Mathematical Experiences Research Articles

Identifying competent problem posers and exploring their characteristics

In a study involving 66 masters and 60 sixth-grade students, we conducted Principal Component Analysis to identify more-and-less competent problem posers based on performance criteria rather than, as in prior research, relying on participants’ mathematical experience or background. Also, to cast light on characteristics of competent posers, we explored possible patterns in the problem-posing process based on the two identified groups’ self-reports and eye-movements. The results showed that: masters students had a significantly lower proportion of the more-competent group and a higher proportion of the less-competent group than sixth graders; more-competent posers perceived a better understanding of the problem-posing tasks than less-competent posers; more-competent posers exhibited significantly more fixation time on completing the entire problem-posing activities than less-competent posers, though this pattern disappeared across particular stages of the problem-posing process; and more-competent posers appeared to engage in a more purposeful search and processing to construct their problems than less-competent posers.

Undergraduate students’ modular experiences in learning mathematics in the new normal education

<span lang="EN-US">The modular approach has been proven to be an effective tool in mathematics learning. However, this approach presents challenges regarding students’ learning. Hence, this study was conducted to determine and compare the modular experiences of 55 Bachelor of Secondary Education (BSED) Math students of Eastern Samar State University (ESSU) Salcedo based on gender, age, and year level. The study utilized a descriptive-comparative design and a survey questionnaire. Percentage, mean, t-test, and </span><span lang="EN-US">analysis of variance </span><span lang="EN-US">(</span><span lang="EN-US">ANOVA) were used to treat the data. The study revealed that respondents were satisfied with their modular experience in learning mathematics in the new normal education. Specifically, the respondents rated their experience satisfactory in good teaching, high in clear outcomes, manageable in appropriate workload, moderate in appropriate assessment, and average in generic skills. Furthermore, the study found a significant difference in good teaching, clear outcomes, appropriate workload, appropriate assessment, generic skills, and satisfaction with modular learning across the respondents’ year level, but insignificant across age and gender. Based on the findings, it is recommended that teachers should attend intensive seminars and training on current trends in math teaching and module development. Modules’ quality must be improved considering the workload, assessment, outcomes, and skills development.</span>

Simple Game Application For Developing Mental Arithmetic For First Grade Elementary Students Using The Challege-Based Learing (CBL) Framework With Swift UI

Mathematics is one of the fundamental sciences that underlies the rapid development of technology and knowledge in the present era. Counting is a basic skill that should be acquired and mastered since elementary school. However, the reality is that many first-grade students still struggle with their counting abilities. Some of the problems include lack of motivation for learning, ineffective learning methods, and math phobias. Math phobia refers to a condition where students feel disturbed and stressed when confronted with anything related to mathematics. The factors contributing to math phobia include triggering events, influence from others, and conventional teaching methods in schools. One way to address this issue is by developing students' mental arithmetic skills, as it has been proven to be highly beneficial in shaping their thinking process. Recognizing the potential of utilizing technology, a simple interactive game using Swift UI can be developed to enhance first-grade students' mental arithmetic skills, providing them with an enjoyable learning experience in mathematics.

A Comparative Study of Computer Programming Challenges of Computing and Non-Computing First-Year Students

The learning of computer programming comes with unique difficulties that vary among students depending on their backgrounds, learning methods, and objectives. This paper investigates the programming challenges first-year students from non-computing at the North-West University, South Africa, and computing backgrounds at the University of Dschang, Cameroon face. A questionnaire-based data collection method is utilized and categorizes participants based on their gender, age, fields of study, prior experiences in mathematics, statistics, English, and programming languages, lab use/access, learning strategies, and material preferences. The aim is to identify and analyze the student's understanding of the basic programming concepts and the specific challenges met during introductory programming modules. Analysis of the collected data shows that while a considerable percentage of non-computing students have prior experience in mathematics and English, they lack familiarity with programming. Equally, while most computing students are proficient in spoken English, they face significant challenges in programming, mathematics, and written English. Notable difficulties are experienced in grasping concepts like recursion, arrays, error handling, and function/procedure methods. Moreover, a comparative study reveals that both groups of students encounter similar challenges, however, non-computing students’ difficulties are more than their computing counterparts. This paper, therefore, suggests designing teaching methods and learning materials to specifically meet the needs of non-computer science students, and enhance their understanding and proficiency in computer programming.

Pendekatan Pemecahan Masalah sebagai Strategi Pembelajaran Matematika di Sekolah Dasar

This research discusses many approaches to teaching mathematics to children, including problem solving techniques. It investigates the value of critical thinking skills for arithmetic investigations and demonstrates the benefits of using these techniques in an elementary school climate. This explanation thus goes a long way to managing critical thinking and how this approach can be used in numerical training. It also examines potential problems educators can see when implementing this framework and provides tips for implementing them. Overall, this paper showcases the importance of making assertive reasoning a profitable developmental experience in learning basic mathematics and providing pointers for teachers to try out instructive practices.

또래 상호작용에서 나타나는 만2세 영아의 수학적 경험

This study tried to explore the contexts of young children’s mathematics experiences with peers during block play activities at the classroom in a child care center. Seven two-year-old infants were observed for eight months in their classroom. This study found several findings of infants’ mathematics experiences with peers during their free play activities as follows: first, interests in peer play set off the mathematics experience of infants during free play, second, infants with competition during play with peers connected to the mathematics experiences, third, peers’ various information on mathematics during play made the infants mathematics experience during play, and forth, infants’ everyday conversation with peers was an important context to get any mathematics experience. This study implies that the results will be useful for making basic data and information for teachers to interact with infants on mathematics communication and experiences with peers. Also this study will be a great help for supplying teachers for infants to interact with peers on mathematics experiences.

Simulation-based mathematics and social justice activities

In this paper, various dimensions of care involved in mathematics education are linked to the need to develop classroom activities that connect mathematics and social justice issues. Drawing from literature that shows cognition is situated and embodied, the importance of meaningful contextualization and social interaction when learning mathematics is highlighted. The concept of “simulation-based mathematics and social justice activities” is presented as an approach for the work of bringing social justice issues that have mathematics at their core to the classroom. Theoretical constructs and examples are discussed, to illustrate what such simulations may entail and what may be learned from scholars, in different educational fields, who use simulations in classroom activities. Potentially beneficial features of social justice simulations are related to various educational goals, such as: decreasing arbitrary boundaries between mathematical sub-areas and between mathematics and other disciplines; providing opportunities for choice and the embodiment of different perspectives; and offering opportunities for inter-personal learning. I report on a simulation-based mathematics and social justice activity, conducted in a teacher education classroom. Students—in this case future teachers—were prompted to write reflectively about their participation in the activity. My interest lies in finding out what, if any, cognitive and affective benefits these prospective teachers connect with their experience of mathematics in the activity. To investigate this, I analyze six themes that are present in the data and illustrate each theme using excerpts of student writing. The thematic analysis allows us to learn about connections made by these students, between mathematics, in the context of the activity, and issues that are personally meaningful to them, such as: their own future teaching practice, learning and interacting with peers, beliefs and feelings about mathematics and the learning of mathematics, and different perspectives on complex decisions, involving cooperation or lack thereof, that are encountered in real life situations.

Community college mathematics instructors of color on the pursuit of supporting developmental students’ self-efficacy

As of 2017, colleges in the state of Texas in the United States of America are transitioning to a corequisite model where students take developmental and traditional mathematics classes concurrently. Using a self-efficacy framework, this qualitative study aimed to explore the perceptions of four mathematics instructors of color at two community colleges in Texas that have adopted the corequisite model mentioned above. Semi-structured interviews were used to inquire how instructors perceived to best support students through this new model. Using thematic analysis, five overarching themes emerged: feelings of encouragement, vulnerability, and empathy, challenges in supporting students’ development of self-efficacy, relatedness to students. The instructors voiced many challenges in helping students. However, most of the instructors also displayed some level of attending to their student’s social and emotional needs to overcome these challenges. In many ways, instructors expressed that they have to be vulnerable with their students to overcome challenges and open themselves up so students are more willing to learn. Instructors discussed instances in which they have been oppressed, which have shaped their educator identity, influenced their current practice, and impacted their relatedness with students. Furthermore, instructors expressed constantly trying to form connections with their students. These instructors discussed how their similar social identities, such as language, race, national origin, and mathematical experiences, are an important middle ground that connects them to their students. Through relatedness and vulnerability, instructors discussed getting students to open up and become more receptive to learning, achieving the necessary outcomes to succeed. The five themes discussed in this paper foreground (a) instructors’ ability to provide student encouragement, typically through vulnerability, (b) challenges that negatively influence students’ self-efficacy and (c) relatedness and empathy to help students succeed, resulting in a higher perceived self-efficacy in their students’ part.

Foregrounding black African immigrants in mathematics education research

Generally, research with Black youth/population in mathematics education have largely focused on their mathematics experiences in the context of United States with a special focus on issues of race/racism, equity, and social justice. While these studies are important and have informed our understanding of the schooling experiences of Black youth, there is a dearth of research with specificity on the mathematics learning experiences of Black African immigrant youth. In this paper, using duoethnography, we analyze our previous projects with Black African immigrant youth/families to argue for more nuances in the theoretical and methodological lenses when engaging with this population.

Students’ perspectives on Critical Mathematics Education

Theoretically, critical mathematics education (CME) differs markedly from traditional, teacher-centered mathematics teaching approaches. In addition to meeting mathematical goals, a main focus of CME lies on fostering students’ critical consciousness and positioning them as active and informed actors in the classroom and beyond. However, only few empirical studies explicitly focus on how students experience CME instruction and curriculum. In this contribution, we draw on interview data to examine how K-12 students in one Austrian and one American school setting respond to and perceive CME lessons. The analysis revealed that, within both classroom settings, students’ perceptions vary greatly, with some perceiving CME lessons as being completely different from prior experiences in school mathematics to some seeing little-to-no difference. Additionally features of CME instruction that mathematics teachers and researchers might consider to be the most salient are not necessarily the ones that students report attending to. Reasons for that might be manifold, and students might need more time with CME instruction and especially with reflecting on such lessons to identify the rationale behind the instructional approach. Moreover, researchers should be aware that students might not share their understanding of critical instructional reforms and might have diverse or even divergent perceptions.

Towards an Integrative Model of Math Cognition: Interactions between Working Memory and Emotions in Explaining Children's Math Performance.

Individual variation in mathematical skills can be ascribed to differences in cognitive ability, but also to students' emotional experiences of mathematics, such as enjoyment and anxiety. The current study investigated how the interplay of working memory with math anxiety and enjoyment explains mathematical performance in primary school students. We also explored whether these relations differed with the type of math test and students' age. Using mixed effect models, we reanalyzed data from 4471 Dutch primary school students (grades 2-6) who had completed two computerized working memory tasks, had filled out a questionnaire on math emotions, and had completed two math tests: story problems and speeded arithmetic. Findings showed that working memory, anxiety, and enjoyment were linear (but not curvilinear) predictors of performance on both tests, while some relations were stronger for the math (story)-problem-solving test. Higher math anxiety negatively impacted performance more strongly for students with stronger working memory skills, but only on the arithmetic test. No interaction between working memory and enjoyment was found. The relation between math anxiety and math performance increased with grade level, but no other age-related changes were found. Interpretations and recommendations focus on situated views on learning and emotion.

Volume of geometric solids on the Desmos platform – A didactic experience in Cape Verde

This work intends to disseminate a didactic experience in mathematics, in times of pandemic, in an emergency remote teaching situation, at the Portuguese School of Cape Verde, using the Desmos digital platform. The topic addressed was the study of the volume of geometric solids. The main objective was to contribute to the learning of mathematical concepts, using digital tools that promote students’ autonomy while respecting their learning pace, thus improving teaching practices through more assertive methodologies and more innovative resources.<br /> In order to understand how the Desmos platform contributes to improve the learning of geometry an explanatory case study was conducted. The participants in the study are 9th grade students from a Cape Verde school. Preliminary analysis of the data collected through several techniques, using diverse data collecting mechanisms, indicates that the contribution is very positive with clear advantages in the construction of knowledge on the part of the students, centered in a logic of skill development.

Algebra discourses in mathematics and physics textbooks: comparing the use of algebraic symbols

It is agreed that algebra has an important role in physics, particularly through handling symbols. A lot of previous research has focused on how mathematics is used in physics from perspectives where mathematics is taken for granted, and not addressing potential differences of mathematics in the physics classroom and in the mathematics classroom. Studies addressing differences between both subjects have been based on researchers’ own experiences of mathematics in both subjects. Thus, more focused empirical research is needed. The purpose of this study is to clarify similarities and differences between mathematics and physics concerning the use of algebraic symbols. Analyses were based on comparisons between upper secondary textbooks in mathematics and in physics from a discourse perspective. Statistical methods were used to decide if there were any significant differences between the subjects. Results showed an overlap in the algebra discourse in both subjects, but also several differences concerning core aspects of algebra. For example, a higher number of different algebraic symbols in equations in physics than in mathematics, and algebraic symbols are more seldom referred to by words in mathematics than in physics. This can make it difficult for students to identify similarities in the algebraic discourses in both subjects.

Factores subyacentes en las actitudes de los estudiantes hacia las matemáticas: un análisis factorial y sus implicaciones educativas

Attitudes towards mathematics influence student performance and subsequent choices in scientific studies, necessitating their in-depth understanding. These attitudes can be influenced by various factors and are not limited solely to the understanding of mathematical concepts; they are also shaped by internal and external factors. Therefore, this study aims to analyse students' attitudes in relation to mathematics, as well as the existence of possible underlying factors of these attitudes. An exploratory investigation has been conducted using a sample of students from basic and secondary education institutions, which range from the fourth to the eleventh grade, in municipalities of the metropolitan area of Cúcuta, Colombia. An instrument consisting of 14 items was administered in printed format. With the participants' responses, an exploratory and confirmatory factorial analysis was performed with a good fit to a two-factor model. The first factor is linked to elements such as commitment and the perception of the teacher's role in mathematics learning. The second factor is associated with elements such as self-perception and perception of the mathematical context. These results are consistent with previous research, highlighting the multifaceted nature of attitudes towards this discipline. The analysis emphasizes that a positive relationship with the teacher and favourable self-perception are essential elements to promote positive attitudes. These aspects could be considered when designing future pedagogical interventions. The study provides a multidimensional perspective on attitudes towards mathematics, laying the groundwork for future research. It is essential to explore how these identified factors can influence and optimize students' educational experience in mathematics

Contextualized Question-Embedded Video-Based Teaching and Learning Tool: A Pathway in Improving Students’ Interest and Mathematical Critical Thinking Skills

Filipino students exhibit lower levels of performance in mathematics and science competency compared to neighboring countries based on national and international surveys. The root cause of this issue is the decline in students’ interest in learning mathematics alongside their insufficient critical thinking skills. This has posed challenges among mathematics teachers to innovate ways on how to enhance students’ critical thinking skills and motivate students towards better performance in mathematics. The primary objective of the study was to determine the effectiveness of a contextualized question-embedded video-based teaching and learning tool on the interest and mathematical critical thinking skills of Grade 10 students. The study used a descriptive experimental research design with the REACT and Socratic methods to contextualize and embed questions in the video tool. A survey questionnaire was used to assess students’ interest before and after utilization, and a pretest and posttest assessment was conducted to evaluate students’ interpretation, analysis, evaluation, and inference skills. Based on the findings, using a contextualized question-embedded video-based teaching and learning tool is effective in increasing students’ interest and critical thinking skills. Moreover, there was a significant difference between students’ mathematical interest in terms of their attitude, initiatives, mathematics experience, and the utilization of contextualized question-embedded video-based teaching and learning tool. The pretest and posttest results of the experimental and control groups also showed significant differences in critical thinking skills. The study concludes that using contextualized question-embedded video-based as teaching and learning tools effectively improves students’ interest and critical thinking skills in Mathematics. Further larger-scale studies with different grade levels can validate the findings of the current study.

Time and Space to Thrive: Mathematics Graduate Students in a Team Teaching Model

Pedagogical training of mathematics graduate students is often disconnected from the actual experience of teaching. Even with the support offered by standard instructor training models, mathematics graduate students find it hard to connect with students, mature pedagogically and contribute meaningfully, especially under the overwhelming conditions of teaching for the first time. In this paper, we discuss features of instructor training that support mathematics graduate students' pedagogical development. Using self-reported experiences of mathematics graduate students who taught in a team teaching model, we single out three features of the model and advocate integrating these features into existing instructor training.

The experiential construction of mathematics teacher identity and the impact of early mathematical failure

It is broadly accepted that teachers’ professional identities influence how they teach and what their pupils learn. In this paper, drawing on semi-structured interviews with 22 experienced primary teachers from the Republic of Cyprus, we explore the construction of informants’ professional identities with a specific focus on mathematics teaching. Analyses, undertaken according to the constant comparison method, yielded three broad themes, implicated in differing ways in the construction and manifestation of informants’ identities: prior experiences of mathematics, mathematical competence, and images of the self-as-teacher. Overall, teachers fell into two groups, which analyses led us to construe as either mathematical victors or mathematical victims. Mathematical victors had experienced success as learners of school mathematics, from which pleasure, pride, and confidence in their mathematical knowledge for teaching emerged. Their teaching, which emphasized pupils’ attainment of similar enjoyment and success, focused on abstraction and mathematical reasoning. Mathematical victims had experienced failure as learners of school mathematics, from which anxiety and a restricted mathematical knowledge for teaching emerged. Their teaching, which emphasized positive pupil experiences, focused on affect rather than cognition and an avoidance of “traditional” teaching. However, both groups, despite their confident assertions, appeared unaware of the potential of their actions for creating new victims. The findings, which are discussed in relation to existing literature, confirm the complex nature of mathematics teachers’ identities and highlight, in particular, the need for further research into the formative role of teachers’ prior experiences of mathematics, whether positive or negative.

Key Patterns of LGBTQ Experiences in STEM: From Institutional Barriers to Transnationality

For decades, scholars have researched social inequalities of race, gender and other minority groups experiences in science, technology, engineering, and mathematics (STEM). Nonetheless, whether lesbian, gay, bisexual, transgender and queer (LGBTQ) professionals experience parallel disadvantaged circumstances remains to be further surveyed substantively. This paper draws on relevant literature concerning the normative STEM environment and different views (constructivism, liberalism, etc.), seeking to unpack the intersectionality between LGBTQ and STEM. Through conducting surveys targeted at international LGBTQ students regarding their academic, social, and mental experiences in STEM specifically, this paper argues that there exists a shared common dilemma for this group: sexual objectification and extra stress to increase their STEM competence. This paper comparatively analyzes the results and reveals the institutional and transnational barriers for those LGBTQ students of different cultural backgrounds in the context of globalization and international interactions and cooperation. This paper also contends that LGBTQ professionals in STEM become victims of sexual objectification mainly due to hypermasculinity and male-female dichotomy.

Teaching Mathematics Through Online at the University Level: An Ethnographic Inquiry

Teaching mathematics at the university level expects a more complex form of algorithmic and theoretical exploration which sometimes could not be delivered as enough as the curriculum demands. In this context, this study primarily focused on exploring the opportunities and challenges of online classes while teaching-learning mathematics at the university level. It is an ethnographic study in which three students and a teacher who had a long experience in online teaching-learning practices were taken as the key respondents. The key informants were requested for writing the reflection about their experiences of learning mathematics through online mode. And, the responses of the students were analyzed and presented in different themes. Based on the responses of the key respondent students, poor networking, unavoidable disturbance, teacher’s artificial pretending, negligence of the teachers, and less ICT-friendly curriculum & teachers were found as the major challenges for the online class. From the perspective of teachers' preparing documents for teaching, students’ negligence, ICT being used only as a means of sharing, taking more time to complete the course, less interactive class, and evaluating the students were found as the major challenges. However, online education provided the teachers and student both with a friend in crisis, sitting home reaching school, reducing unnecessary expenditures, and utilizing video records of the classes. Similarly, for teachers; providing opportunities for professional development, web browsing, any time anywhere teaching-learning, and developing the skills for designing different online evaluation tools have been observed as the major opportunities. Based on these conclusions, even having many challenges of using ICT in teaching university mathematics, its appropriate use leads for the deeper and wider understanding of mathematical contents.

Rarely Discussed and Often Ignored: Classroom Factors Affecting Black Students’ Experiences in Developmental Mathematics

We present findings from a study about obstacles that Black students who succeeded in developmental mathematics in community college reported having endured in those mathematics classrooms. To understand the types of obstacles that can arise for students in these classrooms, we analyze data using two frameworks: mathematics identity and dimensions of mathematics classrooms. Study participants faced obstacles in three categories: (a) impressions of faculty’s instructional practices for problem solving; (b) negative race-related perceptions they believed classmates had about them; and (c) perceptions about instructors’ expectations. These findings contribute to literature on Black students’ progress in mathematics by identifying obstacles experienced by students who achieve in these courses and can also inform professional development learning for mathematics faculty.