Mathematical Beliefs Research Articles

Success Indicators of Mathematical Problem-Solving Performance Among Malaysian Matriculation Students

This study identifies the success indicators of mathematical problem-solving performances among Malaysian matriculation students divided into four indicators: mathematical beliefs, mathematics attitudes, mathematics self-efficacy and metacognitive skills. For this purpose, 368 matriculation students from three matriculation colleges were selected as respondents using proportioned stratified sampling. This study utilized a descriptive correlational design approach. A set of questionnaires and a mathematics test were used as the instruments. Independent variables were measured using a questionnaire, while mathematical problem-solving performance was measured using a mathematics test. The findings show students had a high level in mathematics beliefs, attitude towards mathematics, mathematics self-efficacy and metacognitive skills. Statistical tests to determine success indicators predicting mathematical problem-solving performance revealed that mathematics self-efficacy does not contribute significantly to these variables and that metacognitive skills make the most decisive contribution, followed by mathematics attitude and mathematics beliefs. Hence, this study suggests that problem-solving should be included as an essential part of the mathematics matriculation syllabus to enable students to improve their problem-solving abilities.

Epistemological beliefs in relation to the Content, teaching and learning of mathematics teachers

One result of the research is the paper "integral intervention of mathematics' teaching and learning processes" developed in a public university in Colombia, Latin America. The analysis of the epistemological beliefs of a group of academics from the Mathematics Department, who teach subjects to engineer and technology students is presented. We performed descriptive and quantitative cohort research. The objective was to identify the beliefs regarding mathematics' content, learning, and teaching. The 56 participants were included from a voluntary sample, in which the majority were engineers. A questionnaire adapted from Vizcaíno, with a specific domain of mathematical beliefs, approached from the multidimensional model de Schommer was used as a measuring instrument. The results showed that, in general, the teachers' system beliefs are naive or simple and in some specific topics sophisticated. It was observed a percentage of teachers who didn't assume a precise position in their beliefs when responding neutrally to the questionnaire, which could be interpreted as a lack of reflection on their teaching practice, which revealed the need to generate discussion spaces for promoting reflective practices that improve the mathematics' learning. Likewise, the need for training in mathematics' history, epistemological knowledge, and didactics was evidenced, which promotes better mathematics teaching practices.

Beliefs About Mathematics, Its Teaching, and Learning: Contrast Between Pre-service and In-service Teachers

The present research inquired about beliefs of in-service and pre-service mathematics teachers as well as the analysis and comparison between the beliefs that they declare, argue, and reflect in their lessons plans, and the use of those beliefs in their practical exercises. Five pre-service teachers studying a Bachelor’s in Mathematics, and three in-service teachers who were Ph.D. candidates in Mathematics Education participated in the study. A multiple case study was carried out using mixed methods. Closed questionnaires, semi-structured interviews, and lesson plans were used as instruments for information collection. The obtained data show how participants have been structuring their beliefs. Moreover, it was possible to determine that in-service teachers have more firm beliefs which were evidenced in their classroom proposals, whereas pre-service teachers have more tentative beliefs that, in general, do not align with what is evidenced through their lesson planners. The training received at the undergraduate and postgraduate levels has permeated the formation of participants’ beliefs which can be evidenced in the obtained results. Some implications and suggestions for initial and continuous education programs for mathematics teachers and future research suggestions are presented.

Constructivist Teachers Beliefs, Instructional Practices and Students’ Mathematics Performance

This study determined the role of teachers’ constructivist beliefs in the teaching and learning mathematics and the use of instructional practices in the mathematics performance of Grade 7 secondary students in the Pacific Towns of Northern Samar for the school year 2016-2017. This study utilized the descriptive-correlational research design.
 The demographic profile of teachers in mathematics such as constructivist beliefs, constructivist instructional practices and performance of students was described as it exists at the present time. Multiple regression analysis was used to determine the relationship between the beliefs in mathematics and students’ mathematics performance. Similarly, statistical analysis was used to determine the relationship between instructional practices and mathematics performance of the students.
 The findings showed that more than 50% of the mathematics’ teachers are aged less than 30 suggesting that most of the teachers are neophyte in the teaching career. As to educational attainment, most of the respondents are enrolled in master’s program. Only one-third have already completed master’s degree. In terms of relevant trainings, almost a half of the respondents have attended one to two trainings.
 Most of the teachers believe that teaching should involve real world connections. Teachers believe that they should create real-world environments that employ the context in which learning is relevant. Beliefs about emphasizing prior knowledge were also manifested by the teacher-respondents. Highly demonstrated beliefs include encouraging the use of multiple modes of representation to facilitate easy understanding and recall and the learner's previous knowledge constructions, beliefs and attitudes are considered in the knowledge construction process. In terms of social interaction beliefs, teachers manifested support for collaborative construction of knowledge through social negotiation.
 Result of the test conducted in mathematics by the researcher showed that more than half of the students got fair performance. Only one performed satisfactorily. Beliefs about emphasizing prior knowledge and beliefs in social interaction significantly predicted mathematics performance of students. Real world connection did not significantly predict mathematics performance.
 Respondents’ constructivist instructional practices did not offer a significant role in developing the mathematics ability of the students. Teachers did not play an active role in assimilating knowledge into students’ existing mental framework and reconstructing new knowledge.

Preservice teacher belief on nature of mathematics and mathematics teaching and tearning: a quantitative study

A quantitative study aims to investigate preservice teacher’s beliefs in mathematics and mathematics teaching and learning. The participants were 103 preservice mathematics teachers who were studying at the Musamus University of Merauke. The TBTP questionnaire was used to measure the beliefs of preservice teachers. The results showed that there were differences in the beliefs of preservice teachers when teaching in classes dominated by high ability students and low ability students. Preservice teachers tend to have platonist beliefs when teaching in high ability classes and when teaching in low ability classes preservice teachers have instrumentalist beliefs. Most preservice teachers have instrumentalist beliefs in mathematics. The implications of the study provide recommendations for teacher educators to change the beliefs of preservice mathematics teachers into problem-solving views.

Mathematical Beliefs Held by Costa Rican Pre-Service Teachers and Teacher Educators

Beliefs have been conceived as a hidden variable in mathematics education. It is important to know teachers’ beliefs as they can inform the way that teachers teach mathematics, make decisions in the classroom, and form opinions about the abilities of students. In Costa Rica, studies about beliefs have been conducted with in-service teachers, but there is no research on pre-service teachers and the beliefs they bring to the classroom from their teacher education programs (TEPs). This research aims to describe the beliefs held by 76 pre-service teachers and 19 teacher educators from four Costa Rican public universities, using the Teacher Education and Development Study in Mathematics (TEDS-M) questionnaire. The results suggest that both pre-service teachers and teacher educators believe in a constructivist orientation focused on the learner. Both groups support the view of mathematics as a process of inquiry and active learning and agree that mathematical skills are not fixed or associated with gender or culture. In the literature, the beliefs manifested by the participants are associated with positive results regarding student outcomes and teaching practices. Therefore, policymakers should be concerned with providing environments that allow and encourage teachers to continue with these belief orientations when they start teaching.

Development and Validation of Teachers’ Assessment Belief of Mathematical Thinking Instrument

<p style="text-align: justify;">This study was conducted to corroborate in understanding the teachers’ beliefs about assessment practices. The prior studies related to teachers’ assessment beliefs in mathematics have been done to assess teachers’ beliefs in the general context of mathematics teaching. This study developed an instrument to assess teachers’ assessment beliefs of mathematical thinking. The research aimed to develop and validate a scale of assessment beliefs of mathematical thinking by using the confirmatory factor analysis. The first draft of the scale contained 25 items. The sample of the study consisted of 537 mathematics teachers from public schools in Oman. The instrument was a questionnaire with a 5-point Likert scale. The scale was validated by asking a number of experts in mathematics educational measurement and evaluation. Exploratory and confirmatory factor analysis was applied to test the model of assessment beliefs of mathematical thinking scale using AMOS 25.0. All constructs had acceptable reliability. The model had a good model fit for the assessment beliefs of mathematical thinking scale which obtainable from the fit indices tests. The findings revealed that all fit criteria indices were realized. The results also showed acceptable validity and construct reliability for the scale.</p>

Kemampuan Pemecahan Masalah Mahasiswa pada Kalkulus Integral Dilihat dari Keyakinan dan Pengetahuan Awal Matematis

Integral calculus is a course where students tend to have difficulties in problem-solving. This study examines differences in mathematical beliefs in students' problem-solving skills based on mathematics prior knowledge. This study's subjects were 120 students of the Mathematics Education study program from UPH Faculty of Education. The independent variable is mathematical beliefs, the moderator variable is prior mathematics knowledge, and the dependent variable is students' problem-solving skills. This study is an ex post facto quantitative research with instruments in a Likert scale questionnaire for mathematical beliefs, problem-solving, and mathematics prior knowledge test scores. Hypotheses were tested statistically with a two-way Anova test using SPSS 16.0. The results of the study were: (1) students' problem-solving of logical consistency beliefs is higher than memorized and procedural beliefs, (2) there is an interaction between mathematical beliefs and mathematics prior knowledge on problem-solving, (3) students' problem-solving in high mathematics prior knowledge group of logical consistency beliefs is higher than memorized, and procedural beliefs, and (4) students' problem-solving in low mathematics prior knowledge group of logical consistency beliefs is lower than memorized and procedural beliefs.

Relevance Interventions in the Classroom: A Means to Promote Students’ Homework Motivation and Behavior

Many students suffer from motivational problems when doing homework. To investigate whether an intervention that effectively promoted value beliefs in mathematics promoted students’ homework motivation and behavior, we analyzed data from a cluster randomized controlled study with two classroom-based relevance interventions (writing a text or evaluating quotes from interviews) with 82 classrooms and 1,978 ninth-grade students. Students’ math-specific homework motivation and behavior were assessed with homework diaries over a period of 4 weeks after the intervention. Latent growth curve analyses revealed that students in the text condition reported higher triggered interest but also lower homework completion than students in the control condition in the first week after the intervention. Students in the quotations condition reported higher utility of homework for future life, and higher homework effort directly after the intervention. The study highlights the potential of classroom-based relevance interventions to foster homework-specific outcomes, when considering situational, behavior-related measures.

Platonism and Mathematical Explanations

Ontological parsimony requires that if we can dispense with A when best explaining B, or when deducing a nominalistically statable conclusion B from nominalistically statable premises, we must indeed dispense with A. When A is a mathematical theory and it has been established that its conservativeness undermines the platonistic force of mathematical derivations (Field), or that a non numerical formulation of some explanans may be obtained so that the platonistic force of the best numerical-based account of the explanandum is also undermined (Rizza), the parsimony principle has been respected. Since derivations resorting to conservative mathematics and proofs involved in non numerical best explanations also require abstract objects, concepts, and principles under the usual reading of “abstract,” one might complain that such accounts turn out to be as metaphysically loaded as their platonistic counterparts. One might then urge that ontological parsimony is also required of these nominalistic accounts. It might, however, prove more fruitful to leave this particular worry to the side, to free oneself, as it were, from parsimony thus construed and to look at other important aspects of the defeating or undermining strategies that have been lavished on the disposal of platonism. Two aspects are worthy of our attention: epistemic cost and debunking claims. Our knowledge that applied mathematics is conservative is established at a cost, and so is our knowledge that nominalistic proofs play a genuine theoretical role in best explanations. I will suggest that the knowledge one must acquire to show that nominalistic deductions and explanations do indeed play their respective theoretical role involves some question-begging assumptions regarding the nature and validity of proofs. As for debunking, even if the face value content of either non numerical claims, or conservative mathematical claims, or platonistic mathematical claims didn’t figure in our causal explanation of why we hold the mathematical beliefs that we do, construed or understood as beliefs about such contents, or as beliefs held in either of these three ways, we could still be justified in holding them, so that the distinction between nominalistic deductions or non numerical explanations on the one hand and platonistic ones on the other turns out to be spurious with respect to the relevant propositional attitude, i.e., with respect to belief.

Epistemic and Mathematical Beliefs of Exemplary Statistics Teachers

Education research has established that teachers' beliefs matter because they can affect classroom practices and student outcomes, and beliefs are viewed as an important construct within statistics education. However, relatively little research about the beliefs of in-service statistics teachers has been conducted. Additionally, little research has been conducted with highly-experienced statistics teachers rather than pre-service teachers or typical teachers. Using two survey instruments, this study describes the beliefs about knowledge and beliefs about mathematical problem-solving for a sample of exemplary statistics teachers. The exemplary statistics teachers in this study responded to the Epistemic Beliefs Inventory and the Indiana Mathematics Belief Scales. Results show that the exemplary statistics teachers in this study had mature epistemic beliefs and strongly positive beliefs toward mathematical problem-solving, but notable patterns of similar responses that run counter to these trends were observed and are discussed.

Characteristics of Mathematics Teachers' Practices and Beliefs about Project-based Learning and Teaching Mathematics in Ukraine

This empirical study determines the obvious and hidden factors that affect the Ukrainian Mathematics teachers to use Project-Based Learning and Teaching (PBL and PBT) Mathematics. A survey of 126 practicing Mathematics teachers was conducted using a Standard closed ended questionnaire. The study confirms that modern Mathematics teachers believe that it is impossible to teach Mathematics for modern students without using PBL and PBT. On the one hand, teachers demonstrate their beliefs in these educational techniques. On the other hand, the survey reveals hidden factors that are inhibitory in the practice of PBL and PBT Mathematics. The study shows the following statistically confirmed factors in teachers' beliefs concerning the use of PBL and PBT Mathematics: Content-Technological Factor; Result & Age Factor; Factor of the Target Audience on the expediency of using PBL and PBT Mathematics; Teacher's Overload Factor; Praxeological Factor; Locality Factor; Teacher's Awareness Spectrum Factor. The previous assumption that the experience of a Mathematics teacher is an influential factor in the use of PBL and PBT has not been statistically confirmed. The results show that an influential factor is the Locality Factor. So, it's important if a teacher teaches Mathematics in a city or a village. Its origins (genesis and causes) and the consequences of this factor influence on educational processes in Ukraine need more detailed study.

Movement and Song Idiom Traditional to Enhance Early Mathematical Skills: Gelantram Audio-visual Learning Media

Movement and Song Idiom Traditional to Enhance Early Mathematical Skills: Gelantram Audio-visual Learning Media

Examining the Effect of Students Early Numeracy Activities at Home on Later Mathematics Achievement via Early Numeracy Competencies and Self-Efficacy Beliefs

This study examines the influence of early numeric activities at home on children’s mathematics achievement in fourth grade. It also examines the mediating effects of early numeracy competencies and self-efficacy beliefs in mathematics on this relationship. We used Trends in International Mathematics and Science Study 2015 Korean data, selecting nationally representative samples of fourth-grade elementary students (N = 4 669) and their parents. We conducted confirmatory factor analysis and structural equation modeling to analyze the data. Our findings revealed that students who engage in more early numeracy activities at home are more likely to have high mathematics achievement in fourth grade. Early numeracy competencies and self-efficacy beliefs positively mediate this relationship. Moreover, we found sequential mediating effects of early numeracy competencies and self- efficacy beliefs on this relationship. Based on the findings of the study, we propose several implications.

Do gender differences in academic attainment correspond with scholastic attitudes? An exploratory study in a UK secondary school

AbstractResearch has examined how standardized tests give rise to gender differences in English and STEM attainment, but little research has explored gender differences in classroom‐based attainment and the degree to which these correspond to differences in school‐related attitudes. To explore the extent to which gender‐achievement gaps in classroom‐based performance parallel differences in self‐perceptions and scholastic attitudes. An independent sample of first (n = 187, age 11–12, Study 1) and second‐year students (n = 113, age 12–13, Study 2) from a UK comprehensive secondary school completed a questionnaire measuring academic mindset, self‐efficacy, self‐concept, competence beliefs, personal and social self‐esteem, and endorsement of gender‐subject and career stereotypes. Responses were then matched to their respective classroom grades in English, mathematics, science, and computing. Girls outperformed boys in English in their first year but reported lower global self‐esteem and greater endorsement of science‐career stereotypes. Conversely, girls outperformed boys in mathematics in their second year, but paradoxically reported lower self‐concept and competence beliefs in mathematics and science, and higher competence beliefs in English. Across both studies, mindset, self‐efficacy, competence beliefs, and social self‐esteem were positively related to English attainment; academic self‐efficacy was positively related to mathematics attainment; and mindset, self‐efficacy, self‐concept, and competence beliefs were positively related to science attainment. Gender‐achievement gaps in classroom‐based academic attainment are complex and highly nuanced; they appear to vary between school subjects across years and may not correspond with similar differences in self‐perceptions and scholastic attitudes.

Student-Teachers’ Beliefs towards Learning Mathematics and Beliefs of Mathematics Teaching Efficacy and their Relation to their Perception of the Development of Pupils’ Understanding of Mathematics

The present study aimed at investigating the student-teachers’ beliefs towards learning mathematics, and beliefs of mathematics teaching efficacy and their relation to their perception of the development of pupils’ understanding of mathematics. Three measures were used in this study: The beliefs towards learning mathematics, the mathematics teaching efficacy beliefs, and the mathematics teacher's perception of the development of pupils’ understanding. Validity and reliability were established. A sample of student-teachers participated in the study. The results of the study showed that the more the positive student-teachers’ beliefs towards learning mathematics, the greater their mathematics teaching-efficacy was. Similarly, the greater the positive student-teachers’ belief towards learning mathematics, the more they become aware of the development of pupils’ understanding of mathematics. Finally, increasing the teaching efficacy of mathematics student-teachers was associated with an increase in their perception of the development of pupils’ understanding of mathematics. Both beliefs and teaching efficacy explained significant variance in the perception of their pupils’ understanding of mathematics.

Student-Teachers’ Beliefs towards Learning Mathematics and Beliefs of Mathematics Teaching Efficacy and their Relation to their Perception of the Development of Pupils’ Understanding of Mathematics

The present study aimed at investigating the student-teachers’ beliefs towards learning mathematics, and beliefs of mathematics teaching efficacy and their relation to their perception of the development of pupils’ understanding of mathematics. Three measures were used in this study: The beliefs towards learning mathematics, the mathematics teaching efficacy beliefs, and the mathematics teacher's perception of the development of pupils’ understanding. Validity and reliability were established. A sample of student-teachers participated in the study. The results of the study showed that the more the positive student-teachers’ beliefs towards learning mathematics, the greater their mathematics teaching-efficacy was. Similarly, the greater the positive student-teachers’ belief towards learning mathematics, the more they become aware of the development of pupils’ understanding of mathematics. Finally, increasing the teaching efficacy of mathematics student-teachers was associated with an increase in their perception of the development of pupils’ understanding of mathematics. Both beliefs and teaching efficacy explained significant variance in the perception of their pupils’ understanding of mathematics.

Linking university mathematics classroom environments to student achievement: The mediation of mathematics beliefs

This study examined the relationships between university mathematics classroom environments, mathematics beliefs, and achievement in the context of mainland China. As a type of affect in mathematics learning, mathematics beliefs including mathematics conceptions and efficacy were examined as mediators. Based on analysis of a sample of 1443 undergraduate students from a university in northern China, the study not only found that the mathematics classroom environment was associated with both affective and cognitive mathematics outcomes, but also confirmed the mediating role of mathematics beliefs. Specifically, a desirable classroom environment was related to students’ cohesive conceptions, enhanced self-efficacy, and higher mathematics achievement. In contrast, students’ perceived difficulty of learning mathematics was connected to their fragmented conceptions, reduced self-efficacy and lower mathematics achievement. Implications of the study are discussed.

Fostering Mathematical Creativity While Impacting Beliefs and Anxiety in Mathematics

This quantitative study examined the notion of mathematical creativity and its relationship to epistemological beliefs of the nature of mathematics and mathematical anxiety. A counterbalanced design was employed, randomizing a class of elementary pre-service teachers into two groups and giving a pre- and post-test to determine if significant differences exist in the participants who are exposed to problem posing, divergent thought, and invented strategies, that is, a punctuated, intentional experience with mathematical creativity. This difference in mathematical anxiety, beliefs, and creativity was also gauged using repeated measures during the study. Furthermore, beliefs and anxiety were correlated with mathematical creativity employing pre- and post-test measures. The findings of this study suggest that mathematical creativity can be fostered and sustained under certain conditions. Also, the results indicated that mathematical beliefs and anxiety are significantly impacted by intentional experiences with mathematical creativity – alternative algorithms, divergent thought, invented strategies, and problem posing.

Preservice teachers’ beliefs in a mathematics/science course

ABSTRACT Background Little research exists which describes how mathematics and science constructivist beliefs are developed in a dual content mathematics/science methods course, and if beliefs within one discipline inform the other. If mathematics and science beliefs inform one another, then this would enrich learning in both disciplines. Purpose The study’s purpose was to (a) understand how a dual content methods course centered on problem-solving was able to concurrently enrich PSTs’ mathematics and science beliefs, and (b) determine if PSTs entered the course with similar mathematics and science beliefs, and how these similar beliefs changed throughout the course. Sample PSTs (N = 113) participated in ten iterations of the course. Design and methods PSTs completed a mathematics and science belief instrument at the start and end of the course. An exploratory factor analysis was conducted to determine if PSTs entered the course with similar or different beliefs in mathematics and science, and independent samples t-test was conducted to look for significant changes between the factors from the pretest and posttest. Results Findings show that (a) the course caused PSTs’ beliefs to become more constructivist-based; and (b) PSTs entered and exited the course with similar beliefs in mathematics and science. Conclusion PSTs may have holistic constructivistic beliefs – which stand in contrast to discipline-specific beliefs – that inform the teaching and learning of both mathematics and science. Implications include that education programs should emphasize problem-solving and constructivism in courses outside of mathematics and science, to enrich instruction and learning in all courses.