**Initial Thoughts on the CUNY 2012 Mathematics Conference**About two weeks ago, I had the good fortune of attending the CUNY 2012 Mathematics Conference on Effective Instructional Strategies. To a large degree, this is a product of CUNY's Improving Undergraduate Mathematics Learning (IML) program, which in 2009 vetted and funded 10 research programs at various of the school's colleges. Many of the final papers were presented at this conference, and I'll plan to spend several posts presenting some of my thoughts on them -- you can see the final reports here.

As noted in many places, several of the reports, and on this blog previously, at least half our (my) job is teaching non-credit remedial Arithmetic and Algebra classes for students who can't initially pass a placement test for those subjects, and so many of the research projects were looking for ways to improve that teaching. (Again: Nationwide, about 60% of CC students need such remediation, and only about 30% complete it after some number of years.) Interestingly, within the hour of my sitting down to write this, a top AP headline crossed the news wire on exactly this issue: "Experts: Remedial College Classes Need Fixing".

The strategies looked at in the different CUNY research projects were fairly wide-ranging, and usually required total overhauls of the classes in some way. In general, they seemed to usually be one of: (1) group work/project-based exploratory learning, (2) online/software-based homework and exercise applications, and (3) "inverted" classrooms where video lectures were watched before class, and discussion and exercise drills run in-class.

Compare to my previous blog post. On the one hand, the

*American Educator*article by Clark, et. al., on "Fully Guided Instruction" had me thinking that the group-work-exploration craze was petering out, but apparently that's not quite the case. Consider also, say, David Klein's anti-reformist essay "A Brief History of American K-12 Mathematics Education in the 20th Century" (section "Public Resistance to the NCTM Standards"):

I would say that each of these identifiers from the 1990's programs appeared in at least one of the research programs from the IML.To understand the public backlash against the NCTM math programs of the 1990s, one needs to understand some of the mathematical shortcomings of these programs... Student discovery group work was the preferred mode of learning, sometimes exclusively, and the guidelines for discovery projects were at best inefficient and often aimless... Arithmetic and algebra were radically de-emphasized. Mathematical definitions and proofs for the higher grades were generally deficient, missing entirely, or even incorrect. Some of the elementary school programs did not even provide books for students, as they might interfere with student discovery.

At a certain point, one of the speakers referred to Clark's research that expert learners do well with discovery-based methods, and novices do better with fully-guided instruction -- that being the same Clark who inspired my previous blog post (see more here). I was nodding along with this line of reasoning as very important, and then the speaker concluded with the line, "And since most of our students are aged 20-25, they count as experts, and need self-directed methods", at which point I almost fell out of my chair. (If our students can't pass a basic arithmetic/algebra test, then I don't see how it's valid to conclude that they're experts.)

More thoughts later.