Mathematical Discoveries - Small and Great
Mathematical discoveries, small or great, are never born of spontaneous generation. They always presuppose a soil seeded with preliminary knowledge and well prepared by labour, both conscious and subconscious.
- Jules Henri Pointcare
Purpose of the study
The purpose of this study was to investigate the pervasive and ever elusive wonder of those who teach mathematics: how do we best meet the needs of a group of diverse learners in a classroom community?
Brief description
This research occurred in three school communities and involved student in 12 classrooms, 12 host-teachers, 3 principals, 2 numeracy co-ordinators and the SWST. The research was structured to honour the successes and findings of the previous year's Student Work Study project which included working with an entire division within a school. Qualitative data that was used during the iterative process of continuous collaborative inquiry was collected in classrooms through observations, conversations, student work samples, annotated photographs, video, and interviews.
Analysis
Some of the key/pivotal findings that have emerged from our work together include:
- A divisional book study of a carefully chosen text (Number Sense Routines, Shumway, 2013) that is combined with the Student Work Study Structure of observation, documentation, close examination of students work, is a very effective vehicle for building teacher's pedagogical content knowledge and specialized mathematical content knowledge and knowledge at the mathematical horizon (Ball, 2008).
- building of knowledge of mathematics content allowed for teachers to be able to be more precise in assessing student knowledge for and as learning. In our work, teachers' new knowledge led to the creation, application and refinement of a screen for the early number sense learning trajectory.
- collaboration within divisions began with the mediation of the SWST was powered by the harnessing of student voice and work, created excitement, confidence and developed the productive disposition in teachers which led to the incorporation of new pedagogical approaches and strategies.
- Responsive instructional practices have resulted in the creations of rich mathematical learning environment (i.e. increased use of manipulatives and different representations - rekenreks, five and ten frames; technology to record student thinking - iPads video capture, annotated photographs; more flexible groupings and different forms of small group instruction)
Implications for further study
Questions that remain at the end of this research cycle include:
- Would continued professional development that occurs in the format help to minimize in-school variance in students' mathematics education?
- Would such rich learning for teacher which impacts students' learning and productive disposition continue if it wasn't mediated through divisional groups?
- Is it possible for a principal to lead such a structure?
- How do we sustain the growth that we have experienced this year?
References
Loewenberg-Ball, D., Hoover Thames, M, Phelps G. (2008). Content Knowledge for Teaching, Journal of Teacher Education 59, 389–407.
Shumway, J. (2011). Number sense routines: Building numerical literacy every day in grades K-3. Portland, Me.: Stenhouse
Shumway, J. (2011). Number sense routines: Building numerical literacy every day in grades K-3. Portland, Me.: Stenhouse