Wednesday, February 17, 2016

The Three Part Lesson Mindset

We are often taught that there is a "thing"', a lesson plan, a framework, perhaps, called "the three part lesson". I discovered this video here, from the project I was involved in, offers some plain talk and background on the three part lesson, from Lucy West, Marian Small, and others.

It's mentioned in the clip that perhaps it's an Ontario thing, but it has its own Wikipedia entry, and John van de Walle is credited with coining the term. 

When people in jobs like mine get pushback from teachers about how difficult, unwieldy, and time consuming it is to teach through the three part lesson, I often think, "they''re going about it wrong." We do get this kind of pushback-I have seen it myself in social media groups, comments along the lines of, "don't even get me started on the three part lesson!" 

I don't blame them. Classroom teachers do a lot, and to be fair to teachers, designing a minds on/working on it/and consolidating the learning sequence for EVERY single lesson is probably impossible. That said, as the Ontario curriculum has it, "problem-solving is the mainstay of mathematical instruction"", and we are obliged to structure our teaching through interesting problems.  

It's probably more useful and humane to think of the three part lesson as a mindset in itself. 
Our math coordinator, Mary Fiore, has been making this point for a long time. 

As she says:
Here is how we like to talk about this mindset:
Don't think in terms of a set lesson plan, with time-bound sections. Activate student thinking with something interesting-something that inspires math to happen. If they explore this problem for an hour, a day, or even three days, so be it. Go where they take you. Watch and listen, and plan where you want to go next in your instructional sequence. Take note of any misconceptions you need to give lessons on.

Above all, a lesson is only as good as its consolidation. Think about how you want to discuss the math at the end of the task.  Consider whether your students will be sharing their work out loud, if you will be directing the consolidation, or if they will. Be purposeful and responsive. Teach through the three part lesson mindset!

Friday, February 5, 2016

Have a Goal for Each and Every Math Class #assessment #curriculum #intentionalteaching

I once laminated a few cards that I thought I would put up at the start of each class. I had thought that there were only a certain few types of things we would be doing in any given class: explore or investigate, consolidate learning on a concept, or practice with a skill or concept.

The reality of the middle school teacher is often 40 or 45 minute periods. You need a clear learning intention for each class. Broadly speaking, you might be said to be in one phase of a three part lesson too, although we can classify those three actions as:

-activating thinking
-developing thinking
-consolidating thinking

By that measure, you might argue you are always in one phase of the three part lesson (primary, junior, or high school teachers might find you can make it through an entire iteration of a lesson on a given day).  I like the plain talk on the three part lesson from Lucy West, Marian Small, and others, in this clip.  It's a mindset, not a lesson plan, as my friend Mary always says!

We have spent a lot of time thinking about how best to use learning goals in the math classroom, and I think, regardless of how you do it, you must have clear intentions for each class. Whether you post the learning goals at the beginning, articulate them verbally, or develop them as you go, be intentional.

We must always be accountable to the math that the curriculum requires of us. Further, Growing Success asks those of us in Ontario to be accountable to the overall expectations in the curriculum. 

Further, we must have thought about the progression of learning. Is it a brand new concept? Building on something in previous grades? Is it best suited to investigation? Problem-solving? Is direct teaching needed, perhaps a mini-lesson, or small group guided instruction?

Here is an example of an overall expectation from grade 7, on integers, and some thoughts about it.

-represent, compare, and order numbers, including integers
-demonstrate an understanding of addition and subtraction of integers

What does being accountable to this expectation mean? What instructional actions could  you take? Depends on your class culture and context, but here are some general ideas, and one possible lesson sequence. Let's assume each of these is one class, of whatever length that is.

-explore contexts for integers, such as temperature, sea level, elevator floors, etc.
-make a human number line to explore counting in the "opposite direction"
-explore the concept of plus/minus in hockey (*only if hockey is a good and meaningful context for your class*)
-explore the idea that each integer has an opposite by using two colour chips to make zeroes (the zero principle)
-use number lines to add integers
-use two colour chips to add integers
-explore contexts for subtracting integers-  how does it work, to take away a negative?
-use two colour chips and the zero principle to subtract
-do some practice work on adding and subtracting (games, worksheets, etc.)
-play Integer war with cards to practice
-explore some interesting problems using contexts for integers
-attempt to reason through some generalization problems- is a negative subtract a negative always negative?, eg.

Implicit here is that lots of observations, conversations, and paper and pencil checks for understanding will happen. That's a possible 12 classes, barring the fact that some could expand past one day, and also barring any quizzes, tests, larger projects, or evaluation pieces.

Each of these could be turned into a nice neat learning goal, and you could certainly develop success criteria for this sequence with your students. What matters is approaching each and every class with an intentional goal, staying accountable to curriculum, and knowing your students.

Thursday, February 4, 2016

Do They Understand It? Just Ask! Assessing Math Through Conversations

In doing some reading about teacher efficacy, I found the above quote, from a teacher who participated in mathematics professional learning.

This is a recurring theme for our teachers. It comes up, again, and again, and again.

We recently facilitated professional learning which included looking at student work to try and figure out where the students were at in their mathematical thinking. I talked to one teacher for almost 10 minutes, trying to figure out what a student was thinking with a piece of work. We had our inferences, but really, we need the kid there to ask him. It would have been cleared up, just like that.

If you want to know what a student is thinking? Ask him. Ask her. As I went around the room that day, a big theme was: don't you just want to go back and ask some clarifying questions?

Gone are the days when the paper artifact of the work was assumed to tell us all we need to know about student mathematical learning. Look for the absences, look for the gaps- and ask. Ask the specific questions you need to ask to get at their mathematical understanding. I would have to say we are obliged to do so- Growing Success tells us to assess through conversations, observations, and products. I have been less and less interested in products over time. In the moment and current thinking in the math classroom is far more interesting to me.

Don't be content to give grades based on the absences, gaps, or lacks. Ask questions. Listen for the answers. Seek understanding. Seek it, and, usually, you will find it.