Birgit Pepin

Mathematics and Its Value for Engineering Students: What Are the Implications for Teaching?.

Mathematics has long been known to be problematic for university engineering students and their teachers, for example, Scanlan.[1] This paper presents recent data gathered from interviews with engineering students who experienced problems with mathematics and their lecturers during their transition through the first year in different programme contexts. Our interviews with the students reveal how they understand the relation between engineering and mathematics and we draw on the concept of ‘use- and exchange-value’ to explore this relationship more fully. This paper challenges both the pedagogical practice of teaching non-contextualized mathematics and the lack of transparency regarding the significance of mathematics to engineering. We conclude that the value of mathematics in engineering remains a central problem, and argue that mathematics should be a fundamental concern in the design and practice of first-year engineering.

Inclusion in Schools: Who is in Need of What?

The history of schooling of children with special needs has been described as going from neglect early in the twentieth century to segregation based on individual needs in the 1920s–1960s to integration in the 1960s to the present (Casey, 1994). This picture could be complemented by the current movement towards inclusion in schools, which is responsive to the needs of children as well as to their rights as citizens, and to the needs of all of us to learn to live in a world of differences (Thomas & Loxley, 2001). The global dimension of this movement has been described by Mittler (2000) as connected to places like Jomtien (Thailand) and Salamanca (Spain). In Jomtien, ministers of education and officials from 155 governments met in 1990 and committed their countries to set national targets for the coming decade in five domains:

Mathematics Textbooks and Their Use by Teachers: A Window Into the Education World of Particular Countries

Education in particular is concerned with making available to the next generation what society regards as the most valuable aspects of culture. Certain kinds of knowledge, certain beliefs and concepts concerning teaching and learning are regarded as so important that their transmission to the next generation is not left to chance. In most societies it has been selected and determined what, sometimes how and why, educational professionals (teachers) have to convey to pupils in their classrooms. ‘What knowledge is of most worth’ and ‘how to teach and learn it’ appear to be some of the crucial issues of educational theory.

Students’ Attitudes Towards Mathematics Across Lower Secondary Schools in Shanghai

Whilst students in Shanghai were top-ranked internationally in the 2009 and 2012 PISA (Programme for International Student Assessment) studies, much less is known about Shanghai students’ attitudes towards mathematics and how this varies across the 11–15 age range. This chapter reports on a study of attitudes towards mathematics of Shanghai students in lower secondary schools, in terms of their emotional disposition towards mathematics and their perceived competence in mathematics. Data were obtained from 4,236 students across grades 6 to 9 in eleven schools across four school districts in SH. Our study found that across the grades an increasing proportion of Shanghai students reported a positive disposition towards mathematics, with only slight drop in Grade 8. We also found that the combinations “I like it although I can’t do it” and “I can do it but I dislike it” were not rare. Interestingly, in seven out of the eleven schools surveyed, more than half of the students who disliked mathematics conveyed that they could do it. Noticeably, the seven schools were all top or above-average achieving schools (according to school district and city-level examinations). Our study also found that more boys expressed a positive emotional disposition than girls. Nevertheless, there was no difference between boys’ and girls’ perceived competence in mathematics.

AN INVESTIGATION OF MATHEMATICS TEXTBOOKS IN ENGLAND, FRANCE AND GERMANY: SOME CHALLENGES FOR ENGLAND

This paper reports on an analysis of mathematics textbooks used in lower secondary classrooms in England, France and Germany. The examination was carried out using an analysis schedule based on existing literature on textbooks. In this paper we look first at the development of the analysis schedule and then at the how particular textbooks treat the topic of angle. From this we conclude that learners in the different countries are offered different mathematics. In particular, learners in England are offered few challenges in the mathematics they are offered compared with their French and German counterparts.

From Text to 'Lived' Resources

Nowadays, mathematics teachers are confronted with a myriad of resources that are available through technological means and through the internet in particular. However, teachers may perceive difficulties in orchestrating education which makes use of technological tools and resources. With instrumental orchestration as a theoretical lens, the main question addressed in this chapter is into which types of orchestrations teachers transform the technological resources. In the setting of a pilot teaching sequence in grade 12 on using applets for practicing algebraic skills, this question is investigated, through a case study of one participating mathematics teacher, through questionnaires among the 69 participating teachers, and through interviews with six of them. The results show that teachers privilege orchestrations in which students work individually or in pairs, at the cost of whole-class orchestration types. Within the performance of these student-centered orchestrations, we recognize elements already known from previously identified orchestrations. Compared to their regular teaching practices and their expectations before the pilot, the involvement in the pilot causes teachers to adapt their orchestrations during the pilot.

Word problems versus image-rich problems: an analysis of effects of task characteristics on students’ performance on contextual mathematics problems

ABSTRACT This article reports on a post hoc study using a randomised controlled trial with 31,842 students in the Netherlands and an instrument consisting of 21 paired problems. The trial showed a variability in the differences of students’ results in solving contextual mathematical problems with either a descriptive or a depictive representation of the problem situation. In this study the relation between this variability and two task characteristics is investigated: (1) complexity of the task representation; and (2) the content domain of the task. We found indications that differences in performance on descriptive and depictive representations of the problem situation are related to the content domain of the problems. One of the tentative conclusions is that for depicted problems in the domain of measurement and geometry the inferential step from representation of the problem situation to the mathematical problem to be solved is smaller than for word problems.

Open Educational Resources: A Chance for Opening Mathematics Teachers’ Resource Systems?

This chapter proposes a theoretical frame, the documentational approach to didactics (DAD), as a tool for analyzing the changes brought about by digitalization in the design and uses of mathematics teaching resources. One of the major changes appears to be initiated by the profusion of Open Educational Resources (OER), which provide new opportunities for the design and use of teaching resources. In order to analyze the effects of such opportunities, we focus on two cases: the French Sesamath association, providing OERs at a large scale; and a French mathematics teacher using OERs as a means for accomplishing her teaching. Through the lens of DAD, we investigate the implication of this provision of ‘resources-on-offer’ for teachers’ practices.

Rethinking algebra teaching in the light of 'orchestration of signs'- Exploring the 'equal sign' in an Norwegian mathematics classroom.

Algebra continues to be the focus of reform efforts and research in mathematics education in many countries worldwide (e.g., Kieran, 1992 & 2006; National Council of Teachers of Mathematics (NCTM), 2000; Watson, 2009). There is a general concern (e.g., from policy makers, teachers and Higher Education councils) that students leave compulsory schooling with inadequate understandings of and preparation in algebra, and that they seem to be ill-prepared for future educational or professional opportunities (Moses & Cobb, 2001).

Enhancing Teacher Learning with Curriculum Resources

In this commentary paper I start from the chapters of the book (and related research), and develop an argument for a complementary line of research, which (in my view) deserves additional (and increased) attention in mathematics education research. Whilst curriculum materials have been examined in terms of their quality and support for student learning, less research has focused on teacher learning with educative curriculum materials. This is especially relevant, as teachers are increasingly expected to design their own materials, in particular in times of curriculum change and profusion of digital materials on the web. In this chapter I discuss design criteria and suggest selected design specifications, and their functions, for educative curriculum materials. Moreover, I argue for ‘flexible design criteria’ aligning my suggestions with my earlier work on teacher design capacity.