International Journal for Mathematics Teaching and Learning http://www.cimt.org.uk/ijmtl/index.php/IJMTL <p><span style="font-size: small;">This journal&nbsp;is published&nbsp;only in electronic form. It focuses on&nbsp;mathematics teaching and learning for all ages up to university through relevant articles and&nbsp;reviews&nbsp;from around the world.<br> It is aimed at researchers, practitioners and teacher educators providing a medium for stimulating and challenging ideas, offering innovation and practice in all aspects of mathematics teaching and learning.</span></p> <p>&nbsp;</p> en-US j.hunter1@massey.ac.nz (Jodie Hunter) Mon, 27 Aug 2018 10:04:00 +0100 OJS 3.1.1.2 http://blogs.law.harvard.edu/tech/rss 60 The Analysis of a Novice Primary Teacher’s Mathematical Knowledge in Teaching: Area Measurement http://www.cimt.org.uk/ijmtl/index.php/IJMTL/article/view/13 <p class="Keywords">The purpose of this paper is to investigate a novice primary teacher’s mathematical knowledge in teaching on area measurement.  Data was collected from a novice primary teacher of fourteen students in a primary school located in Ankara, Turkey using field notes, video recordings of lessons, and audio recordings of interviews before and after her teaching. Her teaching were analyzed according to dimensions of Knowledge Quartet (KQ) model which included Foundation, Transformation, Connection, and Contingency. Results revealed that the KQ model is an alternative and effective tool for the primary mathematics teaching. Specifically, the novice primary teacher’s mathematical knowledge in teaching for area measurement was found to be effective regarding the Foundation and Contingency dimensions. However, she lacked the ability to make connections and use appropriate representations and examples regarding the Connection and Transformation dimensions respectively.  Implications and suggestions for the improvement of teachers’ mathematical knowledge in teaching are presented.</p> Sümeyra Doğan Coşkun, Mine Işıksal Bostan ##submission.copyrightStatement## http://www.cimt.org.uk/ijmtl/index.php/IJMTL/article/view/13 Wed, 22 Aug 2018 00:00:00 +0100 Conceptual and procedural angle knowledge: do gender and grade level make a difference? http://www.cimt.org.uk/ijmtl/index.php/IJMTL/article/view/61 <p><span lang="EN-US">The study examined differences in students’ conceptual and procedural knowledge of angles among two grades and gender. Participants were 382 sixth and 376 seventh graders from a metropolitan city in [Country]. [Nation] students’ conceptual and procedural knowledge of angles declined from sixth to seventh grade. Gender differences were found for procedural knowledge, but not for conceptual knowledge. Since conceptual and procedural knowledge of angles may have significant influences on the essential subsequent topics in geometry, we need to seriously consider the implications of these gender- and grade-related differences and pay attention particularly to males in Grade 7. The patterns of [Nation] students’ conceptual and procedural angle knowledge were discussed, and educational implications were offered. </span></p> Utkun Aydın ##submission.copyrightStatement## http://www.cimt.org.uk/ijmtl/index.php/IJMTL/article/view/61 Mon, 27 Aug 2018 09:50:02 +0100 Algorithms . . . Alcatraz: Are children prisoners of process? http://www.cimt.org.uk/ijmtl/index.php/IJMTL/article/view/112 <p class="CONFAbstract">Multiplicative thinking is a critical component of mathematics which largely determines the extent to which people develop mathematical understanding beyond middle primary years. We contend that there are several major issues, one being that much teaching about multiplicative ideas is focussed on algorithms and procedures. An associated issue is the extent to which algorithms are taught without the necessary explicit connections to key mathematical ideas. This article explores the extent to which some primary students use the algorithm as a preferred choice of method and whether they can recognise and use alternative ways of calculating answers. We also consider the extent to which the students understand ideas that underpin algorithms. Our findings suggest that most students in the sample are ‘prisoners to procedures and processes’ irrespective of whether or not they understand the mathematics behind the algorithms.   <strong><em></em></strong></p> Chris Hurst ##submission.copyrightStatement## http://www.cimt.org.uk/ijmtl/index.php/IJMTL/article/view/112 Mon, 13 Aug 2018 00:00:00 +0100 Problem Solving Trajectories in a Dynamic Mathematics Environment: The Geometer’s Sketchpad http://www.cimt.org.uk/ijmtl/index.php/IJMTL/article/view/72 <p>Student problem solving in the context of a dynamic mathematics environment (DME) has previously been investigated primarily through the lens of whether or not the student could complete a problem solving task. Herein, we investigate what trajectories students employ in the realms of mathematics, technology, and problem solving as they attempt to complete tasks and which of these trajectories are more helpful than others. Notably, it was determined that these trajectories are idiosyncratic, nonlinear, and iterative and that, while some trajectories help problem solving, others harm the problem solving process. Among other findings, it was determined that student access to technology may not assist their mathematical problem solving and may at times hinder it even further.</p> Michael J. Bosse ##submission.copyrightStatement## http://www.cimt.org.uk/ijmtl/index.php/IJMTL/article/view/72 Wed, 22 Aug 2018 10:07:38 +0100 Investigation of Pre-Service Teachers’ Pedagogical Content Knowledge Related to Division by Zero http://www.cimt.org.uk/ijmtl/index.php/IJMTL/article/view/117 <p class="CONFHeading1"><span lang="EN-AU">Although the topic of division by zero has been widely discussed in the literature, this subject is still confusing for students, pre-service teachers and teachers. Because of this, teachers at various grade levels may encounter difficulties in conveying the concept to their students. Therefore, in order to provide students with a strong conceptual understanding of division by zero, it is important to examine the ways that teachers and pre-service teachers structure their instructional explanations about division by zero. The aim of this study was to explore the instructional explanations given by pre-service teachers concerning division by zero, as well as the effects of teacher training programs on these explanations. The study consisted of a cross-sectional design and was carried out with 197 pre-service teachers of elementary mathematics. To determine the pre-service teachers’ instructional explanations given at different grade levels, a written questionnaire was used. Analysis of the results revealed that although most of the pre-service teachers gave correct answers related to division by zero, few of them provided conceptual-based explanations. Rather, those who gave correct explanations mainly responded with rule-based statements.</span></p> Fatih Karakus ##submission.copyrightStatement## http://www.cimt.org.uk/ijmtl/index.php/IJMTL/article/view/117 Thu, 23 Aug 2018 01:21:36 +0100 Secondary School Students’ Conception of Quadratic Equations with One Unknown http://www.cimt.org.uk/ijmtl/index.php/IJMTL/article/view/94 <p class="CONFAbstract"><span lang="EN-AU">In recent years, quadratic equations have started to become of greater interest to researchers. This study explored what conceptions high school students have about quadratic equations with one unknown using concept definition and concept images as theoretical concept. The data was gathered through semi-structured interviews with 14 eleventh grade high school students. Analysis of data displayed that students could not provide a proper definition of quadratic equations with one unknown, and their definitions were not consistent with the formal (standard) definition of quadratic equations. Moreover, the findings showed that students’ concept image of quadratic equation is quite limited and dominated by ideas factoring. Students’ conception of quadratic equations also showed that participating students lacked three types of prerequisite knowledge, degree of polynomial, variable and equals sign. To enrich students’ concept images both procedurally and conceptually, this study has implications for teachers. The implications of the findings are discussed. </span></p> Makbule Gozde Didis Kabar ##submission.copyrightStatement## http://www.cimt.org.uk/ijmtl/index.php/IJMTL/article/view/94 Mon, 27 Aug 2018 09:59:44 +0100 Traditional vs Non-traditional Teaching and Learning Strategies – the case of E-learning! http://www.cimt.org.uk/ijmtl/index.php/IJMTL/article/view/21 <h3>The traditional teaching approaches are generally teacher-directed and where students are taught in a manner that is conducive to sitting and listening. It is true that the traditional expectations and department philosophies often allow us to continue with the lecture-based model with some useful results as evident by the past accomplishments of many and this cannot be disputed as much. However it is often argued that the traditional approach may not provide students with valuable skills and indeed some even go as far as saying the traditional method leads to a student not retaining knowledge after exams - they have little or no recall of the body of knowledge learnt beyond the end of a semester, for example. The teaching of mathematics that is usually referred to or called non-traditional uses constructivist philosophy as its basis; this implicates strategies in which the individual is making sense of his or her universe. So the student is an active participant, which allows an individual to develop, construct or rediscover knowledge – a major goal that can be very time consuming process if taken literally for each student; alternately, there is also a philosophical position known as social constructivism; which suggests group work, language and discourse to be vital for learning in a cultural framework of the knowledge base; so the use of group work, discussion, and group solving problems in a cooperative manner lead to a discourse which is believed to be the most important part of learning process. It is argued that the non-traditional teaching is done using a problem solving approach; where the learner is the problem solver.</h3><p>Typically, university lecturers in mathematics and engineering are often not trained in the non-traditional classroom methods. Some have argued that even if they included non-traditional teaching in their universities in fact they may not be in reality using the so called non-traditional methods and goals. They argue that lecturers are often lacking the underlying philosophical knowledge of the non-traditional goals and objectives, and therefore they are not in a position to implement such methodologies and assessment techniques, in reality, even when they say they are.</p><p>The non-traditional teaching and learning (NTTL) in mathematics and engineering needs to be well understood before any appropriate comparisons can be made with the older techniques if we are to do it in professional manner. For example the teachers of engineering courses need to reflect where the students are coming from, and where will they need to be after completing the course; also lecturers need to keep the context and goals of the course the degree program in mind while preparing for their class teaching content for the semester. So, we need to consider the knowledge, procedures, skills, beliefs and attitudes that will be expected for each student of mathematics or engineering at the end of the course that is to be taught in a time frame of 12 to 13 weeks; in addition to keeping the economic constraints of a university in modern times in check at all times.</p><p>The computer based teaching technology (e-learning) is now constantly used in mathematics and engineering courses. The e-learning methodology is considered to be in line with the non-traditional approaches than the traditional teaching approaches; and this paper critically reviews the literature on mathematics and engineering that have made comparisons of the approaches outlined. The paper will specifically examine the advantages/disadvantages of the approaches as well the manner in which they influence performance of students in mathematics and engineering courses.</p> Gurudeo Anand Tularam ##submission.copyrightStatement## http://www.cimt.org.uk/ijmtl/index.php/IJMTL/article/view/21 Mon, 27 Aug 2018 02:10:35 +0100