Incorporating the dynamic mathematics software GeoGebra into a history of mathematics course

The purpose of this study was to investigate pre-service teachers’ views about the history of mathematics course in which GeoGebra was used. The qualitative research design was used in this study. The participants of the study consisted of 23 pre-service mathematics teachers studying at a state university in Turkey. An open-ended questionnaire was used as a data collection tool. Qualitative data obtained from the pre-service teachers were analyzed by means of content analysis. As a result, it was determined that GeoGebra software was an effective tool in the learning and teaching of the history of mathematics.     

Learning fraction comparison by using a dynamic mathematics software – GeoGebra

GeoGebra is a mathematics software system that can serve as a tool for inquiry-based learning. This paper deals with the application of a fraction comparison software, which is constructed by GeoGebra, for use in a dynamic mathematics environment. The corresponding teaching and learning issues have also been discussed.     

ICT integration in mathematics initial teacher training and its impact on visualization: the case of GeoGebra

This case study investigates the impact of the integration of information and communications technology (ICT) in mathematics visualization skills and initial teacher education programmes. It reports on the influence GeoGebra dynamic software use has on promoting mathematical learning at secondary school and on its impact on teachers’ conceptions about teaching and learning mathematics. This paper describes how GeoGebra-based dynamic applets – designed and used in an exploratory manner – promote mathematical processes such as conjectures. It also refers to the changes prospective teachers experience regarding the relevance visual dynamic representations acquire in teaching mathematics. This study observes a shift in school routines when incorporating technology into the mathematics classroom. Visualization appears as a basic competence associated to key mathematical processes. Implications of an early integration of ICT in mathematics initial teacher training and its impact on developing technological pedagogical content knowledge (TPCK) are drawn.     

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.     

Preservice Teachers' Beliefs and Attitude About Teaching and Learning Mathematics Through Music: An Intervention Study

This article presents exploratory research investigating the integration of music and a mathematics lesson as an intervention to promote preservice teachers' attitude and confidence and to extend their beliefs toward teaching mathematics integrated with music. Thirty students were randomly selected from 64 preservice teachers in a southern university. A 90‐minute mathematics lesson integrated with a music composition activity was taught by the first author. Pre‐ and postquestionnaires were provided to evaluate the change in preservice teachers' attitude and beliefs toward mathematics. The results demonstrated that the mathematics lesson integrated with music had a positive effect on preservice teachers' attitude and beliefs toward mathematics teaching and learning.     

Establishing the link between the graph of a parametric curve and the derivatives of its component functions

ABSTRACT

This study aimed to explore the effects of an instructional intervention in which GeoGebra and the think-pair-share method were used to teach the relationship between the graph of a parametric curve and the derivatives of its component functions. The participants in the study were 19 prospective mathematics teachers. To assess the understanding of the participants regarding the content of the instruction, two comparable tests were administered as a pre- and post-test. In order to determine whether there was a difference between the students’ performance on the two tests, a paired samples t-test was conducted on the test scores; the results revealed a significant difference in favour of the post-test. Thus, it was concluded that the adopted teaching method, which included the use of GeoGebra, in delivering the focused content had a positive impact on the students’ understanding.     

建构主义学习理论下的数学教学原则与策略

本文从建构主义学习理论出发，分析了传统数学教学中存在的弊端。提出了建构主义学习理论下的数学教学原则和策略，对于充分认识建构主义学习、教学理论，对促进数学教学改革，提高数学教学质量具有重要的意义．     

Teacher's reflections on experimenting with technology-enriched inquiry-based mathematics teaching with a preplanned teaching unit

According to previous studies, inquiry-based mathematics teaching enhances learning. However, teachers need support in implementing this type of teaching. In this study, a high school teacher was given a short preplanned inquiry-based mathematics teaching unit that included activities with GeoGebra. The teacher was interviewed after every lesson to explore her reflections after teaching. I analyzed how the teacher described the differences between her regular teaching style and the teaching unit and the pros and cons of the teaching unit. The teacher reflected on the roles of the teacher and students, depth of students’ knowledge, her stance toward the teaching unit, constraints for using this type of teaching approach, and challenges in guiding the students. The results give insights to what kind of reflections on technology-enriched inquiry-based mathematics teaching it is possible to initiate with short preplanned teaching units.     

MATLAB in first-year engineering mathematics

The paper details the integration of the mathematical software MATLAB into the teaching of core mathematics to first-year university engineering students. The engineering faculty requested that the mathematics staff allocate one hour per week for students to learn and use MATLAB in a computer pool and that group projects involving the use of MATLAB and other similar tasks be included in the overall assessment of the subject. The central concept in achieving this integration was the production of a guide A Focused Introduction to MATLAB which provides a bridge between the software and the core subject material covered in the textbooks and lectures. Recent extensions involve the construction of a Web site dedicated to this subject where students can obtain all information concerning the subject, including a copy of all MATLAB code and corresponding graphical demonstrations used in the lectures. Feedback has been very positive.     

Observing mathematics teaching in three different countries lessons learnt?

It has been reported that the students’ level of mathematicswhen entering university has changed in recent years. A surprisingnumber of students struggle with mathematics or have a mathematicsanxiety. Although this was widely reported within the UK, therewas some uncertainty if colleagues in other countries were experiencingthe same challenges. Therefore, lectures in three countrieswere observed and the effects different educational backgroundsand cultures have on the students’ attitudes towards mathematicswere determined. Experiences and ideas were exchanged and itbecame clear that the problems lecturers face in the UK withrespect to teaching mathematics are in fact not limited to thiscountry but that their approach to lecturing at university isdifferent. This article discusses the outcomes of analysing and observingmathematics taught in three different countries. Similaritiesand differences are presented, together with feedback on thesuccess of implementing new ideas at Birmingham.     

The functions of function discourse – university mathematics teaching from a commognitive standpoint

This paper addresses a topic within university mathematics education which has been somewhat underexplored: the teaching practices actually used by university mathematics teachers when giving lectures. The study investigates the teaching practices of seven Swedish university teachers on the topic of functions using a discursive approach, the commognitive framework of Sfard. In the paper a categorization of the construction and substantiation routines used by the teachers is presented, for instance various routines for constructing definitions and examples, and for verifying whether an example satisfies a given definition. The findings show that although the overall form of the lectures is similar, with teachers using ‘chalk talk’, and overt student participation limited to asking and answering questions, there are in fact significant differences in the way the teachers present and do mathematics in their lectures. These differences present themselves both on the level of discursive routines and on a more general level in how the process of doing mathematics is made visible in the teachers’ teaching practices. Moreover, I believe that many of the results of the study could be relevant 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.     

Integrating technology into mathematics teaching at the university level

The emergence of new computing technologies in the second half of the twentieth century brought about new potentials and promised the rapid transformation of the teaching and learning of mathematics. However, despite the vast investments in technology resources for schools and universities, the realities of schooling and the complexities of technology-equipped environments resulted in a much slower integration process than was predicted in the 1980s. Hence researchers, together with teachers and mathematicians, began examining and reflecting on various aspects of technology-assisted teaching and learning and on the causes of slow technology integration. Studies highlighted that as technology becomes increasingly available in schools, teachers’ beliefs and conceptions about technology use in teaching are key factors for understanding the slowness of technology integration. In this paper, I outline the shift of research focus from learning and technology environment-related issues to teachers’ beliefs and conceptions. In addition, I highlight that over the past two decades a considerable imbalance has developed in favour of school-level research against university-level research. However, several changes in universities, such as students declining mathematical preparedness and demands from other sciences and employers, necessitate closer attention to university-level research. Thus, I outline some results of my study that aimed to reflect on the paucity of research and examined the current extend of technology use, particularly Computer Algebra Systems (CAS) at universities, mathematicians’ views about the role of CAS in tertiary mathematics teaching, and the factors influencing technology integration. I argue that due to mathematicians’ extensive use of CAS in their research and teaching, documenting their teaching practices and carrying out research at this level would not only be beneficial at the university level but also contribute to our understanding of technology integration at all levels.     

Traditional instruction in advanced mathematics courses: a case study of one professor’s lectures and proofs in an introductory real analysis course

It is widely accepted by mathematics educators and mathematicians that most proof-oriented university mathematics courses are taught in a “definition-theorem-proof” format. However, there are relatively few empirical studies on what takes place during this instruction, why this instruction is used, and how it affects students’ learning. In this paper, I investigate these issues by examining a case study of one professor using this type of instruction in an introductory real analysis course. I first describe the professor’s actions in the classroom and argue that these actions are the result of the professor’s beliefs about mathematics, students, and education, as well as his knowledge of the material being covered. I then illustrate how the professor’s teaching style influenced the way that his students attempted to learn the material. Finally, I discuss the implications that the reported data have on mathematics education research.     

Student performance and attitudes in a collaborative and flipped linear algebra course

Flipped learning is gaining traction in K-12 for enhancing students’ problem-solving skills at an early age; however, there is relatively little large-scale research showing its effectiveness in promoting better learning outcomes in higher education, especially in mathematics classes. In this study, we examined the data compiled from both quantitative and qualitative measures such as item scores on a common final and attitude survey results between a flipped and a traditional Introductory Linear Algebra class taught by two individual instructors at a state university in California in Fall 2013. Students in the flipped class were asked to watch short video lectures made by the instructor and complete a short online quiz prior to each class attendance. The class time was completely devoted to problem solving in group settings where students were prompted to communicate their reasoning with proper mathematical terms and structured sentences verbally and in writing. Examination of the quality and depth of student responses from the common final exam showed that students in the flipped class produced more comprehensive and well-explained responses to the questions that required reasoning, creating examples, and more complex use of mathematical objects. Furthermore, students in the flipped class performed superiorly in the overall comprehension of the content with a 21% increase in the median final exam score. Overall, students felt more confident about their ability to learn mathematics independently, showed better retention of materials over time, and enjoyed the flipped experience.     

An Outlook in Teaching and Research in Mathematics in Educational Institutions

The present paper outlines some basic principles upon which an outlook in teaching and research in mathematics in educational institutions can be developed. Defining applied mathematics, the author analyses the basic topics of mathematics which permeate throughout the wider fields and diversified aspects of this branch of mathematical science.

For the institutions of learning, a course curriculum has been proposed which will gradually motivate, orient and prepare individuals through the process of learning to understand the methods and techniques, so as to apply them to physical problems. This has been illustrated in the fields of fluid dynamics and aerodynamics through the analysis of complex function theory and differential equations.

Because of the frustrating situations prevailing amongst students and teachers in the institutions of learning in the present day, a critical analysis has been made to identify the respective roles of the academicians and administrators, and with a view to improving the situation, some remedy has been suggested regarding teaching and research in educational institutions.     

Applying an alternative mathematics pedagogy for students with weak mathematics: meta-analysis of alternative pedagogies

Student mathematics performance and the need for work-ready graduates to be mathematics-competent is a core issue for many universities. While both student and teacher are responsible for learning outcomes, there is a need to explicitly acknowledge the weak mathematics foundation of many university students. A systematic literature review was undertaken of identified innovations and/or interventions that may lead to improvement in student outcomes for university mathematics-based units of study. The review revealed the importance of understanding the foundations of student performance in higher education mathematics learning, especially in first year. Pre-university mathematics skills were identified as significant in student retention and mathematics success at university, and a specific focus on student pre-university mathematics skill level was found to be more effective in providing help, rather than simply focusing on a particular at-risk group. Diagnostics tools were found to be important in identifying (1) student background and (2) appropriate intervention. The studies highlighted the importance of appropriate and validated interventions in mathematics teaching and learning, and the need to improve the learning model for mathematics-based subjects, communication and technology innovations.