My favorite college professor always said in intro-level math classes, “You’ll learn about that more in Number Theory,” without further explanation. By the time we took number theory of course we were CURIOUS about topics such as, “for all real numbers…” and somehow dealing with the abstract made all of the concrete calculations we’d done over the years make much more sense. We started thinking not about how to multiply radical numbers but how multiplication itself worked and even, when it didn’t work. We went from learning in the relatively concrete to seeing in the abstract.
Teaching Math is itself a bit of the same. The first year of teaching – even with a great student teaching program – is often an eye opening thing. I still remember the first time the door shut to MY CLASSROOM at McLane High School in 2006 (old photo gallery) and the feeling of, “oh crap,” there was! There were about 200 students that I was to teach math to that year. Of course there were some classic first-year teacher stories later told with glee to newbies. My next door neighbor teacher wasn’t hired yet, so there was a sub for 30 days while paperwork was finished. I should say a series of subs. I often had to open the door in between classrooms to get the other kids to quiet down – which in retrospect actually improved my level of respect from my own kids because they thought I was a little bit of a badass. But teaching-wise, I didn’t have quite the arsenal that I would today. I went through the book for the most part, coming up with cool ideas when I could. Famously I took a picture of my Toyota Corolla’s windshield because I thought it’d be cool to have kids find out the area their family car’s windshields measured as part of a unit on circles – finding sector areas to be exact. Of course, in a school with 94% poverty (average income for a family of four was about 2200 a month, which although that was about 400 more a month than what I brought in, not much…).
But that experimenting made me stronger. I shared my ideas with colleagues at my school (twitter had just been invented so wasn’t yet an option), and that first summer had the great experience to attend a two week institute put on by the San Joaquin Valley Math Project. It was like a two week summer camp of math mentoring and even as a first year teacher I felt respected and challenged to think about better ways to challenge kids – and myself – to teach math differently. It was liberating to be around others as passionate about math and kids as I was – when I would make a mistake, I was ASKED about it, not just told no… which made it a high-growth camp for everyone! (Thanks Lori Hamada, now Exec Director of AIMS!)
I taught mostly Geometry that first year – and in the years following did Algebra 2 for a couple of years, Alg/Geo III, CAHSEE, Algebra I, Independent Study which I turned into History of Math sometimes… and later Pre-Algebra when I changed schools to help start a middle school water polo program. Every class influenced the others and that deep exposure across grades 7-12 definitely helped me deliver professional development and now at OpenEd. And when opportunities to grow as an educator – always at my own expense except for the SJMP training – I went!
Not all teachers have the time or motivation; that I know. The best PD experiences I had were hands-on MATH experiences with supportive and mentoring peers(Pre/Algebra University in FUSD, 2011-12?). I remember once going to a lesson where we were to trace Functions from 7th grade through high school. There was a group of middle school teachers who proclaimed – “Why do we need to know this? We don’t teach high school…” I wanted to shout something about the Progressions or, as a former high school teacher, how tricks like FOIL and even PEMDAS don’t hurt but actually hurt students mathematical understanding if that’s all they’re taught. Yet as we did the hands-on math, some teachers didn’t know the rationale behind the tricks either! This isn’t their fault – they probably took the CSET or got an emergency credential or – just forgot after years of teaching lower mathematics.
I’ve spent several years since that time doing as much as I can to help Math teachers. Leading Math Mindset Book Studies, starting a Facebook Math Teacher group, Math and Beer Nights, attending and speaking at California Math Council conferences, leading the content arm of an outstanding mathematics formative assessment and resources company, being an adjunct professor of technology at Fresno Pacific, and even helping with the social media arm of CMC.
All of this because as a high school and college student, I struggled with math because it was presented to me as something to memorize, not something to think creatively about. That failure meant I had to stop- not regroup and ask questions about my failure to learn through it. Long before growth mindset was popular, I had a sign in my classroom – Celebrate Mistakes.
That first year of teaching, I went off on a rant once at the end of class how if, (paraphrased)”You were that kid who played the game of school just good enough to get an A, who asked for extra credit from your teacher and that’s what helped you pass the class, you know that those teachers actually failed you. Because in this class there aren’t games to play and I don’t give extra credit. You will work hard for and earn your grade, and you will pass this class and be ready for Algebra 2 and college.”
A young man taller than myself came up to me after class and said that I must have been talking to him. He admitted he didn’t really know his times tables and other basic math, so for a couple of months would come in around 7:30am a few days a week (which turned into almost every day) to just practice. We just kept it about math and he started feeling more confident, even asking questions and answering others in class.
As educators in and now out of education we need to find ways to help teachers express their unknowns in math. We need to encourage and mentor them, let them ask WHY they need to know where functions are going unlike judgmental old me. Like my mentors at McLane and the SJMP, teachers like students need support in going from a fixed to a growth mindset! Of course, once they all read Math Mindsets, with Math They Can!