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.

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