Two steps for incorporate PBL learning in math class

I've been thinking, experimenting and testing out ideas about how to move math instruction forward in my classroom, using technology and Problem-Based Learning (PBL) as much as I can.  It's a daunting task even if I've done it before in science....very different set of inputs and outputs in a math class.

I've also been wondering what "Teaching in the Age of Siri" really means.  I believe we have students who believe they can Google the answer to anything that is asked.  When they run up against questions that aren't Google-able, it stumps them.

This week, I gave students pretty tough problems about functions that involved square roots.  They really didn't know anything about square roots.  So rather than just telling them....I took a bit to explain that we were going to learn what to do when you can't find the answer on Google or have a friend tell you.  I gave them 10 minutes to find everything they could about a square root that seemed like it might help answer the two-part question I gave them. 

Update from 12.06.12--- I'm inserting a little revision in here to clarify what I first wrote about last week.  I received so many requests for the problem, I thought I'd post it here in addition to leaving it in the comments.  I also think I may need to restate that it is really two questions.  Knowing about square roots help with answering both questions which is why I called it a tw0-part problem in my original writing.

The problem they were solving is really pretty simple

x----> SQRTx    and the second problem was

 x----> SQRT ABS(x).

For these problems, they had to define what inputs, if any, were not valid.

Connecting it to the real world...(educational-speak would be career-ready skills)

I wanted to connect it to the real-world and explained that rarely have I had a boss/supervisor that takes the time to show me how to do my job....most of the time, they expect me to know how already.  That was very puzzling for my students.  Why wouldn't my boss help me, they wondered?  It wasn't until I explained that bosses (or at least the kind I've had) hire me to do something that they I can either already do or that I'm smart enough to teach myself.  It wasn't that they were being mean to me.  In fact it was the opposite, it was that they had confidence in me to solve the problems of my job assignments.  That was a huge flip of a circumstance.....something none of my 8th graders had considered before.  I assured them that I wasn't going to suddenly assume they knew all of algebra and be like my boss, but the experimental learning style we were about to do was a first step towards being that kind of independent learner.

They used laptops, the Algebra references books I have in the room, the textbook, notes that I have given throughout this unit, their phones and some even asked Siri for help.  I really didn't care where or what they brought back to the table.  Then I led them in a class discussion about what they thought was relevant in all that they found to solving the problem.  Once the class decided (and I have to tell you that they learned a ton that they didn't need to know but was just there for the learning) what was most helpful, we started a discussion about what do you do now that you've found info that could help you solve the problem.

Honestly....I don't think many of them have ever thought about that kind of reasoning.

Turning found info into useful knowledge and something that solves the problem

And they really loved it....they argued and wrestled with all the info they collected and then built their conjectures.  After conjectures they had to use evidence from "tests" they could run with their graphing calculators to see the info they found matched up.  My role wasn't to teach...it was to coach them.  I helped them realize that once they had info NOW they had to something with it. 

It's a bit like taking a recipe and a bunch of ingredients...and creating delicious cookies.

And that was thinking...tying all the little discrete factoids they had from prior knowledge and this mini-research into a new problem.  Eventually they correctly solved the problem....along the way we discovered way more than the single answer to the two-part problem. I think they'll probably retain the info better.

I realized most of all....they need some hand-holding and practice as they learn how to take "found" information and "think it" into meaning.  I'm definitely doing this again....try to refine the process and sharpen it.  This isn't all the way to PBL yet.  But I think it's the foundational shift of responsibility for learning onto the student's shoulder that will be a precursor for doing a full-blown PBL or maybe a STEMy kind of lesson.

http://www.morguefile.com/archive/display/541092 ---map picture

http://www.morguefile.com/archive/display/83127--- recipes

Comments

[David Sundstedt]

What was the given problem?

[Philomena Hughes]

Can you tell us more about the actual lesson?

[Krista McKeague]

Great blog! What was the question that you asked them?

[Julie]

What was the two part question you gave them to solve?

[Blaisej]

Hi Marsha,

Thanks for writing a very interesting post. I would be keen to see the two-part problem to which you refer in order to get a better sense of what the students were up against. As well, what age are the kids in your class? I realize that you are presenting here a more general approach to problem-solving but I am interested in the specifics as well.

Thanks again,
Blaise

[Cara]

Hi, I'm gearing up to teach my students about square roots and exponents after the break. I also have 8th graders and they're learning algebra. I love the lesson on self-directed learning that you incorporated! Would you mind possibly sharing with me the resources you used or are using for this?

[Jarius Jones]

When I opened my school email this morning, I noticed your article in the Dec. 5th NCTM SmartBrief and became interested; especially when I saw the name Marsha Ratzel. You and I served on the committee for the Center for Teaching Quality in KS several years ago.
I found this article to be quite intriguing; particularly, the way in which you challenged students to search for information they needed in order to make sense of a concept(s) they may be unfamiliar with. Presently, I am the Teacher Leader (fka Instructional Coach) at F.L. Schlagle High School in Kansas City, KS. For the last 2.5 years I have wondered/brainstormed ideas that may elicit improved and increased engagement in Math classes, but I've managed to only think of a few options that seem to help with certain teachers. However, your strategy seems to be effective regardless of the personality or experience of a teacher, which is what I encounter throughout my daily practice of coaching.
Sorry for the long response, but I am so proud of your success and innovation. Thank you for sharing with the rest of the educational community your professional expertise.

[Cindie Donahue]

I loved hearing about your experience. What was the two part problem that you gave them?

[Roland Roberts]

You're killing me...what was the problem you had them work on?

[Natalie House]

Thank you for posting this. I have been struggling with how to incorporate PBL into math. It was easy when I taught science, but math seems to be a different beast when designing work.

[Marsha Ratzel]

Thanks Natalie for your comment. I agree it has taken a bit of thinking and re-designing to figure out how to apply that empowered learner model (ie PBL) to math. It's worth the struggle I think.

[Marsha Ratzel]

The problem they were solving is really pretty simple

x----> SQRTx

and the second problem was

x----> SQRT ABS(x).

For these problems, they had to define what inputs, if any, were not valid.

[Marsha Ratzel]

Dear Blaise,

My students are 12, 13 and 14 year olds in 8th grade. They come hetergenously mixed ability classes and we use a inquiry-oriented, real-world problem based math curriculum.

Do you work with math students? How have you tackled this problem of finding information but not knowing how to use it for solving problems?

[Basil]

Great job! I'm attempting to shift my students to a PBL enviornment; however, they have been instructed traditionally much of their lives. It's been a struggle so far, but we are getting there.

[Josh]

School online should make a way on how to really work things out in teaching. Math is a hard subject and should be really taught well on students.

[dissertation writing service reviews]

This is a good way of learning. This can surely nourish students mind especially in mathematical skills which is actually the most important thing to know about.