Investigation of eighth-grade students' understanding of the slope of the linear function

This study aimed to investigate eighth-grade students' difficulties and misconceptions and their performance of translation between the different representation modes related to the slope of linear functions. The participants were 115 Turkish eighth-grade students in a city in the eastern part of the Black Sea region of Turkey. Data was collected with an instrument consisting of seven written questions and a semi-structured interview protocol conducted with six students. Students' responses to questions were categorized and scored. Quantitative data was analyzed using the SPSS 17.0 statistical packet program with cross tables and one-way ANOVA. Qualitative data obtained from interviews was analyzed using descriptive analytical techniques. It was found that students' performance in articulating the slope of the linear function using its algebraic representation form was higher than their performance in using transformation between graphical and algebraic representation forms. It was also determined that some of them had difficulties and misunderstood linear function equations, graphs, and slopes and could not comprehend the connection between slope and the x- and y-intercepts

Flu viruses a lucky community and cosine graphs: the possibilities opened up by the use of a socio-political perspective to study learning in an undergraduate access course in mathematics

This is an Accepted Manuscript of an article published by Taylor & Francis in African Journal of Research in Mathematics, Science and Technology Education on 20 August 2013 available online: http://www.tandfonline.com/10.1080/10288457.2009.10740656.In this paper I present a perspective of mathematics education and learning, termed a 'sociopolitical perspective'. Classroom mathematical activity, in which certain ways of acting, behaving and knowing are given value, is located in a wider network of socio-political practices. Learning in mathematics is regarded as coming to participate in the discourse of the community that practises the mathematics. I argue that the use of a socio-political perspective allows the researcher and teacher to view classroom mathematical activity as a product of the network of socio-political practices in which it is located, rather than as a product of individual cognitive ability. I illustrate the use of this perspective by drawing on a study of learning in a first-year university access course in Mathematics at a South African university. Fairclough's method for critical discourse analysis, supplemented with work by Sfard and Morgan in mathematics education, was used to analyse both the text of a 'real world' problem in mathematics and a transcript representing the activity as a group of five students solved the problem. This analysis suggests that, despite containing traces of discourses from outside of mathematics, the problem text constructs the activity as solving a mathematical problem with features of a school mathematical word problem. When solving the problem the students draw on practices associated with school mathematics and their university mathematics course, some of which enable and others constrain their participation. For example, they refer to named functions learned at school, they have difficulty making productive links between the mathematical functions and the 'real world' context, and they have varied opportunities for mathematical talk in the group. The study identifies as key to the students' progress the presence of an authority (in this case a tutor) who can make explicit the ways of thinking, acting, and talking that are valued in the discourse of undergraduate mathematics, and who provides opportunities for mathematical talk

Methodological Considerations in the Analysis of Classroom Interaction in Community College Trigonometry

We report analyses of classroom interaction in trigonometry classes taught at an American community college focusing on two dimensions: the mathematical novelty of questions that instructors and students ask and the interactional moves that the instructors use to encourage student involvement in the lesson. The analyzed lessons were particularly challenging because existing frameworks that analyze classrooms did not account for the cases in which the delivery mode was lecture. We discuss the analytical strategies we used and show data to illustrate how they help us in capturing the complexity of classroom interaction and differences between instructors when lecture is the primary mode of instructional delivery. We conclude with suggestions for further work.National Science Foundation CAREER award DRL-0745474 to the first authorPeer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/96961/1/Mesa_Lande_MetConsClassInt_DEEPBLUE.pd

Designing and enacting instruction that enhances language for mathematics learning - a review of the state of development and research

After four decades of research and development on language in mathematics classrooms, there is consensus that enhancing language is crucial for promoting students’ mathematics learning. After briefly sketching the theoretical contexts for work on this topic, the article presents six design principles for instruction that enhance language for mathematics learning. It then reviews the research that provides an empirical foundation for these principles, (a) concerning the design of learning environments to enhance language for mathematics learning and (b) on teaching practices (including teacher moves and classroom norms) involved in the enactment of those designed learning environments. Without claiming completeness, this review of the state of development and research shows that some aspects of design and instruction that enhance language for mathematics learning have been well researched, whereas research gaps for other aspects persist