March 30, 2014

Project Based Learning - My Questions


Oh good, did you like that image and follow it here from twitter or Pinterest?
Were you thinking I was going to give you a lovely list of bullet pointed answers for all those questions?
HA! Not a chance! I don't have those answers!
But I would like to invite you to stick around, continue reading, and contribute your ideas.

All edits and updates will be in red.

*I'm attempting my first full PBL experience - Eekkkk!!! Wish me luck!!! Even if I don't soar on this one, at least I'm headed in the correct direction, right? I'm focusing on having a "growth mentality" like Tim talks about HERE. I'll chronicle my journey in this post.

This post might ramble and meander a bit; my thoughts are not completely formed yet and I'm sure that will show...

I'm not content with my current level of technology integration. I recently posted an update on my workshop/stations model and it really has me thinking. These stations are helping lots of students, less are falling through the cracks, but it's all in the context of a very teacher-directed atmosphere. I do not do stations every day, we recently did a volume investigation with rice, but I still feel like that was more me-centered and student-centered than I would like.

I've read a lot of articles about project-based learning and really want to move towards that model, but I just can't quite figure it all out. I'm hoping you can help me think through these questions and together we can figure it all out. I'll update this post over time (a thousand times if I need to) if we can start a conversation and pull together resources. I'd love to host that! I think it'd be beneficial for a lot of teachers!! Or if someone is already curating and hosting that, please point me in their direction and I'll jump on that wagon. I just need to see this thing in motion; I need to see it working.

Here are some current questions/thoughts rattling around in my head:

-- I can begin a unit/project cycle with an entry event that peaks the students' interest and gets them curious. It needs to be a real and relevant problem that is understandable to 8th graders and yet complex enough to require driving questions and a real solution.
Emergent Math's PBL Curriculum Maps HERE
Intel Unit Plans HERE
PLB U by Buck Institute HERE 

--After peaking their interest, I can lead a discussion to provoke some driving and enduring questions. Here is my first conundrum. If I want these questions to be student-created, what if they don't think of the right things to allow for enough mathematical discovery? I guess I could prompt/lead them? I should make sure my entry event can lead to enough? So in reality these questions are not completely student created, I knew what I wanted them to create, I just let them get there on their own without me giving them here are your questions to answer. Right??
Conversation with @RossCoops31 on twitter regarding driving questions:
ME Do different students work on different driving questions or do all students answer the same few questions?Thx!
ROSS: I usually do one essential (driving) question that is decided upon by my class (Google Form).
ME: So do all finished products cover relatively the same information? Do you have Ss work individually or groups?
ROSS: Either group/individual works! All products different, but demonstrate same understandings.

--Now that we have our guiding questions I will give my students the requirements of the project. "In X many days you (or your group) will be responsible for _____." This will be some sort of synthesis of information and presentation that utilizes technology and is published to a global community, I'm thinking a blog. Wouldn't the best way to give these requirements be a rubric? Does someone out there already have and use a wonderful rubric that I could see?
Rubrics from the Buck Institute (
Project Design Rubric HERE
Collaboration Rubric HERE
Critical Thinking Rubric HERE
Creativity and Innovation Rubric HERE

--Alright, so students have their interest piqued, they are genuinely curious, they have formed their questions, and I have given my rubric. Now they research and synthesize and create. I roam around the room for however many days it takes to finish up these projects, giving feedback and guiding, and then students present. I really like the following quote from the Buck Institute for Education regarding this phase: In real inquiry, students follow a trail that begins with their own questions, leads to a search for resources and the discovery of answers, and which ultimately leads to generating new questions, testing ideas, and drawing their own conclusions. With real inquiry comes innovation - a new answer to a driving question, a new product, a new solution to a problem. The teacher does not ask students to simply reproduce teacher- or textbook-provided information in a pretty format. Are you inspired yet?!?! I know! There are so many great resources like the Buck Institute that make me want to jump in with both feet but I have trouble finding real teachers talking about doing this in their classrooms. I feel like I'm moving that directions, using Mathalicious and 3-Act Math and similar things, but I don't think I'm quite there. These are engaging and definitely better than traditional lecture, but I'm not pulling off a true PBL classroom.

This is one of my largest question marks at this point. How big of a problem do I really need? I feel like the lessons at Mathalicious and YummyMath and Robert Kaplinsky aren't big enough. They have pre-determined questions and a set order of business. These are fantastic problems, but I don't think I'm letting the students really ponder, inquire, and direct their own learning. People doing this, what types of tasks do you use? Are they on a blog somewhere I could see?? 

--Sorry, little bit of a tangent there, back on track.

--So students have created and presented, to both their classmates and a global community online, and I've made sure we've nailed down all the mathematics that were needed throughout this unit. I figure at this point I might have a day or two of formalizing. Here is how mathematicians write about/talk about/use the ideas we all just learned about.

--So did we do it? Are we done? Was that Project Based Learning? Is that how my units can all look in the future?  How long should one of those cycles take?

Here is where I definitely need your help!
Are you currently doing this? Do you know someone who is? Do you have any rubrics created that you'd be willing to share? Do you have any of those entry events that are large problems and could facilitate lots of mathematics? Can you share about part of this process that I completely missed the boat on? Please share your thoughts, ideas, wisdom! Please!! This is an area I'm very unsure about (as if you couldn't already tell) and I'm definitely leaning on my PLN here.

If you don't have anything to share, are you a teacher that is also hesitant and curious about this whole process? Could you please comment and let me know I'm not alone! :) Maybe a few of us together can convince those with the answers to share the goods. I promise to come back and update any useful information I receive.

Other teachers' comments/emails:
Ben Mahas (@greenemiddle) posted on twitter: "Help answer @MrsHestersMath questions are about implementation of pbl. I'm interested as well #mtos #mathchat"
Shelley via email to me: Thank you for your post about PBL. I have many of the same hesitations and have been looking for a place where someone is sharing what really works in a classroom. I hope you can get some answers to those questions and thank you, in advance, for posting those answer.
Rick via email to me: I have a lot of the same project based leaning questions. Thanks for the post. I'm right there with you. You're not alone!

So - those of you with some expertise, please share!!!!

Some Twitter People to follow for PBL
Buck Institute for Education @biepbl
Geoff Krall @emergentmath
Michael Gorman @mjgormans
Dayna Laur @daylynn
Chris Fancher @cfanch
Jerry Blumengarten @cybraryman1
Mrs. Telannia Norfar @thnorfar
Ross Cooper @RossCoops31
Jolene Speckman @JoleneSpeckman

Some General PBL Links
Edutopia's page HERE
Buck Institute HERE
Buck Institute's Recommendations for Teachers HERE
Jerry Blumengarten's page HERE
High Tech High HERE (a school pulling this off on a very large scale!)

March 25, 2014

Math Stations - Update

Well, I've been using stations for a few weeks now and wanted to post an update and ask for some advice.

Here's a tweet from a few weeks ago so you can see the general layout. I've changed it a bit lately, but generally it's the same. The back right grouping is where they work on computers doing TenMarks, the back left group is quizzes/hw/etc, and the front 12 are new content with me.

Things I'm loving!
  • Students are getting targeted remediation. I am setting student-specific goals through TenMarks. I also have this taped onto each desk in the TenMarks station... very helpful!
  • I feel like I'm reaching more students since I'm only giving instruction to about 12 at a time.
  • 8th graders have a relatively short attention span - 17 minutes and then rotating is helping to keep them focused.
  • Students are accomplishing a lot in one class period. Targeted, timed things to accomplish are working very well.
Things I need to improve:
  • I still feel the need to monitor/watch the back groups. I need to let this go! 
  • I want to give students more than 17 minutes for TenMarks. Hopefully when I get for more computers (I'll have 10 total soon) I can move to only having three rotations of about 25 each.
  • It's really hard to say the same thing over and over, especially now I'm doubling up in each class period. I have to be very careful and not leave anything out because I've already said it about 12 times!
Sorry I don't have pictures of this workshop thing in motion - I'm always with a group of kids! That's another thing that's hard. I used to grade during the few minutes that students were working on quizzes or homework. Now, I'm with a group of students while others are quizzing, meaning I don't have time to grade/check email/nothing! Bell to bell!! It's hard!

So what are your suggestions? Any ideas for my 'improved' list? Any general thoughts or ideas to add?

March 23, 2014

Pythagorean - Part 2

Part 1 with my new intro for this year is HERE.

Our finished right triangle pages looked like this...
I know that's kind of a crazy picture. I used my CamScanner app and sent it to a student that was in ISS so she could check her work before moving to the next activity. 

If you don't have CamScanner I highly recommend it! I can scan and save as a high quality pdf right from my classroom - huge time saver!

Anyway... next we completed this little booklet. 

It was all about the relationships between areas and side of the squares formed. Never once did my students plug into a formula while completing their book - I love this! The types of problems are from Christa Lemily here, I just made it into a little booklet for their INB. The students were all commenting about how easy it was and how much sense it made. When we completed our town map next, the students were breezing through. I had to show one example about how mathematicians organize their work because we hadn't been showing work before. But conceptually, they did great!

They completed the map with more ease than my students did last year, and these students are classified as "less advanced" than my students were last year. That, to me, says the intro and conceptual booklet worked!! YAY!

Next we calculated distance between points.

When you flip the flap down that says "Calculating Distance Between Two Points" it looks like this...

Yes, I know, the distance formula is not explicitly an 8th grade standard. But if I'm doing distance between points on a coordinate grid why wouldn't I mention it?! We talked about how they would see this formula later and it contains the same math as the Pythagorean Theorem. We color coded the same work in both methods so students could see the connections. Hopefully they'll remember this at least a little next year and go look it up. Fingers crossed!

So there it is, my week of Pythagorean Theorem and distance. Got any helpful critiques or suggestions?

Here are your files:

March 21, 2014

Making Sense of Linear Inequalities

We were treasure hunters today!!!! And the students LOVED IT!!!!

I gave them a map of our town (a different region than I used here) and told them I was going to give them clues about some recently confirmed buried treasure. They laughed and got into it - thank goodness - because I would have sounded like an idiot even more than I already did trying to talk in my best pirate voice.

I told them that part of their clues were going to include roads and part were not, they needed to show those things differently on their map. Many used a darker line to show included roads.

The clues were:
  • The treasure is somewhere south of 8th street.
  • The treasure is either on Tiger Boulevard or east of it, but definitely not west of Tiger Blvd.
  • The treasure is either on or north of 14th street.
  • The treasure is west of J street.
This gave them a relatively small region of town where the treasure could be located.

Then they did a partner activity. They had to build a barrier and I gave each partner a paper with two maps, one with a shaded region and one without. They had to describe their shaded region to their partner using clues like mine, and then listen as their partner described. It really made them focus on precise language and boundary lines.

When we transitioned to inequalities on a coordinate grid they were pros already! The dotted line/solid line made prefect sense and shading towards the region that satisfies the inequality also made sense. Success!!

I will definitely be using this type of introduction in the future!

What innovative ways do you use to introduce this (or any other!) topic. I'd love to steal them :)

March 11, 2014

Pythagorean Theorem - A New Intro!

I've never started Pythagorean with an investigation like this before and so far I'm loving it!!

I got the awesome idea from Christa Lemily at Here's her wonderful stuff.

I've always talked about the two leg lengths squared and we've even gotten blocks out before, but I've never had students determine if it's a right triangle on the first day using this method. We haven't named what we're doing as the "Pythagorean theorem" yet, but we're using it and it's converse.

We did this on the same day that students were finishing a retest opportunity so I had kiddos in all different places. I posted on the board that once they completed their retest they needed to go to From there they scrolled through the pictures and were self-guided.

Here's a fun desk picture from yesterday!! :)

Part 2 is here.

March 5, 2014

Organizing Resources

Do you ever have those days where one or all classes make you feel like What the heck am I even accomplishing here?!?!?! Yeah... today was one of those days... Anyway, on to something positive, right?! :)

As I become more and more active in my online PLN, I am constantly amazed and thankful for the wonderful resources being shared. Now, how do I keep up with and make these things useful?! Isn't that the million dollar question. I know we all have our own system, but I wanted to given an overview of what is currently working for me in case anyone needs a starting place.

Up until about a month ago I wasn't a big Diigo fan. Boy was I missing out!! If you haven't played around with Diigo I definitely encourage you to do so! I had been finding resources through blogs I follow and twitter. Those are my two main sources. I was then creating Pinterest pins of everything I wanted to save. Now, this system is not horrible, it just wasn't working well as I collected more and more resources. My pinterest boards are getting very large and searching for a particular document/activity/foldable was becoming cumbersome. You know what dreaded feeling I've seen something awesome for this... now where did I put it??????

I have a FANTASTIC principal who is very knowledgeable and is helping our staff become more intentional with our PLN time and how we find/organize all our resources. He introduced me to Diigo back in the fall but I didn't fall in love with it then - I am now a Diigo lover. Here's what I'm doing and loving with Diigo...

I find a resource anywhere on the internet and save it to my Diigo library. I tag everything I save by the content, ie: quadratics, linear function, point-slope, residuals, etc. I also use the tags "inb" and "activity" to signify which things are more useful for interactive notebook pages and which are more classroom activities. As I'm finding things online I'm saving and tagging everything useful to Diigo. I may not need it now but I'll probably need it soon. For example, when planning this last unit for Math-8, I went to my Diigo library and filtered by the tag "pythagorean." It looked like this...

I can click on any of those links and quickly access the the resources. I can also quickly see I have three things that might be good class activities, one that might be fun in a challenge packet, and one that relates the Pythagorean Theorem to the distance formula. Score!!

Like I said, I've only really be using and loving Diigo for about a month. My library and tagging system is growing quickly. There will probably be many more resources than just 4 in this area soon. :)

Now, no judging as I'm getting ready to be transparent and share :) Here is the link to my Diigo library in case you want to poke around and see how I've set mine up. I'd love if you left a link in the comments below to your Diigo library if you use one. Or, please let me know how you organize and manage all your resources. I'd love to learn a few tricks from you!

Also, here's my principal's library in case you need to see how the masters use Diigo :) Now, don't be overwhelmed or intimidated like I first was; he'll be the first to tell you his is 10 years in the making!

Alright, time to go play with the pup for the evening. How can you resist this sweet face?!
Happy Wednesday everyone!