In the 9th grade Waldorf math unit, it is important that students learn to factor a variety of polynomial expressions, and eventually develop the ability to solve quadratic equations. Time needs to be taken here in order to ensure mastery before moving forward in the Waldorf high school math curriculum.
It is best for the students to formulate their own rules for when it is possible to factor a binomial expression. They may formulate a rule such as: “A binomial which has no greatest common factor can only be factored if it has even exponents, coefficients that can be square rooted, and a negative sign between the two terms.” Of course, this can be expressed in a variety of ways, but the point here is to have the students articulate the rule as clearly as possible.
When factoring trinomials, where the lead coefficient equals 1 (a = 1), again, the theme is to have students come up with strategies for solving these problems. It can then be quite valuable to have students share their own strategies with their classmates. Of course, there are varied opinions about which strategy is best. The important thing is that it isn’t just presented to the students as a blind procedure to follow in order to get an answer. From Jamie York’s 9th Grade Waldorf High School Math Curriculum.