Confucian heritage culture learner’s phenomenon: from “exploring the middle zone” to “constructing a bridge”

In the past decades, the CHC (Confucian heritage culture) learner’s phenomenon has spawned one of the most fruitful fields in educational research. Despite the impression that CHC learners are brought up in an environment not conducive to learning, their academic performances have been excelling their Western counterparts (Fan et al. in How Chinese learn mathematics: perspectives from insiders, 2004). Numerous explanations were offered to reveal the paradox (Morrison in Educ J, 2006), and there were challenges of whether there is “over-Confucianisation” in all these discussions (Chang in J Psychol Chin Soc, 2000; Wong and Wong in Asian Psychol, 2002). It has been suggested that the East and the West should come and discuss at the “middle zone” so that one can get the best from the two worlds. On the other hand, at the turn of the new millennium, discussions on mathematics curriculum reform proliferate in many places. One of the foci of the debate is the basic skills—higher-order thinking “dichotomy”. Viewing from the perspective of the process of mathematisation, teaching mathematics is more than striking a balance between the two, but to bridge basic skills to higher-order thinking competences. Such an attempt was explored in recent years and the ideas behind will be shared in this paper.     

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.     

CDIO模式下高等数学与理工专业其它后续课程的教学探讨

作为"做中学"战略下的一种模式,CDIO是对以课堂讲授为主的传统教学模式的革命.针对CDIO教学模式的12标准中第3条--一体化课程计划以及目前教学实践中表现出的高等数学课程不能很好的为一般院校不同专业后续课程学习服务的现状,本文在对我院一般理工科类相关专业后续课程的调研的基础上,对高等数学课程教学的改革方案进行了初步...     

Teachers and didacticians: key stakeholders in the processes of developing mathematics teaching

This paper sets the scene for a special issue of ZDM—The International Journal on Mathematics Education—by tracing key elements of the fields of teacher and didactician/teacher-educator learning related to the development of opportunities for learners of mathematics in classrooms. It starts from the perspective that joint activity of these two groups (teachers and didacticians), in creation of classroom mathematics, leads to learning for both. We trace development through key areas of research, looking at forms of knowledge of teachers and didacticians in mathematics; ways in which teachers or didacticians in mathematics develop their professional knowledge and skill; and the use of theoretical perspectives relating to studying these areas of development. Reflective practice emerges as a principal goal for effective development and is linked to teachers’ and didacticians’ engagement with inquiry and research. While neither reflection nor inquiry are developmental panaceas, we see collaborative critical inquiry between teachers and didacticians emerging as a significant force for teaching development. We include a summary of the papers of the special issue which offer a state of the art perspective on developmental practice.     

Elementary teachers’ mathematical beliefs and mathematics anxiety: How do they shape instructional practices?

This quantitative study investigated the relationships among practicing elementary teachers’ (N = 153) beliefs about mathematics and its teaching and learning, mathematics anxiety, and instructional practices in mathematics. When viewed singly, the findings reveal the teachers with higher levels of mathematics anxiety tend to use less standards‐based instruction and those with beliefs oriented toward a problem‐solving view of mathematics reported more standards‐based teaching. A combined analysis shows that after controlling for mathematical beliefs, teaching longevity, and educational degree attainment, there is no relationship between teachers’ mathematics anxiety and instructional practices. These findings suggest a spurious relationship between anxiety and practices, with beliefs having the strongest relationship with practices. Several suggestions for positively influencing the mathematical beliefs and affect in general of elementary teachers while learning mathematics are offered.     

An accessible,justifiable and transferable pedagogical approach for the differential equations of simple harmonic motion

Recently, Gauthier introduced a method to construct solutions to the equations of motion associated with oscillating systems into the mathematics education research literature. In particular, Gauthier's approach involved certain manipulations of the differential equations; and drew on the theory of complex variables.

Motivated by the work of Gauthier, we construct an alternative pedagogical approach for the learning and teaching of solution methods to these equations. The innovation lies in drawing on factorization techniques of differential equations and harmonizing them with Gauthier's approach of the theory of complex variables. When blended together to form a new approach, the significance lies in its accessibility, justifiability and transferrability to other problems.

We pedagogically ground our approach in the educational development theory of Piaget, with the results informing the learning and teaching of solution methods to differential equations for lecturers, teachers and learners within universities, colleges, polytechnics and schools around the world.     

Inquiry as an entry point to equity in the classroom

ABSTRACT

Although many policy documents include equity as part of mathematics education standards and principles, researchers continue to explore means by which equity might be supported in classrooms and at the institutional level. Teaching practices that include opportunities for students to engage in active learning have been proposed to address equity. In this paper, through aligning some characteristics of inquiry put forth by Cook, Murphy and Fukawa-Connelly with Gutiérrez's dimensions of equity, we theoretically explore the ways in which active learning teaching practices that focus on inquiry could support equity in the classroom.     

Beliefs and beyond: affect and the teaching and learning of mathematics

The importance of beliefs for the teaching and learning of mathematics is widely recognized among mathematics educators. In this special issue, we explicitly address what we call “beliefs and beyond” to indicate the larger field surrounding beliefs in mathematics education. This is done to broaden the discussion to related concepts (which may not originate in mathematics education) and to consider the interconnectedness of concepts. In particular, we present some new developments at the conceptual level, address different approaches to investigate beliefs, highlight the role of student beliefs in problem-solving activities, and discuss teacher beliefs and their significance for professional development. One specific intention is to consider expertise from colleagues in the fields of educational research and psychology, side by side with perspectives provided by researchers from mathematics education.     

Adult Education and Ethnomathematics: appropriating results, methods, and principles

This article aims at discussing the ways that Youth and Adult Education have been taking on the production, methods and principles of Ethnomathematics in the last decades, especially in Brazil. First, it focuses on how Youth and Adult educators found Ethnomathematics to be a resource to know their students and the mathematics they use and produce better. The second part discusses how intercultural studies undertaken by Ethnomathematics research offered a new perspective under which mathematics knowledge and educational practices of Youth and Adult Education are conceived. Finally, the interlocutive and interdiscursive dimensions of teaching and learning practices are approached to present a reflection about the relations among Youth and Adult Education, Ethnomathematics and the search for the meanings of teaching and learning mathematics at school into an Inclusion project.     

Teaching and learning mathematics in the collective

In this paper we analyse and explore teaching and learning in the context of a high school mathematics classroom that was deliberately structured as highly interactive and inquiry-oriented. We frame our discussion within enactivism—a theory of cognition that has helped us to understand classroom processes, particularly at the level of the group. We attempt to show how this classroom of mathematics learners operated as a collective and focus in particular on the role of the teacher in establishing, sustaining, and becoming part of such a collective. Our analysis reveals teaching practices that value, capitalize upon, and promote group cognition, our discussion positions such work as teaching a way of being with mathematics, and we close by offering implications for teaching, educational policy, and further research.     

Active learning: a case study of student engagement in college Calculus

This paper presents a case study for strategic engagement of students in a Calculus course in order to produce increased learning in the classroom. Since it has been shown that active learning can promote greater comprehension for students in science, technology, engineering, and mathematics (STEM) courses, the researcher utilized many types of active learning techniques to enhance classroom instruction. The key components implemented are presented as a model of enhanced learning through developed classroom engagement. This course redesign model entitled, Strategic Engagement for Increased Learning (SEIL), has the potential to (1) contribute to the body of knowledge on ways to improve mathematics skills for college students, (2) identify successful teaching strategies and technologies that will promote the retention of STEM students, (3) increase the success rate of students taking Calculus, and (4) help produce more STEM graduates needed for the STEM workforce in the United States of America.     

Investigating undergraduate mathematics learners’ cognitive engagement with recorded lecture videos

The use of recorded lecture videos (RLVs) in mathematics instruction continues to advance. Prior research at the post-secondary level has indicated a tendency for RLV use in mathematics to be negatively correlated with academic performance, although it is unclear whether this is because regular users are generally weaker mathematics students or because RLV use is somehow depressing student learning. Through the lens of cognitive engagement, a quasi-experimental pre- and post-test design study was conducted to investigate the latter possibility.

Cognitive engagement was operationalized using the Revised Two-Factor Study Process Questionnaire (R-SPQ-2F), which measures learning approaches on two major scales: surface and deep. In two mathematics courses at two universities, in Australia and the UK, participants were administered the questionnaire near the course start and finish. Overall findings were similar in both contexts: a reduction in live lecture attendance coupled with a dependence on RLVs was associated with an increase in surface approaches to learning.

This study has important implications for future pedagogical development and adds to the sense of urgency regarding research into best practices using RLVs in mathematics.     

Explanation,motivation and question posing routines in university mathematics teachers' pedagogical discourse: a commognitive analysis

This paper investigates the teaching practices used by university mathematics teachers when lecturing, a topic within university mathematics education research which is gaining an increasing interest. In the study, a view of mathematics teaching as a discursive practice is taken, and Sfard's commognitive framework is used to investigate the teaching practices of seven Swedish university mathematics teachers on the topic of functions. The present paper looks at the discourse of mathematics teaching, presenting a categorization of the didactical routines into three categories – explanation, motivation and question posing routines. All of these are present in the discourses of all seven teachers, but within these general categories, a number of different sub-categories of routines are found, used in different ways and to different extent by the various teachers. The explanation routines include known mathematical facts, summary and repetition, different representations, everyday language, and concretization and metaphor; the motivation routines include reference to utility, the nature of mathematics, humour and result focus; and the question posing routines include control questions, asking for facts, enquiries and rhetorical questions. This categorization of question posing routines, for instance, complements those already found in the literature. In addition to providing a valuable insight into the teaching of functions at the university level, the categorizations presented in the study can also be useful for investigating the teaching of other mathematical topics.     

Mathematics university teachers' perception of pedagogical content knowledge (PCK)

Teaching mathematics in university levels is one of the most important fields of research in the area of mathematics education. Nevertheless, there is little information about teaching knowledge of mathematics university teachers. Pedagogical content knowledge (PCK) provides a suitable framework to study knowledge of teachers. The purpose of this paper is to make explicit the perception of mathematics university teachers about PCK. For this purpose, a phenomenological study was done. Data resources included semi-structured interviews with 10 mathematics university teachers who were in different places of the mathematics university teaching experience spectrum. Data analysis indicated a model consisting of four cognitive themes which are mathematics syntactic knowledge, knowledge about mathematics curriculum planning, knowledge about students' mathematics learning and knowledge about creating an influential mathematics teaching–learning environment. Besides, it was found out that three contextual themes influenced on PCK for teaching mathematics in university levels which were the nature of mathematics subjects, university teachers' features and terms of learning environment.     

Implementation and outcomes of inquiry-based learning in mathematics content courses for pre-service teachers

This mixed-methods study describes classroom characteristics and student outcomes from university mathematics courses that are based in mathematics departments, targeted to future pre-tertiary teachers, and taught with inquiry-based learning (IBL) approaches. The study focused on three two-term sequences taught at two research universities, separately targeting elementary and secondary pre-service teachers. Classroom observation established that the courses were taught with student-centred methods that were comparable to those used in IBL courses for students in mathematics-intensive fields at the same institutions. To measure pre-service teachers' gains in mathematical knowledge for teaching, we administered the Learning Mathematics for Teaching (LMT) instrument developed by Hill, Ball and Schilling for in-service teacher professional development. Results from the LMT show that pre-service teachers made significant score gains from beginning to end of their course, while data from interviews and from surveys of learning gains show that pre-service teachers viewed their gains as relevant to their future teaching work. Measured changes on pre-/post-surveys of attitudes and beliefs were generally supportive of learning mathematics but modest in magnitude. The study is distinctive in applying the LMT to document pre-service teachers' growth in mathematical knowledge for teaching. The study also suggests IBL is an approach well suited to mathematics departments seeking to strengthen their pre-service teacher preparation offerings in ways consistent with research-based recommendations.     

‘The unplanned impact of mathematics’ and its implications for research funding: a discussion-led educational activity

‘The unplanned impact of mathematics’ refers to mathematics which has an impact that was not planned by its originator, either as pure maths that finds an application or applied maths that finds an unexpected one. This aspect of mathematics has serious implications when increasingly researchers are asked to predict the impact of their research before it is funded and research quality is measured partly by its short term impact.

A session on this topic has been used in a UK undergraduate mathematics module that aims to consider topics in the history of mathematics and examine how maths interacts with wider society. First, this introduced the ‘unplanned impact’ concept through historical examples. Second, it provoked discussion of the concept through a fictionalized blog comments discussion thread giving different views on the development and utility of mathematics. Finally, a mock research funding activity encouraged a pragmatic view of how research funding is planned and funded.

The unplanned impact concept and the structure and content of the taught session are described.     

A brief historical introduction to solitons and the inverse scattering transform–a vision of Scott Russell

The objective of this study was to evaluate biomathtutor by (i) investigating the impact of biomathtutor on the mathematics skills competencies of bioscience undergraduates, and (ii) assessing students’ and tutors’ reactions to biomathtutor, identifying whether and how tutors might integrate it into their curricula and blend it with more traditional teaching practices to enhance their students’ learning experiences. A multi-method approach was adopted in which a quasi-experiment and non-experimental evaluation of biomathtutor were used to collect both quantitative and qualitative data, using mathematics tests, questionnaires, tutor interviews and student focus groups. Eighty-nine bioscience undergraduates and eight tutors participated in the study. A comparison of student performance in the quasi-experiment, which adopted a pre-test-intervention-post-test methodology, revealed no significant difference between pre-test and post-test scores for either the ‘control’ group (no intervention) or for any of the mathematics learning support interventions used, including biomathtutor. Despite the limitations of the quasi-experiment which are discussed, tutors’ and their students’ reactions towards biomathtutor were very positive, with both groups agreeing that biomathtutor represents a very well designed and useful learning resource that has a valuable role to play in supporting mathematics learning within bioscience curricula. Students felt that using biomathtutor had helped them acquire new biological and mathematical knowledge and had increased their competence and confidence in mathematics, with many students confirming that they would use biomathtutor again. Tutors felt it would be useful to embed biomathtutor, where possible, into their curricula, perhaps linking it to assessment strategies or integrating it with their current more traditional teaching practices. Students indicated that they too would like to see biomathtutor embedded within their curricula, primarily because it would motivate them to use the resource. Modifications to biomathtutor, which may need to be considered in light of any potential further development of this resource, are discussed.     

Using Primary Source Projects to teach undergraduate mathematics content: analysis of instructor implementation and perceptions

ABSTRACT

This study investigates changes in instructor teaching tendencies, instructor’s perception of impact on student learning and dispositions, and methods of implementation of Primary Source Projects (PSPs). PSPs are curricular modules designed to teach core mathematical topics from primary historical sources rather than from standard textbooks. In essence, they are a form of inquiry-based learning that incorporates the history of mathematics through original source texts. We provide an overview of results from two semesters of implementation reports and surveys administered at the beginning and end of the semester by instructors who implemented PSPs in their undergraduate mathematics classes.