Tag Archives: teacher reflection

Mathematics: Facts or Acts? #mtbosBlaugust


This post is me rambling – trying to sort some thoughts I’ve had for a while now. Things I “should” have known and maybe “did” know but still never actually utilized the ideas correctly in my planning. There have been times tasks just “felt right” to use for a lesson, but I’m not sure I was conscientious as to why it fit.

Last spring, I watched a Global Math Department presentation by Juli Dixon (@thestrokeofluck on Twitter) and many things shared had me pondering. I had intentions of revisiting my notes and her blog posts. Well, here I am now.

Her series of posts on Ways We Undermine Efforts to Increase Student Achievement begins with the idea that posting lesson objectives for conceptual lessons may be an unproductive practice. Okay, so then how do I handle that as a teacher? She states that if a lesson is procedural, it is totally appropriate to post the object at the beginning as suggested by Wiliam (2011). However, Conceptual Lessons will have a different look/structure and teachers can present an essential question in place of the learning objective to help with administrative mandates of “posting” those objectives.

Essential questions have seemed so vague to me in the past and that’s because they need to be, a little bit. The steps she shared made me feel like I had a better understanding of how to approach the task of writing a purposeful essential question. Begin with the lesson objective, is it conceptual? If so, what question do we want students to be able to answer in the end of the learning sequence? Then she suggests zooming-out from that question to develop the essential question. Using this essential question in place of a lesson objective at the beginning allows for some sense of the discovery of connections and big ideas. Ahhh. That was one a-ha for me.

The Miss Rumphius Effect shares a post titled: Mathematically Inclined where she shares reflections from The Glass Wall: Why Mathematics Can Seem Difficult, by Frank Smith and this question from Chapter 12:

Is mathematics something we know or something we do?

Her response, “The answer is both–mathematics is part facts and part act. And there is no clear dividing line between the two.”

Hmmm. Me: So which comes first, the chicken or the egg? I’ve debated writing this post, because I find myself pondering and how I don’t have it exactly sorted in my mind, but as I look at lessons, I find myself asking – is the goal procedural, a skill? conceptual, an understanding of a skill/idea? or application/problem solving using the skill/idea to answer a question? Again, I am not sure I ever really “thought” about the differences in the type of tasks needed to address different goals here.

Several years ago, as I was learning about the formative assessment lessons (FALs) from MathShell site, I knew the lessons had different structures, but when I realized why, that was an a-ha for me.

Concept Development lessons are intended to assess and develop students’ understanding of fundamental concepts through activities that engage them in classifying and defining, representing concepts in multiple ways, testing and challenging common misconceptions and exploring structure.  Problem Solving FALs are intended to assess and develop students’ capacity to select and deploy their mathematical knowledge in non-routine contexts and typically involve students in comparing and critiquing alternative approaches to solving a problem.

Mathematics Assessment Project

My current take-a-way, I no longer have to be “bothered” by the admins request to post the objectives, I can modify – zooming out – and share our Essential Question in place of those objectives. @astrokeofluck has provided me with a structure my brain gets in helping me arrive at quality, purposeful EQs. And of course revisiting the EQ will give students a chance to reflect, hopefully see the learning goal and make connections that are most lasting.

And as I plan, I can now feel not-so scattered in my process. By asking myself if we are looking at procedural, conceptual or problem solving (application) – I can choose tasks that are better suited for the end goal of that learning sequence.

I apologize for my rambling, but am open to ideas and suggestions on how you consider some of these thoughts in your own planning process.