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 International Journal for Mathematics Teaching and Learning 1473-0111 In-Service Teachers’ Perceptions and Interpretations of Students’ Errors in Mathematics http://www.cimt.org.uk/ijmtl/index.php/IJMTL/article/view/119 <p>This paper reports on findings of a research study that investigated in-service secondary school teachers’ perceptions and interpretations of students’ errors in mathematics. The study used a survey research design in which a questionnaire with two sections was used to collect data. The first section sought to find out the teachers’ perceptions of the nature of errors. In the second part the teachers were asked to explain five common errors in algebra. A sample of forty-two mathematics teachers randomly drawn from one university in Zimbabwe constituted the respondents for the study. The findings showed that teachers perceived errors as not solely due to the student, but also as due to other factors arising from teaching and the nature of the subject. The teachers also regarded errors as useful for further inquiry in mathematics, as a normal part of learning, and as a result of previous knowledge not well understood by learners. In their explanations of given errors in algebra the teachers gave mainly procedural explanations, some of which lacked clarity or were incorrect. The study recommends the need for pre-service and in-service teacher professional development programmes to incorporate error analyses so as to develop teachers’ understanding of the nature and role of errors in the teaching and learning of mathematics.</p> Million Chauraya Samuel Mashingaidze ##submission.copyrightStatement## 2017-12-06 2017-12-06 18 3 Preservice Elementary Teachers’ Understanding of Operations for Fraction Multiplication and Division http://www.cimt.org.uk/ijmtl/index.php/IJMTL/article/view/63 <p class="Normal1">This study examined preservice elementary teachers’ change in their understanding of fraction operations while taking a mathematics methods course focused on grades 3-5. The preservice teachers (<em>n </em>= 48) completed an assessment before and after the course’s unit on the teaching and learning of fractions.  Specifically, the preservice teachers were asked to explain why the traditional algorithms for multiplication and division of fractions work.  Additionally, they were asked to identify errors in students’ work and provide rationales for why the strategies were faulty.  All responses on the pre- and post-assessments were coded using an existing framework for the assessment of understanding. Paired t-tests indicated a statistically significant improvement on most items on the assessment and on the total test score.  However, an in-depth analysis of how the scores changed gave insights into the proportion of preservice teachers who demonstrated no change, improvement, or regression on each question.  The percent of teachers improving on each question ranged from 33% to 46%.  Implications for mathematics teacher education programs and future research are discussed.</p> Ashley Whitehead Temple A. Walkowiak ##submission.copyrightStatement## 2017-12-06 2017-12-06 18 3 A snapshot of the role of the textbook in English secondary mathematics classrooms http://www.cimt.org.uk/ijmtl/index.php/IJMTL/article/view/75 <p><span style="font-family: Times New Roman;"><span style="font-size: small;">The role and function of the mathematics textbook has been widely discussed since its inclusion in the Trends in International Mathematics and Science study (TIMSS) in the late nineties.  </span><span style="font-size: small;">They are a common feature in many classrooms worldwide and have been identified as important vehicles for the promotion of curricula. However, there has also been much debate about the role of a mathematics textbook and as a result there is anecdotal evidence to suggest a decline in the use of mathematics textbooks in England.</span><span style="font-size: small;">  </span><span style="font-size: small;">This paper reports on an examination of the current role of mathematics textbooks in secondary and middle schools in the North-West of England based on teachers self-reported use of mathematics textbooks. The data indicates that for all teachers in this sample who used a mathematics textbook, there is a positive correlation between the number of years teaching experience a teacher has and the amount of their classroom time that is ‘textbook driven’ and a negative correlation between the number of years’ experience a teacher has and the likelihood that they will use a mathematics textbook as their key resource for planning. These teachers also identified as having access to a range of different resources to supplement their use of mathematics textbook and using textbooks in varied ways such as to set reading tasks.</span></span></p> Lisa O'Keeffe Bruce White ##submission.copyrightStatement## 2017-12-06 2017-12-06 18 3 WHAT HAPPENS WHEN TEACHERS AND STUDENTS ARE INTRODUCED TO MATHEMATICAL INVESTIGATIONS: AN EXPLORATORY STUDY http://www.cimt.org.uk/ijmtl/index.php/IJMTL/article/view/90 <p>A mathematical investigation (MI) encapsulates the reform movement in mathematics education by addressing content and process simultaneously and providing a novel opportunity for students to develop thinking skills and good mental habits. However, introducing MI to teachers and students who are used to routinized teaching approaches and pen-and-paper testing presents many challenges. This study introduced MI to two junior classes and the mathematics teachers of a regular public high school. After the MI orientation workshops, the students engaged in the processes of pattern-finding, problem posing, conjecturing, verifying, and proving. Data were gathered through focus group discussions, interviews, observations, teachers’ reflection notes, audiotapes, and analysis of students’ outputs. The challenges of doing MI included the teachers’ and students’ lack of exposure to and/or competence in the investigative processes, the teacher’s traditional views and teaching practices, and some sociosystemic factors in schools. Issues raised here could give insights into the areas where teachers and students needed reinforcement and how teachers could redesign mathematics instruction to focus on the development of processes and thinking skills needed for investigations.</p><p><strong> </strong></p> Gladys Celis Nivera ##submission.copyrightStatement## 2017-12-06 2017-12-06 18 3 Pattern Finding Skills of Pre-school Children http://www.cimt.org.uk/ijmtl/index.php/IJMTL/article/view/60 <p>This study investigates the pattern finding skills of pre    school children and the in-class pattern activities conducted by teachers. The research was designed as a descriptive survey study carried out with a total of 162 children aged 60-77 months from families with middle socio-economic status. The findings of the study revealed that the children’s pattern-finding achievement was above average and that there was not a significant difference between the pattern finding skills of the children in terms of gender and age. Lastly, in relation to pattern categories, the results showed that the children were more successful in the repetitive pattern category and pattern sub-categories, and structures were effective in the children’s pattern-finding performance. In addition, the teachers were found to use repetitive patterns more frequently and triple-structured patterns most frequently in in-class pattern activities. </p> Kamuran Tarim ##submission.copyrightStatement## 2017-12-06 2017-12-06 18 3 Visualization of Lines of Best Fit http://www.cimt.org.uk/ijmtl/index.php/IJMTL/article/view/38 <p>Humans possess a remarkable ability to recognize both simple patterns such as shapes and handwriting and very complex patterns such as faces and landscapes.  To investigate one small aspect of human pattern recognition, in this study participants position lines of “best fit” to two-dimensional scatter plots of data.  The study investigates the variation in participants' fits and whether there is some consistent metric being used in fitting the lines.  For example, is there a natural tendency toward fitting lines similarly to one of the standard regression lines: vertical, horizontal, or orthogonal.  This study also investigates the effect of outliers on the line a participant fits to a scatter plot with a strong linear trend and provides guidance for future inquiries. </p> Michael J. Bosse Michael Rudziewicz Gregory S. Rhoads Eric S. Marland ##submission.copyrightStatement## 2017-12-06 2017-12-06 18 3 Fostering Students’ Preparation and Achievement in Upper Level Math Courses http://www.cimt.org.uk/ijmtl/index.php/IJMTL/article/view/33 <p> </p><p><span style="font-family: Calibri;">This study describes an intervention to address motivation and student engagement in upper - level math courses. The effect of the intervention regarding students’ achievements is investigated via students’ opinions and data analysis from students’ assessments. The results of this study show that the featured intervention decreases anxiety, provides confidence, and increases motivation for class preparation which, in turn, fosters students’ ‘in- and out-of- class interactions’ and boosts ‘students’ self-confidence on studying math on their own’. Moreover, students’ assessment scores reveal a significant increase on students’ grades.</span></p><p> </p> Ali Shaqlaih Mehmet Celik ##submission.copyrightStatement## 2017-12-06 2017-12-06 18 3