Category Archives: PBL

NCTM 2017 Presentation: Using Design Thinking to Drive STEM PBL

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Our Slides

Excel Spreadsheet that can help with Project Design.

Here is a 5 minute video with some reflections from students at the end of the Bike Project in 2016.


Alg2 – Investment Project part 3 – My Reflections

I’ve been blogging about an Investment Project I did in my Algebra 2 classes this past semester.  Part 1 gave an overview of the project and shared my docs.  Part 2 gave examples of student work and their feedback.  This last blog in the series shares my reflections.


  • I definitely gave the students too many deliverables in too short of a time period.  The research took longer than I predicted.
  • I also had the students complete some textbook work during the project.  I was so worried about timing of my class and “coverage.”  I would not do this in the future.  We would only focus on the project and nothing else.
  • I like the deliverables and don’t think I’d change any, even though some students disliked the final paper.  I saw too many benefits from what I read in the work.
  • I would extend the project by 2 days if I kept everything else the same.
  • In class, I would make sure students wrapped up their work with 5-10 minutes left so they could journal before leaving for the day.
  • I believe in depth over breadth, I need to remember that and live it in my classroom.

The Project Itself:

  • I like the topic – it is something my students are interested in
  • I wonder how to make the project more authentic and if that matters? Mutual funds don’t grow at the same rate for 50 years.  They are also based on a share price, which I didn’t address.  Is it ok that it’s semi-realistic and gives students a basic intro to investments and how exponential growth works?
  • I like having students create what should be in the presentations.
  • I wonder if I should have students co-create the rubric like I originally planned?  If I did this, I think I might need to add 3 days instead of 2 days.
  • I like having students have to “prove” why they should get top scores on the rubric and have to self-assess.  I would change the rubric so that the top points are next to the topics (on the left) and the lowest points are on the right.
  • I wonder if there is a way to include logarithms without teaching them logarithms?  For example, I could have them determine how long it would take to double their investment by doing guess and check.  We do that with a zombie problem I got from Julie Reulbach.
  • I mentioned in Part 2 that my students were stressed because I was gone from class one day.  I actually think this worked out perfectly.  Good PBL is more about students researching and discovering instead of me being the person with all of the answers.  This forced them to not rely on me as much.  Yes, many of them were annoyed that day; I’m ok with that.  In their final papers & presentations, overwhelmingly they talked about how the project was difficult and challenging at times, but they worked through it and learned so much.  They learned how to persevere as learners.  To me, that made it all worth it.
  • I wonder how I can grade these faster? I spent way too much time grading – it took forever and wasn’t fair to my students.  I think I need tips from my ELA and Social Studies colleagues.
  • I really had a hard time giving up so much class time to a topic I would normally spend one day on.  However, reading the student papers changed my mind completely.  I was teary eyed reading their papers, so proud of their work.  It affirmed to me how important this type of learning is for my students.  I don’t think math classes can completely be taught with project based learning, nor should they, but it should be a part of the course.

Alg2 – Investment Project part 2 – student work & feedback

Yesterday, I blogged the particulars of this project, including the documents I used with students.  If you haven’t looked at that yet, I suggest giving it a quick once over to get some background for this post.  Today I share some student work &  their feedback.  I’ve decided to leave my reflections for part 3 as this blog post got really long!  In the words of Samuel L. Jackson in the original Jurassic Park, “hold on to your butts!”

Student Work:

I wish I had exemplars when the project started to share with the students.  Alas, since it was my first time doing this project, I had nothing; so, I gave fairly detailed instructions (like a checklist), yet also tried to leave room for student ideas and inspiration.  Students completed a notes page of their initial findings, 3 journal writes, predictions of a 1-time investment, predictions when contributions continue, a presentation, and a 3 page-ish summary/review.  For the final paper, each cohort group brainstormed what should be in the presentation and I added it to our class webpages.  They were assessed on whether or not they included the things that we decided as a class should be there.  As a reminder, here is the rubric.  After the project was completed, I shared exemplar work with the students so they could see top level work. This was powerful. I’m so excited I have this in place for next year!

Journal Day 1: Students were to reflect on their investing and the MV Mindset of Ethical Decision Maker.  This is the final paragraph of a student who earned a top grade on the journal.  You can read her entire journal here.

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Journal Day 2:  One student did a video journal instead of a written journal.  It was incredible! I loved that students knew they could step outside of the box.  She probably reflected more in that video journal than anyone did in writing.

Investment Prediction Contributions Continue: Students had to do predictions of one time investments and if they added a total of $1,000/year.  They could determine how to split the $1,000/yr between their 3 funds. These predictions when contributions continue are much more complicated and most students used recursion on their calculator.  This is one of the top pieces of student work.  Here is  snippet of what the student submitted.

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Presentation:  There were many students that rocked the presentation part of the project, both with their content and their presentation skills.  Students were excellent at engaging the audience and using humor.  This presentation stood out for many reasons (you can see the whole presentation here.)

First, look at this slide where the girls put their comparisons on one slide, color coded it, and had the formula in the top right corner.  This was an excellent use of a graph that immediately gave a visual of their results.

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The next two slides were hysterical and, again, you knew exactly what was being communicated by the use of graphs.

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Investment Paper:  This was many students least favorite part of the project.  Many thought it was not necessary.  A few actually enjoyed this part and saw their work coming together.  I do think it was important because of the necessity to summarize their learning.  The paper that was the biggest standout used a lot of graphs and charts well, not just for the sake of adding a graph/chart to take up room.  The student didn’t use MLA and I decided I didn’t care because he went so above and beyond in the layout and content of the paper.  It looked professional.  The entire paper is here.   I’m sharing his introduction, a chart, and his final reflection and feedback for me.  One student did her final paper as an infographic (same student who did the video journal), again, it was amazeballs!

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Student Self-Assessment: I had the students self-assess as the final piece of the project.  They filled out the rubric on themselves and had to defend why they should get the top grade in each category.  If they didn’t submit the rubric, they couldn’t get the highest marks. In general, students did a thorough job of self-assessment.  In 2 of my classes, all students ended up with a grade within 5 points of their self-assessment.  In 1 class, most were close, but there were a few that were way off.  For example, I had one student who didn’t answer any of the journal prompts, just described his work on the project.  He gave himself top marks on the journals and I assessed him at 0 on the journals.  He felt he should get something for the effort because he turned something in.  I disagreed and let him know that his answers to the prompts were similar to me asking a quadratic question on a test about projectile motion and his solution having nothing to do with that particular question.  That helped him seem to get it, but I still think he thought I was being petty.

I’m sharing some assessments where students thought they should get the highest grade and where they acknowledged it wasn’t their best work.

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Student Feedback and Reflections:

All but one student said this was a worthwhile project that should be repeated.  One of the most common comments was that they enjoyed doing math that was “real-world” based.  I pretty much hate that phrase, but that’s ok, I get their point, it was math they saw useful no matter what they were going to do in college and career.  They thought there were too many deliverables in too little time, they would have liked more time to complete the project or less deliverables if the time frame stayed the same.

I was absent one day due to an observation at another school.  Initially, I was stressed out about this, but then was grateful, which I’ll share more about in the next post.  The students were stressed and hated that I was gone one day.

Some individual comments:

  • There was too much writing for a math class
  • I liked how we combined math, literature, social studies, and economics
  • Originally, when we started this project, my main motive for trying so hard was for a good grade.  However, when I really started opening up my mind to this, I began to see I wanted to learn more about the world of finance and investments.  Therefore, the further along I got in this project, I found myself not thinking about the grade as much as I thought about my desire to learn more.  (Side note: Yeah, I got teary reading several of these! Teacher win!)
  • I believe that reflections are what help us grow because we can be learning great things, but if we don’t take time to reflect, it practically goes in one ear and out the other.  (This came from an iDiploma student.  I found the iD students were excellent at reflection.)
  • I would say the most enjoyable part of this project was finding out what to do with my money when given this freedom.  I enjoyed having (fake) responsibility to see what it was like to handle large amounts of money.
  • This project has completely changed my view on how to grow my money by teaching me about a new way to invest.
  • This project has taught me so much about how to invest my money, the most important of which probably being not to wait and start investing now because you can’t make up time, and in Mrs. Mathews’ words, “YOU WILL DIE!”
  • The most important thing I learned through all of this is to invest early and spend smart.
  • I feel like the majority of this was done at home and I wish I could have collaborated more with my partner face to face.
  • Reflection – while this wasn’t my favorite part of the project, I slowly began to understand the importance of reflecting.  At the end of the day it was nice to have that time to contemplate my daily work.  Reflecting really “cemented” the learning.
  • It is challenging for me to accept that some things are going to be confusing and that is ok to leave some things unknown.
  • While I did hear you when you emphasized on the importance of investing early, it was very different to actually see the large amount of money we would gain over fifty years.
  • My dad helped me with some of my confusion.  He showed me his portfolios and what he’s been investing in since before I was born. I’m so glad I asked him because if I didn’t and if he didn’t physically show me what it all means, I probably wouldn’t have understood the project as much as I did.

If you have made it this far, thank YOU! I’m so proud of my students and they gave me a lot of food for thought for next time!

Part 1 – the docs

Part 3 – my reflections

Alg2 – Investment Project for Exponential Growth part 1 – the docs

Last Spring I blogged about a project I was working on for a grad school class.  It was my first attempt at writing a PBL type project, as opposed to what we used to call projects when I was a kid but was basically a diorama or something.  That original blog shares the documents I was using and my brainstorming.

Finally, I implemented that project this past semester.  This post is to share the docs that I used and shared with my students.  My next blog post will share the feedback from the students as well as my own reflections on the project.

In the Fall, we do a systems of equations investigation on Minimum Wage vs. Living Wage that was created by Brad Latimer at Science Leadership Academy.  This gets the conversation about finances going.  My students talk about money type things a lot.  Then, to start the exponential unit in the Spring, we do the Loan Ranger activity from Mathalicious.  I love this activity and have used it twice.  Such a great way for students to see how exponential growth can work against you.  I would plan 2 days for the Loan Ranger Activity.  We only have 50 minute classes, so I cannot get it done well in one class period.  This creates the finance talk in earnest.

Next, I used a randomizer to pair students and told them this would be their partner for the Investment Project.  Since the majority of people retire as couples, I wanted them to think about retirement planning as a couple.  I loved this wording and can’t take credit.  The amazing Jennifer D. Klein of World Leadership School came up with that one and gave me incredible feedback before I implemented the project.

Here is my original planning doc that shows my thinking and changes as I worked on it myself and with Jennifer’s feedback.  I was going to have less days than my original plan called for so I had to consider what changes to make for a shorter time period.  In my next post, I’ll reflect on how that went.

I shared this slide on day 1 of the project to go over the differences in time in saving & growth.  The info is from Dave Ramsey.

On Day 1 of the project, the students got this handout both physically and electronically giving them the details of the project.  They also got this rubric both physically and electronically.  You’ll notice that the rubric doesn’t give descriptors for the lowest or the highest end.  This is also due to my work with Jennifer.  Students needed to make a case for why they deserved the highest score on the rubric.  Additionally, I made the points such that it was basically 50%, 70%, 85%, 100% for each item on the rubric.  Too often rubrics don’t consider percentages and student scores are artificially low.

Part #2 will share student work and feedback.

Part #3 will share my reflections

Interdisciplinary PBL Collaboration (with a side of Design Thinking thrown in!)

I’ve had the pleasure of working with 2 fantastic colleagues, Zach Strother and TJ Edwards, on an Interdisciplinary PBL “Unit”.  TJ had the idea of HMW we redesign a bike for an urban commuter that he wants to use in his Tech, Engineering, and Design (TED) class.  Zach teaches AP Physics.  I teach Algebra 2.  As I left our time of collaboration this morning, I reflected on how fortunate I am to work with these guys, how well we work together, and how learning from them is making me a better math teacher, which benefits my students.  Part of what works in our collaboration is that we chose the project and each other.  We come from similar mindsets to education, though not identical, which probably minimizes the disagreements.  Yet, we also feel comfortable enough to push back on certain things and talk through disagreements as we get to unity.

This started when I was at NCTM Boston in April.  I noticed a lack of Design Thinking at the conference.  I emailed TJ & Zach before I even left Boston asking if they wanted to put together a proposal for the NCTM 2016 conference. And oh, by the way, proposals are due on or before May 1.  They both were in and when I returned to the ATL, we got to work.  TJ already had the idea of the bike redesign.  We worked together as to how we would lead a conference session through parts of the DT process, while also sharing the results of how we implemented the project at our own school. Proposal submitted on exactly May 1 and now we await word if it will be approved.

Zach suggested we apply for summer grant work from our independent school as they were wanting teachers to create interdisciplinary projects.  TJ submitted that proposal, we were approved, and so we have spent time this summer creating the UbD plans for our individual courses, times when we will have the students together, rubrics, and the timeline for the whole project.  (My Alg 2 UbD plan is here.)

It was chance that my CP Algebra 2 class is the same period as Zach AP Physics.  We don’t have any students in common, and we think that makes it better.  TJ’s class will start the DT process with interviewing users (empathy) & 3 bikes, then fill in a project brief to hand off to the AP Physics students.


Zach will have some labs pre-designed, but also have the students design 1 lab from scratch based on the needs of the TED students.  The Alg 2 students will do the labs with the Physics students, take the data back to work on in our classroom, and then fill in the project brief with their results.  The AP Physics students, who are further along in their math career than the CP Alg 2 students, will give feedback on the math to my students! I love students getting directions and then feedback on the results from other students. After all of our labs, the project brief goes back to the TED students for iteration.

We will each be assessing our students on our specific content learning outcomes, content area processes (for example, in math the Standards of Mathematical Practice), and then we picked two of our school’s Mindsets – Collaboration & Communication.  We used BIE’s Collaboration & Presentation rubrics as a guide and merged/changed the pieces we wanted to focus on for this project.  So, all students will be self-assessing, peer-assessing, and have teacher-assessing done on the mindsets using the same rubric across all 3 classes.  Additionally, we’ve picked 3 times during the 1st semester where we will get all students together so that they can give each other in person feedback, not just on the planning brief.

I’m excited.  I’m excited for my students to see how the things we do in Algebra 2 get applied in other disciplines.  I’m excited to do physics labs! I’m excited to learn how to bring more science into my classroom.  I’m excited for my students to be a part of a project and realize that they don’t have to be involved in every aspect – much like teams in various occupations – they pass the baton.  I’m excited that I’m finally doing something like this in my classes.

Thanks MV for giving us the grant to make this happen and trusting us to meet both our content learning outcomes & the MV mindsets.

My first attempt at Project Based Learning – Exponential Investment Project

I’ve been reading a lot about Project Based Learning – I’ll call it PjBL to differentiate from Problem Based Learning, which I refer to as PBL.  I’ve been wanting to incorporate PjBL into my math classes, but have really struggled.  One of my Ed. S. classes this semester will require me to create a project with  LoTi of level 4 or above.  So, in the shower this morning, all that thinking & reading started to come together. (Side bar – am I the only one who does their best thinking in the shower?) I’m sure others have created similar, better projects.  That’s ok.  I’m just excited that I’m actually STARTING to create!

I mentioned LoTi in the first paragraph.  LoTi stands for Levels of Technology Implementation.  There are 6 levels.  Level 4 and above is when the assignment/activity/project is more student directed and constructivist in nature.  Some links for LoTi: Loti Framework, LoTi Level Decision Chart, LoTi Sniff Test.

I’ve also been studying indicators of engagement in the same class.  Using this doc from my Prof as a guide, I think this Investment project would include the following indicators of engagement: standards-based, challenging, authentic/meaningful, student-directed, multi-disciplinary, culturally responsive (possibly), explorer, teacher, producer, facilitator, guide, co-learner/co-investigator, collaborative (if I have them do it in dyads), performance-based, seamless/ongoing.

So, my idea is that students research mutual fund investing, create their own investment portfolio using 3 mutual funds (1 high risk, 1 medium risk, and 1 low risk), and determine what they would have at retirement age of 65.  They would also work at analyzing if this were a true situation, would they keep all 3 until retirement age (most people would sell off the high-risk as they get older).  Additional questions I’ve been brainstorming center around the MV Mindset of Ethical Decision Making and having students analyze their spending, saving, and giving decisions based on this and their own faith tradition.  I know, not earth shattering or ground breakingly new, but new for me! Here is a link to the Google Doc where I’m starting to brainstorm and would happily welcome suggestions and/or links to similar projects,  The doc is set so that people can comment directly.  Thanks in advance for any feedback!