Final ImagineIT Report

A Brief Summary of the Project:

• What you have learned about the whole design process?

I’ve learned that a project like ImagineIT needs to have a well-developed outline with detailed activities and checkpoints for the sake of accountability. External pressures of the project’s requirements, especially developing a student focus group, inspired me to talk math with kids in a meaningful, authentic, interesting way. I found that allowing for flexibility throughout the process is vital, too. Inserting ideas related to the Real Number Line into the curriculum at key moments – even when they were not part of the initial design process – was one of the high points of the project. The Concept Check that students and parents completed together about whether 1=0.999… or 1 is approximately equal to 0.999… is the best example of this.

• Informally reach out to your peer and student focus groups from the fall.  Ask them to share about how this experience/project has impacted them.  This provides you with an opportunity to see the outcome of your ImagineIT from different perspectives.  We rarely get time to do this, so take advantage and soak it all up!  Share their insights and/or the overall message that is shared in these conversations.  Does anything surprise you that is shared?

One student wrote that the discussions ‘make the math more meaningful. [The discussions] give meaning to the things we learn. There’s more stuff behind it.’
This was surprisingly profound. ‘There’s more stuff behind it'; that is, math is more than a list of seemingly arbitrary procedures. It has substance, life, meaning.
 
Another student wrote the following:
Dear Mr.Stricker,
 
Although the concept of imaginary numbers were really frustrating it allows me to discover this realization that math never stops. It's made everything so unbelievable for the fact that "i" is an actual number, and not a placeholder as "x" would be. It honestly blew my mind, I'll never be a math expert with all the infinite methods in math out there. It was hard to wrap my head around imaginary numbers and that [they’re] actually there. Although it was difficult, I understand that anything can be achievable. Even learning about "imaginary" numbers. 
I enjoyed how this student described imaginary numbers as something that ‘blew [her] mind’. This brought to mind one of my favorite quotes: A ‘mind, once stretched by a new idea, never regains its original dimensions’ (Oliver Wendell Holmes).
 
In talking with one of my co-teachers, she said we did a nice job of creating time and space to discuss ideas of the RNL with various topics, especially with respect to fractions and really large numbers, like a googol. I was surprised – and pleased – to hear her say that this went as well as she said it did. At times, I don’t think that we’ve spent enough time on the RNL. She thought, however, that we looped back to the idea pretty often, and the kids benefited from this.
 

• What you have learned in the teaching itself?  How has it influenced your teaching as a whole?

Carving out time and space for students to wrestle with important, deep mathematical ideas, even given the constraints of the curriculum, benefits and inspires both the students and me. This is worthwhile because it helps each of us make sense of a rich subject. Understanding and appreciating how our number system was built becomes more important to me every year: as time goes on, I see my ImagineIT project blossoming. I enjoy discussions with kids about numbers – and I think they do, too. Instead of math feeling like a bunch of arbitrary procedures, we can learn from thinkers before us who struggled at least as much with these ideas. This is the fun stuff with math. I am motivated to push the ideas I’ve presented even further to make my class a more mathematically rich environment.