Looking Back & Looking Forward

Looking Back...

One of my main goals this past school year was to have my Geometry students see math from multiple perspectives.  This goal was a direct result of Jo Boaler's "How to Learn Math" MOOC.  The fact that very simple problems can be seen from multiple perspectives is one aspect of mathematics that I truly love and my hope was to instill that love, or at least an appreciation, with my students during the last school year. My second goal was to have my students see the value of mistakes - that mistakes are part of learning.  Not all student answers are perfect, but we can learn from all student answers.

So...how did I do?  I asked students at the beginning of the year to use 2 words to describe math and I had them do that again at the end of the year.  The first Wordle was based on the words students used from the beginning of the year and the second Wordle was based on the words students used from the end of the year. The larger the words, the more the students used that word. (Note: There are some interesting words that only a few students used.  I recommend zooming in on the pic to see them.)

Beginning of School Year	What are the "Top 5" words students used to describe math prior to the school year starting? 1) interesting 2) challenging 3) complex 4) fun 5) ubiquitous
End of School Year	What are the "Top 5" words students used at the end of the school year? 1) useful 2) challenging 3) interesting 4) fun 5) ubiquitous

It is interesting to note that not many words in the "Top 5" list changed.  Although some students still found math "confusing" or "intimidating" at the end of the school year, there are many new words in this list had including, rewarding, elegant, stimulating and exhilirating.  Not all of my students loved math like I did, but there was more of an appreciation of its power at the end of the school year.

But what about my orignial goals: math from multiple perspectives and students valuing mistakes for what can be learned from the mistakes.  I asked about this in a google form and although some students said simply "Yes" or "Sure", others gave more detailed responses.

One student said the following: I think that mistakes were also seen as ways to learn in the class, but not personally because I hate making mistakes. I do realize that I should learn from them more now, from this class.  Embracing mistakes is something that I still personally find challenging and I can relate to the struggles of this student.

Another student said: Viewing math from different perspectives not only showed us the many dimensions of mathematics, but also helped those who may learn differently than others. By looking at math in different ways we grow to appreciate the different ways of thinking of our classmates. And here I wanted my students to see math from multiple perspectives to help them understand the beauty and connections within mathematics.  But this student gets that different perspectives are important because (drumroll, please) not all students learn the same way!  I know this, but didn't think of this as a reason for pursuing the goal of multiple perspectives.

Looking Forward...

In the fall, I will continue to teach Honors level Geometry.  But I will also have a section of College Prep Geometry.  How do I get this group of students to undertand that there is value for them in seeing math from multiple perspectives?  How will I get them to embrace mistakes as a form of learning?  Of course I can do some of the same things I did last year, but these students haven't had as much success with math and are less enamored with the subject.

What will I try? We need something that is accessible to all students, but can challenge those students who are ready for higher order thinking. Enter Low Floor High Ceiling tasks, some of which can be found at youcubed.org and others at nrich.maths.org.  In the next week or two, I have the opportunity to try out a problem or two in a summer transitions program. Two tasks I am considering using are What's the Secret Code? and Beelines. Beelines seems quite challening, but I like the visual aspect of this problem and the ability to link it to GeoGebra or keep it simple with paper and pencil. Here is a video about the Beelines problem.  Looking forward to hearing the Buzzzzzing of voices as students tackle this one.