If you ever question the value of being a mathematics educator, read this:

Much of the commentary on mathematics and science in the United States focuses on national economic competitiveness and the economic well-being of citizens and enterprises… but it is yet more fundamental to recognize that the safety of the nation and the quality of life—not just the prosperity of the nation—are at issue.
— National Mathematics Advisory Panel (2008)¹

We have made progress in meeting those needs, but still have significant work to do.  The National Assessment of Educational Progress (NAEP) shows an overall positive trend in 4th and 8th grade math scores over the last ten years.  Despite this positive trend, less than 40% of 4th and 8th graders scored at the proficient level in 2009.²

The 2007 Trends in International Mathematics and Science Study (TIMSS) also shows progress and room for improvement.  The five highest scoring countries have much larger percentages (two to seven times larger) of 4th and 8th grade students scoring at the Advanced International Benchmark than does the United States.³

We are currently preparing students for many jobs that do not yet exist and to solve problems that have not yet been posed.  We know that the demands our students will face in the future cannot be met through rote-oriented learning of basic procedures and facts. The powerful, meaningful learning that the national and international studies call for involve critical thinking, making sense of problems, and applying skills and knowledge to new situations.4

However, many people have experienced mathematics as a set of rules and procedures that doesn’t necessarily make sense. "Ours is not to reason why; just invert and multiply."  But mathematics truly is the discipline of making sense of mathematical phenomena.  Teaching for sense making differs from the traditional 'presentation and practice' mode of instruction.  There is broad consensus that curricula should help students develop mathematical processes as they learn mathematical content.  Both content and process are essential.  Mathematical processes include solving problems and reasoning, communicating effectively mathematically, making connections, and using various representations fluently.5

Schoenfeld reports that virtually all of the available scholarly evidence indicates that teaching for understanding in mathematics is worth the effort.  "If one teaches for skills, skills will come—but little else.  If one teaches for skills, conceptual understanding, and problem solving, all three will come—and there will be little or no difference along the skills dimensions when you compare performance with instruction on skills alone."6

1 National Mathematics Advisory Panel (2008).  The Final Report of the National Mathematics Advisory Panel.  US Dept. of Education. p. 1
2 The Nation’s Report Card (2010). Institute of Educational Studies. US Dept. of Education. p. 1
3 Gonzales, P. et al. (2009).  Highlights from TIMSS 2007. National Center for Education Statistics.  US Department of Education. p. 16
4 Darling-Hammond, L., et al, (2008) Powerful Learning: What We Know About Teaching for Understanding. Jossey-Bass, San Francisco, CA. p. 2
5 Schoenfeld, A. H. (2008) “Mathematics for Understanding”, in Powerful Learning: What We Know About Teaching for Understanding, Darling-Hammond, L., et al, Jossey-Bass, San Francisco, CA. pp. 113-150
6 Ibid.  p. 133

When the final version of the Common Core State Standards is published, Teacher to Teacher Publications
will post a "crosswalk" from the NCTM, Washington and New Jersey editions of Making Sense of
Problem Solving to those new standards online at:

www.teachertoteacher.com