E-learning in secondary–tertiary transition in mathematics: for what purpose?

Mathematics is a challenging subject for many science freshmen, and failing mathematics exams is a major factor in university dropout rates. Many factors, including metacognitive, affective and linguistic ones, play a role in students?? difficulties in mathematics. Starting from this perspective, we conducted a theoretical exploration of the potential of online environments in helping students counteract the mathematical difficulties they face in the transition from secondary school to university. Although this secondary?Ctertiary transition and the use of technology are both widely researched issues in mathematics education, the potential of technology in helping students in the ??rite of passage?? to tertiary education has not yet been researched. This paper reports on the developed theoretical framework and on the preliminary findings from the implementation of an e-learning course that we designed with the aim of supporting students in the critical phase of transition from secondary school to university.     

Students’ Activity in Computer-Supported Collaborative Problem Solving in Mathematics

The purpose of this study was to analyse secondary school students’ (N = 16) computer-supported collaborative mathematical problem solving. The problem addressed in the study was: What kinds of metacognitive processes appear during computer-supported collaborative learning in mathematics? Another aim of the study was to consider the applicability of networked learning in mathematics. The network-based learning environment Knowledge Forum (KF) was used to support students’ collaborative problem solving. The data consist of 188 posted computer notes, portfolio material such as notebooks, and observations. The computer notes were analysed through three stages of qualitative content analysis. The three stages were content analysis of computer notesin mathematical problem solving, content analysis of mathematical problem solving activity and content analysis of the students’ metacognitive activity. The results of the content analysis illustrate how networked discussions mediated mathematical knowledge and students’ questions, while the mathematical problem solving activity shows that the students co-regulate their thinking. The results of the content analysis of the students’ metacognitive activity revealed that the students use metacognitive knowledge and make metacognitive judgments and perform monitoring during networked discussions. In conclusion, the results of this study demonstrate that working with the networked technology contributes to the students’ use of their mathematical knowledge and stimulates them into making their thinking visible. The findings also show some metacognitive activity in the students’ computer-supported collaborative problem solving in mathematics.     

高师生数学解题的元认知模型及其特点研究

从实证的角度探讨数学解题的元认知模型.以数学解题中的元认知知识、元认知体验、元认知策略三者为基本因素,研制一份元认知问卷;施测问卷,对数据进行探索性因素分析和验证性因素分析,检验因素假设与数据之间的拟合程度.施测正式问卷于高师生,结果表明,高师生数学解题的元认知模型还保持一定程度的发展,而且发展不平衡.总体水平而言,女生比男生好;大三学生明显高于大二、大一学生,大一优于大二,大二年级是个转折时期.     

The relationship between mathematical problem-solving skills and self-regulated learning through homework behaviours,motivation, and metacognition

Studies highlight that using appropriate strategies during problem solving is important to improve problem-solving skills and draw attention to the fact that using these skills is an important part of students’ self-regulated learning ability. Studies on this matter view the self-regulated learning ability as key to improving problem-solving skills. The aim of this study is to investigate the relationship between mathematical problem-solving skills and the three dimensions of self-regulated learning (motivation, metacognition, and behaviour), and whether this relationship is of a predictive nature. The sample of this study consists of 323 students from two public secondary schools in Istanbul. In this study, the mathematics homework behaviour scale was administered to measure students’ homework behaviours. For metacognition measurements, the mathematics metacognition skills test for students was administered to measure offline mathematical metacognitive skills, and the metacognitive experience scale was used to measure the online mathematical metacognitive experience. The internal and external motivational scales used in the Programme for International Student Assessment (PISA) test were administered to measure motivation. A hierarchic regression analysis was conducted to determine the relationship between the dependent and independent variables in the study. Based on the findings, a model was formed in which 24% of the total variance in students’ mathematical problem-solving skills is explained by the three sub-dimensions of the self-regulated learning model: internal motivation (13%), willingness to do homework (7%), and post-problem retrospective metacognitive experience (4%).     

How can self-regulated learning support the problem solving of third-grade students with mathematics anxiety?

The study compares 140 third-grade Israeli students (lower and higher achievers) who were either exposed to self-regulated learning (SRL) supported by metacognitive questioning (the MS group) or received no direct SRL support (the N_MS group). We investigated: (a) mathematical problem solving performance; (b) metacognitive strategy use in three phases of the problem-solving process; and (c) mathematics anxiety. Findings indicated that the MS students showed greater gains in mathematical problem solving performance than the N_MS students. They reported using metacognitive strategies more often, and showed a greater reduction in anxiety. In particular, the lower MS achievers showed these gains in the basic and complex tasks, in strategy use during the on-action phase of the problem solving process and a decrease in negative thoughts. The higher achievers showed greater improvement in transfer tasks and an increase in positive thoughts towards mathematics. Both the theoretical and practical implications of this study are discussed.     

元认知在高等数学教学中的作用及培养途径

元认知是认知主体对自身认知活动的认知,大学生的元认知能力对高等数学教学具有很大的影响作用.在高等数学教学中应通过多种途径,把培养和发展大学生的元认知能力作为一项重要教学任务来完成.     

The impact of metacognitive practice and teacher feedback on academic achievement in mathematics

The purpose of this study is to determine the effects of metacognitive strategies and content‐specific feedback on student achievement in high school mathematics. Participants consisted of a convenience sample of students in honors geometry. An analysis of variance with repeated measures was employed to address the research questions. For both the posttest and retention test, students in the experimental group significantly outperformed the students in the comparison group. However, students scored lower in the retention test than the posttest. The findings of this study offer a modest contribution to the body of empirical research on the impact of metacognitive practice and content‐specific feedback on academic achievement at the high school level.     

Predictive factors of students’ motivation to succeed in introductory mathematics courses: evidence from higher education in the UAE

The purpose of the study is to examine whether there is a significant relationship between students’ motivation to succeed in introductory mathematics courses offered by universities in the United Arab Emirates (UAE) as the dependent variable of the research and another five independent variables including cognitive mathematics self-concept, affective mathematics self-concept, extrinsic motivation as expectations of future career and income, students’ age and the number of mathematics courses taken by students. The rationale of the study is based on the significance of mathematics achievements for students and academic institutions in particular, as well as for the society in general. The study is designed based on a quantitative research methodology and a sample of 685 students participated in completing a survey questionnaire. The sample is drawn from students who were registered in different introductory mathematics courses at four academic institutions of higher education in the UAE. The quantitative correlation analysis among students’ motivation, cognitive mathematics self-concept, affective mathematics self-concept, extrinsic motivation, students’ age and the number of mathematics courses taken by students reveals theoretically consistent interrelationships. The quantitative multiple regression analysis indicates that the five independent variables explain 71.3% of the variation in students’ motivation to succeed in introductory mathematics courses.     

The Effect of Journal Writing on Achievement in and Attitudes Toward Mathematics

A teaching experiment was conducted to investigate the effect of journal writing on achievement in and attitudes toward mathematics. Achievement variables included conceptual understanding, procedural knowledge, problem solving, mathematics school achievement, and mathematical communication. Subjects were selected from first intermediate students (11–13 years) attending the International College, Beirut, Lebanon, where either English or French is the language of mathematics instruction. The journal-writing (JW) group received the same mathematics instruction as the no-journal-writing (NJW) group, except that the JW group engaged in prompted journal writing for 7 to 10 minutes at the end of each class period, three times a week, for 12 weeks. The NJW group engaged in exercises during the same period. The results of ANCOVA suggest that journal writing has a positive impact on conceptual understanding, procedural knowledge, and mathematical communication but not on problem solving, school mathematics achievement, and attitudes toward mathematics. Gender, language of instruction, mathematics achievement level, and writing achievement level failed to interact with journal writing. Student responses to a questionnaire indicated that students found journal writing to have both cognitive and affective benefits.     

Preservice Teachers of High School Mathematics: Success,Failure, and Persistence in the Face of Mathematical Challenges

The goal of this study was to identify variables related to success and resilience in an undergraduate, high school mathematics teacher education program. Over a five‐year period, we tracked the academic performance and achievement motivation goals of multiple cohorts of students. Students who successfully completed their degrees had higher grade point average (GPAs) upon entering the program, earned higher grades in their first college mathematics course, and failed fewer courses than students who left the program or university. Learning and performance motivational goals did not predict success in the program. Performance goals decreased over time. Nearly half the successful students repeated one or more mathematics courses. Ten students completed their degrees, obtained a teaching license, and are teaching despite the need for multiple repetitions of the same mathematics courses. These persistent students did not differ from their peers in motivational goals. Our results suggest that although students with higher GPAs and initial mathematics grades were more likely to complete the program, students who experienced challenges in mathematics courses were able to succeed. We discuss the implications of these results for recruiting, advising, and retention of students in mathematics education programs.     

Assessing science students’ attitudes to mathematics: a case study on a modelling project with mathematical software

This article reports the attitudes of students towards mathematics after they had participated in an applied mathematical modelling project that was part of an Applied Mathematics course. The students were majoring in Earth Science at the National Taiwan Normal University. Twenty-six students took part in the project. It was the first time a mathematical modelling project had been incorporated into the Applied Mathematics course for such students at this University. This was also the first time the students experienced applied mathematical modelling and used the mathematical software. The main aim of this modelling project was to assess whether the students’ attitudes toward mathematics changed after participating in the project. We used two questionnaires and interviews to assess the students. The results were encouraging especially the attitude of enjoyment. Hence the approach of the modelling project seems to be an effective method for Earth Science students.     

Changing students’ beliefs about the relevance of mathematics in an advanced secondary mathematics class

ABSTRACT

This study shows that using authentic contexts for learning differential equations in a differentiation-by-interest setting can enhance students’ beliefs about the relevance of mathematics. The students in this study were studying advanced mathematics (wiskunde D) at upper secondary school in the Netherlands. These students are often not aware of the relevance of the mathematics they have to learn in school. More insights into the application of mathematics in other sciences can be beneficial for these students in terms of preparation for their future study and career. A course differentiating by student interest with new context-rich curriculum materials was developed in order to enhance students’ beliefs about the relevance of mathematics. The intervention aimed at teaching differential equations through guided small-group tasks in scientific, medical or economical contexts. The results show that students’ beliefs about the relevance of mathematics improved, and they appreciated experiencing how the mathematics was applied in real-life situations.     

Factors affecting the process of proficient mental addition and subtraction: case studies of flexible and inflexible computers

The relationship between mental computation and number sense is complex: mental computation can facilitate number sense when students are encouraged to be flexible, but flexibility and number sense is neither sufficient nor necessary for accuracy in mental computation. It is possible for familiarity with a strategy to compensate for a lack of number sense and inefficient processes. This study reports on six case studies exploring Year 3 students’ procedures for and understanding of mental addition and subtraction, and understanding of number sense and other cognitive, metacognitive, and affective factors associated with mental computation. The case studies indicate that the mental computation process is composed of four stages in which cognitive, metacognitive and affective factors operate differently for flexible and inflexible computers. The authors propose a model in which the differences between computer types are seen in terms of the application of different knowledges in number facts, numeration, effect of operation on number, and beliefs and metacognition on strategy choice and strategy implementation.     

Measurement of students’ mathematics motivation and self-concept at institutions of higher education: evidence of reliability and validity

ABSTRACT

The study aims at proposing a quantitative instrument tailored to measure the level of mathematics motivation and self-concept of students in mathematics courses at academic institutions of higher education. The significance of this study stems from its endeavour to measure mathematics motivation and self-concept of students in courses of mathematics at academic institutions of higher education which ultimately contributes to the success of students, academic institutions and societies. A quantitative research methodology has been employed in this study in which a 55-item survey instrument has been tailored and piloted. The results of factor analysis indicate that the instrument’s items loaded into mathematics motivational factors and mathematics self-concept factors. The cumulative percentage explained by mathematics motivational factors is 55.3% and the cumulative percentage explained by mathematics self-concept factors is 53.2%. The factors of mathematics motivation and mathematics self-concept explain the majority of variance in the dataset. The findings of validity and reliability tests show that 35 items measure mathematics motivation through four subscales which include importance and necessity of mathematics; perception of success in mathematics; enjoyment of mathematics; and expectations of future career and income. The other 20 items measure mathematics self-concept through two subscales which include cognitive mathematics self-concept and affective mathematics self-concept.     

A case study: assessment of preservice secondary mathematics teachers’ metacognitive behaviour in the problem-solving process

The purpose of the present study was to investigate preservice secondary mathematics teachers’ metacognitive behaviour in the mathematical problem-solving process. The case study methodology was employed with six preservice mathematics teachers, enrolled at one university in Ankara, Turkey. We collected data by using the think aloud method, which lasted for two sessions. It was found that there was no relationship between academic achievement and frequencies of metacognitive behaviour. However, the types of problems could affect these frequencies. Furthermore, there was no pattern in metacognitive behaviour with respect to achievement and type of problem.     

Handling errors as they arise in whole-class interactions

There has been a long history of research into errors and their role in the teaching and learning of mathematics. This research has led to a change to pedagogical recommendations from avoiding errors to explicitly using them in lessons. In this study, 22 mathematics lessons were video-recorded and transcribed. A conversation analytic (CA) approach was then taken to examine how mathematical errors are treated by teachers and students when they arise in interaction. Despite pedagogical recommendations, in these interactions, errors continue to be predominantly treated as something to avoid. There is a tension between the affective aspects of managing errors in interactions and the cognitive aspects. Close examination of classroom interactions enable us to see how these tensions are managed both by teachers and students.