How do we do PBL Math?

Repetition + Rigor + Relevance = Retention

1 - Make it as real and relevant as possible.

Students engage when they see the project connects with them. When projects have enough personal autonomy, students will value their work and it won't likely be trashed afterwards.

Answer the student's question, "When will I ever use this in my life?"

2 - The repetitive use of the content creates the product.

Start with a standard or group of standards you'd like to create into a project. If you would normally assign 40 problems for practice, think of how the project should allow students to practice that concept the same number of times or more.

Answer the question, "How can students repeatedly use this concept to create a product?"

3 - Don't be afraid to think BIG.

Think outside the box, take some calculated risks, set up guest speakers, don't be afraid to teach above grade level, and learn a new skill if you have to. Answer the question, "How far can the students take this project?"

4 - Have an example of what excellence looks like.

Doing your own project, especially a new one, will help you figure out many of the pitfalls students will go through. After a few years, you'll collect enough exemplary work to display. At the very least, do the project with them. Answer the question, "What exemplary work do my students have to model their projects after?"

Example

Standard(s): Operations with fractions.
Project Idea: Read, write, and play music (relevance).

Notes are fractional. Have students dissect a popular song like Twinkle, Twinkle, Little Star. What are the numerical equivalence of each note in the score? What do they notice about the sum of notes in each bar (repetition)?
Move on to songs that are longer and have more varied fractional notes (more repetition).
Then have students write their own songs (personal autonomy) with certain requirements such as having a number of halves, quarters, eigths, and even sixteenths notes (repetition, relevance, rigor).
Require a certain number of bars (rigor). There are open source software for writing music. Discuss how loudness is related to amplitude, which is related to multiplication of fractions. Bring in string instruments and demonstrate harmonics as fractions of a string (rigor).
Discuss octaves and show how strings tuned to the same notes resonate (rigor). Show the Pythagorean music scale uses fractions.
Finally, have students play music. Bring in a keyboard and have them play their song. Or have a computer play it for them! OR have their song played by professionals (think BIG)! What if students want to write parts to different instruments in a song (think even BIGGER!)? Remember to complete a full project (with all parts of the process) as an example for students.

PBL IS NOT:

The trifold
The webpage
The Power Point/slide show
A Product without drafts, processes, and a few math problems.
80% made of fluff, 20% made of math
80% fluff time, 20% math time
80% fluff-weighted Grade, 20% math-weighted Grade
A classroom of projects that all look exactly alike.
A project where you have to "look for the math".
A project where you're not proud to publicly display.
A project students can't wait to trash.
Where you have to reteach the topics after the project.

PBL IS:

OOOOOOZING with Math!
Full of Numbers, Equations, Graphs, and Calculations!
A Project with Drafts, Processes, reviews and critiques, and LOTS of Math!
A Project that Uses a Design Cycle!
20% Made of Fluff, 80% Made of Math!
20% Fluff Time, 80% Math Time!
5% Fluff-Weighted Grade, 95% Math-Weighted Grade!
Unique with Students' Interests All Around!
When someone exclaims, "There's that much math in that?!"
Something that will be Publicly Displayed.
Something Students want to Keep!
Achieving the goal of learning and retention in infinitely many ways!

☙ Try something...anything.

Start small. Maybe a week-long project requires students to create a mosaic tile display using multiplication tiles (just their 3s). Assign colors to each multiplication fact. Have them create 9 sets with the product written on each tile (repetition). Let students rearrange them into different designs (drafts) until they finalize on one. Ask them why they chose their final design. Have them document the process, showing the drafts, the calculations, how multiplication relates to the length, width, and area of a tile. If you extend it into art, maybe use color swatches to learn about complimentary colors or cool and warm colors. But at the end of the day, "put the go to the know!"

☙ Collaborate with people of different strengths.

Different people have different strengths.

Ideation - Look for people who can give you ideas. They love taking boring things out of the box to become exciting ideas.
Connectors - Look for people who can make connections. They know how math and art connects, or how math and science connects, or how math and cooking connects.
Strategic - Look for people who can create a logical plan. They can see the logical progression of a project.
Achievers - Look for people who want to see success. If you're lucky to team teach with them, you'll accelerate quickly. They love to encourage people to succeed.
Creators - Look for people who want to get their hands dirty. They will show you (rather than tell you) what they're thinking.

Don't do it alone unless you have most of these strengths.

☙ Be aware of the math around you.

Math is all around us. Look for ways to incorporate the world into math. Even if it's a single lesson, it will plant a seed of ideas that may flourish into a week-long or month-long project!

☙ Be aware of your students' interests.

Figure out what your students like. Design projects with that in mind. When I taught fractions to a group of students in a remedial class who were more than three years behind in math, I realized that the traditional methods of teaching fractions wasn't getting across to them. However, I noticed that they all had earbuds on listening to music all the time. I rewrote the entire's semester's curriculum to center around music. They read music, wrote music, played music, and even created their own little guitar from scratch. I took music classes and learned to play a guitar (I had very little music background). By the end of the year, the class went from 0% passing the standardized test to 86% passing.

☙ Bring in your own interest.

We teach what we're most passionate about. If it's gardening, figure out how math can be repeatedly used. Regardless of your interest, students will see how excited you are when you're teaching something you absolutely love. For example, at two schools, I managed to get a pool table into my classroom. I taught a lot of math on that pool table. Students got to hear about some of the tournaments I was playing in. Another hobby I have is art. That is why many of my projects are centered around art.

Again, bring in your interests and students will get to see the human side of you.

☙ Recycle, Redesign, and Refine.

If the project was a success, then recycle the project. "Recycling" a project means taking it through the stages of redesign again. If we ask students to learn the design cycle and create drafts, we should be doing the same things when it comes to project designs. Immediately after completing a project, figure out some of the pitfalls that you or your students encouter. Give a student survey and ask students what they liked and didn't like about the project. Ask them what were some of the troubles they went through. Ask them how they would improve the process for upcoming students next year. Refine or redesign certain parts based on the surveys and from your own observations to make the project more efficient.