Math Perceptions Research Articles

Cognitive Network Science Reveals Bias in GPT-3, GPT-3.5 Turbo, and GPT-4 Mirroring Math Anxiety in High-School Students

Large Language Models (LLMs) are becoming increasingly integrated into our lives. Hence, it is important to understand the biases present in their outputs in order to avoid perpetuating harmful stereotypes, which originate in our own flawed ways of thinking. This challenge requires developing new benchmarks and methods for quantifying affective and semantic bias, keeping in mind that LLMs act as psycho-social mirrors that reflect the views and tendencies that are prevalent in society. One such tendency that has harmful negative effects is the global phenomenon of anxiety toward math and STEM subjects. In this study, we introduce a novel application of network science and cognitive psychology to understand biases towards math and STEM fields in LLMs from ChatGPT, such as GPT-3, GPT-3.5, and GPT-4. Specifically, we use behavioral forma mentis networks (BFMNs) to understand how these LLMs frame math and STEM disciplines in relation to other concepts. We use data obtained by probing the three LLMs in a language generation task that has previously been applied to humans. Our findings indicate that LLMs have negative perceptions of math and STEM fields, associating math with negative concepts in 6 cases out of 10. We observe significant differences across OpenAI’s models: newer versions (i.e., GPT-4) produce 5× semantically richer, more emotionally polarized perceptions with fewer negative associations compared to older versions and N=159 high-school students. These findings suggest that advances in the architecture of LLMs may lead to increasingly less biased models that could even perhaps someday aid in reducing harmful stereotypes in society rather than perpetuating them.

Biology Students' Math and Computer Science Task Values Are Closely Linked.

Quantitative and computational skills are required of 21st-century biologists. While biology student abilities and attitudes toward math have been studied extensively, less is known about corresponding attitudes toward computer science (CS). It is important to understand how students perceive math and CS subjects and whether those perceptions are linked or operate contradictorily to determine instructional best practices. This study 1) determined biology students' perceptions of math and CS in biological contexts, 2) measured the linkage of those perceptions, and 3) examined additional factors affecting attitudes. Students (N = 272) were surveyed using the original and a CS-adapted version of the Math-Biology Values Instrument to determine interest, perceived utility, and perceived costs toward math and CS in biological contexts. Mixed-effects models were used to determine correlations between task values and investigate effects of exposure to topics and demographic factors. Math and CS values exhibited positive correlations, but utility and cost were more negative for CS, possibly due to less exposure to CS before college, and overall attitudes were influenced by CS background and gender. Given these findings, we make educational recommendations for CS and math exposure early, often, and embedded in the biology curriculum.

The Role of the Home Learning Environment on Early Cognitive and Non-Cognitive Outcomes in Math and Reading

The home learning environment (HLE) has been considered to contribute to children’s early math and reading development. Previous studies examined the HLE by examining the influence of parent-child math and reading activities on math and reading outcomes, however also parents’ own perceptions of math and reading and their math anxiety (MA) and reading anxiety (RA) contribute to the HLE but the latter factors have been scarcely explored. The aim of this study was to provide a more holistic view of the HLE and its relations with children’s cognitive and non-cognitive outcomes in math and reading at the start of primary school. This paper examined the relations within the HLE, and the relations between the HLE and children’s early math and reading outcomes. Participants were 301 first-grade children and their parents. The HLE was measured by the parent questionnaire. Children’s digit comparison, number line estimation, letter knowledge and phonological awareness skills were measured as well as their math and reading anxiety levels. The results demonstrated a significant association between parents’ perceptions and their anxiety towards math and reading. No significant associations were found between parents’ perceptions towards math and the frequency of home numeracy activities, whereas significant relations were found in the domain of reading. Socioeconomic status was found to provide a unique contribution in children’s digit comparison and math anxiety, while no significant relations were observed between other HLE factors and children’s outcomes. The current study suggests the importance of including parents’ perceptions and feelings to explore the dynamics of the HLE and its impact on children’s math and reading outcomes.

A scholarship of teaching and learning study of hospitality students’ attitudes toward and perceptions of math

ABSTRACT Some college professors may be concerned about students’ mathematics skills because they believe that their students lack the math skills required for career success and are anxious about math. For this Scholarship of Teaching and Learning (SoTL) study, hospitality students were surveyed to explore their perceptions of and attitudes toward math. Findings indicated that students had higher math anxiety related to tests than to other math-related activities; their math test anxiety was related to their overall exam anxiety; if students perceived that they were good at math, they enjoyed math more, and the more students perceived that math was important to their careers, the more they enjoyed math; and the less students were anxious about math tests, the more they enjoyed math. Based on the findings, implications for teaching and learning are described, and ideas for future research are proposed.

중학생들의 수학흥미와 수학가치인식이 수학학업성취도에 미치는 영향력에 대한 유형탐색

This study detects heterogeneous latent classes and their models applying REBUS-PLS analysis based on the path model of math interest, math perception and math achievement using TIMSS 2015 8th grade data of Korea, under the context that the influence of related factors on the achievement of mathematics is different. As post-hoc analysis, the distribution for latent classes as dependent variables is analyzed by using math self-confidence and engaged math-learning as predictors. According to the analysis results, two latent classes were captured, and the math-interest oriented class and the math-perception oriented class were named. As a result of post-hoc analysis, CHAID analysis showed that students with high self-confidence in mathematics were distributed in the math-perception oriented class at a high proportion, while those with low self-confidence in mathematics were distributed in the math-interest oriented class at a high proportion. Next, under the classification by math self-confidence, students with more engaged math-learning in both high confidence and low confidence group were more distributed in math interest oriented class, and the less engaged math-learning, in math perception oriented class. This study presented a new method of research on school mathematics by applying the REBUS-PLS analysis method to detecting unit segments based on the path model.

Elementary teachers\u2019 attitudes and beliefs about spatial thinking and mathematics

Considering how spatial thinking connects to Science, Technology, Engineering and Mathematics (STEM) outcomes, recent studies have evaluated how spatial interventions impact elementary students’ math learning. While promising, these interventions tend to overlook other factors affecting math learning; perceptions of math abilities, beliefs about math, and math anxiety can also impact math performance. Additionally, perceptions of spatial skill and spatial anxiety impact spatial performance. This study investigated how elementary teachers’ perceptions of spatial thinking connects with math perceptions. Specifically, we focused on teachers’ attitudes and beliefs around three topics: teaching and learning math, spatial abilities, and spatial thinking in mathematics. We found that lower spatial anxiety related to lower anxiety about teaching math, greater alignment between math beliefs and math standards, and greater efficacy in teaching and learning math. Further, a factor analysis showed one factor that connected stereotypical math thinking with both math and spatial anxiety, and another that connected spatial competencies, teaching and learning math, and spatial thinking within math. To further evaluate spatial thinking in math, we introduced a math categorization and verified it using teachers’ ratings of teaching difficulty, visualization helpfulness, and spatial-thinking involvement. Structural equation models revealed that the level of spatial-thinking categorization was the best model of all three of the teachers’ ratings. Overall, results showed numerous connections between teachers’ attitudes and beliefs about mathematics and spatial thinking. Future intervention studies should consider teachers who are spatial and/or math-anxious, and future research should investigate the role of stereotypical thinking in spatial and math anxiety.

Ortaokul Öğrencilerinin Matematik Algılarının Resmetme Yoluyla İncelenmesi

Bu çalışmada ortaokul öğrencilerinin matematik algıları çizim (resmetme) tekniği ile ortaya çıkarılmaya çalışılmıştır. Çalışma kapsamında 2017-2018 Eğitim-Öğretim yılında Ordu il merkezinde öğrenim görmekte olan ve 2017 yılında yapılan TEOG sınavı sonuçlarına göre başarı sıralamasın-da üst, orta ve alt gruplarda yer alan ortaokullardan seçi-len 682 öğrenci ile çalışılmıştır. Çalışma nitel olarak desen-lenmiş ve nitel araştırma yaklaşımının yöntemlerinden biri olan olgu bilim yöntemi kullanılmıştır. Verilerin ele alınarak yorumlanmasında içerik analizi tekniğinden yararlanılmış ve bu kapsamda öğrenci çizimleri beş ana kategori ve on altı alt kategori altında değerlendirilmiştir. Sözü edilen ana kategoriler Duyguları ifade eden/içeren çizimler, Öğrenci görüşlerini/fikirlerini içeren çizimler, Matematiğin yaşamla ilişkisine yönelik çizimler, Okul ortamına yönelik çizimler ve Matematiksel nesneleri içeren çizimler’dir. Çalışma sonu-cunda öğrencilerin yapmış oldukları çizimlerde sırasıyla matematiğe yönelik görüşlerine, duygularına, matematiksel nesnelere, okul ortamına ve matematiğin yaşamla ilişkisine yer verdikleri görülmüştür. Öğrencilerin genel olarak ma-tematiğe yönelik görüşleri ve duyguları olumlu olmakla birlikte, öğrenme süreçleri ile ilgili görüş ve duygularının olumsuz olduğu gözlenmiştir. Öğrenciler matematiği sev-mekle ve değer vermekle birlikte, öğrenme süreçlerinde zorlanmaktadırlar. Sınıf seviyeleri dikkate alındığında ise matematiğe yönelik olumlu görüş ve duygularda sınıf sevi-yesi yükseldikçe azalma olduğu gözlenmiştir. Özellikle 8. sınıf öğrencilerinin matematiğe yönelik duygu ve görüşleri-nin, diğer sınıf seviyelerine nazaran olumsuz anlamda ve büyük ölçüde farklılaştığı görülmüştür. Çalışma sonuçları ile ilgili olarak öğretim ortamlarına ve yapılacak farklı akademik çalışmalara yönelik önerilerde bulunulmuştur.

Why and How Parents Promote Math Learning with their Young Children: A Mixed-Methods Investigation

SYNOPSISObjective. This study examined parental characteristics that related to children’s early math learning. Specifically, we examined how parents engage in math activities with their children in the home and how their practices were informed by parents’ experiences with and perceptions of math. Design. Using a mixed-methods design, we first quantitatively examined associations between two parental characteristics, past math experiences and current math anxiety, and various types of math activities to understand factors that predict home math engagement in a sample of 34 parents. We then conducted semi-structured interviews with a sample of 15 parents to identify additional factors that relate to parents’ engagement in math activities with their young children. Results. We found that parents’ math anxiety predicted their reports of math activity frequency in the home, controlling for demographics as well as prior measures of math enrichment. Through qualitative analyses, we demonstrated considerable variability in the way that math activities are implemented and described by parents and identify a novel theoretical construct – parents’ goals for children’s math learning – which relates to parents’ practices. Conclusions. These results suggest that survey measures may fail to capture important heterogeneity in parents’ practices and that additional predictors such as parental goals should be explored in future quantitative research.

The Perceptions of Math and Math Education in Midville, Illinois

By means of a qualitative research method known as folknography, a concerted effort was made to discern perceptions of math and math education in the rural Midwest. A community that will be referred to as Midville, located in the state of Illinois, was chosen as the target population for this study. The community and surrounding region stands over one hundred miles from the nearest metro complex. The study was conducted in May of 2006. After completion of the initial field work, data were collected, analyzed, and summarized, producing this document.

PERANAN MOTIVASI BELAJAR MATEMATIKA, PERSEPSI TERHADAP PELAJARAN MATEMATIKA, DAN TINGKAT PENDIDIKAN ORANG TUA TERHADAP PRESTASI BELAJAR MATEMATIKA

This research aims to find: 1) the relation between the motivation and the achievement in learning Mathematics. 2) The relation between the perception to Mathematics and the achievement in learning Mathematics. 3) The relation between the parents’ education level and the achievement in learning Mathematics. 4) The role of motivation and perception in learning Mathematics and parents’ education level in the achievement in learning Mathematics.The hypotheses in this research are: 1) There is a positif relation between the motivation and the achievement in learning Mathematics. 2) There is a positif relation between the perception to Mathematics and the achievement in learning Mathematics. 3) There is a positif relation between the father’s education level and the achievement in learning Mathematics. 4) There is a positif relation between the mother’s education level and the achievement in learning Mathematics 5) The motivation in learning Mathematics, the perception to Mathematics, and the parents’ education level have a role in the achievement in learning Mathematics. The research’s subject is 100 students class X and XI of SMAN 2 Yogyakarta. The data were collected by using scale, documentation, and identity. The scale used was math motivation scale and math perception scale. The data analysis were done by using multiple linear regression and product moment correlation.Based on the correlation analysis done was known that there was positive and significant relation between motivation and achievement in learning Mathematics and between the perception of Mathematics and the achievement in learning Mathematics, but there is no positive and significant relation between father and mother’s education level and the achievement in learning Mathematics. Based on the result of multiple linear regressions analysis, it was known that motivation and perception in learning Mathematics as well as parents’ education level have a role in the achievement in learning Mathematics. It is based on the significant result of F testing, i.e. α = 0.05. The determination of coefficient was 0.162 meant that the percentage of the effect of motivation and perception in learning Mathematics and parents’ education level to the achievement in learning Mathematics was 16.2%, while the rest of 83.8% was influenced by other variables which were not included in this research.Key words: Motivation in learning Mathematics, perception to Mathematics, parents’ education level, the achievement in learning Mathematics.

Motywacja do uczenia się a lęk przed matematyką w klasach starszych szkoły podstawowej

<p>Motywacja do uczenia się stanowi jeden z ważniejszych czynników wpływających na osiągnięcia matematyczne uczniów. Może ona ulegać zmianom pod wpływem lęku przed matematyką. Wśród licznych typologii motywacji, ze względu na szczególne odniesienie do doświadczeń w uczeniu się, na uwagę zasługują motywacja samoistna i celowa. W artykule opisano efekty poszukiwań zależności między typami motywacji do uczenia się wyróżnionymi w modelu Amabile i in. (1994) a lękiem przed matematyką. W badaniach uczniów z klas IV (n = 43) i VI (n = 45) szkoły podstawowej zastosowano Inwentarz Orientacji Motywacyjnych (Amabile i in. 1994, Karwowski 2009) obejmujący 30 stwierdzeń, które dotyczą motywacji samoistnej i celowej, oraz Kwestionariusz Lęku Matematycznego składający się z 54 stwierdzeń (Mulhern, Rae 1998). W obu grupach wystąpiły umiarkowane dodatnie korelacje między motywacją samoistną a lękiem przed matematyką. W klasie VI istotna okazała się korelacja między klarownością celów jako aspektem motywacji celowej a lękiem przed matematyką. Nie uzyskano istotnych różnic w większości aspektów motywacji do uczenia się. Jedynie wyzwanie różnicowało grupy istotnie. Lęk przed matematyką oraz postrzeganie nauczyciela były istotnie większe w klasie IV. Uzyskane rezultaty mogą mieć znaczenie dla planowania edukacji matematycznej i jej rozwoju w kierunku redukcji lęku przed matematyką i zwiększenia się motywacji samoistnej u uczniów.</p>

Student math perceptions and skills in an equine nutrition class

Student math perceptions and skills in an equine nutrition class

Why Don’t More American Indians Become Engineers in South Dakota?

American Indians are among the most under-represented groups in the engineering profession in the United States. With increasing interest in diversity, educators and engineers seek to understand why. Often overlooked is simply asking enrolled tribal members of prime college age, “Why don’t more American Indians become engineers?” and “What would it take to attract more?” In this study, we asked these questions and invited commentary about what is needed to gain more engineers from the perspectives of enrolled tribal members from South Dakota, with some of the most poverty-stricken reservations in the nation. Overall, results indicated that the effects of poverty and the resulting survival mentality among American Indians divert attention from what are understood to be privileged pursuits such as engineering education. The study’s findings indicated American Indian interviewees perceived the need for consistent attention to the following issues: 1) amelioration of poverty; 2) better understanding of what engineering is and its tribal relevancy; 3) exposure to engineering with an American Indian cultural emphasis in K-12 schools; 4) presence of role-model engineers in their daily lives; 5) encouragement and support from their peers, families, teachers, Elders, and tribal governments to value science, technology, engineering, and mathematics (STEM) education, particularly engineering fields; and (6) the embedded perceptions of math as a barrier to engineering studies.

Why Don’t More American Indians Become Engineers in South Dakota?

American Indians are among the most under-represented groups in the engineering profession in the United States. With increasing interest in diversity, educators and engineers seek to understand why. Often overlooked is simply asking enrolled tribal members of prime college age, “Why don’t more American Indians become engineers?” and “What would it take to attract more?” In this study, we asked these questions and invited commentary about what is needed to gain more engineers from the perspectives of enrolled tribal members from South Dakota, with some of the most poverty-stricken reservations in the nation. Overall, results indicated that the effects of poverty and the resulting survival mentality among American Indians divert attention from what are understood to be privileged pursuits such as engineering education. The study’s findings indicated American Indian interviewees perceived the need for consistent attention to the following issues: 1) amelioration of poverty; 2) better understanding of what engineering is and its tribal relevancy; 3) exposure to engineering with an American Indian cultural emphasis in K-12 schools; 4) presence of role-model engineers in their daily lives; 5) encouragement and support from their peers, families, teachers, Elders, and tribal governments to value science, technology, engineering, and mathematics (STEM) education, particularly engineering fields; and (6) the embedded perceptions of math as a barrier to engineering studies.

Stereotype Threatening Contexts Enhance Encoding of Negative Feedback to Engender Underperformance and Anxiety

In a recent meta-analysis, women exhibit varied performances on mathematic aptitude tests yet report more negative math perceptions compared to men. One explanation for this is that stereotype threatening (ST) contexts, that is, stressful contexts that engender negative emotions, arousal, and error vigilance, facilitate encoding of stereotype confirming information. Two studies tested this hypothesis. Study 1 found that ST women encoded error feedback better than correct feedback received on a math task compared to non-threatened women and men. Study 2 extended this effect to neutral information presented in conjunction with negative feedback. Furthermore, ST-based negative memory encoding mediated underperformance on a future difficult math test, which in turn engendered post-task anxiety. Findings indicate ST fosters negative math affect via biased memories even when women's initial performance is comparable to men.

Gender in STEM Education: an Exploratory Study of Student Perceptions of Math and Science Instructors in the United Arab Emirates

The current study addresses student perceptions of math and science professors in the Middle East. Gender disparity in science, technology, engineering, and math (STEM) education continues to exist in higher education, with male professors holding a normative position. This disparity can also be seen in the United Arab Emirates. As female participation in STEM education lags behind men, it is possible that gender stereotypes may influence students’ first impressions of male and female instructors. The United Arab Emirates provides a unique context to study this phenomenon as it is a traditional patriarchal society that is highly dependent on the engineering discipline, especially within the oil and gas sectors. A total of 176 undergraduate students from 2 universities in the United Arab Emirates completed a survey about teaching effectiveness based on their perceptions of photographs of hypothetical male and female instructors. A factor analysis of survey items revealed 2 main subcategories of teacher effectiveness: namely teacher warmth and professionalism. A 2-way between-groups analysis of variance was conducted to explore the impact of teacher gender and student gender on perceptions of overall teaching effectiveness, as well as their perceptions of teacher warmth and professionalism. Findings revealed that there was a significant cross-gender effect on student perceptions of math and science instructors in the United Arab Emirates.

Teachers' and students' perceptions of self-regulated learning and math competence: Differentiation and agreement

Teachers' diagnostic competence is a crucial determinant of their teaching quality. However, prior research has indicated only a moderate association between teachers' and students' assessments of students' competence/self-concept and motivation. Furthermore, it is unclear how well teachers are able to differentiate between students' overall competence and other competence-relevant characteristics. The present article therefore investigated teachers' and students' perceptions of math competence/self-concept and two aspects of self-regulated learning (preactional and actional strategies), using a sample of 73 teachers and their fifth-grade students (N=1289). Exploratory structural equation modeling revealed three-factor solutions, indicating that both teachers and students differentiated between the assumed self-regulated learning factors and math competence/self-concept. Latent correlations between teachers' and students' perceptions were small to moderate; their assessments of students' math competence/self-concept showed the highest agreement. The findings are discussed with respect to their implications for assessing and improving teachers' diagnostic competence of students' learning.

Stereotype Internalization, Math Perceptions, and Occupational Choices of Women With Counter-Stereotypical University Majors

Based on Eccles’ (1987) model of academic achievement-related decisions, we tested whether women, who are engaged in mathematical fields at university, have internalized, to some extent, the stereotype about women’s inferiority in math. The results indicate that men and women do not assess their ability self-concept, subjective value of math, or performance expectancies differently. However, women’s degree of stereotype endorsement has a negative impact on their ability self-concept and their performance expectancies, but does not affect their value of the math domain. Moreover, members of both genders envisage stereotypical careers after university graduation.

An Investigation of the Factors Influencing Student Performance in Physical Chemistry

A variety of diagnostics were administered to students enrolled in a first-semester physical chemistry course throughout the course of the semester: the Group Assessment of Logical Thinking (GALT), a math skills assessment, an inventory of student perceptions of the course, an inventory of student perceptions of math, and a survey of the students' past history in chemistry and math courses. The responses from these diagnostics were then correlated to students' achievement in the class. A correlation analysis revealed significant relationships between students' grades and their performance on the GALT as well as on several of the math problem solving questions from the math skills assessment (p < .05). It appears that achievement in a physical chemistry course designed for chemistry fields is significantly related to students' logical thinking skills, rather than to their previous chemistry knowledge, math exposure, or attitudes toward the course.

Attributional patterns and perceptions of math and science among fifth-grade through seventh-grade girls and boys

A culturally and economically diverse group of fifth to seventh graders (n = 361) from Boston-area public schools rated their perceptions for liking and difficulty of core academic subjects, including math and science, and their attributions for explaining performance on a math test. Inconsistent with earlier work, girls and boys reported similar perceptions of core subjects, with all students reporting a relatively high liking of math and science. Girls' and boys' attributional patterns for success in math were somewhat consistent with earlier findings, but not their attributions for lack of success. Observations of the math and science classrooms in the study indicated that most teachers, aware of gender equity issues, attempted to teach their students in a gender-fair manner. This factor may account for differences between current findings and those from past studies.