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!