CMEF Geometry Curriculum

From MathWiki

This is an overall page for a working group preparing for the Canadian Mathematics Education Forum in Vancouver 2009. The contact person is Walter Whiteley whiteley@mathstat.yorku.ca

Links

Here are a couple of links just to get things started, but we will have more!

  • 1967 Geometry Report Summary is the summary of a longer report on the Geometry Curriculum K-13, by a distinguished panel including Donald Coxeter and W.W. Sawyer. In these times of shrinking curriculum, it is refreshing to reread their proposals.
  • Primary Recommendations is the Primary Level Recommendations of a longer report on the 1967 Geometry Curriculum K-13, by a distinguished panel including Donald Coxeter and W.W. Sawyer.
  • Intermediate Level Recommendations is the Intermediate Level Recommendations of a longer report on the 1967 Geometry Curriculum K-13, by a distinguished panel including Donald Coxeter and W.W. Sawyer.
  • Senior Level Recommendations is the Senior Level Recommendations and Final Recommendations of a longer report on the 1967 Geometry Curriculum K-13, by a distinguished panel including Donald Coxeter and W.W. Sawyer.

Some personal preliminary observations

We have found a number of pointed pieces of evidence that there are no current answers to key questions.

I have concluded, catalyzed from conversations at the weekend conference at Chicago on Geometry and Algebra curriculum, and possible Curriculum/Technology integrating them, (CSMC conference), that the key finding to date is:

- there is a great need for research / conversations proofs of concept, to even find the network of concepts / skills/ activities which we want to include in a good curriculum, and which parts of this are sequenced / closely connected.

We do not have a curriculum to propose. We do not have 'hypothetical learning trajectories' because that assumes some agreement on where we want to end up by grade 12, or grade 14. It would also assume some agreement on the starting points. We do not know the real capacity of children, with and without guidance / technology etc. We do not know the real needs of students and practitioners in many fields in university, college, and beyond. We know so little.

Recent research is confirming obstacles, including some obstacles created or reinforced by gaps in the current curriculum, texts, cultural presentations of geometry. We know that teacher's prior knowledge has an impact on what students will learn and retain, and knowledge of, say, algebra cognition does not impact geometry learning. Is this kind of conclusion suitable for a report in Vancouver:

question all geometry/spatial reasoning curriculum, 
question all neglect and gaps in geometry curriculum, 
question all teacher knowledge of 'geometry', 
question all preparation of teachers and curriculum writers
question all claims of professions about what geometry is needed, 
question all assessments of geometry...

The State of Geometry in our Schools

There is general agreement that the time spent on geometry, and the quality and continuity of the geometry curriculum in the Canadian (and US) schools is in decline.

The recent revisions of the Ontario curriculum have reduced (again) the geometry content.

Teachers in BC are considering a 'Eulogy to Geometry' in response to the new revised Western Curriculum.

Here is a paper I wrote back in 1999, about the general decline (and rise) of geometry in North America:

 http://www.math.yorku.ca/~whiteley/cmesg.pdf

The theme is that geometry will not disappear - it is essential to work in many areas. It might disappear from the MATHEMATICS curriculum, in secondary schools and in Universities, and live in other areas. So the failure is within our conception of Mathematics, in particular the choices being made in mathematics departments (and in the preparation of teachers).

Here is a more recent polemic on Why Learn Geometry. It has been published in several magazines for Teachers (The OAME Gazette and the St. Louis Convergence). This gives, in summary form, some of the same arguments for Why geometry is necessary for our students.

I have chosen to focus on early childhood geometry because I think this is an area where there is the most room for significant improvement in understanding, and in materials/pedagogy. As this happens, there will be pressure on the curriculum and the schools to continue to trajectory and develop stronger geometry curriculum that has a rich set of connections and engages more of the students.