Year Students of Mathematics Education

The main objective of this study was to measure the level of computational thinking readiness in prospective first-year mathematics education students. In addition, this study also aims to identify factors that influence their level of readiness towards computational thinking. This research is qualitative and descriptive in nature. This study describes first-year mathematics education students' mathematical computational thinking ability based on the theory of mathematical computational thinking. This study was conducted on first-year mathematics education students in the academic year 2023/2024. There were 16 first-year mathematics education students, all of whom were taken as samples in this study, to obtain more in-depth information about the computational thinking ability of first-year mathematics education students for further research development. The instruments used to collect data on first-year mathematics education students' mathematical computational thinking ability are (1) a mathematical computational thinking ability test and (2) an interview. The data obtained were calculated using statistical tests, and the results will be explained in depth. The mean score of the first-year mathematics education student's computational thinking ability test was 59.68, indicating that students generally have a fairly good level of computational thinking ability.

Вычислительный эксперимент в преподавании высшей математики. Комбинаторика и её приложения

<p>The article continues the cycle ([1] – [12]) of methodological developments of the authors. It discusses some problems related to ways to improve the culture of mathematical thinking of mathematics students. The authors rely on the experience of working at the Faculty of Information Technology of MSUPE.</p>

Editorial: Mathematical thinking, practices, and processes in non-formal learning environments

Editorial: Mathematical thinking, practices, and processes in non-formal learning environments

Digital educational resources in the development of mathematical logical thinking in middle school students

This article "Digital Educational Resources in the development of mathematical logical thinking in high school students" arises from the scientific problem: how do digital educational resources contribute in the development of mathematical logical thinking? The main objective is to analyze the importance of the contribution of digital educational resources in the development of mathematical logical thinking in high school students of the following educational institutions: Mariscal Sucre, Coronel Olmedo Alfaro and José María Velasco Ibarra. The research is descriptive with a mixed approach; for the development of the research techniques and instruments were used, where interviews and surveys were recorded, in addition, the difficulties presented by students in the development of mathematical logical thinking were detected, therefore, as an alternative solution to the problem, the guide of digital educational resources for strengthening skills in the subject of mathematics is presented.