THE EFFECT OF PURPOSEFUL MATHEMATICS DISCOURSE IN THE CLASSROOM ON STUDENTS’ MATHEMATICS LANGUAGE IN THE CONTEXT OF PROBLEM SOLVING

This study examines how one secondary school teacher’s use of purposeful oral mathematics language impacted her students’ language use and overall communication in written solutions while working with word problems in a grade nine academic mathematics class. Mathematics is often described as a distinct language. As with all languages, students must develop a sense for oral language before developing social practices such as listening, respecting others ideas, and writing. Effective writing is often seen by students that have strong oral language skills. Classroom observations, teacher and student interviews, and collected student work served as evidence to demonstrate the nature of both the teacher’s and the students’ use of oral mathematical language in the classroom, as well as the effect the discourse and language use had on students’ individual written solutions while working on word problems. Inductive coding for themes revealed that the teacher’s purposeful use of oral mathematical language had a positive impact on students’ written solutions. The teacher’s development of a mathematical discourse community created a space for the students to explore mathematical language and concepts that facilitated a deeper level of conceptual understanding of the learned material. The teacher’s oral language appeared to transfer into students written work albeit not with the same complexity of use of the teacher’s oral expression of the mathematical register. Students that learn mathematical language and concepts better appear to have a growth mindset, feel they have ownership over their learning, use reorganizational strategies, and help develop a discourse community.

Preservice Elementary Teachers’ Beliefs toward Mathematics and Mathematics Teaching

As they began their one-year teacher education program 138 elementary school teacher candidates completed a questionnaire designed to measure their beliefs concerning the nature of mathematics, measured on a scale from absolutist to fallibilist, and their beliefs concerning effective mathematics instruction, measured on a scale from traditional to constructivist. Interviews were conducted with volunteer questionnaire participants, with selection based on the questionnaire results and using two sets of criteria. Study 1. involved 8 teacher candidates showing distinct absolutist or fallibilist views of mathematics and individual interviews explored participants' beliefs concerning the use of information and communication technology, particularly interactive whiteboards (IWB), in the teaching and learning of mathematics. Participants with absolutist beliefs about the nature of mathematics tended to focus on the IWB as a presentation tool, while those with fallibilist beliefs appreciated the use of the IWB to support student exploration. Study 2. involved 8 teacher candidates with apparently misaligning absolutist beliefs concerning the nature of mathematics and constructivist beliefs concerning teaching. Interviews exploring participants' favoured instructional approaches, particularly those involving the use of manipulatives, showed that constructivist views involved essentially surface beliefs and that in fact manipulatives would be employed to support traditional direct instruction.

Using WebCT to Support a Community of Practice

Reflecting a view of “teaching as both an intellectual and practical activity” the Queen’s University Bachelor of Education program has multi-week in-school practicum sessions separated by periods of on-campus course work. The expectation is that teacher candidates will bring together theory and practice as they reflect upon their daily classroom experiences. The reality often is that, while isolated from the university environment and caught up in the pressures of teaching, little deep reflection takes place. For reflection and critical examination of experience to occur, teacher candidates need to share and discuss on a daily basis their practice teaching experience. For the past few years, students in my secondary school mathematics curriculum course, through a WebCT based conference, have been provided, while away from campus, with a place for on-going sharing of teaching stories and dilemmas. In the Fall of 2004 eight-five percent of the class took part in the discussions, posting a total of 667 messages over a 9 week period. In an effort to increase the value of this practicum conference we have analysed the topic threads arising in the conversation, surveyed the participants concerning their impressions of the sharing experience, and conducted in-depth interviews with a sampling of the class. This session will present the results of this study and provide an opportunity to discuss ways in which an online discussion can support the building of community and the exchange of experience while students in professional programs are disbursed in practice/clinical settings.

Math-Towers: Online Interactive Collaborative Mathematics Explorations & Problem-Solving for Students Ages 11 to 15 years (Grades 6 to 10)

Math-Towers (www.math-towers.ca) is an online resource for students in grades 6 to 10 that supports collaborative problem-solving and investigations. This paper presents the philosophical position motivating the development of Math-Towers and describes how the site presents and motivates the mathematical challenges and supports participants' exploration and collaboration.