Secondary Students’ Attitudes Toward Learning Mathematics with Computer Algebra Systems (CAS)

The purpose of this study was to explore the relationship between behavioral and emotional engagement of Iranian EFL learners and their attachment to their teachers. Both teachers’ and students’ perceptions of their relationships and students’ engagement have been taken into account. Questionnaire data provided by 311 EFL students and 70 EFL teachers was used to investigate the relation between (a) teacher-student attachment and EFL learners’ engagement, (b) teacher-student secure attachment and EFL learners’ engagement, (c) teacher-student insecure attachment and EFL learners’ engagement, (d) teacher-student secure attachment and EFL learners’ behavioral engagement, (e) teacher-student insecure attachment and EFL learners’ behavioral engagement, (f) teacher-student secure attachment and EFL learners’ emotional engagement, and (g) teacher-student insecure attachment and EFL learners’ emotional engagement. The analysis of teachers and students’ questionnaire data showed that teacher-student attachment was correlated with learners’ engagement. The student participants reported that secure attachment positively affected behavioral and emotional engagement while insecure attachment had a negative effect. The teacher participants reported that attachment with students had weak and non-significant relationship with their students’ behavioral and emotional engagement. These findings and their major pedagogical implications are discussed.

This study aims to analyze self-confidence in learning mathematics through a constructivism approach assisted by geogebraic applications. The research method used descriptive qualitative with the population of all students of SMPN 4 Ngamprah. The sample used was 32 students in class VIID on triangular triangle material. The instrument used is a scale of self-confidence with 25 questions that have positive responses or negative responses. The self-confidence scale is used to find responses from respondents to students' self-confidence in mathematics learning in triangle triangle material using a constructivism approach assisted by geogebraic applications. The results of this study show that the level of self-confidence of students in triangle triangle material with the help of geogebra applications shows positive results with a response rate of 61%. The average is obtained by each indicator of the confidence questionnaire that has been given to each respondent

If the use of a computer algebra system (CAS) is to be meaningful and have an impact on students, then it must be grounded in good pedagogy and have some clearly defined goals. It is the authors' belief that an important goal for teaching mathematics with the CAS is that courses be designed so that students can become active participants in their learning experience, planning the problem-solving strategies and carrying them out. The CAS becomes an important tool and a partner in this learning process. To this end, here the authors' have linked the use of the CAS to an existing classification scheme for Mathematical Tasks, called the MATH Taxonomy, and illustrated, through concrete examples, how the goals of teaching and learning of mathematics can be set using this classification together with the CAS.

Based on Ellis’s three-dimensional learner engagement framework, this study examined the learner engagement in multiple feedback of nine second language learners with different language proficiency through writing texts, retrospective interviews, and semi-structured interviews. It was found that (1) learners generally have a positive attitude towards multiple feedback; they experience positive emotions while negative emotions such as disappointment, doubtful, angry, guilty are also generated in the process of revision; learners tend to absorb more teacher feedback and more meaning-level feedback and they are relatively poor at self-regulated learning. (2) Language proficiency has an effect on learner engagement, with a more significant effect for lowerlevel learners. Learners with lower language proficiency tend to be opposed to multiple feedback and show lower behavioral and cognitive engagement. (3) There is a correlation between the three dimensions of learner feedback engagement: Affective engagement influences behavioral and cognitive engagement, and the behavioral engagement is inspired by learners’ cognitive engagement. This study provides insights into the implementation of multiple feedback and second language writing, which is beneficial to the cultivation of second language talents in the new era.

An increasing number of studies have explored the effects of collaborative writing on written outcomes; however, few studies have examined the influence of collaborative processing of feedback. This study addresses this gap by focusing on learner engagement. While collaborative writing involves co-authoring a text, which requires negotiation and idea sharing, collaborative processing of feedback focuses on jointly interpreting and responding to feedback. Utilizing a mixed-methods design, this study examined 24 learners of French as a Foreign Language (FFL) over an 8-week period. It compared their engagement with written corrective feedback (WCF) when processed individually versus in pairs. The findings provide insights into how different feedback processing modes influence learner engagement and highlight the potential benefits of collaborative feedback processing. The instructor provided indirect WCF, and learners revised their essays with think-aloud sessions. The study examined cognitive and behavioral engagement through writing analysis and used think-aloud reports examining affective engagement. Results indicated that learners’ cognitive engagement varied between individual and collaborative processing, with individuals employing fewer high-depth and low-depth processing strategies. However, affective engagement was found to be independent of task completion mode, and behavioral engagement did not differ between individual and collaborative processing of WCF.

With the rapid development of information technology in recent years, learning and teaching approaches are facing profound changes. This study uses a structural equation model to analyze the influence mechanism of blended teaching on the autonomous learning ability of college students through a questionnaire survey of 295 students who have taken a blended course at universities in Heilongjiang Province. In this study, a structural equation model of the relationship between blended teaching, student involvement and autonomous learning ability was constructed and SPSS22, AMOS24.0 were used to test the reliability, validity and fit degree. Research shows that teaching content, teaching methods and teaching attitudes in blended teaching have a significant positive impact on students' autonomous learning ability. Teaching content and teaching methods can affect students' behavioral engagement, emotional engagement and cognitive engagement, thereby affecting students' autonomous learning ability. Teaching attitudes affect students' autonomous learning ability by influencing students' behavioral and emotional engagement. In order to improve the effect of blended teaching, colleges and universities should pay attention to the design and implementation of blended courses, change teaching concepts, increase Student engagement, stimulate students' learning motivation and then improve students' autonomous learning ability.

The present study aimed to examine whether and to what extent university student online learning performance was influenced by individual-technology fit (ITF), task-technology fit (TTF), environment-technology fit (ETF), and whether the influence was mediated by their behavioral, emotional, and cognitive engagement. A theoretical research model was developed by integrating the extended TTF theory and student engagement framework. The validity of the model was assessed using a partial least squares structural equation modeling approach based on data collected from 810 university students. Student learning performance was influenced by TTF (β = 0.25, p < 0.001), behavioral engagement (β = 0.25, p < 0.001), and emotional engagement (β = 0.27, p < 0.001). Behavioral engagement was affected by TTF (β = 0.31, p < 0.001) and ITF (β = 0.41, p < 0.001). TTF, ITF, and ETF were observed as significant antecedents of emotional engagement (β = 0.49, p < 0.001; β = 0.19, p < 0.001; β = 0.12, p = 0.001, respectively) and cognitive engagement (β = 0.28, p < 0.001; β = 0.34, p < 0.001; β = 0.16, p < 0.001, respectively). Behavioral and emotional engagement served as mediators between fit variables and learning performance. We suggest the need for an extension to the TTF theory by introducing ITF and ETF dimensions and demonstrate the important role of these fit variables in facilitating student engagement and learning performance. Online education practitioners should carefully consider the fit between the individual, task, environment, and technology to facilitate student learning outcomes.

There is an increasing use of and rapid advancements in technologies in education. In particular, there is a take-up of advanced calculators (graphing calculators and calculators with computer algebra system [CAS]) in senior secondary high-stakes examinations. Each year, tens of thousands of students in Australia, Singapore, and other regions, use advanced calculators in mathematics examinations that directly affect their entry into tertiary education. Thus, it was pertinent to investigate the ways in which students use these technologies when learning mathematics, and the factors that influenced them. This study was built upon a bricolage of theories from various fields such as mathematics education, educational technology, learning theories, learning styles, and gender studies. From a review of the literature in the different fields, it was hypothesised that factors such as students’ gender, beliefs about and attitudes toward mathematics and technology, approaches to studying mathematics, and learning preferences, influence their ways of using technology. A mixed methods research design was used, consisting of two parts: a quantitative large scale online survey of 964 Singaporean and 176 Victorian senior secondary mathematics students, and a qualitative small scale study of nine students in a Singaporean school. There were several main results found in this study: (i) How students interact with advanced calculators was influenced by their beliefs about and attitudes toward mathematics and their approaches to studying mathematics. Students’ ways of knowing and learning mathematics best explained their ways of interacting with the calculator. (ii) Students' learning preferences were situated, and the use of advanced calculators was associated with visual and kinesthetic modes and a preference to work cooperatively. (iii) There were regional differences (in favour of Victorian students) in how students use the advanced calculators and their attitudes toward calculators. (iv) There were gender differences (in favour of males) in students' attitudes toward mathematics and advanced calculators, and how they used the calculators. Although there were more student factors with gender differences in the Singaporean than the Victorian data, the effect sizes were larger in the Victorian sample. The findings have implications for mathematics teaching practice, in that deep understanding, intrinsic interest, beliefs about the creative, inter-connectedness and contextual aspects of mathematics are associated with using calculators as a partner and collaborator for learning. Additionally, students tend to employ visual and kinaesthetic modes when learning how to use the calculators. Students were also found to have a preference for working on the calculator cooperatively with friends. Therefore, teachers can employ methods such as encouraging students to try out the calculator keys and to work cooperatively in groups when learning how to use the calculators. Another significant contribution of this study was in the use of Facebook to recruit participants. More research can be done on the participation and response rates associated with this recruitment method. Further research can also be conducted to translate the implications of the study into practical classroom strategies and to investigate longitudinally the dynamic interplay between these factors and students’ interactions with the advanced calculators.

Based on the self-system model of motivational development, we examined the mediating role of school engagement, including cognitive engagement and behavioral engagement, in accounting for the relation between mastery goal orientations and subjective well-being in school among elementary school students. A total of 974 Chinese children (440 females, 534 males; Mage = 9.52, SD = 0.95) completed multiple self-report questionnaires at four time points, 6 months apart, across a 2-year period. Structural equation modeling was used to examine the hypotheses, controlling for the initial levels of mediating and dependent variables, and demographic variables (i.e., gender, age, and parental education levels). Results indicated that (a) mastery goal orientations at Time 1 positively related to subjective well-being in school at Time 4; (b) cognitive engagement at Time 2 mediated the relation between mastery goal orientations at Time 1 and subjective well-being in school at Time 4; and (c) mastery goal orientations at Time 1 displayed indirect effects on subjective well-being in school at Time 4 successively via the chain mediation of cognitive engagement at Time 2 and behavioral engagement at Time 3. These findings suggested that, in order to promote positive subjective well-being in elementary school students, school professionals and parents should simultaneously encourage students to cultivate mastery goal orientations and high levels of cognitive and behavioral school engagement.

Mathematics plays a vital role in a student's academic as well as everyday life. A large number of students experience mathematics anxiety, which negatively affects their performance in educational settings. The present study aimed to examine the overall level of mathematics anxiety among secondary students and also aimed to compare the mathematics anxiety based on demographical variables such as gender, type of school and medium of instruction. This study adopted a cross-sectional survey research design to conduct the study, and a total number of 220 secondary school students (13-15 years old) were selected as the sample through non-proportional stratified sampling techniques. The relevant data were collected using a standardized Mathematics Anxiety Scale and the collected data were analysed using descriptive statistics and t-tests. The findings of the study revealed that secondary school students experience a moderate level of mathematics anxiety. Further, the study revealed significant differences between male and female students, with male students showing higher mathematics anxiety in comparison to female students. Government secondary school students experience a higher mathematical anxiety compared to the private secondary school students and students who are studying in Odia medium secondary school had higher levels of mathematics anxiety than their English medium counterparts. The overall findings indicate that mathematics anxiety is influenced by various factors such as contextual, institutional, and medium of instruction. The study highlights the need for learner-friendly, concept-based, and supportive teaching practices to reduce mathematics anxiety among secondary school students. Improving instructional resources, reducing examination pressure, and adopting context-sensitive pedagogy may help in enhancing students’ confidence and performance in mathematics.

This study investigates the influence of students’ perceptions on mathematics performance at a selected South African secondary school. The influence of factors such as strength and weaknesses in mathematics, teacher support/learning material, family background and support, interest in mathematics, difficulties or challenges in doing mathematics, self-confidence and myths and beliefs about mathematics were identified as constructs of perceptions that influence students’ performance. Five of the seven constructs were found to be influential on students’ performance in mathematics. Quantitative methods were used to analyse the data collected from a questionnaire which was administered to randomly selected secondary school students (n=124) in Polokwane, South Africa. From the regression analysis of the data, the following hierarchy of themes emerged as components of students’ perceptions of mathematics. These were (i) weaknesses in mathematics (ii) family background and support, (iii) interests in mathematics, (iv) self-confidence in mathematics, (v) myths and beliefs about mathematics (vi) teacher /learning material support, (vii) difficulties in learning mathematics. Results from t-tests, Anova and suggest that there were significant differences in the perceptions and beliefs about mathematics between males and females, between mature and juvenile students and among students from different language backgrounds respectively. Correlation analysis results showed strong positive relationships between performance and perception constructs such as self-confidence, interests in mathematics, teacher and learning support material as well as myths and beliefs .The respondents tend to view lack of proficiency in mathematics as a challenge, and attribute success in mathematics to effort and perseverance. Students also perceive difficulty in mathematics as an obstacle, and attribute failure to their own lack of inherited mathematical ability. These findings suggest that differences in (i) myths and beliefs about mathematics success, ( (ii) motivation given by mathematics teachers and parents, (iii) mathematics teachers' teaching styles and learning materials and (iv) self confidence in mathematics may lead to differences in perceptions about mathematics. These in turn may lead to differences in attitudes towards mathematics and learning mathematics which have a bearing on performance. DOI: 10.5901/mjss.2014.v5n3p431

The current popularity of flipped learning may be attributed to its reported successes in bringing about enhanced learner engagement and positive learning outcomes. This study aims to improve our understanding of flipped learning (FL) outcomes by examining factors of learner engagement, academic capability, and epistemological beliefs. Data were collected and statistically analyzed from 231 undergraduate students enrolled in a general biology or general chemistry course at a Korean university implemented with the FL model. The results indicated that learners’ epistemological beliefs influenced neither pre‐class nor in‐class engagement, but that academic capability did affect both pre‐class and in‐class engagement. Only content/learning‐related outcomes, not generic competencies or satisfaction, were affected by both academic capability and epistemological beliefs. Both pre‐class and in‐class engagement levels affected most types of FL outcomes except generic competencies, which were only affected by the extent of in‐class engagement. Learners’ affective engagement was not influenced by epistemological beliefs, but directly and indirectly affected FL outcomes via behavioral and cognitive engagement. Theoretical and practical implications are discussed along with recommendations.

Mathematics is an important subject as a skill and foundation to further learning at the university level. In this regard, the engagement of students in the learning of mathematics is required so that mathematical knowledge and skills can be learned and mastered as much as possible. Previous study showed that student engagement, parental involvement, and peer influence affect mathematics achievement at a university. The purpose of this is to examine the relationship between mathematics achievement, the three aspect of student engagement, parental involvement, and peer influence. Data were collected from a total sample of 284 undergraduate students at a private university in Malaysia. Descriptive statistics and multiple regression analyses were used to analyse the data. Mathematics achievement was positively related to cognitive engagement and affective engagement, while behavioural engagement did not affect their achievement. Parental involvement and peer influence, on the other hand, are negatively related with mathematics achievement. More studies that concentrated on the relationship between parental involvement, peer influence, and student engagement in the future are encouraged to establish students' engagement in mathematics learning that vital to increase their mathematics achievement. A qualitative study should be considered in order to obtain more information from respondents.

This paper examines the process through which students learn to make functional use of computer algebra systems (CAS), and the interaction between that process and the wider mathematical development of students. The result of ‘instrumentalising‘ a device to become a mathematical tool and correspondingly ‘instrumenting’ mathematical activity through use of that tool is not only to extend students' mathematical technique but to shape their sense of the mathematical entities involved. These ideas have been developed within a French programme of research – as reported by Artigue in this issue of the journal – which has explored the integration of CAS – typically in the form of symbolic calculators – into the everyday practice of mathematics classrooms. The French research –influenced by socio-psychological theorisation of the development of conceptual systems- seeks to take account of the cultural and cognitive facets of these issues, noting how mathematical norms – or their absence – shape the mental schemes which students form as they appropriate CAS as tools. Instrumenting graphic and symbolic reasoning through using CAS influences the range and form of the tasks and techniques experienced by students, and so the resources available for more explicit codification and theorisation of such reasoning. This illuminates an influential North American study– conducted by Heid – which French researchers have seen as taking a contrasting view of the part played by technical activity in developing conceptual understanding. Reconsidered from this perspective, it appears that while teaching approaches which ‘resequence skills and concepts’ indeed defer – and diminish –attention to routinised skills, the tasks introduced in their place depend on another –albeit less strongly codified – system of techniques, supporting more extensive and active theorisation. The French research high lights important challenges which arise in instrumenting classroom mathematical activity and correspondingly instrumentalising CAS. In particular, it reveals fundamental constraints on human-machine interaction which may limit the capacity of the present generation of CAS to scaffold the mathematical thinking and learning of students.

Student’s attitude towards 21st-century mathematics teaching is affected by factors such as content knowledge, knowledge of teaching and learning activities, attitude towards mathematics and technology knowledge. The aim of this study was to construct structural equation models for investigating 21st-century mathematics teaching and learning among secondary mathematics students in the Secondary Educational Service Area Office Lopburi (SEAOL). Quantitative research used the 21st-century TPACK framework. The research sample consisted of 400 SEAOL students from the 1/2022 semester using multi-stage sampling. A questionnaire was used to assess 21st-century secondary school mathematics teaching and learning with a 0.934 confidence of. The data was analyzed using the appropriate software and revealed key components and their relationships. The results show that teaching and learning, fundamental technology capability, content knowledge, specialized technology use, and mathematical content implementation all affected mathematics teaching in the 21st-century for SEAOL students. Influence was .89, .70, .63, .25, and .21. School technology support has a .59 effect on students’ basic technological skills. Technology's role in learning influenced students' technology use by .21. This research shows how each aspect affects 21st-century mathematics education at the SEAOL, and math overload had the least effect. Teachers and stakeholders should investigate and innovate to improve the use of specialized technology in teaching to help students acquire higher-level mathematical content and apply it in their daily lives. Keywords: mathematics secondary students, mathematics teaching, structural equation model, Thailand