Planning for Discovery

As an educator, I have been very lucky.  I have been blessed with an abundance of game changing opportunities:  planning time with teachers of the same subject and grade built into my regular schedule, access to mentors and math coaches who have worked with me side-by-side in my classroom, and plenty of choices in accessing meaningful and timely professional development.  

In that common, scheduled time with my school-based professional learning community or PLC, teachers meet and plan together with student achievement at the core of the work.  We have guiding questions that frame what we do so everyone comes to the meetings with similar intentions and a common purpose.  These questions are:

What am I teaching?
Why am I teaching it?
How will I teach it?
How will I know if students have learned it or not?
What is next…if this works?  If it doesn’t work?
Where do I go for help?

At the start of a professional development session, we might also hear or be reminded of these same guiding questions.  During staff meetings we are sure to hear these questions again, and without a doubt when we meet to problem solve ways to engage and inspire students that have yet to meet targets, you better believe these questions will show up once more.

It was no surprise then, that on the first day of a new course at Mount Holyoke College these guiding questions seemed to resurface.  Jan Szymaszek, one of my favourite teachers of all time, started asking those same questions that have been at the center of my planning, and the focus of my professional learning community:

What do I want my students to learn?
Why do I want them to learn that?
How am I going to make it possible for them to figure it out for themselves?

Wait what?  What was that last line again?

I stopped…literally frozen in time.  It is not an exaggeration for me to say that I felt like everything around me took on a new and exciting glow.  That guiding question was different…and in such an important way.  While I know and have known that offering chances for discovery have lasting effects on understanding and retaining new ideas, I did not approach planning with this idea as a core component.  Discovery happened for sure, but planning for discovery was different. It was intentional.  Impactful.  Powerful.  This was the focus question that I needed to bring to my planning each and every single day.  This was the question that would change everything for me.

Jan kept talking in that lovely soft, curious, warm and inviting way that she does, oblivious to the fact that she had just blown up my whole thought process and changed my mindset forever.  I am sure it looked like my screen was frozen for the next ten minutes with a dazed and crazed look on my face as I thought about how this idea would fundamentally change how I operated, how I planned, and how my students learned.  I did not hear the rest of her list, or really anything else for a solid chunk of time as I let that idea and everything it entailed wash over me and take hold.  When I finally refocused and tuned into the class conversation, our other amazing facilitator, Zak Champagne, was in the middle of his humble brag that his previous class claimed, “…he didn’t teach them anything all year!  He just happened to be there when they figured things out.”  Yasssssssssssss!  That’s it.  That’s my new goal, my new focus:  planning for discovery.

I started thinking about this amazing program I was in at Mount Holyoke and realized that so much of the content and organization of my classes were conducted in this manner.  Course creators and facilitators designed and selected activities that would lead participants to notice and wonder.  We could make conjectures, test theories, prove with representations, extend to other number domains, then reword generalizations as new information gets consolidated with previous knowledge.  Facilitators did not tell us the answers to problems.  We examined and discussed student work, ideas and conversations but they didn’t tell us how to teach content.  They were planning for discovery. 

So how does this translate into my daily practice?  Well here’s a quick example from something on deck for this week.  Halving and doubling.  A great computational strategy when opportunities to use it are recognized.  

One way to introduce this concept to students is to simply show them: 
Hey kids!  Did you know that 18 x 5 has the same product as 9 x 10?  It does!  In fact anytime that you have a multiplication problem to do you can take half of one factor and double the other factor and the product stays the same.  Isn’t that cool?  Let’s test it out and practice with these examples!  

If I am planning for discovery, however, I would approach this idea differently.  I might have students give all the factor pairs that have a product of 100.  (…or another product. I like 100 since the factor pairs might be easy to access for many and we can focus on the upcoming strategy without getting bogged down with unfamiliar facts)

1 x 100
2 x 50
4 x 25

5 x 20
10 x 10

I might record what students share this way so that the pattern is easier to notice.  Then I might ask if they notice anything?  Is there a pattern? Students will notice that, “one side doubles and the other side gets cut in half…and the answer stays the same!”  I’ll record their noticings using their words.  I might wonder if there is a way to represent what is happening with a picture or context.  Or wonder if this only works for a product of 100.  What do we think?  Some students will start scrambling to test other products and draw pictures while some might need more direction.  Why don’t we test other possibilities!  I’m going to test a product of 36.  You can choose another number if you like…

As we go, I might ask if this works for other numbers as well, or only certain products.  I might ask if this only works for multiplication. Does this only work with halving and doubling…does quartering and quadrupling work? What about taking a third then tripling? Whole numbers only or will fractions and decimals work? My questions might be for the whole class or might be for particular students depending on what they are ready to investigate. I might wonder when or if this information is useful.  I might present some carefully selected examples and ask if or how we could use our generalization to change these problems to equivalent problems.  Why might we want to change them?  Letting the students test and check and play.  Letting them discover.  Being flexible with how far we get that day in the process and being open to letting students take an unproductive path before embarking on a new route.  Letting kids share what they learned and what they still wonder about. Planning for discovery.

It may seem as though planning for discovery is more time consuming than simply telling students how to do something and hoping they trust your expertise and take your word at face value.  But do we want that?  Compliance over engagement? Will students be able to recognize opportunities to use this strategy without the notice and wonder?  Maybe…maybe not.  What I do know is that there is no better feeling than being present when a student makes a discovery for themselves.  That satisfied, confident look when they notice, test, and confirm the patterns they see in their own examples.  When they compare notes with their buddies and decide something works every time – I can prove it!  Lighting kids up with discovery beats any regurgitation satisfaction every day of the week.  And deep understanding that comes from digging into the content and testing your own examples?  Well that’s the stuff that sticks.  

My new guiding question is really just an important edit of what I have been using for years.  Instead of, “How will I teach it”, I think, “How am I going to make it possible for students to figure it out for themselves?”  You know – planning for discovery.

I laugh when I think about that moment when Jan said those words that shifted my focus. I have yet to find out how she finished that list of questions.  But that gave me another insight.  When your words have a deep impact – your students might not hear another word that day.  Big ideas need time and space.  You will repeat yourself – and not because students weren’t listening.  Maybe…just maybe (and this is what I choose to believe) you are repeating yourself because the impact of your words just changed everything.

My big moment

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