Thoughts and Research on Improving Math Instruction

Wow. They amount of information about how we are teaching math in the US versus how we need to be teaching math is a little overwhelming for a middle school math teacher. I literally spend hours and hours pouring over websites and resources looking for what research has proven to work. Here is a summary:
1. Success in Algebra II is the best indicator of success in college. Really.
2. Success in Algebra I is dependent on a student's understanding of fractions, which leads to understanding ratios, proportions, rates of change, and, eventually, slope. Of course, this should be done in a well-thought out sequence following the concrete-representational-abstract method of teaching mathematics.
3. Students who have learning difficulties in mathematics do best with explicit teacher instruction.
4. Students who are gifted in math can accelerate with no negative impact, as long as they are comfortable with the pace.
5. Planning for effective instruction takes a lot of time, and collaboration with fellow math teachers is key. Math teachers must understand the concepts being taught in the grade levels before and after their own.
6. Graphic organizers are essential to organizing thinking around a concept.
7. Math class cannot be scary! If students feel fear, their fight-or-flight mode turns on, and their problem-solving frontal cortex turns off.
8. It takes a lot of practice to acquire a skill, and time for the young brain to "file" it (grow dendrites to connect new learning with old learning).
9. Teaching procedures before concepts does not develop deep understanding, just momentary memorization that actually hurts students when they try to apply math properties to abstractions in algebra.
10. Allowing students to teach other students is a valuable strategy; teaching a concept is a higher form of learning.
11. Understanding the terminology of math can never be over-emphasized. Use the correct terms!
12. Modeling complex problem-solving is another terrific strategy; let students see you, as a mathematician, struggle with the math as they do. I always tell my students Albert Einstein died trying to solve a math problem (the unification of the universe into one equation).

I will add more as I research and study, but reminders of where we are and where we are going are always welcome!

My Philosophy

I never thought I was good at math. I never thought I was good at anything, except maybe art. I didn't take many upper level classes in high school; I thought I would be getting married and staying home to have children. In May of 1980, a month before graduating, I put a halt to my wedding and "ran away" to a small college in NC. I got an apartment, a dog, a bike, and a job. I started out as an art major, but true to my history I backed out and changed majors because everyone else in the class had had lessons, won contests, had something called a portfolio. For a child psychology class I had to spend time in a middle school classroom. I loved every minute of it, and changed my major to intermediate education (4th through 9th grades at the time). Fast forward a few years, and I graduated from UNC at Wilmington with a B.A. in Intermediate Education with endorsements in language arts (my primary focus) and math (because I tested out of several classes and had enough credits by default). Even I was surprised when my final GPA was 3.76. This from a girl who worked through high school and was absent 52 days in her senior year!

That next fall I took a job in NC teaching a little of this and a little of that at a city middle school. The lead math teacher, who had all the gifted classes, left in the middle of the year to have a child and decided not to come back. In order to appease the parents, the principal decided to put me in her place and get a long-term sub for my classes. I got my gifted certification and taught gifted language arts and math to several grades for five years, then moved to the county school closer to my house to do the same. Somewhere during all that time math became fun. Maybe it was the graphing calculators during my 7th year; I really don't know. But I started to love math. I already loved the kids!

Now to my philosophy. School was a scary place for a sensitive introvert like me. Sometimes it still is, but never when I am with my children. When I am teaching and we are in the zone it is pure delight. I love hearing their little a-ha moments, and making what seems like a fairly simple problem into a teachable moment full of connections and deep thinking. But to get my kids to buy-in, they have to get past their own fear of math. I've heard "I've never been good at math" from parents and other teachers many times. To get past the fear, I have to make my kids believe it is fun, understandable, and I will always be there to catch them. That means they have to love me first, and find safety in my classroom. No one can think through a problem if they are nervous or frustrated; that part of the brain shuts down while the "fight or flight" takes over. So, in short, love the kids unconditionally, show them how magical and fun math is, and then teach them to enjoy tackling the big problems. It seems to work for me!