“One of the participants in my Making Sense in Algebra 2 workshop had an interesting criticism. That anonymous participant pointed out that I presented no coherent pedagogical framework for the activities I shared. Good point! I did not present a coherent [pedagogical] framework because, well, I do not have one to present.”I was puzzled. Which coherent pedagogical frameworks was the participant referring to? Webster states that a framework is a basic structure underlying a system, concept, or text. For math education that structure is a curriculum. Pedagogical refers to the myriad of approaches that a teacher can take in presenting a curriculum to students. And a coherent pedagogical framework would be a pedagogical framework that made sense. So conjuring up the meaning of those three words together Henri continues with why he doesn’t have one to present.

“During my four-plus decades in the classroom, I've seen many math edu-fads come and go: new math, individualization, manipulatives, problem-solving, group work, constructivism, constructionism (yes, that's a thing), portfolios, complex instruction, differentiation, interdisciplinary-ism, backward design, coding, rubrics, problem-based instruction, technology, Khan Academy, standards-based grading, making, three acts, flipping, inquiry learning, notice-wonder, growth mindset... not to mention various generations of standards.”So instead of following some fad-like frameworks, Henri says:

“We need to be eclectic, and select "what appears to be best in various doctrines, methods, or styles." Instead of rejecting the fads wholesale, we need to consider each one as it comes along, as all (or almost all) have some validity. Instead of shutting our classroom door and continuing business as usual, we should keep it wide open. Without becoming a dogmatic across-the-board adopter of each pedagogical scheme, we need to learn what we can from it, and incorporate that bit into our repertoire. This is how we get the sort of flexibility that makes for good teaching. If we do that, our lessons will not fit a standard mold. Quite the opposite: they will depend on the myriad variables that make teaching such a complex endeavor.”I too like Henri have spent more than 4 decades working in math education. I’ve also worked with many of the edu-fads he mentions. In my private school teaching days I eclectically developed my own curriculum which included lessons borrowed liberally from Harold Jacobs’ “Mathematics: A Human Endeavor.” In fact, Harold’s work helped me to develop a coherent pedagogical framework - a classroom strategy model - that served extremely well in my modeling how to teach coherent lessons to the teachers I worked with. My model went something like this.

Each lesson (approximately 45 minutes) had three parts.

The first part I called:

**Set the Stage**. This part would motivate the activity that followed. (I never wrote objectives on the board.)

The second part was:

**Do the activity**. Students would usually work in groups. They would discuss and record their findings on a handout I would give them. (See 5th grade example.)

Finally (and maybe most importantly) was

**Debrief**. What did we learn today? This is where the objective is revealed or left open for further noticing, wondering and even debating.

This was the model I used with teachers who were teaching math in conventional ways. For teachers who were interested in exploring more innovatively, I also modeled a collaborative project approach - usually referred to as Project Based Learning (PBL) which was an edu-fad back in the 1920s, but recently is undergoing a revival according to the Buck Institute. What I like about PBL is that it takes into consideration student interest. My example of PBL is the Noon Day Project which is a recreation of the measurement of the earth done by Eratosthenes in 200 BC. See my blog entry about it here.

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