Cool math abounds in this new school year as we start our study of linear functions/expressions. Common Core asks students not to only be procedurally strong, but also to be able to discuss and "prove" your answers are sound. I think it said this way..."They make conjectures and build a logical progression of statements to explore the truth of their conjectures." That also matches up with the fact that if you're investigating the truth of your conjecture, you are probably going to uncover questions that are far beyond those that the teacher posed.

Applying what I've learned over the past year and a half about inquiry based learning has been easier than I thought it might be. Students liked this way of learning, for the most part, because it was informal, it gave them plenty of time to talk and catch with their peers and then talk some more for the product. If you can't guess, I work with middle schoolers....talking is a huge deal for them.

I offered several open-ended questions to kickoff the school year...pretty much reviewing the last quarter of the previous grade. Students worked in pairs to answer those questions and pose any new questions they thought were important. They had three days to prepare answers they could give as we discussed each question.....

They brought posters, presented their ideas on the SmartBoard or use the document camera (borrowed one from an ELA teacher). A super cool byproduct of the document camera is snapping pictures of particularly effective presentation pictures. Ones that we can re-use in On the Bell problems or even in quizzes.

It was amazing was to hear students talking math and using math vocabulary. This was a much better review plan for me because I watched them work alone and in their partner.

I could immediately tell

- who would be good partners and who might need to be encouraged to pick a different partner next time
- who was understanding the ideas and who didn't understand
- who could do the computational part of the assignment but didn't really know why it worked and couldn't explain.

I came away with a very comprehensive view of the 160 students in my classes...and it really only took 5 class days. Students did invent lots of their own questions and they started to see how they can and should test out their ideas by solving a practice problem or two.

I've now taken all that data, entered formative marks in the gradebook along with specific comments so that parents will know where their student is starting from...and developed lesson plans. I can tell that when I give the pre-test, I will probably have a big percentage of people who demonstrate mastery of the unit before I even start. I will have another big group of people who have almost no idea what I'm talking about.

So at the end of my 6th day of school, I think I've collected enough data that I can effectively ability group, target lessons to reteach the places where there are holes in the previous year's learning and to project out the new learning we need. Who knew that exploring the truth of their mathematical conjectures was going to be interesting?

I teach "Application of Number" to adults and teenagers UKside and was very interesting to see in your standards link the bit about "...

perseverein solving them." (my emphasis)This is a big issue with our learners and not really reflected anywhere in our syllabus. How do you measure/encourage that? (And find the time!)

Posted by: Ourlearning.wordpress.com | August 28, 2012 at 05:26 AM

What a wonderful course....Application of Number!!! It sounds so intriguing and if I was closer I'd enroll.

To start off with, I think it's a subjective thing. And while you can describe it, it never going to be something that you can truly measure.

I guess I start off by talking with students about their ideas and getting scenarios they think demonstrate that quality. Sometimes they reference a sports thing where they thought they couldn't sink 5 free throws in a row, but they practiced and then they could. We sort of group-think our way through what that might look like in math.

As we go through the year, I keep up the teacher feedback chit-chat about how they are "this close" and pinch my fingers together....and how they are on the right track if they don't give up. As odd as this might sound, just that kind of direct encouragement really makes them trust me because they know they're going to figure it out soon or that I will bale them out. I usually do this when they are really just on the verge OR if I know they're at that tipping point of frustration and they know I'll give them a hint that will get them over the hump.

Lastly with my higher performing students, I do lots of think alouds and give me another way. Actually in my rubric, it specifically addresses problem solving strategies. Did they solve it one way and then try to get the same answer using a different strategy? That's particularly useful where my students are....they can use guess & check to figure out the answer, so this way I ask them to try using algebraic reasoning to find the same answer. By the end of the year, they can often find 2-4 different ways to solve the same problem.

While this isn't exactly persevering....it builds those same endurance muscles. And I can more objectively measure how many strategies they tried.

Does that help? What have you thought about doing to build these skills within your learners?

Thanks for dropping by and leaving a message. It's always great to hear from someone.

Posted by: Marsha | August 28, 2012 at 05:42 AM