As I read about continuing efforts to improve our education system, I am reminded of the following quote:

Ask not what your country can do for you—ask what you can do for your country. (John F. Kennedy; United States presidential inaugural address, 1/20/ 1961.)

Thus, I paraphrase Kennedy’s statement to:

Ask not what your educational system can do for you—ask what you can do for your educational system.

For me, this is a top-down versus a bottom-up issue. It is very easy to be critical of what exists and of what the ubiquitous “they” are doing about it. It is far harder to understand that “they is us” and that we—as individuals and small groups of individuals—can make a difference. You may have recognized the “they is us” statement

Pogo's statement, "We have met the enemy and he is us," still gets quoted by environmentalists. (Pogo comic strip by Walt Kelly. See http://en.wikipedia.org/wiki/File:Pogo_-_Earth_Day_1971_poster.jpg.)

Finally, I am reminded of what is perhaps my favorite quote:

“Never doubt that a small group of thoughtful committed citizens can change the world: indeed; it's the only thing that ever has.” (Margaret Mead; American Cultural Anthropologist; 1901–1978.)

The year 2011 is coming to an end, and we are about to begin the year 2012, please pause for a moment and think about what you, personally, have done during this past year to improve our education system. What have you done to improve your own education? What have you done to improve the education of others? In these endeavors, what has worked well for you, and what has not been as successful as you would like? What will you do the same and what will you do differently during the coming year?

One of the personal things I have worked on is to improve my educational-related conversations with some of my grandchildren and their parents. I still ask the children,  “What did you do in school today?” But then I quickly change this into something more specific such as, “What did you learn in math today?” I lead the conversation into an interactive discussion about what was studied, how was it studied, was it interesting and fun, how it relates to what has been learned in the past, what is it good for, and so on. I take a combined top down (question strategy) and a bottom up (help me learn what you are learning) approach.

If the child’s parents are present, I broaden the conversation to include them in my ideas about what is good and what is not so good about their child’s math teaching/learning environment. In essence, I am role modeling how they might interact with their children and math education ideas that they might want to learn more about.

Here are two key ideas about math education:

1. Math is a very broad and very deep subject. The vertically organized curriculum is a challenge to many students because they forget what they “supposedly” covered and learned in the past. The “lose it” part of “Use it or lose it” tends to win out as students progress through the math curriculum.
2. It is difficult for learners to transfer their math learning from the math-period instruction time to the rest of their formal schooling and to their lives outside of school. Note that this relates closely to “use it or lose it.”

These two ideas can help form a basis for math education interactions that you have with children, grandchildren, students, and others. They also form the basis for you to do something about our educational system.