Hi Paul! I'm a part of the research team for this project. Thanks for your question! We look forward to our findings as well! We find that the coding enhances the math because it helps student see the patterns from the general expressions they come up with in an automated way. There certainly is a tension of balancing the coding with the math for students though, so we make sure to have a lesson introducing Python and some basic Python skills before diving into the content.

Hello Paul,

I wanted to jump in and piggy-back off of what Mindy said regarding your question.  The CPR2 Instructional Model was designed to enhance mathematical knowledge by pushing learners to generalize concepts.  To be clear, we are not teaching coding.  We only teach enough coding so that students can use Python programs as a tool to explore mathematical concepts.  As stated by Mindy, we usually begin with a quick lesson introducing students to the programming basics they need to get started on their exploration.  From there, any additional programming is introduced as needed. As a result, the mathematics remains front and center.  Thanks for your question!

Thanks to both of you for responding.  My experience working with students on Arduino coding to develop environmental sensors resonates with what you are saying.  The focus is on collecting and analyzing the data; the coding is a means to the end.  My students have not been concerned with the coding and often find resources to help them develop the instrument.

Hi Paul,  I'm not on this project and visited the video just because it looked interesting, but your question caught my attention. It is absolutely the right question to be asking, and the project's responses are quite on point. Any time something new is added, there is potential for distraction or overhead. But programming—properly designed and used—can be so powerful as a means for letting kids do the mathematics that it can (again, with proper design and use and attention to the classroom) repay any overhead it creates with extra dividends.

Our own project focuses on elementary school. It also uses programming as a language for expressing and exploring the mathematics kids are studying in their regular classes. Because it is elementary school, we are using a language (Snap!) with fewer extra syntactic demands than Python, but the principle is the same. A mathematical expression you write on paper just sits there, right or wrong, and gives you no feedback as to its correctness and no easy way to generalize it. An expression or command in computer code can be run, allowing the child to tinker with it and really understand it, to assess its correctness, and to extend it. That can be really powerful.

I don't think any of us have the final word here—these are new ideas and new implementations—but what we see on our project so far is extremely exciting, and quite full of (nice) surprises we'd never have anticipate. I can easily believe the same is true for this CPR2 project. 

BTW, CPR2 people, I'm really curious and would love to learn more and be in touch!

Paul, what a wonderful comment! We here at CPR2 whole heartedly agree that computer programming can assign meaning to a general expression.

We have worked with elementary age school children and our findings align with yours. 

I look forward to continuing this conversation with you!

Paul, we agree. We have a science lesson published in the JAAS if you would like to check it out.  
Attack of the Ice Aliens: a transdisciplinary approach to physics education.

https://aasjournal.org/index.php/journal/articl...

Thanks.  I will check out the article.

Joan, You are spot on! I have worked with Ed Dubinsky for over 20 years. CPR2 is inspired and motivated from my work with him. He was a keynote at one of our CPR2 Summits Agee years back.….and thank you for that insightful question. We are looking at abstraction (similar to the object level of APOS) as a next step after generalization (similar to process level of APOS).

Hi Joan,

Thank you for your questions and comments.  We have definitely thought about how this approach can be used across various disciplines and have utilized it in several science classes as well as math classrooms.  The forensics lesson Cindy linked to above has been used by several teachers in local high schools and was developed in conjunction with a Physics faculty member and local science teacher.  We have also used the approach with 8^th grade science students in a waves lesson and high school students in a bioinformatics lesson.  It is our belief that this method can be useful across many academic disciplines and leads nicely into interdisciplinary lessons. 

Joi, thank  you for these thoughtful questions. We feel that mathematical reasoning skills such as generalization and abstraction are most frequently expected to be “caught” rather than taught. This is one of the motivations behind the inception of our project over 10 years ago.

Already we do see this instructional model, emphasizing giving meaning to general expressions,  shaping the way teachers think about the subject.

Thank you for bringing this up.

Hello Haviaire,

Thank you for your comment!  One of the biggest issues we hear with getting teachers on board is related to time.  Of course all teachers have their course of study items that must be covered, and if they view CPR2 as something "extra" instead of something to utilize for required content, then the buy in is less.  Once they recognize that the instructional model can be used with their existing content, then they get excited to have a new tool in their toolbox.  Students definitely seem to enjoy it and often times ask the teachers when they will get to program some more, which is awesome! 

I enjoyed the Passion-Driven Statistics video! One difference between the projects may be that CPR2 uses Python for exploring various relationships between numbers and making conjectures about them, while it looks like Passion-Driven Statistics is more focused on statistics. 

Yes that is correct.

Hi Jeni, we are humbled and grateful to be working with outstanding teachers like you. The days I have spent observing you in your classroom as you stepped out into new uncharted territory (programming in the math classroom !) simply because you believe it benefits your students, have encouraged me about the future! I hope our partnership will continue for years to come.