Abstract: Many people know ‘Mathematics needs practice!’ statement or similar ones from their mathematics lessons. It seems important to practice when learning mathematics. At the same time, it also seems important to practice how to learn mathematics. This paper places neuroscientific-radiological findings on “practicing” while learning mathematics in a context of mathematics education. To accomplish this, we use a literature-based discussion of our case study on practice. We want to describe neuroscientific-radiological findings in the context of mathematics education and point out stimulating connections between both perspectives. From a connective perspective we expect incentives that lead discussions in future research in the field of mathematics education.
Abstract: Interest in (STEM) Science Technology Engineering
Mathematics education especially Computer Science education has
seen a drastic increase across the country. This fuels effort towards
recruiting and admitting a diverse population of students. Thus the
changing conditions in terms of the student population, diversity
and the expected teaching and learning outcomes give the platform
for use of Innovative Teaching models and technologies. It is
necessary that these methods adapted should also concentrate on
raising quality of such innovations and have positive impact on
student learning. Light-Weight Team is an Active Learning Pedagogy,
which is considered to be low-stake activity and has very little or
no direct impact on student grades. Emotion plays a major role in
student’s motivation to learning. In this work we use the student
feedback data with emotion classification using surveys at a public
research institution in the United States. We use Actionable Pattern
Discovery method for this purpose. Actionable patterns are patterns
that provide suggestions in the form of rules to help the user achieve
better outcomes. The proposed method provides meaningful insight
in terms of changes that can be incorporated in the Light-Weight team
activities, resources utilized in the course. The results suggest how
to enhance student emotions to a more positive state, in particular
focuses on the emotions ‘Trust’ and ‘Joy’.
Abstract: Understanding the concept of function has been important in mathematics education for many years. In this study, the models built by a group of five business administration and accounting undergraduate students when carrying out a population growth activity are analyzed. The theoretical framework is the Models and Modeling Perspective. The results show how the students included tables, graphics, and algebraic representations in their models. Using technology was useful to interpret, describe, and predict the situation. The first model, the students built to describe the situation, was linear. After that, they modified and refined their ways of thinking; finally, they created exponential growth. Modeling the activity was useful to deep on mathematical concepts such as covariation, rate of change, and exponential function also to differentiate between linear and exponential growth.
Abstract: The present study aimed to evaluate the understanding of the students in Tehran universities (Iran) about the numerical representation of the average rate of change based on the Structure of Observed Learning Outcomes (SOLO). In the present descriptive-survey research, the statistical population included undergraduate students (basic sciences and engineering) in the universities of Tehran. The samples were 604 students selected by random multi-stage clustering. The measurement tool was a task whose face and content validity was confirmed by math and mathematics education professors. Using Cronbach's Alpha criterion, the reliability coefficient of the task was obtained 0.95, which verified its reliability. The collected data were analyzed by descriptive statistics and inferential statistics (chi-squared and independent t-tests) under SPSS-24 software. According to the SOLO model in the prestructural, unistructural, and multistructural levels, basic science students had a higher percentage of understanding than that of engineering students, although the outcome was inverse at the relational level. However, there was no significant difference in the average understanding of both groups. The results indicated that students failed to have a proper understanding of the numerical representation of the average rate of change, in addition to missconceptions when using physics formulas in solving the problem. In addition, multiple solutions were derived along with their dominant methods during the qualitative analysis. The current research proposed to focus on the context problems with approximate calculations and numerical representation, using software and connection common relations between math and physics in the teaching process of teachers and professors.
Abstract: This paper discusses Sfard’s commognitive approach and provides an empirical study as an example to illustrate the theory as method. Traditionally, research in mathematics education focused on the acquisition of mathematical knowledge and the didactic process of knowledge transfer. Through attending to a distinctive form of language in mathematics, as well as mathematics as a discursive subject, alternative views of making meaning in mathematics have emerged; these views are therefore “critical,” as in critical discourse analysis. The commognitive discourse analysis method has the potential to bring more clarity to our understanding of students’ mathematical thinking and the process through which students are socialized into school mathematics.
Abstract: Many African countries, such as Zimbabwe and South Africa, have curricula reform agendas that include incorporation of Indigenous Knowledge and Nature of Science (NOS) into school Science, Technology, Engineering and Mathematics (STEM) education. It is argued that at high school level, STEM learning, which incorporates understandings of indigenization science and NOS, has the potential to provide a strong foundation for a culturally embedded scientific knowledge essential for their advancement in Science and Technology. Globally, investment in STEM education is recognized as essential for economic development. For this reason, developing countries such as Zimbabwe and South Africa have been investing into training specialized teachers in natural sciences and technology. However, in many cases this training has been detached from the cultural realities and contexts of indigenous learners. For this reason, the STEM curricula reform has provided implementation challenges to teachers. An issue of major concern is the teachers’ pedagogical content knowledge (PCK), which is essential for effective implementation of these STEM curricula. Well-developed Teacher PCK include an understanding of both the nature of indigenous knowledge (NOIK) and of NOS. This paper reports the results of a study that investigated the development of 3 South African and 3 Zimbabwean in-service teachers’ abilities to integrate NOS and NOIK as part of their PCK. A participatory action research design was utilized. The main focus was on capturing, determining and developing teachers STEM knowledge for integrating NOIK and NOS in science classrooms. Their use of indigenous games was used to determine how their subject knowledge for STEM and pedagogical abilities could be developed. Qualitative data were gathered through the use dialogues between the researchers and the in-service teachers, as well as interviewing the participating teachers. Analysis of the data provides a methodological window through which in-service teachers’ PCK can be STEMITIZED and their abilities to integrate NOS and NOIK developed. Implications are raised for developing teachers’ STEM education in universities and teacher training colleges.
Abstract: Parental expectations often differ to that of their children and the influence and involvement of parents, at home, may affect the student performance in the classroom. This paper presents results from a survey of Asian and European background secondary school mathematics students (N=128) in Melbourne, Australia. Student responses to survey questions were analysed using confirmatory factor analysis, followed by t-tests and ANOVA. The aim of the analysis was to identify similarities and differences in parental expectations in relation to ethnicity, gender, and the year level of the students. The notable findings from the analysis showed no significant difference (at 0.05 level) in parental expectations and student performance, in relation to ethnicity or gender. Conversely, there was a significant difference in both parental expectations and student performance between year 7 and year 12 students. Further, whilst there was a significant difference in parental expectations between year 7 and year 11 students, the students’ performances were not significantly different. The results suggest further research may be needed to understand the parental expectations and student performance between the lower and upper secondary school mathematics students.
Abstract: We present a framework of researcher knowledge
development in conducting a study in mathematics education. The
key components of the framework are: knowledge germane to
conducting a particular study, processes of knowledge accumulation,
and catalyzing filters that influence a researcher decision making.
The components of the framework originated from a confluence
between constructs and theories in Mathematics Education, Higher
Education and Sociology. Drawing on a self-reflective interview with
a leading researcher in mathematics education, Professor Michèle
Artigue, we illustrate how the framework can be utilized in data
analysis. Criteria for framework evaluation are discussed.
Abstract: In this article, we discuss project-based learning in the context of a wheel garden as an instructional tool in science and mathematics education. A wheel garden provides multiple opportunities to teach across the curriculum, to integrate disciplines, and to promote community involvement. Grounded in the theoretical framework of constructivism, the wheel garden provides a multidisciplined educational tool that provides a hands-on, non-traditional arena for learning. We will examine some of the cultural, art, science, and mathematics connections made with this project.
Abstract: This study aims to specify to what extent students
understand topology during the lesson and to determine possible
misconceptions. 14 teacher trainees registered at Secondary School
Mathematics education department were observed in the topology
lessons throughout a semester and data collected at the first topology
lesson is presented here. Students- knowledge was evaluated using a
written test right before and after the topology lesson. Thus, what the
students learnt in terms of the definition and examples of topologic
space were specified as well as possible misconceptions. The
findings indicated that students did not fully comprehend the topic
and misunderstandings were due to insufficient pre-requisite
knowledge of abstract mathematical topics and mathematical
notation.
Abstract: This study has been prepared with the purpose to get the views of senior class Elementary Education Mathematics preservice teachers on proving. Data have been obtained via surveys and interviews carried out with 104 preservice teachers. According to the findings, although preservice teachers have positive views about using proving in mathematics teaching, it is seen that their experiences related to proving is limited to courses and they think proving is a work done only for the exams. Furthermore, they have expressed in the interviews that proving is difficult for them, and because of this reason they prefer memorizing instead of learning.
Abstract: The main issue of interest here is whether individuals
who differ in arithmetical reasoning ability and levels of imagery ability display different brain activity during the conduct of mental
arithmetical reasoning tasks. This was a case study of four
participants who represented four extreme combinations of Maths –Imagery abilities: ie., low-low, high-high, high-low, low-high respectively. As the Ps performed a series of 60 arithmetical reasoning tasks, 128-channel EEG recordings were taken and the
pre-response interval subsequently analysed using EGI GeosourceTM
software. The P who was high in both imagery and maths ability
showed peak activity prior to response in BA7 (superior parietal cortex) but other Ps did not show peak activity in this region. The
results are considered in terms of the diverse routes that may be employed by individuals during the conduct of arithmetical reasoning
tasks and the possible implications of this for mathematics education.
Abstract: The purpose of the study is to determine the primary mathematics student teachers- views related to use instructional technology tools in course of the learning process and to reveal how the sample presentations towards different mathematical concepts affect their views. This is a qualitative study involving twelve mathematics students from a public university. The data gathered from two semi-structural interviews. The first one was realized in the beginning of the study. After that the representations prepared by the researchers were showed to the participants. These representations contain animations, Geometer-s Sketchpad activities, video-clips, spreadsheets, and power-point presentations. The last interview was realized at the end of these representations. The data from the interviews and content analyses were transcribed and read and reread to explore the major themes. Findings revealed that the views of the students changed in this process and they believed that the instructional technology tools should be used in their classroom.
Abstract: The aim of this study is to point out whether personalization of mathematical word problems could affect student achievement or not. The research was applied on two-grades students at spring semester 2008-2009. Before the treatment, students personal data were taken and given to the computer. During the treatment, paper-based personalized problems and paper-based non personalized problems were prepared by computer as the same problems and then these problems were given to students. At the end of the treatment, students- opinion was taken. As a result of this research, it was found out that there were no significant differences between learners through personalized or non-personalized materials, and also there were no significant differences between gender through personalized and non-personalized problems. However, opinion of students was highly positive through the personalized problems.
Abstract: Students often adopt routine practicing as learning
strategy for mathematics. The reason is they are often bound and
trained to solving conventional-typed questions in Mathematics in
high school. This will be problematic if students further consolidate
this practice in university. Therefore, the Department of Mathematics
emphasized and integrated the Discovery-enriched approach in the
undergraduate curriculum. This paper presents the details of
implementing the Discovery-enriched Curriculum by providing
adequate platform for project-learning, expertise for guidance and
internship opportunities for students majoring in Mathematics. The
Department also provided project-learning opportunities to
mathematics courses targeted for students majoring in other science or
engineering disciplines. The outcome is promising: the research
ability and problem solving skills of students are enhanced.
Abstract: The link between coordinate transformations in the plane and their effects on the graph of a function can be difficult for students studying college level mathematics to comprehend. To solidify this conceptual link in the mind of a student Microsoft Excel can serve as a convenient graphing tool and pedagogical aid. The authors of this paper describe how various transformations and their related functional symmetry properties can be graphically displayed with an Excel spreadsheet.