Common Framework for Mathematics – Discussions of Possibilities to Develop a Set of General Standards for Assessing Proficiency in Mathematics
pp. 13-39 | Article Number: iejme.2018.002
The article discusses the challenges of and solutions of developing a common, general standards-referenced student assessment framework for mathematics. Two main challenges are faced. First, the main challenge is the lack of commonly accepted standards as the basis for the criterion- and standards-referenced assessment. Second challenge is that, even if having criteria and standards for the assessment, the descriptions of the standards are, in many cases, so vaguely worded that it is not possible to create unambiguous test items on the basis of a specific level of the standards. An initial common framework for mathematics standards is introduced on the basis of Common European Framework in Reference for Languages (CEFR) – a common framework for mathematics (CFM).
Keywords: assessment, standards-referenced assessment, criterion-referenced assessment, Mathematics
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Problematization and Research as a Method of Teaching Mathematics
Iran Abreu Mendes, & Carlos Aldemir Farias da Silva
pp. 41-55 | Article Number: ..2018.003
In this article we present our arguments in favor of a teaching of mathematics by means of problematization and investigation, one that includes in the classroom multiple ways and meanings for the students to read the world around them. In this respect, we propose a teaching-learning process of mathematics grounded on the relationships between society, cognition, and culture, in the way of practices that exercise multiple readings of reality and give meaning to mathematical construction as learning of culture, through culture. Argumentative reflections have lead us to conclude that mathematics characterizes the social and imaginary interactions manifested in culture, under multiple explanatory ways, for the sociocultural experiences, evidenced in the ways of reading, comprehending and explaining the human cultures emphasized by multiple methods and codes of mathematical reading of sociocultural realities. The article is organized in the following way: initial problematization of the study, foundations and assumptions, followed by the epistemological basis of argumentation, on to the appointment of epistemological and didactic implications about problematization, research for a learning beyond disciplinarity, as a way of including these methodological procedures in the classroom. We end with our reflections and referrals for the practice of the mathematics teacher
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Seeing and the Ability to See: A Framework for Viewing Geometric Cube Problems
Kok Xiao-Feng Kenan
pp. 57-60 | Article Number: ..2018.004
Perceiving a 3-dimensional (3D) diagram on a 2-dimensional (2D) surface or plane can be a challenging endeavor for students at the elementary or primary grade levels. Adding to this challenge are the intricacies present in understanding the processes involved in geometric problems of such a nature. To ease the comprehension of these processes, this paper proposes a framework that traces the processes in viewing 3D diagrams represented on a 2D plane. This framework, abbreviated as SMS, espouses three main processes; (1) Seeing the 2D plane, (2) Making sense of the 3D diagram on the 2D plane, and (3) Seeing the 3D diagram. Implications for teaching and learning are also offered.
Keywords: cube, geometry, 3-dimensional, 2-dimensional, visual perception, visualisation, spatial visualisation
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Applying van Hiele’s Levels to Basic Research on the Difficulty Factors behind Understanding Functions
pp. 61-65 | Article Number: ..2018.005
Functions is considered an important mathematical literacy concept within the Organization for Economic Cooperation and Development’s (OECD’s) Programme for International Student Assessment (PISA), and it has been shown that Japanese junior high school students are experiencing problems understanding functions. This paper examines the difficulty factors behind the understanding of functions by referring to van Hiele’s theory of learning levels. This paper focuses on the prototypical stages for understanding functions from the perspective of the mathematical concept process model of gradual understanding: ‘[I] Extract a variate from a phenomenon and [II] Relate the 2 extracted variates’. The subjects of the study were junior high school students, who completed a questionnaire. The results of the analysis of the questionnaire responses found that for a certain number of students, concept formation for stages [I] and [II] was lacking, and that the situation was not necessarily improving as the class progressed, thus, suggesting that this may be a difficulty factor that affects the understanding of functions.
Keywords: function understanding, difficulty factor, van Hiele’s theory, extract variables, relate the two extracted variates
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Scaffolding Based on Cognitive Conflict in Correcting the Students’ Algebra Errors
Indah Puspitasari Maharani, & Subanji Subanji
pp. 67-74 | Article Number: ..2018.006
The purpose of the research is to describe and analyze the implementation of Scaffolding based on Cognitive Conflict in correcting the students’ errors in Algebra material. The research uses Mix Method, that is a combination of quantitative and qualitative methods. There are 25 students that are involved and tested on Algebra material. They are collected from the Second Grade Students of Junior High Schools in Malang. The quantitative data are collected through essay test, while the qualitative data are collected through interview and observation. The findings of the research are: (1) Cognitive Conflict can increase the students’ reasoning ability, (2) Scaffolding is required to overcome the students’ errors based on their Cognitive Conflict, (3) Cogtnitive Conflict needs to be improved in the classroom learning.
Keywords: scaffolding, cognitive conflict, algebra errors
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Mathematics Teachers’ Subject Matter Knowledge and Pedagogical Content Knowledge in Problem Posing
Yujin Lee, Robert M. Capraro, & Mary Margaret Capraro
pp. 75-90 | Article Number: ..2018.007
Since the National Council of Teachers of Mathematics ([NCTM], 2000) and the National Research Council ([NRC], 2005) revealed that problem posing needed to be incorporated into mathematics classrooms, the importance of teachers’ roles in problem posing has been emphasized in K-12 mathematics curriculum because of instructors’ impact on students’ mathematical performance. In the present study, researchers investigated teachers’ subject matter knowledge (SMK), knowledge of content and teaching (KCT), and knowledge of content and students (KCS) in terms of problem-posing. A qualitative study design and inductive analysis were used to gather and interpret data from interviews conducted with four mathematics teachers. Results indicated that participants had SMK of problem posing, but their actual problem-posing results did not reflect their SMK well. In terms of KCS and KCT, teachers were aware of the importance of problem posing for students’ mathematical development but felt that there were several significant factors impeding the effective incorporation of problem posing within their classes. These findings underscore the importance of professional development for teacher pedagogical knowledge in problem posing.
Keywords: problem posing, subject matter knowledge, knowledge of content and teaching, knowledge of content and students, pedagogical content knowledge
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Innovative Strategies for Learning and Teaching of Large Differential Equations Classes
pp. 91-95 | Article Number: ..2018.008
Ordinary Differential Equations I, is one of the core courses for science and engineering majors. Practical problem solving in science and engineering programs require proficiency in mathematics. Improving student performance and retention in mathematics classes requires inventive approaches. At the University of Central Florida (UCF) the Department of Mathematics developed an innovative teaching method that incorporated computers, Canvas (Webcourses@UCF), WileyPlus software, and application sessions in large Ordinary Differential Equations I classes. Introduction of new technology, in-class problem solving and application (or discussion) sessions are important factors in the enhancement of students’ deep understanding of mathematics. We will detail various components of the course (online homework sets, application sessions and projects, in-class tests, and comprehensive final exam) and discuss how we obtained optimal results enhancing the traditional teaching techniques. Also, how to obtain optimal results without sacrificing the traditional teaching techniques will be brought out. We hope that the details of our experiences and the lessons we learned along the way will be helpful to others who are struggling with the same issues. Also, we provide solutions for quality education and the student-growth. Furthermore, this technique can be used to teach large classes in Science, Technology, Engineering and Mathematics (STEM).
Keywords: differential equations, teaching and learning, technology, retention, large class, STEM education
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