Investigating spatial skills and math anxiety as mediators in a sequential mediation model: A pilot study

Prior research showed a gender effect on spatial ability, math anxiety, and math achievement. Lacking, however, is a comprehensive study that testedthe mediation effects of spatial ability and math anxiety between gender and math achievement in a sequential mediation model. To fill this gap, this pilot study tested two mediation relationships, one with spatial ability as a mediator, gender as a predictor, and math anxiety as an outcome variable; the other with math anxiety as a mediator, spatial ability as a predictor, and math achievement as an outcome variable. In addition, the study tested the relative strengths of the relationship between specific spatial skills that included perspective-taking, spatial imagery, and mental rotation and collegiate math achievement that included trigonometry, calculus, and linear algebra) via canonical correlations. Lastly, gender differences in spatial skills, math anxiety, and math achievement were investigated. The results of the independent t-tests showed that none of the well-documented gender differences in spatial ability was found. Canonical correlation analysis showed that a single canonical variable is sufficient in accounting for math-spatial relationship. The sequential mediation model, with spatial ability and math achievement serving as themediators in the model, fitted reasonably well. However, none of the mediation effects was statistically significant. Implications of these findings and future directions of this research are discussed

The relationship between grade 11 learners’ procedural and conceptual knowledge of algebra

The acquisition of procedural and conceptual knowledge is imperative for the development of problem solving skills in mathematics. However, while there are mixed research findings on the relationship between the two domains of knowledge in some branches of mathematics, the relationship between learners’ procedural and conceptual knowledge of algebra has not been well explored. This research paper examined the relationship between Grade 11 learners’ procedural and conceptual knowledge of algebra. Data for the study was collected using an algebra test administered to 181 grade 11 learners in Gauteng province, South Africa. Descriptive statistics and Pearson’s correlation coefficient were used to analyse the data in SPSS. The study revealed that the learners have low levels of both procedural and conceptual knowledge of algebra. However, they displayed better procedural knowledge than the conceptual knowledge of algebra. In addition, a statistically significant moderate positive linear relationship was found between the learners’ procedural and conceptual knowledge of algebra.

Multivariate analysis on performance in statistics, self-efficacy and attitudes of senior high school students

Over the past few years, teaching and learning of statistics have been influenced by the emergence of the reform movement in education such as the K-12 basic education curriculum. Those of statistics concepts have changed both elementary and secondary level. Considering the educational reform in the Philippines, the study was conducted to determine whether there are significant differences of the determinants such as gender, type of school, parent’s educational level, family monthly income, family size and Senior High School track preference to students’ self-efficacy beliefs, attitudes towards Statistics, and performance in Statistics. The causal-comparative research design was used for comparing two or more groups to find the differences or determine whether the independent variable influences the dependent variable. The data were gathered from 570 senior high school students of both public and private schools in Mindanao, Region XI. The study adopted the questionnaires on self-efficacy beliefs and attitude towards Statistics while it utilized a researcher-made questionnaire for performance in Statistics. Multivariate Analysis of Variance (MANOVA) was used to determine whether multiple levels of independent variables on their own or in combination with one another influence the dependent variables. The findings revealed that among the demographic factors, only type of school has a significant difference to the self-efficacy beliefs, attitudes towards Statistics, and performance of senior high students in Statistics. Implications from the findings of this study might suggest that improving of K-12 school facilities by the school public administrators and collaborative effort of teachers to enhance the students’ self-efficacy, attitudes towards statistics and teaching statistics reveals optimistic results. Also, school administrators may provide opportunities for Statistics teachers to hone their pedagogical skills in promoting and building students’ self-confidence and interest in the subject.

Ethnomathematics: Modelling the volume of solid of revolution at Buginese and Makassarese traditional foods

Ethnomathematics can empirically improve the cognitive abilities of students in elementary and secondary schools. However, in undergraduate study, there are still limited studies on integrating ethnomathematics in learning resources. This study aims to apply interpolation in modelling polynomial functions and integral volume on the shape of Buginese and Makassarese traditional foods. Furthermore, it can be used by students as relevant learning resources regarding interpolation and the concept of volume of solid of revolution (VOSR). This is a qualitative study using an ethnographic approach. The data were collected through observations to obtain general information, interviews with informants to find out food-making techniques, and documentation to obtain physical models of each type of food. Data Analysis Techniques consist of the domain analysis to obtain an overview of Buginese and Makassarese traditional foods and the taxonomic analysis to categorize mathematical concepts obtained from the modeling and simulation. The result of this research reveals that lammang is suitable with the slabs. It can be represented as constant functions that revolved around the x-axis or the y-axis. While paso, bolu cukke, and cantik manis as well as barongko batara, Putu, and cucuru can be outlined in linear functions rotating about the x-axis, y-axis, or others fixed-line. They meet the criteria of the disks method. However, they are described in the function of polynomials of n-degree. The use of washers can be described in the model of blundered and sarang semut with a hole in the middle caused by the intersection of two curves rotated about the x-axis or the y-axis. For shells, the model can be applied to determine the cover volume of the cover of pisang ijo flour and onde-onde. Thus, all types of traditional foods in this study can be appropriate objects for a learning resource in modelling the VOSR.

Learning design of lines and angles for 7th -grade using Joglo traditional house context

Lines and angles are essential for students because of geometry and its many applications in daily life. However, there are still many students who have difficulty grasping the material. Therefore, it is necessary to design learning using the right approach, context, and media. This study aims to produce a learning trajectory that can assist students in understanding the concept of lines and angles, maximize the effectiveness and efficiency of learning, create meaningful learning, and motivate student learning. This study used the Joglo Traditional House context as a starting point and the design research method developed by Gravemeijer and Cobb with three main steps: preparing for the experiment, designing the experiment (pilot experiment and teaching experiment), and retrospective analysis. However, in design experiment step is limited to the pilot experiment. In this study, all activities were designed based on Indonesian Realistic Mathematics Education. It involves six 7th-grade students from one of the junior high schools at Juwana Resident with three different abilities, namely two students for each level with high, moderate, and low ability. The learning trajectory generated in this study consists of a series of learning processes in four activities that can be used to develop local instructional theories and develop designs for further activities. Those are observing Joglo traditional house video for understanding lines and angles concepts, deducing line positions, discovering the angles' properties on parallel lines intersected by other lines, and solving lines and angles problems.

Chess, visual memory and geometric transformations

This work shows how playing chess creates capacities in the student such as increasing visual memory. This helps to classify information in an orderly manner in the mind and contributes to a better understanding of geometric transformations such as displacements, turns and similarities. This was done with a mixed technique (Quantitative and Qualitative), starting with a structured questionnaire that was applied to 487 students. A case study was carried out with two students (one with and the other without notable chess skills) in two schools in Bogotá-Colombia, with the aim of understanding chess as a tool that can help the teacher to teach mathematics¡. In the quantitative part, data were collected by a structured questionnaire, and in the qualitative part, recordings and transcripts were made of what the two students reported in the case study. So, favorable results were achieved for students who usually play chess, because they show a great capacity for visual memory (in the long and short term) that contributes to a more optimal learning of displacements and similarities in the Cartesian plane. This research shows a powerful tool (chess) that can be used in the teaching of mathematics, thanks to the skills and concepts that are generated in the experience with the game.

Undergraduate basic sciences and engineering students’ understanding of the concept of derivative

Derivative is one of the most important topics in calculus that has many applications in various sciences. However, according to the research, students do not have a deep understanding of the concept of derivative and they often have misconceptions. The present study aimed to investigate undergraduate basic sciences and engineering students’ understanding of the concept of derivative at Tehran universities on based the framework of Zandieh. The method was descriptive-survey. The population included all undergraduate students of Tehran universities who passed Calculus I. The sample included 604 students being selected through multi-stage random cluster sampling. The measurement tool was a researcher-made test for which the reliability coefficient was obtained using Cronbach's alpha (r=.88). Inspired by Hähkiöniemi’s research, nine tasks on derivative learning were given to the students. The students’ responses were evaluated using a five-point Likert scale and analyzed using descriptive responses. The results indicated that students have no appropriate understanding of the basic concepts of derivatives in numerical, physical, verbal, and graphical contexts. Basic sciences students performed meaningfully were better in understanding the tangent line slope compared to engineering students, while engineering students performed meaningfully were better than basic sciences students in the rate of change.

Introducing a measure of perceived self-efficacy for proof (PSEP): Evidence of validity

It is widely recognized that students encounter difficulties with proof across all grades and beyond, yet standardized instruments related specifically to students’ perceived self-efficacy for mathematical proof have not been readily available. The purpose of this study was to develop and investigate preliminary validity evidence for a new instrument for measuring self-efficacy for mathematical proof that can be of importance to the field. The new Perceived Self-Efficacy for Proof (PSEP) questionnaire is a self-administered, 8-item questionnaire that quantifies experimentation, conjecturing, inductive reasoning, justification, and validation. To validate the PSEP, two studies with 260 eleventh grade students—recruited from three Dinaledi schools in EThekwini metropolitan area, South Africa—were conducted. In Study 1 (n=128), face and content validity were evaluated, and an exploratory factor analysis (EFA) was performed. In Study 2 (n=132), a confirmatory factor analysis (CFA) was conducted and external validity was investigated. In both samples, the PSEP was found to possess good internal consistency reliability with relatively high factor loadings on a single component. Although the findings in this report represent preliminary validation evidence, it can be concluded that the PSEP is a valid, reliable and sensitive measure of 11th grade students’ perceptions of their ability to construct a proof and may serve as a meaningful outcome in mathematical proof research and classroom proof education.

Pre-service primary school teachers’ metacognitive awareness and beliefs about mathematical problem solving

Metacognitive awareness is a variable that is thought to affect beliefs in problem solving. When the literature is examined, it is seen that the studies mostly focus on metacognitive awareness and problem solving skills. Therefore, the aim is to determine pre-service primary school teachers’ metacognitive awareness and beliefs in mathematical problem solving. In this study, it is thought that it will contribute to the researches that will be carried out regarding the investigation of the relationship between metacognitive awareness and beliefs about problem solving and its implementation with pre-service primary school teachers. The study, designed as the correlational survey model, included a total of 284 pre-service primary school teachers attending a university in the Aegean Region of Turkey. The data were collected with the “Metacognitive Awareness Inventory” and the “Scale of Beliefs about Mathematical Problem Solving”. In the analysis, descriptive statistics, difference test, correlation and regression analyses were used. As a result, the pre-service primary school teachers’ metacognitive awareness was found to be high and their beliefs about mathematical problem solving were found to be medium. While metacognitive awareness was found to be not varying significantly by gender, beliefs about mathematical problem solving were found to be varying significantly by gender in favor of the male pre-service teachers. Moreover, a medium and significant correlation was found between metacognitive awareness and beliefs about mathematical problem solving. It was also found that metacognitive awareness explained 13% of the variance in the dependent variable of beliefs about mathematical problem solving.

Professional competency: Pre-service mathematics teachers’ understanding toward probability concept

The ability to understand mathematics is a faculty crucial to be possessed by pre-service teachers who will enter into the education sphere. It is one of the professional competencies essential for teachers since satisfactory lessons’ delivery engenders more comprehensible instruction in teachers’ students. Qualitative research employs a descriptive approach relevant to the research purpose, describing mathematics pre-service teachers’ professional competency of understanding the concept toward probability observed based on mathematical abilities; advanced, intermediate, and basic mathematics ability. The subjects are three pre-service teachers having passed discrete mathematics course in a college in Madura. The criteria to select the subjects are the GPA (Grade-point Average) of the last semester and information from the lecturer. It is because unlikely to administer the test due to online learning applied at the college. Findings indicated that the subject with advanced mathematics ability could meet individual concepts, relate concepts and connect concepts with the operations. The subject with intermediate mathematics ability could meet individual concepts, but could not relate to some concepts. However, he could connect concepts with the operations. The subject with basic mathematics ability could not meet individual concepts, relate concepts, and connect concepts with the operations. In terms of the advancement indicator of understanding the concept, the subjects have not attained it since they have not apprehended concept definition well, particularly the probability concept, although the subject with advanced mathematics ability was procedurally prodigious.