Mathematical Activity Research Articles

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.

Students’ use of technological tools to engage in collective mathematical proof activity

Students’ use of technological tools to engage in collective mathematical proof activity

Evolution of the Four Fours Problem

Summary Besides being popular and entertaining, recreational mathematics problems are often of historical interest. We highlight the origin and evolution of one such simply-stated yet deep problem. For nearly three centuries the four fours problem has been generalized and expanded, providing hours of mathematical activity for enthusiasts as well as inspiring some intriguing discoveries.

Elements of the methodology of routine mathematical activity in teaching undergraduate and graduate students

Elements of the methodology of routine mathematical activity in teaching undergraduate and graduate students

Predicting and analysis of urban wastewater quantity to be treated by using Neural Network and ODE model: A case study

Wastewater data, including Population of the Municipality Served by the Wastewater Treatment Plants (WWTPs), Capacity, Number of WWTPs, Amount of Daily Wastewater Discharged per Person and Wastewater Treated in WWTPs (y(t)) obtained from Turkish Statistical Institute (TUIK) for Kayseri province for 2003-2020 were mathematically modelled and analysed with Artificial Neural Network (ANN) and Differential equations. Firstly, the data were augmented through ARIMA since TUIK data numbers are insufficient to ANN training and later the data were normalized. The augmented normalized data was trained with ANN twice, thus the effect of other variables on the y(t) variable was shown and mathematical ANN activation functions in the form of a tangent hyperbolic function was proposed for this variable. Then, arbitrary parameters used for a linear system consisting of differential equations representing the five variables mentioned above were estimated using normalized original data and thus the ODE (ordinary differential equation) model was proposed. Two ANN models and ODE model were evaluated on normalized real TUIK data and the performances of these three models were compared. Among these mathematical models, the model that gave the minimum MSE (mean squared error) has been determined as the ODE model. Finally, future predictions were made for the y(t) variable with the ODE model.

Do home mathematical activities relate to early mathematical skills? A systematic review and meta-analysis.

Children's foundational mathematical skills are critical for future academic attainment. While home mathematical activities (HMAs) have been proposed to support these skills, the extent to which engaging in them supports mathematical skills remains unclear. This preregistered systematic review and multilevel meta-analysis identified 351 effect sizes from 72 samples in 20 countries, exploring the relation between frequency of HMAs and mathematical skills in children aged 7 years and under (Mage = 61 months). A small significant positive relation was found (r = .13), moderated by risk of bias, with larger effects associated with a higher risk of bias. Specific ways the field can move forward are discussed to better understand the role of the home mathematical environment in early mathematics.

An investigation of students’ mathematical connection and metacognitive skills in the mathematical modelling process

The purpose of the study is to investigate the changing mathematical connection and metacognitive skills of students in the process of applying mathematical modelling. The data used for the study were collected from modelling activities, students’ written responses to modelling activities, audio recordings, semi-structured interviews, and observation notes. The data obtained were analysed using content analysis. As a result of the data analysis, it was found that metacognitive skills were used in each activity in the mathematical modelling process and were developed in interaction with each other. Although inter-concept and real-world connection skills are most commonly used in mathematical connection skills, modelling activities were found to enhance connection skills by allowing students to use connection skills with different disciplines and between different representations of the concept. It was found that metacognitive skills and mathematical connection skills develop interdependently, and it was found that mathematical modelling activities can be used as a tool for developing both of these skills.

Parental involvement in students’ mathematics activities: A bibliometric analysis

This study is focused on investigating parental involvement in students’ mathematical activities. It presents a comprehensive bibliometric analysis that examines new areas of research to discover current trends and future research opportunities related to parental involvement in their children’s mathematics activities. This study intends to provide a meaningful contribution toward enhancing educational interventions in the future. The metadata of the publications included in this analysis was extracted from the Scopus and ERIC databases using the search criteria “(parent OR parent) AND (involvement OR support) AND (math or math) AND student.” After the screening step, a comprehensive analysis was conducted on a total of 944 articles using the tools Harzing’s Publish or Perish 8, Biblioshiny, and VOSviewer 1.6.20. The findings indicated that studies on this topic covered 42 years and accumulated a total of 17,392 citations. The most prolific year in terms of publications was 2023, with a peak of 80 studies published. The leading contributors to this body of research were Jianzhong Xu and James Reed Campbell, each authoring six papers. The keyword mapping results revealed several interesting research avenues for future investigation, such as the incorporation of psychological interventions, longitudinal studies, multidisciplinary approaches, and the utilization of technology.

Structural and functional model of formation of STEM-competencies of students of professional higher education institutions in mathematics teaching

Abstract This study focuses on the vocational preparation of learners in professional pre-higher educational establishments. The primary objective is to provide a theoretical foundation for, construct, and empirically evaluate the efficacy of a structural-functional paradigm for cultivating STEM proficiencies among students in these institutions through mathematics instruction. The pedagogical experiment corroborated the research postulate that attaining advanced STEM competencies in mathematics among professional pre-higher education students can be facilitated through a learning model that incorporates specific pedagogical conditions: motivating and stimulating students to engage in educational, cognitive and research activities in mathematics through engagement in cooperation and the use of individual and group coaching; implementation of STEM projects in mathematics teaching; usage of ICT to ensure visibility and research orientation of mathematics teaching. The experimental outcomes and accompanying educational resources have enabled a comprehensive analysis of the challenges associated with implementing STEM methodologies in mathematics instruction. This article aims to elucidate the key attributes of the devised structural-functional model and evaluate its implementation efficacy, with particular emphasis on the application of the authors’ developed pedagogical support materials.

Investigating Students' Problem Solving Achievements, the Modeling Steps reached and Modeler Types in the Process of Mathematical Modeling Activities

The aim of this study is to identify the effect of mathematical modeling activities applied as action plans on the development of students' achievement in solving algebraic verbal problems, as well as to investigate the mathematical modeling competencies they use during these mathematical modeling activities and the modeling steps they reach. Moreover, the types of mathematical modelers that the students demonstrated during this application process were examined in the study. The study was conducted as an action research with a total of 15 7th grade students in rural areas. It was aimed to reveal the mathematical modeling competencies that students achieved during mathematical modeling activities through observations, researcher and student diaries, as well as interviews conducted with students. Content analysis was implemented to analyze the data. During the study, the mathematical modeling competencies demonstrated by the students in each mathematical modeling activity and the mathematical modeling steps they reached were identified. As a result of the study, it was confirmed that students' mathematical modeling competencies were related to competencies such as general mathematical knowledge or verbal comprehension, and it was also revealed that students' mathematical knowledge competence could be examined in more detail. It was also observed that students could achieve competencies through group work and it was found that students' success in solving the verbal algebraic problems generally improved based on their mathematical modeling competencies.

Secondary teachers’ guided reinvention of the definitions of reducible and irreducible elements

Informed by Realistic Mathematics Education, we designed a hypothetical learning trajectory on graduate students’ guided reinvention of reducible and irreducible elements in rings. We created experientially real context problems for use in a teaching experiment, in which secondary in-service and pre-service teachers used algebra tiles as an emergent model of factoring integers and quadratics in Zx. In their mathematical activity, this became the teachers’ model for abstracting the shared structure of (ir)reducible elements in Z and Z[x], which they used to formally define (ir)reducible elements. In this paper, we discuss the progression of the teachers’ reasoning and defining activities that were evident as they reinvented the definitions of reducible and irreducible elements of integral domains.

Eksplorasi Etnomatematika pada Tradisi Saprahan Etnis Melayu Sambas dan Pengintegrasiannya dalam Pembelajaran Matematika Sekolah Dasar

This study focuses on ethnomathematics in the Sambas Malay ethnic Saprahan tradition which aims to answer three questions: (1) Describe the mathematical fundamental activities in the Sambas Malay ethnic saprahan tradition, (2) Tools used in the Sambas Malay ethnic saprahan tradition related to mathematical concepts, (3) Describe the integration of ethnomathematics in the Sambas Malay ethnic saprahan tradition in elementary school mathematics learning. The method used is a qualitative research method in the form of ethnography. Researchers as the main instrument that plays a role in collecting data through interviews, observations and documentation. The data validity technique uses source triangulation and triangulation techniques. The results of this study show that there is ethnomathematics in the Saprahan tradition of the Sambas Malay ethnicity. In counting activities there is the concept of counting operations, measuring activities (measuring) there is the concept of measuring and flat building, locating activities there are the concepts of addition and flat building and inactivity, designing activities there are the concepts of counting and flat building operations, and explaining activities there are the concepts of counting and flat building operations. The concepts of elementary school mathematics in the tradition of Saprahan Malay Sambas can be developed by designing a suitable learning tool such as evaluation questions so as to provide new innovations in mathematics learning in schools.

Negotiating Knowledge Through Mathematical Activities in Classroom Interactions

What students are learning in mathematics classrooms can be analysed from a wide range of perspectives, focusing on the mathematical content, the mathematical processes or the mathematical activities. There is also a social dimension intertwined with this cognitive dimension that focuses on what mathematical activities in particular are established as socio-mathematical norms within a classroom. It is through these norms that students learn what it is to both learn mathematics and what it means to do mathematics. In this article I add a further epistemic dimension to illustrate how these socio-mathematical norms are co-constructed through interactions in a dynamic way. The analysis reported in this paper draws on video data of 65 lesson segments where students made their thinking explicit, taken from an original sample of 133 naturally occurring mathematics lessons with 81 teachers identified as including cognitively demanding mathematics. Using ethnomethodological conversation analysis and the epistemic dimensions of interaction initially outlined by Heritage and colleagues, a fine-grained sequential analysis of the interactions including students’ detailed contributions around cognitively demanding activities within these lessons illustrates how epistemic access, primacy and responsibilities are continually negotiated in interaction. Students’ rights to make knowledge claims or obligations to demonstrate their knowledge are negotiated in ways that influence students’ and teachers’ epistemic authority and stance. The analysis shows how the cognitive and social dimensions are intertwined both at an individual level but also at the classroom level that establish and reinforce the norms around the access and primacy of ideas and knowledge in interaction. These epistemic negotiations have consequences on the nature of mathematical activities that students experience and participate in, and subsequently their opportunities to learn mathematics.

МАТЕМАТИКАЛЫК КЕЧЕЛЕРДИ УЮШТУРУУДА ТАРЫХЫЙ ЭЛЕМЕНТТЕРДИ ПАЙДАЛАНУУНУН НАТЫЙЖАЛУУЛУГУ

Increasing the interest of modern schoolchildren in the subject of mathematics still remains one of the problematic issues. For this reason, activities to introduce various approaches are carried out in order to retain in the child’s memory the material learned by different methods and to develop the skills to use it in everyday life. In particular, to increase students' interest in mathematics, it was noted that, along with the requirement to explain it simply and clearly, adding historical information on this topic also motivates the achievement of the intended goal. Particularly among extra-curricular mathematics activities, the main purpose of organizing math nights is to arouse students' interest in the subject and encourage them to try to solve the problem on their own. At the math evening, not only the mathematical knowledge of schoolchildren is formed, but also their general cultural values, which have great educational significance, grow. This article examines how historical data can be of interest to students at a math evening, and provides a scenario for a math evening. It is also said that supplementing information from historical facts as an approach to increasing students' interest in mathematics helps achieve the intended goal.

UPAYA PENINGKATAN KEMAMPUAN BERPIKIR ANALISIS MATEMATIKA MELALUI MODEL MAKE A MATCH SISWA SEKOLAH DASAR

The aim of the research is to determine the application of the Make A Match model as an effort to improve the mathematical analytical thinking skills of class IV students at SDN 5 Tegalrejo in corner material with the help of paired cards. This research method is classroom action research on 21 class IV students at SDN 5 Tegalrejo. Collection techniques through pre-cycles, model application, evaluation tests, observation of learning activities and interviews. The results of the research showed an increase in the mathematical analysis thinking skills of fourth grade students at SDN 5 Tegalrejo in applying the Make A Match model with the help of paired cards in corner material. The scores obtained in the Pre-cycle were with a class average of 62.85, the first cycle had a class average of 72.61, and the second cycle had a class average of 88.09. Increasing mathematical analysis skills takes place in mathematical problem-solving activities through paired cards and evaluation of cycle I and cycle II through the ability to differentiate, organize and attribute. Students are able to achieve analytical thinking skills when the student's score has successfully achieved 3 indicators of students' analytical thinking skills, namely differentiating, organizing and attributing. Students gain knowledge of the concept of angles through understanding problems and surrounding angles, organizing mathematical and applied problems and making attributions in mathematical problems. The percentage of students' analytical thinking ability is achieved if it exceeds ≥ 60% of the classical percentage of students in the high category

Teaching Staff Mathematics University: Catalyst of the Emotional-Techno-Ontological Logic

The relevance of the study lies in the necessity to investigate the psycho-emotional state of teachers during the transition to remote teaching in universities and its impact on academic performance and emotional state of students. The aim of the research was to develop a theoretical approach to describe the emotional and techno-ontological logic of mathematics teachers during distance learning during the COVID-19 pandemic and the impact of their emotional state on the learning process. The study involved teachers and students from universities in Ecuador, both private and public. The study observed the behavior of teachers and students, analyzed the use of technology in mathematical activities, and analyzed personal opinions about the learning process of the participants of the study. A digital observation guide and open-ended interviews were used to collect data. The qualitative analysis program Atlas.ti was used to analyze the data. The program created three categories: andragogical retrotopia of mathematics, emotional scar in teacher preparation, and perceptions of the educational process. As the results of the research showed, there was a deficit of digital professional training of teachers in the university teaching of mathematics. And it was also found that the teacher played the role of a catalyst for the emotional-techno-ontological state of the educational process. As a result of the research work carried out, a theoretical approach is proposed, through which it is possible to avoid the manifestation of techno-ontological logical emotions in mathematics teachers in Ecuadorian universities.

It’s mathematics all the way down: revealing mathematical activity in non-formal learning spaces

We offer this synthesized framework as a tool to reveal mathematical activity in a non-formal making-space. In particular, we connect research at different grain sizes to illustrate and explain how mathematics plays a crucial, if often implicit, role in making activities. We begin by describing the Approximate Number System and the Ratio-Processing System, and explaining how those systems connect to both embodied cognition and Thompson’s (1994) conceptualization of quantities. Then, we examine how prediction and anticipation relate, with a particular emphasis on how social feedback guided the emergent mathematical activity. We offer this framework as a way to perceive, account for, and understand the multi-layered nature of experiencing mathematical activities.

An engineering design-based mathematics activity example based on STEM approach in middle school: Cold storage design

Engineering design practices in STEM education focus on reflecting the discipline-specific work of engineers in a manner that is suitable for the student level and course learning objectives. Using an engineering design context also facilitates student identification of global problems and feasible solutions to address such problems. In this article, within the framework of STEM approach, an engineering design activity that can be applied in middle school mathematics course is presented. Additionally, examples of students’ experiences of the engineering design-based mathematics activity are given. The "Cold Storage Design Activity" was executed in a classroom setting, and the implementation process underwent examination and evaluation. 12 eighth-grade students from a middle school in Turkey took part in the implementation. The middle school were able to successfully perform an engineering design process and effectively overcome challenges through teamwork. The results of the activity show that middle school students are excited and eager to participate in a design activity.

Mathematical Work of a Future Teacher in Teaching the Box Plot Diagram

Objective: The study aims to characterize the teaching proposals of the future Mathematics teacher in the context of their practical training in the final year of their university studies. Theoretical Framework: To achieve this, we consider the theory of Mathematical Workspaces, which allows for the analysis of both the mathematical activity that an individual engages in while solving a mathematical task, and the activity that is promoted during teaching. Method: A qualitative methodology is adopted through the design of an instrumental case study. The case pertains to a future teacher conducting a class on constructing a box plot. This class was observed and transcribed for analysis in light of the proposed mathematical work. Results and Discussion: The mathematical work exhibited by the future teacher includes a strong semiotic component and the use of non-material artifacts for quartile calculations. Students' prior knowledge is utilized in this context, with procedural aspects taking precedence over statistical thinking. Implications of the Research: The study raises concerns about the statistical education of mathematics teachers and its impact on future teaching proposals. Originality/Value: This research contributes to the study of statistics and initial teacher training in their influence on the future practices of Mathematics teachers. It provides a characterization of the mathematical work promoted by a future teacher and offers insights into concerns regarding the development of statistical thinking.

The potential of photography for mathematics education and research–A literature review

This literature review examines the use of photography in educational research and in education, to learn how photography could be better used in teaching and learning mathematics and mathematics education research. The authors analyzed 125 publications published between 1975 and 2023 to identify different research methods and teaching solutions that utilize photography. Within educational research two main approaches that are often used combined were photo-elicitation (photographs are used in an interview as a stimulus) and photovoice (taking photographs is a way the participant communicates their perspective). Mathematics education research could also combine these methods, for example in identity research. Our findings regarding teaching show that photographs have an important role in connecting mathematics to the real world and for visualizing mathematics. The best way to engage students is when they take photographs of themselves as a starting point to mathematical activity. Based on this review we identify future exploratory directions and various research gaps.