Connections (in response to Praboda's post)

My comment in response to your post got too long so I decided to make a separate post:


I completely agree with you: we're walking in circles and having the same conversation, over and over again!

You brought up several key points in your post. There are two that specifically reminded me of some previous readings:

1."Although reform-oriented mathematics education seeks to de-emphasize procedural knowledge, we certainly cannot dismiss it entirely."

I agree and so do Hiebert et al. (1997).  They had this to say about teaching skills (procedural understanding) and conceptual understanding:

  

In spite of our belief that understanding and skills can and should develop together, we must make it clear that we assume the primary goal of mathematics instruction is conceptual understanding.  But we must also make it clear that setting conceptual understanding as the primary goal does not mean ignoring computation skills (p. 6).

2."If we are to ‘authentically’ promote the notion of interconnected-ness in mathematics, then can we have a curriculum that communicates a high degree of specificity in terms of individual expectations?"

Alan Schoenfeld (2002) referred to this exact point in terms of the Curriculum and Evaluation Standards for School Mathematics from NCTM in 1989:

..the Standards were long on direction and short on detail - it was a vision statement rather than a blueprint.  In hindsight, that was a good thing, for both political and intellectual reasons (p. 15)

He goes on to argue 'no set of curricular recommendations would have been politically viable" and that we would have missed out on 'significantly enriched curricular discourse" among the mathematical community.

Interestingly, Reys and Reys (1998) disagreed with Schoenfeld years earlier when they wrote this:

Ultimately, without clear direction, teachers make their own decisions on the basis of the mixed messages received from the collective forces of parents. fellow teachers, standardized assessments, curriculum materials, backgrounds that their students bring to the learning environment, and their own beliefs about how children learn (p. 237)

Surprisingly, NCTM did get specific by releasing Curriculum Focal Points:

NCTM's Curriculum Focal Points

Personally, I adopted a philosophy a while back to take my cues from my students.  They told me which parts on the curriculum to focus on.  My circle walking days are not nearly over though :-)

References:

Hiebert, L., Carpenter, T.P. & al. (1997) Making Sense: Teaching and Learning Mathematics with Understanding.  Portsmouth, NJ: Hieneman. Preface & Chapter 1, p. 1-15

Reys, B.J., & Reys, R.E. (1998) Computation in the Elementary Curriculum: Shifting the Emphasis.  Teaching Children Mathematics, 5(4), p. 236-241

Schoenfeld, A. (2002) Making Mathematics Work for All Children: Issues of Standards, Testing, and Equity.  Educational Researcher, 31(1), p. 13-25