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.

Prudent Budget Planning and Budgetary Process Effectiveness: The Canadian Federal Government’s Experience (Working Paper 47)

In 1994, the Liberal government introduced a structured approach to prudent budgeting to provide the fiscal discipline needed to meet its debt reduction targets in which explicit prudence factors were introduced into the fiscal framework to reduce the amount of fiscal flexibility available for allocation in each annual budget. Although that framework was successful in contributing to the elimination of persistent budgetary deficits, this paper advances three linked arguments: • that additional but undisclosed prudence factors were also introduced into the fiscal framework to attenuate the political risk of missing budget targets; • that these undisclosed prudence factors are one cause of a number of unintended budgetary outcomes that put the effectiveness of the budgetary process at risk; and • that there is nothing inherently politically partisan about the Liberal’s approach to prudent budget planning and, changes to terminology and display notwithstanding, the present Conservative government has continued to apply most elements of that framework in its budgets. Moving from a single-year budget target to one that is expressed as a cumulative total over the election cycle is discussed as one option that would help preserve the merits of prudent budgeting.