Introducing new math topics in the Waldorf lower grades

All too often, if a teacher is asked, “Why are you teaching this math topic to your Waldorf students now?” the response is “Because that’s when everyone does it.” An example is borrowing. Most teachers introduce borrowing (and have the children practice it a great deal) in second grade. Why? “Because that’s when everyone does it.” We should instead ask, “When is the best time to introduce borrowing?”

If a math topic is introduced too early, or studied too deeply too soon, then two things are likely to happen: many students in the Waldorf class will get left behind, and even the ones that can keep up will end up simply doing things mechanically without understanding what they are doing. They are then simply following blind procedures instead of developing strategies, developing mental arithmetic skills, and developing flexibility in thinking. The other extreme – introducing a topic too late – is also problematic. It is best to take the middle road and look for the developmentally appropriate time to bring the topic to the students. Then they will learn the material more deeply, in less time, and with wonderful enthusiasm.

Generally, we should ask the question, “Why do we do what we do and when do we do it?” As Waldorf teachers, we need to be able to articulate our answer to this important question to ourselves, to our colleagues, and to our parents. Our answers need to be soundly based upon the pedagogical principles of Waldorf education and upon the developmental stage and needs of the children.


2 Responses to Introducing new math topics in the Waldorf lower grades

  1. As a Waldorf and state school teacher, I always enjoy getting ideas from different sources and appreciate the effort that people go to make educatin accessible to all. I am always looking for resources and ideas for mathematics and spend much of my time transforming the state education mathematics ( which I find very useful and appreciate the work that goes in to it) into Waldorf methodology. I notice you use the concept of borrowing but I find this , if I may be so bold , as not true, because we do not borrow we actually take . I know that borrowing is a device but we actually take from the tens and never give it back. what is your comment on this?
    Thanks Sue

    • I realize that many would prefer not to use the term “borrow”, and the reason given is usually what you have stated.
      The reason I use the term “borrowing” (when speaking with a broad group of teachers) is because it’s familiar; if I say “borrowing”, then teachers know what I am speaking about. I don’t personally have great issue with the term. Words often have different meanings. There is not a commonly accepted and acceptable word that I know of. I have heard “regrouping”, but that is not specific to the subtraction process. “Vertical subtraction” is a term I use, but that doesn’t really capture it either. What is actually meant is: “taking from another place value when there isn’t enough in the current place value when doing vertical subtraction”. So what is the perfect word?
      I encourage teachers to invent their term to use with their students in the classroom.
      Thanks, Jamie