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Educational Consultant and Online Educator

Matthew, thank you for your

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Matthew, thank you for your help in pointing teachers to specific places to look for those learning targets that will work for them. You suggestions are insightful and useful! I appreciate it. As I'm sure you know, my focus is on multiple tips, so I appreciate that you could go in depth on ones I articulated.

Michael, I share your hesitancy about Standards Based Instruction. It does have its pitfalls. In fact, one of my favorite books is Beyond Standards, by Carol Jago, current NCTE president. She goes in depth on many of these pitfalls I'm sure you have experienced. I believe in Standards Based Instruction, as long as those pitfalls are avoided.
However, my audience is teachers. Standards, both state and common core, are part of the teacher world and reality. Teachers are addressing and targeting specific standards in order to increase student performance. PBL can be challenging when it comes to aligning standards, but it can be done. I want teachers to feel confident that what they are designing to targeted standards and that PBL can help students learn them. PBL is standards based, and thus their needs to be support for teachers around this.

Thanks for the feedback and comments!

mathematics coach

Is it REALLY necessary to

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Is it REALLY necessary to kow-tow to bad ideas like the Common Core and its many bastard off-spring (coming soon to a nation near you)? You've got some nice points to make about PBL. Why sully them with the "standardista" stuff?

Program Director at NC New Schools Project

Where to look when you don't know or haven't seen in real life

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I'm a HUGE PBL advocate, taught wall-to-wall math PBL for 3+ years, and want all math teachers to read this post and take your advice. However, I'm afraid that your remark...

  • "Pick standards that you know or have seen used in real life. If you are unsure, ask you colleagues. I like to say, "The Wisdom is in the room." I'm sure your colleagues, whether it be math teachers or CTE teachers have some great ideas. Pick standards that clearly can have a practical purpose in analyzing a problem and/or design a solution to that problem."

...doesn't necessarily leave teachers with enough information to get started if they are feeling lost or their colleagues aren't able to help. And I don't want to make the case here, but there is evidence that many teachers don't necessarily have the content knowledge or real-world experience to draw upon for project creation.

I'd like to propose a strategy that I used when I found it difficult to find connections in designing math PBL experiences: Dust off that old technology, the TEXTBOOK, and look at those "Challenge Problems" that have all of the stars next to them at the end of problem sets. Some very smart people have put a lot of time into those little nuggets and they can serve as seeds for quality projects.

Case in point: In fall 2007, as a rookie PBL teacher, I was looking to design a project that taught exponential equations in Algebra 2. I came across a problem in the back of section that was asking student to calculate the "Apparent Magnitude" (A.M.) of different objects in the night's sky (A.M. is how bright objects seem to us from a distance). Not understanding the topic myself, I dove deep to learn that A.M. works with distance and luminosity (actual brightness) in an exponential fashion (see and That exploration, and a conversation with a physics teacher friend (your recommendation), led to a project where students designed space goggles, using two polarized lenses that could adjust to different brightnesses, for astronauts to use when visiting other (and far brighter) solar systems. A video of that project presentations can be seen here:

I like this strategy paired with your advice for several reasons:

  1. Textbooks are already in the hands of teachers and bring the thoughts of many scholars who authored the books
  2. Looking in depth at one example will often present logical connections to other topics we must teach--in this case I had to also bring in logarithms to help students solve the exponential equations. Talk about a great feeling...students asking ME to show them how logarithms could be useful in their work.
  3. There are these "challenge problems" in nearly every section of a course (granted they are of varying quality)

Just thought I'd share what has worked for me. Thanks for the great post, Andrew. I agree whole-heartedly that, "Designing PBL for Math can be a different beast." And while so many teachers/schools are hungry for math PBL, there are too few resources available.

Best regards,


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