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.

Using the interact system model to analyze computer mediated communication during a small group problem-solving task

The Interact System Model (ISM) developed by Fisher and Hawes (1971) for the analysis of face-to-face communication during small-group problem solving activities was used to study online communication. This tool proved to be of value in the analysis, but the conversation patterns reported by Fisher (1980) did not fully appear in the online environment. Participants displayed a habit of "being too polite" and not fully voicing their disagreements with ideas posed by others. Thus progress towards task completion was slow and incomplete.

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.

A HARD PUSH FOR SOFT SKILLS: AN EXAMINATION OF POLICY AND RESEARCH ON NON-COGNITIVE SKILLS IN CANADIAN K-12 SCHOOLING

Non-cognitive skills have caught the attention of current education policy writers in Canada. Within the last 10 years, almost every province has produced a document including the importance of supporting non-cognitive skills in K-12 students in the classroom. Although often called different names (such as learning skills, cross curricular competencies, and 20th Century Skills) and occasionally viewed through different lenses (such as emotional intelligence skills, character skills, and work habits), what unifies non-cognitive skills within the policy documents is the claim that students that are strong in these skills are more successful in academic achievement and are more successful in post-secondary endeavors. Though the interest from policy-makers and educators is clear, there are still many questions about non-cognitive skills that have yet to be answered. These include: What skills are the most important for teacher’s to support in the classroom? What are these skills’ exact contributions to student success? How can teachers best support these skills? Are there currently reliable and valid measures of these skills? These are very important questions worth answering if Canadian teachers are expected to support non-cognitive skills in their classrooms with an already burdened workload. As well, it can begin to untangle the plethora of research that exists within the non-cognitive realm. Without a critical look at the current literature, it is impossible to ensure that these policies are effective in Canadian classrooms, and to see an alignment between research and policy. Upon analysis of Canadian curriculum, five non-cognitive skills were found to be the most prevalent among many of the provinces: Self-Regulation, Collaboration, Initiative, Responsibility and Creativity. The available research literature was then examined to determine the utility of teaching these skills in the classroom (can students improve on these skills, do these skills impact other aspects of students’ lives, and are there methods to validly and reliably assess these skills). It was found that Self-Regulation and Initiative had the strongest basis for being implemented in the classroom. On the other hand, Creativity still requires a lot more justification in terms of its impact on students’ lives and ability to assess in the classroom.