Immaculate Kizito Namukasa

New Media and Online Mathematics Learning for Teachers

In this chapter we offer a case study of an online Mathematics for Teachers course through the lens of four affordances of new media: democratization, multimodality, collaboration and performance. Mathematics, perhaps more so than other school subjects, has traditionally been a subject that people do not talk about outside of classroom settings. However, we demonstrate through the case of the Mathematics for Teachers course that this does not have to be the case. Mathematics, even mathematics that traditionally has been seen as abstract or inaccessible, can be talked about in ways that can engage not only adults but also young children. The affordances of new media can help us rethink and disrupt our existing views of mathematics (for teachers and for students) and of how it might be taught and learned, by (1) blurring teacher/student distinctions and crossing hierarchical curriculum boundaries; (2) communicating mathematics in multimodal ways; (3) seeing mathematics as a collaborative enterprise; and (4) helping us learn how to relate good math stories to classmates and family when asked “What did you do in math today?”

Selection of Apps for Teaching Difficult Mathematics Topics: An Instrument to Evaluate Touch-Screen Tablet and Smartphone Mathematics Apps

Manipulatives—including the more recent touch-screen mobile device apps—belong to a broader network of learning tools . As teachers continue to search for learning materials that aid children to think mathematically, they are faced with a challenge of how to select materials that meet the needs of students. The profusion of virtual learning tools available via the Internet magnifies this challenge. What criteria could teachers use when choosing useful manipulatives? In this chapter, we share an evaluation instrument for teachers to use to evaluate apps . The dimensions of the instrument include: (a) the nature of the curriculum addressed in the app—emergent , adaptable or prescriptive, and relevance to current, high quality curricula —high, medium, low; (b) degree of actions and interactions afforded by the app as a learning tool—constructive, manipulable, or instructive interface; (c) the level of interactivity and range of options offered to the user—multiple or mono, or high, moderate or low; and, (d) the quality of the design features and graphics in the app—rich, high quality or impoverished, poor quality. Using these dimensions, researchers rated the apps on a three-level scale: Levels I, II, and III. Few apps were classified as Level III apps on selected dimensions. This evaluation instrument guides teachers when selecting apps. As well, the evaluation instrument guides developers in going beyond apps that are overly prescriptive, that focus on quizzes, that are text based, and include only surface aspects of using multi-modality in learning, to apps that are more aligned with emergent curricula, that focus also on conceptual understanding, and that utilize multiple, interactive representations of mathematics concepts.

Studying Student Teachers’ Voices and Their Beliefs and Attitudes

Learning to teach mathematics is a complex undertaking, and in the last twenty years there has been a great deal of research looking at aspects of the process. There are many ways one might structure an analysis of research on learning to teach mathematics. It is clear, though, from all the research on learners in all kinds of situations that what student teachers bring to their teacher education courses in terms of prior knowledge, experience, attitudes, beliefs, goals, fears, hopes, and expectations has to be a key factor in preparing for and teaching those courses and hence for research. This particular focus for research in our field is not new; my own doctoral studies, completed in 1986, looks at connections between student teachers’ beliefs about the nature of mathematics and their perceptions of teaching mathematics (Lerman, 1990).1 It remains, however, of great importance, and there are new insights drawing on a range of theoretical frameworks emerging in the field. Central to research in the study of student teachers’ attitudes and beliefs and any changes in those beliefs during pre-service teacher education courses are issues of methodology. Access to student teachers’ beliefs and experiences is inevitably through their voices, expressed in interviews, conversations, and their writing, but the interaction of beliefs and practice is a necessary consideration too. First, regarding students’ voices, what must concern us is how to read across a number of stories in order to be able to say something about how these voices are produced (Arnot & Reay, 2004). Without that focus we produce a spiral of more and more detailed stories with no possibility of making sense of the data (see Brown & McNamara, 2005, for an excellent example of the struggle for an appropriate theoretical framework for analysing student teachers’ voices). Second, there is always a gap between what people say about what they do and what they actually do in their practice (Lerman, 2002). Research needs, therefore, to be aware of that gap

Design-based mathematics workshops

Purpose – The purpose of this paper is to present a workshop model for engaging children and parents in mathematics activities in public libraries or other informal education settings. Design/methodology/approach – This paper explores a workshop model for helping the school-aged children learn mathematics outside the school. The model includes five workshop sessions and designs the parent’s role in the mathematics activities. Each workshop session has both a mathematics task activity and a user interface design activity. The model was implemented in a major Canadian city and a major Chinese city over a period of one month. This paper presents the workshop attendees’ experiences and their feedback on the workshop design. It also presents several suggestions on the design of such workshops. Findings – The parents acknowledged that they learned about how mathematics is currently taught in schools and appreciated the opportunities to interact with their children in the workshops. The children participated in ...

Critical Curriculum Renewal in Africa

Uganda suffered a turbulent political history and is challenged by socio-economic diversity. Its school system was inherited from Britain. The government in partnership with bilateral and multilateral agencies is currently expanding the system through programs such as privatization. But most of these programs are focusing on improved access and management of education. Minimal development of curriculum is taking place

The I Teach Mathematics Online Project: Learning and Teaching through Innovative Practices

Providing professional development and support resources that offer additional learning to what teachers might have studied at school, university, and in practice is an increasingly recognized way to support teachers Web-based resources promise to deliver content and pedagogical knowledge in ways enriched by digital technologies. We report on a prototype of a project, I Teach Math project, ITM, developed to deliver pedagogical content knowledge for teaching through problem-solving. ITM was designed from video interviews of selected mathematics teachers on their favorite lessons. On the ITM online database the videos are presented in short clips. Virtual learning objects are used to annotate and illustrate the content. The online environment was harnessed to aid teachers to observe exemplary teaching practices, to build a database of exemplary teaching, and to share ideas on teaching practices. In the process of designing ITM we surveyed existing online projects to select 10 major players for a comparative analysis. This paper reports on the development of ITM. It explores the digital-technologies utilized, the pedagogical content knowledge and pedagogical thinking shared by the teachers.

Teacher Tasks for Mathematical Insight and Reorganization of What it Means to Learn Mathematics

The mathematics-for-teachers tasks we discuss in this chapter have two qualities: (1) they offer teachers opportunities to experience the pleasure of mathematical insight; and (2) they aim to disrupt and reorganize teachers’ views of what it means to do and learn mathematics. Given that many future and inservice elementary teachers fear and dislike mathematics, it is perhaps not too far-fetched to suggest that there is a need for “math therapy.” We believe that a form of mathematics therapy may involve new and different experiences with mathematics. Such experiences, considered broadly to include questions or prompts for mathematical exploration, draw attention to deep mathematical ideas and offer the potential of experiencing the pleasure of significant mathematical insight. In our work with teachers we have developed and used a variety of mathematics tasks as opportunities for experiential therapy. The tasks aim to challenge some of the mathematical myths that future teachers believe to be true and are typically assumed by them in mathematics classrooms. The tasks have potential to disrupt teachers’ view of mathematics, and to start the process for reorganizing their thinking about what mathematics is and what it means to do and learn mathematics. In this chapter we describe and discuss four of the mathematics tasks which involve non-routine mathematics problems that we use in our mathematics-forteachers program. This program is offered annually to our 440 future elementary school (K-8) teachers, who generally lack confidence in mathematics and often fear and/or dislike the subject. It is also offered to inservice teachers through a series of mathematics-for-teachers courses. A student response summarizes the effects of our approach.