I need not touch upon the subject of Mathematics. It is receiving ample attention, and is rapidly becoming an instrument for living teaching in our schools. - Charlotte Mason, School Education (Volume 3), page 236
This quote makes me laugh because Mason had a lot to say about EVERY topic, including math (which she discusses at length in Home Education, or Volume 1). I imagine an interviewer asking her, "Miss Mason, and what do you think about math?" And Mason responding, "I need not touch upon the subject..."
My own ideas about math instruction are influenced by my experience teaching elementary and middle school. At the public school where I work, I teach math using the district-adopted curriculum. I am not able to teach math the way I believe math should be taught, or the way I will teach my daughter.
For example, last week, during our unit on measurement, I taught my fourth graders a lesson on converting standard units of measurement (12 inches equals 1 foot, 36 inches equals ___?). The very next day, the lesson was converting metric units. This is not the way I would teach my own child. This is not the kind of pacing plan that gives children the experience they need to master these skills.
I've posted my math goals for preschool through fourth grade, and I intend to post about math in grades 5 through 7 (pre-algebra).
This example of converting units of measurement is a good example of how I teach vs. how I will teach my own daughter. To be prepared for algebra as an 8th grader, a child does not need to master converting standard units of measurement and converting metric units during the same year, let alone the same week.