Mathematical Experiences Research Articles

Enjoyment, confidence, and broader experiences of teaching mathematics to the under-fives: accounts from students of Early Childhood Studies

ABSTRACT This article examines Early Childhood Studies students’ enjoyment, confidence, and broader experiences of teaching mathematics to the under-fives. The underpinning, two-phase study took place in a university in England using online questionnaires and interviews, with this article focusing on the findings from the interviews. Drawing upon Bronfenbrenner's Ecological Theory (1979), this article builds on current knowledge by highlighting that students’ own broader experiences of mathematics at school and during childhood have shaped their emotional attitude to mathematics by exploring their enjoyment and confidence of teaching mathematics in comparison to other subjects. This has implications for the support and training in the teaching of mathematics of those in the early years workforce and for the course content of Early Childhood Studies degrees.

Validity evidence of the use of quantitative measures of students in elementary mathematics education

AbstractQuantitative measures in mathematics education have informed policies and practices for over a century. Thus, it is critical that such measures in mathematics education have sufficient validity evidence to improve mathematics experiences for students. This article provides a systematic review of the validity evidence related to measures used in elementary mathematics education. The review includes measures that focus on elementary students as the unit of analyses and attends to validity as defined by current conceptions of measurement. Findings suggest that one in ten measures in mathematics education include rigorous evidence to support intended uses. Recommendations are made to support mathematics education researchers to continue to take steps to improve validity evidence in the design and use of quantitative measures.

The connections children develop between science and mathematics: An example of temperature measurement in the kindergarten

Children gain experiences that enables them to build concepts through everyday activities, while the use of cultural tools leads them to the development of early mathematical experiences. This paper presents a case study in a public kindergarten classroom in a semi-urban area of Greece (n=21), where discussion and recording of temperature sparked children’s interest in using the thermometer as a cultural tool. By observing children engaging in mathematical experiences related to number construction through a lesson plan it was evident that children tried to explain the use and function of the thermometer.

Heutagogy in action: Unveiling the transformative power of virtual “air campus” experiences of mathematics trainee teachers

The fourth industrial revolution has brought about significant changes in various fields including the education sector. It is increasingly essential for individuals, particularly student teachers, to embrace lifelong learning and acquire the know-how and skills required to grow into autonomous and critical thinkers. In this paper, we examine the virtual “air campus” experiences of 39 first-year student teachers of mathematics at a rural university in South Africa’s Eastern Cape Province. The heutagogical approach served as a lens for trainee teachers’ virtual “air campus” explorations. An exploratory qualitative case study design was employed to provide answers to two main questions that guided the inquiry. Findings of the study show that trainee teachers had varied experiences regarding what they learned from their virtual “air campus” visits. These include what constitutes effective teaching and how students learn as well as correction of common misconceptions regarding specific concepts in school mathematics. Through virtual lesson observations on the “air campus” of their choice, trainee teachers were also able to create their professional identities in terms of their future goals, ideal teacher traits, and desired teaching and learning environments. These findings demonstrate that integrating virtual learning environments into teacher education curricula and assessment has practical implications for enhancing trainee teachers’ self-directed learning, critical thinking, and professional identity development.

FROM LOOM TO CLASSROOM: EXPLORING THE EDUCATIONAL POTENTIAL OF JOLAHA ART OF WEAVING'S EMBEDDED MATHEMATICAL CONCEPTS

One of the current challenges in mathematics education is how to link school mathematics to student’s culture and everyday activities to improve the quality of the student’s mathematical learning. Drawing ideas from scholarship in ethno-mathematics, this study attempted to comprehend the mathematical concepts embedded in the weaving art of jolaha peoples. The study employed a qualitative research method to unravel the mathematical elements. Evidence of mathematical practices of the Jolaha community in the art of weaving indicated that irrespective of the mathematical experience, they all employed a certain level of informal mathematics in the discharge of their duties. The researcher explored the Jolaha weaving skills from a mathematical perspective and noted the mathematical ideas, concepts of traditional counting systems, traditional measurement units, concepts of translation, and rhombus that can be used to teach mathematics through ethno-mathematical strategies in the classroom, and concluded with discussion of mathematical elements that can be integrated with the mathematics curriculum to enhance mathematics teaching in the classroom.

1. THE MOST POPULAR ARTIFICIAL INTELLIGENCE APPLICATION USED BY AEROSPACE ENGINEERING STUDENTS’ TO LEARN MATHEMATICS

Artificial intelligence (AI) develops over time. Education is concurrently the AI evolution,sometimes in front, sometimes behind. Education underlies AI, and later on, AI is used in education. Therefore, the utilization of AI in education cannot be denied. There are many advantages, but also some limitations and ethical issues that arise from the use of AI in education. There are many applications of AI in mathematics scattered throughout society, but not all of them are useful enough. Thus, the purpose of this research is to gain the famous application AI in mathematics (app AI math) that is mostly used and recommended by the students’ experience in doing and learning mathematics. T-test independent samples were used to test the score of two groups, using the AI math app or not, in order to know whether it was affected or not. The result of this research is that the most popular app is Photomath, followed by ChatGPT and Mathway. But still, many students did not use this app. Relating to their score, the students who have used the AI math app to learn math before are not different from the students who do not use the AI math app.

Burning facial tissue and corroding graphite rods of recycled batteries: two simple experiments in preparation of nanomaterials

This report presents two hands-on activities for high school students that focus on the preparation of nanomaterials in a relatively simple manner. Carbon dots (CDs) were chosen as a demonstration. The article is categorised into two parts. The first part roughly performs the same work as a previous publication by Jumeng Wei, in which ultrasonication was utilised to cleave paper ash. Furthermore, we also attempted to use magnetic stirring or even hand stirring as an alternative method. The second section offers a perspective on the use of an electrochemical method to prepare CDs using graphite rods from recycled batteries. In the scope of this article, instead of using high-analysis techniques to prove the availability of CDs at the nanoscale, our work aims to illustrate green, sustainable physics and demonstrate the way that synthetic physicists utilise waste materials via practical education. The designed experiment suggests an integration between physics and chemistry that might be used for the science, technology, engineering, and mathematics experience of high school students.

The bridging understanding of language and mathematical symbols between teachers and students: An effort to increase mathematical literacy

The research aims to analyze the gap between teachers' and students' understanding of language literacy and mathematical symbols. The study was designed with a concurrent triangulation strategy. The research respondents consisted of 20 teachers and 120 class VII students. Data collection through questionnaires, interviews, and cognitive tests. Qualitative data was analyzed descriptively, and quantitative data was analyzed inferentially. The results of the analysis of quantitative data show that there is a linear (significant) relationship between understanding language and mathematical symbols and mathematical literacy skills. The results of the qualitative data analysis describe that the teacher's understanding of language and mathematical symbols (high criterion) does not necessarily support the students' understanding of language and mathematical symbols. We confirm the suspicion that there is a gap in the ability of teachers and students to understand language and mathematical symbols. Students need to improve their understanding of mathematical language and symbols. The pattern of errors is based on the teacher's conception of learning in the previous class, so the process of transitioning the teacher's knowledge to students' understanding of mathematics experiences obstacles. The implication is that the process of transitioning meaning from mathematical symbols to written and spoken language must be carried out when the teacher introduces or teaches new topics to students, and the context in which mathematical symbols are used must be followed by clarification.

Mathematical experience in game‐based problem‐solving

AbstractBackgroundGame‐based learning can frame problem‐solving as a sense‐making experience with domain‐specific tasks for school students. However, multiple challenges arise when trying to support learners in such a complex, problem‐oriented learning environment.Objectives and MethodsWith an architecture‐themed mathematics learning game, we conducted two mixed‐method studies to explore the impact and design of game‐based mathematical experience on the math problem‐solving performance of middle school students.Results and ConclusionsThe study findings suggested a positive impact of game‐based math experience on math problem‐solving for middle school students. Problematization‐oriented game‐based math tasks with structuring features enhanced students' reasoning with problems and channelled it to doing mathematics.TakeawaysThe current research findings support the initiative to frame learning as a sense‐making experience with domain‐specific tasks and inform the design of game‐based mathematical experience and learning support.

Exploring Challenges Faced by Secondary School Students in Understanding Taxation: An Expert Perspective Using the Nominal Group Technique

Taxation is financial knowledge that all workers in various sectors worldwide need to know. The introduction of the subject of taxation in several countries is aimed at increasing the understanding of students who are future workers to increase awareness among young people. This study explores the challenges faced by secondary school students in understanding taxation concepts, using the Nominal Group Technique (NGT) to gather insights from expert mathematic teachers. Through learning, students tend to struggle to comprehend various important tax laws and procedures. Although tax education is vital for enhancing future tax obedience, a major difficulty arises from the fact that while the topics mentioned above are covered in the Malaysian secondary school curriculum, basic financial literacy is low, and tax content is rather abstract. Based on NGT sessions, five experienced teachers with more than fifteen years of teaching experience in mathematics at the tertiary level engaged themselves in finding out the issues and challenges of the students. The discoveries identified eight significant areas of challenge in regard to the concepts of tax, and these were due to the difficulty in understanding more conceptuality, inadequate focused curriculum and mode of delivery by lecturers/facilitators, and lack of adequate interactivity in the teaching process. Therefore, this research emphasizes the need to provide systematic financial literacy training and to supplement the curriculum with attention-grabbing examples that would make the students more interested in taxation.

Use of Freire's Conscientization in Mathematics Learning

Conscientization in mathematics refers to the process by which students develop a critical awareness of the world view through education with their life experiences in mathematics learning. This qualitative study to analyze the use of Freire's conscientization in mathematics learning. The information was collected through secondary data as research articles, archival documents related with reliable sources. The conclusion showed that by using Freire's conscientization students develop a critical awareness of the world through education with their real-life experiences in mathematics. It advocated critical pedagogy in which teachers and students learn together through dialogue and it always welcomes critical analysis in the mathematics learning. The study has implication in mathematics learning, students share their experiences with other classmates in small groups as contextual teaching strategies in mathematics. It is recommended that a new relationship between teachers and students as well as society for an effective mathematics teaching strategy should be developed.

Reciprocal Learning Mathematics through Honeycomb Patterns

The purpose of this paper is to examine the mathematical ideas, problems, and solutions from the honeycomb patterns. This is a qualitative research design under an interpretive paradigm. I used interview, participant observation, small group discussions, photos, notes taken, and personal reflection for the data collection tools. The information was analyzed by participants generated text, activities, and experience of learning mathematics through the honeycomb patterns. The major themes that generated were algebra and students knowing of in-depth processes and solutions; algebraic and geometrical interpretation of 2D shapes with formulas; and geometrical knowledge of honeycomb patterns. The study showed that honeycomb patterns are the source for reciprocal learning of multidimensional area contents like algebra (quadratic and arithmetic sequence, hexagonal congruent tessellation, and geometry parallel lines, angles, and similar and congruent shapes together). What the students and the teachers need in reciprocal learning is the skill of observing patterns, redrawing, imagining, estimating, and logically intervening and shearing in them. The findings of the study can be helpful to teachers, students, and educators for reciprocal ways of learning, teaching, and training mathematics, connecting such patterns interestingly and meaningfully.

성인에게 필요한 수학 소양에 관한 고찰

In this study, we analyzed the current perception of mathematical literacy among Korean adults and determined their mathematical literacy needs, based on a theoretical review of how the concept of mathematical literacy required for adults has changed. Mathematical literacy, which refers to the mathematical ability currently required, is a concept that integrates mathematical skills, knowledge, and attitudes. Following the theoretical review, it was found that the mathematical literacy provided by lifelong education in Korea falls short of the current requirements for adults. The study revealed that the current mathematical literacy expected of adults involves the application of mathematical skills such as reasoning, modeling, information processing, and communication as well as routine basic arithmetic. Furthermore, adults' perceptions of mathematical literacy closely aligned with the definitions presented by PISA, ALL, and PIAAC. The results of the study suggest the following actions: re-conceptualizing the mathematical skills needed by Korean adults, shifting the perception of mathematics education from a lifelong learning perspective, offering positive mathematical experiences to adults, and identifying areas for further research.

Bridging disciplinary aesthetics: when mathematics meets art through educational technology

In this article, we discuss the way students’ aesthetic experiences can shape the learning of mathematics at higher school levels. We designed a learning environment based on three main design principles: (1) Mathematics as Artistic, where mathematics is used for open artistic creation; (2) Aesthetically rich mathematical experiences, that enable students to appreciate mathematical beauty and aesthetic experiences of wondering, imagining, conjecturing, testing, discovering, making connections, problem posing and solving; (3) Constructionism, where mathematical sense making is interwoven with constructing a personally meaningful digital artefact. Two students of the 11th grade participated in a case study, where they used expressive digital resources for representing, manipulating and exploring periodic functions in order to create an animated artefact based on a piece of music. The collected data fed the formation of a theoretical model for analysing students’ aesthetically driven mathematical meaning making, in an attempt to structure existing theoretical concepts around mathematical aesthetics in education. A part of the analysis of students’ aesthetic experiences based on this model is presented and further reflectively discussed with respect to the prospect of an aesthetically oriented curriculum reform.

Leveraging community-based assets in coaching, wellness and mentorship to increase the African American and Latinx math teacher workforce

Purpose There is some evidence to suggest that the historical challenge associated with recruiting and retaining Black and Brown Science, Technology, Engineering and Math (STEM) collegians is tied to early their teaching and learning experiences in Mathematics. This paper describes an National Science Foundation (NSF) funded project (NSF #2151043) whose goal is to attract, prepare and retain math teachers of color in high need school districts ensure that those teachers remain in the field long enough to make a meaningful impact on the minds and hearts of BIPOC students who are often, extrinsically, and intrinsically, discouraged from pursuing careers in STEM professions.Design/methodology/approach This mixed-methods study, which began in the summer of 2023, seeks to recruit, prepare, support and retain nineteen (19) Black and Brown math teachers for two (2) high need urban school districts. The expectancy value theory will be used to explain the performance, persistence, and choices of the teachers, while grounded theory will be utilized to understand the impact of the intensive mentorship and wellness coaching that applied over the first year of their preservice preparation and subsequent in-service years.Findings Measures of project efficacy won’t begin until 2025 and as such there are no findings or implications to draw from for the study at this time.Originality/value The intention of this paper is to augment the body of knowledge on recruiting and retaining Black and Brown math teachers for urban schools where the need for quality STEM teachers is critical.

How Productive is the Productive Struggle? Lessons Learned from a Scoping Review

Since its first notable appearance in the Second Handbook of Research on Mathematics Teaching and Learning, the phrase productive struggle has garnered support from a few, yet very influential, educational researchers. However, since the phrase was popularized by Hiroko Warshauer in 2011, examinations of the productive struggle have grown substantially within mathematics education. In this article, we present a systematic review of the literature on the productive struggle to quantify the breadth and depth of existing work in the area. Our analysis indicates that many studies: (1) provide a direct implementation of the productive struggle; (2) primarily involve teachers and not students; (3) present primarily qualitative or non-empirical research approaches; and (4) specify the NCTM content area focus less often across studies. Thus, we conclude that there are opportunities for rigorous research designs reporting on observable trends in the implementation of the productive struggle, explicitly targeting underexamined NCTM content and process standards, and focusing on how the productive struggle can support equity in mathematics. We believe that these opportunities should be investigated to provide a broader evidence base for developing meaningful experiences in mathematics for school-aged children that capitalize on the interconnectedness of attribution, meta-cognition, and controlled frustration in mathematics learning.

Geçici Barınma Merkezindeki Okullarda Matematik Öğretmeni Olmak: Türk Öğretmenler ve Suriyeli Öğrenciler

In the study, the difficulties faced by mathematics teachers in schools in Temporary Accommodation Centers in Türkiye and ways of coping were investigated. In this sense, it is focused on the experiences of mathematics teachers working in the schools in the Temporary Accommodation Center, and it is aimed to contribute to the understanding of the teaching processes. The study data were collected from mathematics teachers working in schools in Temporary Accommodation Centers. The research was conducted with a qualitative approach. Phenomenology design was used in the study. The study observed that teachers try to create opportunities to learn mathematics. Teachers have been attempting to enrich the lessons (ethnomathematics) by incorporating the cultures and languages of refugee students into the class, even though they have yet to receive any training. To create the fair learning environments deserved by refugee students in the Temporary Accommodation Center, it is recommended to increase the studies on teachers' mathematics teaching processes and to identify their needs.

Investigating the effectiveness of TPACK and TGT in enhancing histogram learning achievement among eighth-grade students

This study aimed to explore the effects of employing the Technological Pedagogical Content Knowledge (TPACK) model integrated with the Teams Games Tournament (TGT) collaborative instructional approach in teaching the concept of histograms to eighth grade students. Additionally, the research sought to assess the students' satisfaction with this integrated method during the learning process. The participants in the study comprised 44 eighth-grade students from a public school in Thailand. Three primary instruments used in this study are the learning management plan, a learning achievement test and a satisfaction questionnaire. The findings of the study indicate that the integration of the TPACK model with TGT collaborative learning had a positive impact on the participants' comprehension and knowledge of histograms. The interactive and cooperative nature of TGT activities in addition to the integration of technological, pedagogical and content knowledge increased the learning outcomes of the students. Additionally, the participants expressed a high level of satisfaction with the integrated TPACK and TGT frameworks learning experiences. This suggests that the collaborative and technology-enhanced approach fostered a positive and engaging learning environment, facilitating a deeper understanding of the histogram concept. These findings contribute to the existing body of knowledge on innovative instructional methods and provide valuable insights for educators seeking to enhance students' learning experiences in mathematics and other related subjects.

Experiences of Pre-Service Teachers’ on Skill-Based Problem Solving Oriented Lesson Study

This study aims to present the experiences of pre-service mathematics teachers’ on skill-based problem solving-oriented lesson study. In the study, the activities related to the learning environments designed by the lesson study groups before and after the research lesson with a focus on problem solving are investigated. In this way, the study aims to reveal how lesson study affects pre-service mathematics teachers’ awareness of teaching problem solving. In the study, 31 pre-service mathematics teachers first received a comprehensive training on teaching problem solving in mathematics for six weeks. Then, the pre-service teachers received a one-week training on the lesson study professional development model. In the last stage, they carried out problemsolving-focused lesson study processes under the guidance of the researcher with ten lesson study groups that they formed on the basis of volunteerism. Finally, the lesson study groups shared their experiences with the other pre-service teachers participating in the study by presenting the bulletins they prepared. The data were obtained through planning and evaluation meeting minutes, observation notes of research lesson practitioners and observers, initial and final lesson plans and documents. The data obtained in the study, in which the case study design of the qualitative research approach was preferred, were subjected to descriptive analysis using Polya’s (1957) problem solving process steps framework. During the lesson study process that they experienced within the scope of the research, pre-service teachers shared their knowledge and experiences about the problem solving process and teaching with each other, as well as activities such as collaborative work in groups, designing and implementing teaching materials such as lesson plans and worksheets. According to the results obtained in the study, it was seen that the activities in the problem solving-oriented learning environments of the pre-service teachers varied thanks to the collaborative structure of the lesson study. In addition, it was seen that the pre-service teachers had the opportunity to experience the steps of the problem solving process and the instructions they could use in these steps on the students through the research lesson and then make the necessary rearrangements through evaluation meetings. Considering the opportunities offered by the collaborative and school-based structure of lesson study, it is thought that lesson study can be a functional model for pre-service teachers to use theory and practice together in courses on problem solving instruction.

The importance of developing a metric to classify student experience in mathematics within the framework of intensive block teaching

The number of students enrolling in higher level mathematics units at high school have been in decline for a number of years. This is of particular concern when they then continue their studies within undergraduate STEM disciplines at University, leading academics to search for better methods to support mathematical instruction. The aim of this study was to investigate the development of a simple and robust tool to classify students’ mathematical capacity within a time compressed block teaching environment. One hundred and seventy-six first year students completed a survey reflecting on their level of comfort, competence, and enjoyment of mathematics, including their highest level of previous study in the discipline. Students also completed a short quiz to establish a pre-learning numeracy skill baseline. The survey provided data for development of the metric, from which, three groups ranked on their mathematical ability (low, medium and high) were identified which were then matched with scores arising from their baseline assessment. The classification grouping was uniform across all four offerings of the mathematics unit taught and matched with common baseline assessment scores. The importance of this tool shows both reliability and robustness in being able to identify students likely to have difficulty in studying undergraduate mathematics especially within the context of the time limited intensive block teaching, permitting early intervention to help students at risk of failure to succeed.