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.

An exploration of students’ perceptions and attitudes towards creativity in engineering education

This study used a mixed methods approach to develop a broad and deep understanding of students’ perceptions towards creativity in engineering education. Studies have shown that students’ attitudes can have an impact on their motivation to engage in creative behavior. Using an ex-post facto independent factorial design, attitudes of value towards creativity, time for creativity, and creativity stereotypes were measured and compared across gender, year of study, engineering discipline, preference for open-ended problem solving, and confidence in creative abilities. Participants were undergraduate engineering students at Queen’s University from all years of study. A qualitative phenomenological methodology was adopted to study students’ understandings and experiences with engineering creativity. Eleven students participated in oneon- one interviews that provided depth and insight into how students experience and define engineering creativity, and the survey included open-ended items developed using the 10 Maxims of Creativity in Education as a guiding framework. The findings from the survey suggested that students had high value for creativity, however students in fourth year or higher had less value than those in other years. Those with preference for open-ended problem solving and high confidence valued creative more than their counterparts. Students who preferred open-ended problem solving and students with high confidence reported that time was less of a hindrance to their creativity. Males identified more with creativity stereotypes than females, however overall they were both low. Open-ended survey and interview results indicated that students felt they experienced creativity in engineering design activities. Engineering creativity definitions had two elements: creative action and creative characteristic. Creative actions were associated with designing, and creative characteristics were predominantly associated with novelty. Other barriers that emerged from the qualitative analysis were lack of opportunity, lack of assessment, and discomfort with creativity. It was concluded that a universal definition is required to establish clear and aligned understandings of engineering creativity. Instructors may want to consider demonstrating value by assessing creativity and establishing clear criteria in design projects. It is recommended that students be given more opportunities for practice through design activities and that they be introduced to design and creative thinking concepts early in their engineering education.