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.

Heat Transfer in an Airfoil Shaped Strut

The heat transfer from a hot primary flow stream passing over the outside of an airfoil shaped strut to a cool secondary flow stream passing through the inside of that strut was studied experimentally and numerically. The results showed that the heat transfer on the inside of the strut could be reliably modeled as a developing flow and described using a power law model. The heat transfer on the outside of the strut was complicated by flow separation and stall on the suction side of the strut at high angles of attack. This separation was quite sensitive to the condition of the turbulence in the flow passing over the strut, with the size of the separated wake changing significantly as the mean magnitude and levels of anisotropy were varied. The point of first stall moved by as much as 15% of the chord, while average heat transfer levels changed by 2-5% as the inlet condition was varied. This dependence on inlet conditions meant that comparisons between experiment and steady RANS based CFD were quite poor. Differences between the CFD and experiment were attributed to anisotropic and unsteady effects. The coupling between the two flows was shown to be quite low - that is to say, heat transfer coefficients on both the inner and outer surfaces of the strut were relatively unaffected by the temperature of the strut, and it was possible to predict the temperature on the strut surface quite reliably using heat transfer data from decoupled tests, especially for CFD simulations.