# Category Archives: Pedagogical Content Knowledge

## Your mathoscope is good when Pedagogical Content Knowledge in harmony with Foundations of Math

Your mathoscope is good when pedagogical content knowledge is in harmony with foundations of math.   However, when they are in conflict, your mathoscope is bad, and confusion, rote procedural learning and homework bloat are in your future. When the lesson … Continue reading

## Fractions first then definition of length

Suppose we have defined fractions algebraically and worked out their rules including for adding fractions with different denominators.  Now we are ready to apply this algebraic construct to length.   We consider a function from point sets on the fraction number … Continue reading

## Simple Natural Number Geometric Measure Length

The number first geometric measure second approach is discussed here in terms of natural numbers.  We consider the case of length first. We are dealing only with natural numbers. No fractions and no signs.  We have a number line with … Continue reading