Towards a Pedagogy of Inferential Statistics in Graduate Education Programs: Insights from Cognitive and Educational Research

This study attempts to understand the nature of knowledge base that supports the ability to select statistical techniques for research situations. Findings showed that the largest component of such knowledge was related to research design. One implication is that techniques should be taught in relation to features of research design

Reflections on restructuring of IEJME

As an international journal, one of the goals of International Electronic Journal of Mathematics Education (IEJME) is to stimulate discussions in our field through publishing significant and innovative research studies. To pursue this goal better, IEJME has gone through a restructuring process recently. The journal is now stronger with its two new associate editors, an editorial assistant, and a renewed international editorial board. We now have a shorter and improved review process. There are certain measures and challenges we needed to take into consideration in revising and improving the structure of the journal. The purpose in this article is to share the changes made to the journal and their impact in its progress

On People's Incorrect Either-Or Patterns in Negating Quantified Statements: A Study

People manifest formally incorrect either-or, polarizing re-sponse tendencies when asked to negate quantified state-ments. Our study focuses on students ’ error patterns when ne-gating quantified sentences, which are the single most impor-tant cause for their difficulties with indirect proofs and proofs by contradiction. We found that, contrary to our expectations, the effect of content is relatively small on their negation be-havior; that of the four quantifier categories used, students have by far the most difficulties in negating universally quan-tified sentences; and that the effect of formal logic instruction wears off relatively fast. The significance of our study reaches beyond the classroom: logically literate reasoners are less prone to be manipulated by either-or rhetoric of politicians, and are more conscious of their own limiting beliefs

Mathematical Knowledge and Skills Expected by Higher Education in Engineering and the Social Sciences: Implications for High School Mathematics Curriculum

One important function of school mathematics curriculum is to prepare high school students with the knowledge and skills needed for university education. Identifying them empirically will help making sound decisions about the contents of high school mathematics curriculum. It will also help students to make informed choices in course selection at high school. In this study, we surveyed university faculty members who teach first year university students about the mathematical knowledge and skills that they would like to see in incoming high school graduates. Data were collected from 122 faculty members from social science (history, law, psychology) and engineering departments (electrical/electronics and computer engineering). Participants were asked to indicate which high school mathematics topics and skills they thought were important to be successful at university education in their field. Results were compared across social science and engineering departments. Implications were drawn for curriculum specialists, students, and mathematics educators

Secondary mathematics teachers' noticing of students' mathematical thinking through modeling-based teacher investigations

This study aimed to investigate secondary mathematics teachers' noticing of students' mathematical thinking in the context of a professional development (PD) program utilizing modeling-based teacher investigations. The PD program was conducted with two groups of mathematics teachers from two public high schools. It included seven 1-month-long cycles, each consisting of an introductory meeting, the teachers' classroom implementations of a model-eliciting activity (MEA), and a follow-up meeting focusing on the teachers' collaborative investigation and discussion of students' written work, including their strategies to solve the MEA. Findings suggested that participating in the PD program promoted the teachers' noticing of students' mathematical thinking, albeit differently, over time. We elaborated on the components of the PD program that might have influenced the teachers' noticing of students' mathematical thinking. Implications of the findings on teachers' noticing for researchers, PD leaders, and teacher educators are discussed in terms of potential directions for future research and practice

Evolution of Mathematics Teachers' Pedagogical Knowledge when They are Teaching through Modeling

Use of mathematical modeling in mathematics education has been receiving significant attention as a way to develop students. mathematical knowledge and skills. As effective use of modeling in classes depends on the competencies of teachers we need to know more about the nature of teachers. knowledge to use modeling in mathematics education and how this knowledge evolves. The aim of this study is to investigate how teachers. pedagogical knowledge to use modeling in the classroom is formed and modified through professional development activities based on lesson study cycle from modeling perspective. The professional development program reported in this study included five monthly cycles consisted of meeting before the implementation, implementation of the activity and a follow up meeting. The participants were four in-service mathematics teachers. Results showed that the program provided opportunities for teachers to test, revise, and refine their knowledge. More specifically, teachers generated effective strategies for proper implementation of the modeling activities in the classroom

Mathematical Modeling in Mathematics Education: Basic Concepts and Approaches

Mathematical modeling and its role in mathematics education have been receiving increasing attention in Turkey, as in many other countries. The growing body of literature on this topic reveals a variety of approaches to mathematical modeling and related concepts, along with differing perspectives on the use of mathematical modeling in teaching and learning mathematics in terms of definitions of models and modeling, the theoretical backgrounds of modeling, and the nature of questions used in teaching modeling. This study focuses on two issues. The first section attempts to develop a unified perspective about mathematical modeling. The second section analyzes and discusses two approaches to the use of modeling in mathematics education, namely modeling as a means of teaching mathematics and modeling as an aim of teaching mathematics

Pre-service Teachers’ Developing Conceptions about the Nature and Pedagogy of Mathematical Modeling in the Context of a Mathematical Modeling Course

Adopting a multitiered design-based research perspective, this study examines pre-service secondary mathematics teachers' developing conceptions about (a) the nature of mathematical modeling in simulations of real life problem solving, and (b) pedagogical principles and strategies needed to teach mathematics through modeling. Unlike other studies that have focused on single-topic and lesson-sized research sites, a course-sized research site was used in this study. Having been through several iterations over three teaching semesters, the 15-week long course was implemented with 25 pre-service secondary mathematics teachers. Findings revealed that pre-service teachers developed ideas about the nature of mathematical modeling involving what mathematical modeling is, the relationship between mathematical modeling and meaningful understanding, and the nature of mathematical modeling tasks. They also realized the changing roles of teachers during modeling implementations and diversity in students' ways of thinking. The researchers' conceptual development, on the other hand, involved realizing the critical aspect of the teacher role played by the instructor during modeling implementations, and the need for more experience of modeling implementations for pre-service teachers