UCDMP Building Number Sense Day 1

In late July, I attended a five day Institute on Building Number Sense sponsored by the UC Davis Math Project. I have been attending their professional development offerings for the past several years. Some were sponsored by our district, while others were part of their Saturday Series offered each year. It never disappoints and exists without comparison as the best professional development I have ever experienced for math. Due to a conflict with my admin program coursework this year I am unable to attend any sessions and I miss them terribly. Participation in these trainings over the past several years completely transformed the way that I taught math in my classroom and changed the way I support teachers in teaching math.

I always loved math. I loved it so much, I even took Algebra twice! And it wasn’t because I failed it the first time but rather sought special permission to re-take it because I wanted to learn it better. The first time I took Algebra was during summer session prior to entering high school and at the end of six weeks I had a good grade but didn’t feel like I learned or understood much. I remember it being a bit of a battle to get permission to take it again. All because I wanted to learn it better. Sadly, my naive 13-year old self thought spending a year in Algebra, as opposed to six weeks, would lend itself to deeper learning. I had a great teacher and probably became more fluent in many of my procedures but my counselor was most likely correct that taking Algebra again when I had a good grade the first time was a waste of time. This happened in 1987 and today grades still rarely communicate learning and the experience epitomizes what math education was for me and how I taught my students up until three years ago.

My math experience as a student was very black and white. You followed a procedure and you got an answer. The answer was correct or wrong. That’s it. Then you went on to the next problem. It’s amazing with this experience that I enjoyed math so much and completed calculus in college. Yet I am not surprised that I did not choose to become an engineer or a programmer. Because I never truly understood math at any kind of deep level that would have allowed for conceptual application in mathematical fields until a few years ago.

UCDMP Building Number Sense Days 3 & 4 (partial)

Math is no longer black and white for me and these sketchnotes represent that belief. It was the first time I incorporated color into my notes. (It certainly helped that there were colored pencils in our toolboxes!) When I consider math instruction today, it is full of color and variations that are built upon sense-making as I wish had been my experience in school. This is why I love the Common Core Math Standards. They make sense. The goal is deep understanding of the mathematical concepts. Teachers have time to build important, foundational conceptual understandings with students over multiple grade levels. Students have time to explore and internalize these concepts. They have opportunities to apply these concepts to real-world problems that aren’t the neat problems found in textbooks where everything works out evenly, all assumptions are made for you, and you draw a small box around your answer at the end. Math is messy, colorful, and stunningly beautiful, just like life.

All of these beliefs were part of my math education.

In my work with pre-service elementary teachers, I am honest that I just understood math in the last few years which has equipped me to teach math more effectively. Let’s be honest, I have always been able to “do” the math required of an elementary teacher as can my pre-service teachers. However, was I able to explain the how or why behind an algorithm like long division?  No.  I could do the procedure but didn’t truly understand the meaning. I find my pre-service teachers are very similar. Some that I have worked with have the extra challenge of possessing the “not being a math person” mindset.  However, I find that by rebuilding the content knowledge of teachers whose math education was largely limited to procedural knowledge we can create different outcomes for our students.  Thinking visually and seeing the patterns and relationships everywhere in math are a first step. Add a splash of color to some visual notes in our math classrooms and I think we may be on our way to preparing more students to become engineers or programmers if they so desire.