What I’m going to ask you at the end of this post: I’d love any links in the comments to examples of awesome projects and examples of project based learning for the math classroom. I’d love any projects that you think are actually really good, and any and all examples of project based learning (good or bad).
***
This isn’t a post about something I’m doing in the classroom, but rather me soliciting resources from all y’all so I can do something different in the classroom.
But my basic sentiment at the moment is: AAACK! HELP! AAACK!
Setup: My school is jumping on the Project Based Learning bandwagon. However, no one has been able to give me good examples of what real Project Based Learning in the math classroom looks like. However, no one has yet been able to give me a satisfying example of Project Based Learning in math.
I found this online (thanks twitter) which appears to separate Project Based Learning from Projects:
It’s all very good sounding. But I am a concrete thinker and I haven’t been able to come up with a hundred examples of Project Based Learning. Honestly, I haven’t even seen one that I’d say “hey, this is awesome.”
Also, I am not really good with doing projects in general. I don’t do a lot of them (for a variety of reasons).
So, as I said: I’d love any links in the comments to examples of awesome projects and examples of project based learning for the math classroom. I’d love any projects that you think are actually really good, and any and all examples of project based learning (good or bad).
Mainly I’m just trying to wrap my head around this. I still am unsure what to think about this move my school is making, and if it makes sense for the math classroom. But for now, I am keeping an open mind.
Continuous Everywhere but Differentiable Nowhere 
http://rer.sagepub.com/content/77/2/186.short Which is about how to use cultural historical theory to analyse what happens while working on projects – but the example cases could be interesting to you.
At the bottom of my post (http://teacherleaders.wordpress.com/2012/12/08/creativity-and-imagination-in-the-math-classroom-reframing-projects-and-project-based-learning/) is a brief description of a successful wind turbine PBL I do with my sixth graders. It was created in collaboration with the Siemens STEM Academy and Discovery Education (http://www.siemensstemacademy.com/index.cfm?event=showResource&C=&RESOURCEID=b7ae4c05-1438-bbfa-6026-c7de68579cb3)
Yeah! Perfect timing. I’m adding you to our Sunday Funday this week. :)
There’s gobs of good examples for statistics, but that’s a topic that lends itself to project-based curriculum (here’s a statistical method, now find somewhere to use it).
My colleague who teaches AP statistics recently had students do a bias project. The only direct was that students reveal bias in some way. One group did what they told students was a Coke-Pepsi taste test. They first asked students which was their preferred drink, then filled red and blue cups and asked them which they preferred. However, rather than filling one with Coke and one with Pepsi, they simply picked the preferred drink and filled both cups with the same type. The experiment was solely in the bias involved with the color of cup. They thought Pepsi drinkers would tend to the blue cup and Coke drinkers to the red, but it turned out Coke’s results were evenly split and every student who preferred Pepsi went for the red cup.
That’s fascinating stuff and good for a statistics class (which includes conceptual ideas as much as the number crunching) but not really useful for more computational math topics. It’s trickier when you want to convey (say) long division of polynomials. Even when you carefully gear a topic to include particular bits of algebra, students are good at making end runs around the algebra somehow.
Also, some topics are so science-linked and require so much extra background that the lesson becomes half-science and half-math. Not necessarily a bad thing if your curriculum allows the time — I’ve taught a summer class for several years which was an equal mix of science, math, and engineering, culminating in a bottle rocket competition — but problematic if you actually want to reach the required topics in a particular subject.
One approach is to simply relax the stringent requirements listed in your chart (I notice the lesson Mary links to would not be considered project-based learning by the definition, because it involves a specific problem). Then you’re back to something more Japanese-style where you front-load a problem and let it direct the learning, which might be sufficient for your school.
I incidentally also know of an instance from the 80s-90s of utter project-based failure. Sunnyside (a local district, not mine) experimenedt with 9-12 project based math where ability levels were mixed. It turned out horrible; because of the lack of focus, “calculus” students didn’t know any calculus, at all. So this sort of thing can be risky. Good luck!
Thank you for all your thoughts. My school is also moving towards having more and more interdisciplinary stuff. I’m with you though… I barely do ‘projects’ let alone anything fancier. So I’m going to start slow, with some simple things that wouldn’t fall in the “Project Based Learning” definition, and just get my feet wet.
My concern is primarily about how to introduce interdisciplinary stuff (in order to make a project viable) and still cover the content that we are expected to in a year. More updates, prolly, as I frustratingly go through this…
Don’t be mad at me for infiltrating the math blogosphere but….this is EXACTLY how I feel as a chemistry teacher. I haven’t had that much time to go a-googling yet to find resources, but the very limited feelers I put out are disappointing so far. I’m crossing myfingers for you!
I do projects when I can, but they probably don’t really make the PBL definition. The closest I come is a precalculus project where they design and build a parabolic solar cooker.( We make s’mores and they research a social justice connection). I considered dropping it at one point, but several parents have mentioned how effective it was for their child in tying together the concepts. It also is the far and away the most frequent answer to “what was your favorite part of the course you took with me?” I know there are some out there with Stem connections- the navy has a program where the create a problem for groups to solve. There also is a mathematical modeling competion that might provide some sample questions that can be tweaked for math.
Good luck
Ooooh! PBL or not, I need to know about this. Do you have documents/something I can read on this solar cooker? I want to do it when we do conics!!! Thanks for sharing!
http://www.nctm.org/resources/content.aspx?id=22453
I originally found the idea in a Key curriculum book, but ended up modifying this NCTM activity. Wow I have “borrowed” so many ideas from your blog- it’s great to share one. This year I’m borrowing temperature probes from the physics teachers to find the temperature differential at the focus
I’ve been dying to have students design their own house in Google Sketchup for a Perimeter, Area, & Volume unit, and do calculations for how much it would cost to do flooring, painting, etc. Still am only on the “sketch it out on paper” version though.
Ooooh, you’re going for the Holy Grail! PBL certainly seems very rewarding and authentic but as you’re discovering, it is tantalizing difficult to pull off. Jason Dyer makes a very good point above – PBL is often (almost always?) interdisciplinary.
Back when I did my undergrad a few of us tried to create some PBL lessons that integrated with environmental education: http://www.dryfly.ca/greenmath/ I’m not claiming that they are fantastic or even make sense but a few of the projects are worth looking at. On my site I also link to: http://www.enviromath.com/ChapterProjects.htm
I think the idea of project based learning in math is encapsulated in the LEGO work of Papert. If I was starting from scratch, I would research programming and implementing projects that require math. Sorry, no links but I have no doubt this is a good place to look. By the same token, implementing a mechatronics program would be another useful way to incorporate math into PBL. Here is a link to an interesting article, but there is no free full text (message me for details): http://ieeexplore.ieee.org/xpl/articleDetails.jsp?arnumber=5288530
Close cousins of Project Based Learning are Problem Based Learning and Anchored Instruction. I’ve never used it (probably few people have in the past 15 years), but the Jasper Woodbury series from the Vanderbilt group may have been the creme de la creme of problem based learning. A series of drama videos were produced, and students had to solve problems for the characters. These problems would ultimately lead them to learning about all sorts of math concepts. The Jasper series was novel at the time for many reasons, one of which was that the videos were on Laserdisc!
I think Problem Based Learning is a better place to start, as its easier to design shorter problems that try to target specific learning objectives. In order for Project Based Learning to work best, I believe that learning objectives need to be quite broad – you will likely target enduring understandings as opposed to specific skills/understandings/knowledge. But even Problem Based Learning scenarios are difficult to design in an authentic manner, imo.
Lastly, I think it may be wise to place PBL within a intentional learning cycle. For example, a small project can be produced in order to explore a new mathematical concept. Then through inquiry or more traditional lesson, the concept is explained and expanded. Then perhaps another project is done to extend or examine the concept (sort of a modified 5e learning cycle). The point is to mix PBL with the concrete, so that specific learning objectives are clarified.
Your thoughts and links and everything are awesome. THANK YOU. I’m glad you have sort of said some of the same things that have been going through my head. Much much much obliged.
It is time to google Jasper Woodbury. Now.
Hi Sam,
I’ve run my Applied / Consumer Math classes with PBL for 3 years now. They do projects that last ~ 2 weeks, and normally have several products that are due at the end. An example project is the Buy a Car project. They have to look into the costs of owning or leasing a car, etc.
I like PBL for these classes because the students are using the math that they’ve previously learned (or not learned) to solve problems that they mostly find useful. The students get much better at researching topics online, creating documents, spreadsheets, and presenting in front of their peers. I think they learn quite a bit of non-mathy skills in these classes.
However, I don’t feel PBL is a good basis for learning much new material. I never tried to teach Geometry, Pre-Calc, etc through PBL. Maybe with some sort of mini-project setup where they are being given something more specific to learn about. Having a true PBL setup for these classes would very tough.
We visited Tech Valley HS, who teaches entirely in PBL (https://www.techvalleyhigh.org/). They were new at it when we visited (3 years in), but even though they had a self-selected motivated group of students, their passing rates on the state assessments were poor. I know that state assessments don’t even start to measure learning, but it was one data point.
-Dan
I do a similar one for my financial math unit in IB Math Studies (12th grade). The students have to research the costs associated with a college to which they are applying, then analyze them using the math they have learned in the unit (inflation and compound interest). I wish I had been able to include more math, but couldn’t figure out how to add in depreciation, simple interest, or currency conversion, and am already thinking of ways to revise it.
Just posted it here: http://www.appetite-for-instruction.com/?p=302
Hi Dan;Would you be willing to forward me the materials you use for that course? We don’t currently have it but I feel this would be of great benefit for those who don’t want to go the typical college prep route.
Thanks!
Matt Dion
Pembroke Academy
Sam
I was lucky enough to meet Carmel Schettino at an Exeter summer academy (the Greer Conference) and she is a big proponent of PBL. She keeps her own webpage (http://www.carmelschettino.org/wp/) and writes passionately and clearly about this. Check out her work. She used to work at Emma Willard and is now at Deerfield Academy.
Jim D
I met her at a Boston College math conference–her presentation was great!
Ooh, thank you for posting this. My school is going to try PBL next year, but they haven’t given us any details yet on what it would look like. (It’s not going to be a project here and there, it’s going to be jumping-in-with-both-feet PBL all the time.) This looks like a great blog for seeing how the implementation went at another school.
Here are a few resources.
1) Applying Math Skills to Real World Problems – http://www.youtube.com/watch?v=hxufdpcfpJY
2) Math PBL Video – With specific examples
3)Tips for Using PBL in Math – http://www.edutopia.org/blog/project-based-learning-math-standards
Here is a presentation that I’m still working on, but I tried to list some example projects that either I do myself or that my colleagues do, along with general tips for running successful projects in the math classroom! They’re not as cross-curricular as what you are envisioning… but they might still be a good starting point! https://dl.dropbox.com/u/39075205/AGIS%20-%20math%20projects%20short.pptx
My comment isn’t offering the help pu really asked for, but isn’t it crazy that the school system decided PBL is the thing to do, but doesn’t allow for the interdisciplinarity that PBL actually requires to be a real thing and not just some pointless exercise in “innovation.”
I’m interested in Jason Dyer’s comment because I think it’s examples like that that discourage people from changing educational practices – so people move toward standardization not realizing that was the problem to begin with!
I have been meaning to share something I found online a few months back and was working on modifying for my own use (but then I lost the link and didn’t want to claim what I had made through modifying as my own)
http://www.envisionprojects.org/cs/envision/view/env_p/88
Its a matrix based PBL type assignment.
(a) I would definitely hit up Shawn Cornally with this question. You might consider reaching out to him directly.
(b) I’ll email you the final project I used to use in AP Calculus.
(c) A propos of the whole interdisciplinary dilemma and the what’s-the-definition-of-PBL question, and from the point of view of somebody currently in math grad school and therefore on the verge of embarking on a multiyear, “real life” PROJECT that is not interdisciplinary at all –
I think it’s worth keeping the way math research works in mind as a model for how a project that’s more or less compliant with the def. of PBL in your graphic could look and still be 100% curricular in a math class. For this you need a problem / question that’s juicy enough to stay fruitful over a long period and yield more questions along the way. (But this is how math actually progresses! Example – a problem: “do there exist nonzero integers x,y,z and n>2 such that x^n+y^n=z^n?” Unsuccessful work on this problem led to the entire field of algebraic number theory!) I think some good examples of such problems are the Unit Problems from the IMP curriculum. IMP then traces a particular path through the problem over the course of the unit, but one could leave it more open.
I know that High Tech High does a lot of PBL. They have also done a good job of documenting their work in digital portfolios–choose the drop down menu that is labeled staff–http://www.hightechhigh.org/schools/HTHMA/?show=dp
Candice Director and Mele Sato are both math teachers & you can check the staff directory for more if you like what you see.
This is crazy interesting to explore. THANK YOU!
You might try googling work by Dr. Anthony Petrosino at U.Texas. He does a lot of PBL and STEM research at UT’s School of Education. He is a good friend and hails from Hoboken…but don’t hold that against him (LOL).
Thanks! I def will! For anyone who wants to do the legwork for me, his site is here: http://www.edb.utexas.edu/petrosino/index.html
And I don’t hold ANYTHING against people from NJ. I went to HS in New Jersey!!!
I’ve been doing a lot with my stats class this year and I’m hoping to go even further next year. My favorite project is based on the movie Moneyball and has student draft fictional Ultimate Frisbee teams based on a large spreadsheet of data I give them. The purpose is to figure out which players are the best by analyzing which stats actually matter, boiling them down to a set of summary stats, and sorting so they can make the right decision when their 30 second time to choose a player comes up during the draft. I then run the teams through a simulator I wrote to see how well they did. https://sites.google.com/a/byron.k12.mn.us/stats/projects/ultimate-frisbee-draft.
Another project uses Minute to Win It games as the basis for teaching experimental design and 2 sample observational studies and their analysis. After designing the experiments, we have a game day to collect a bunch of data into online spreadsheets, and then follow up with a team paper that describes their experiment, data, analysis, and conclusions. https://sites.google.com/a/byron.k12.mn.us/stats/projects/minute-to-win-it.
To teach students how to work with scatter plots, analyze lurking variables, etc, I have students choose 2 variables from the Gapminder website and create their own webcasts that explain why the variables are related. Scroll to the bottom for some examples of student videos. https://sites.google.com/a/byron.k12.mn.us/stats/projects/gapminder.
In Algebra, I’m still struggling as it sounds like you are, but I have a few ideas of how to get started. A couple days ago, I created a document that tries to break down the core math skills in different ways, not just the traditional chapter breakdown, thus making it easier to see how projects might fit around it. Read through it and see if you get any ideas (or request edit access and make it better!). https://docs.google.com/a/byron.k12.mn.us/document/d/1E6Vc34gOJpiCCzuCo-YYgk6-J4j0QRutIIFP8EfCPVc/edit.
Tweet at me @rockychat3 if you have questions / ideas!
I’ve been doing a lot with my stats class this year and I’m hoping to go even further next year. My favorite project is based on the movie Moneyball and has student draft fictional Ultimate Frisbee teams based on a large spreadsheet of data I give them. The purpose is to figure out which players are the best by analyzing which stats actually matter, boiling them down to a set of summary stats, and sorting so they can make the right decision when their 30 second time to choose a player comes up during the draft. I then run the teams through a simulator I wrote to see how well they did. https://sites.google.com/a/byron.k12.mn.us/stats/projects/ultimate-frisbee-draft.
Another project uses Minute to Win It games as the basis for teaching experimental design and 2 sample observational studies and their analysis. After designing the experiments, we have a game day to collect a bunch of data into online spreadsheets, and then follow up with a team paper that describes their experiment, data, analysis, and conclusions.https://sites.google.com/a/byron.k12.mn.us/stats/projects/minute-to-win-it.
To teach students how to work with scatter plots, analyze lurking variables, etc, I have students choose 2 variables from the Gapminder website and create their own webcasts that explain why the variables are related. Scroll to the bottom for some examples of student videos: https://sites.google.com/a/byron.k12.mn.us/stats/projects/gapminder.
In Algebra, I’m still struggling as it sounds like you are, but I have a few ideas of how to get started. A couple days ago, I created a document that tries to break down the core math skills in different ways, not just the traditional chapter breakdown, thus making it easier to see how projects might fit around it. Read through it and see if you get any ideas (or request edit access and make it better!).https://docs.google.com/a/byron.k12.mn.us/document/d/1E6Vc34gOJpiCCzuCo-YYgk6-J4j0QRutIIFP8EfCPVc/edit.
Tweet at me @rockychat3 if you have questions / ideas!
ZOMG that’s an awesome set of stuff. PBL lends itself pretty naturally to stats, which is awesome. I suppose one of the things is to get stats more integrated with the rest of our curriculum.
I am totally sending this comment to our AP stats teacher. Thanks!
Hi Sam,
I am a new Math Intiative blogger. (But gosh no, not a new teacher, oy). I appreciate your commitment to stretching and finding the best way to do most everything.
Please forgive my “old schoolness,” in contributing a project. I have tons of enthusiasm for curriculum, sometimes I don’t have the most current methods of delivering/retrieving them. Here goes:
After ride-sharing with the Environment and Sustainability teacher in our High School’s 11-12 core, the WISE Academy, (Windsor Institute of Sustainability and the Environment) we had a lot of time to talk shop. Between the two of us, we came up this project for teaching Scientific Notation, Unit Analysis, and an introduction to Exponents: (Algebra 1 or 1A)
Exponents, the Environment, and Consumerism in the USA
Students watch: http://www.storyofstuff.org/movies-all/story-of-bottled-water/
Students work alone, in pairs or triads to come up with a question of their own. They must research the answer for the town of Windsor, and expand it to the United States.
It must contain a visual…all the unit analysis…commentary…etc…(forgive me for not having any pictures at the moment, I am still on vacation (hello Lake Tahoe!)
Here is an example: One of my Algebra 1A students used deodorant sticks. If each person went through three sticks a year, and if each stick were 3 inches in height, he figured end to end they would cover the distance from Windsor High School to the Statue of Liberty.
Okay, so it wasn’t EXACT science, yet it did get the two ideas across I was trying to make: We need big numbers (or really small), we need unit analysis, and we need to be aware of how what we use effects the Earth.
Forgive shmorgive! You are awesome. Thanks for this idea. I love that your project emphasized the “big picture” ideas (unit analysis, big numbers, sustainability). I often feel trapped in these minutae and you’re reminding me that projects allow us to get to bigger picture things. At the expense of time and other parts of the curriculum. But these bigger picture things are important and I often skip them because they are hard to do.
Thank you, thank you! Sigh…
I love the chart to compare projects and projects based learning. I am in a teaching program and am student teaching in the first grade. I have heard the terms and now it is very clear the definite difference between. Do you believe any grade level could benefit from projects based learning? Are projects in general not valuable at all?
check out http://www.pblproject.com