First Grade Math
I started researching homeschooling when my oldest daughter Aiya was two years old. My husband and I had both taught in a free school (similar to the Summerhill or Sudbury models) so I went in with the idea that we would probably be unschoolers. Still, I wanted to make an informed decision and I was fascinated by all the different philosophies and methodologies that were out there. When I found Waldorf it was like meeting a new friend and feeling like I had known her forever. I don’t consider myself a Waldorf purist though and here’s why: I’m a mother and my first responsibility is to my individual children and not to any philosophy. So I look first to my heart and their hearts and then to the wisdom and experience that I find in the Waldorf tradition. And when I read, I’m often stunned. Inspired. Grateful. The richness of the philosophy, the deeply holistic and respectful perspective, and the incredible insightfulness just blows me away time and time again.
When you start teaching with Waldorf you’ll find that many of the assumptions that we have in our culture are turned on their heads. Assumptions such as more/earlier/faster is better. Or that learning takes place mostly in the head. Or that downtime, sleeping, and summers off are a waste of time and detrimental to learning. Waldorf is a really different approach to childhood, parenting, and schooling. And even if you combine Waldorf with other methods or just look to it for inspiration it’s helpful to understand the ways that it’s really, really different.
Waldorf is at its core a holistic method based on the development of the whole child. In the human being, thinking, feeling, and willing (doing) are integrated and Waldorf methods take advantage of that by including academic, artistic, and active parts in every lesson. In other words, we are educating the head, heart, and hands to provide a much deeper learning experience than if we focused only on the head.
I want to zero in today on what holistic learning looks like in first grade math lessons but for an overview of the essentials of first grade please see this post!
Waldorf is an academically (and artistically) rigorous education but the speed of acquiring understanding and skills is carefully attuned to the developmental capacity (for example, the neurological readiness) of the child at each age. In many subjects, that means introducing concepts later than in other methods. For math, it’s a mixed bag. Math isn’t introduced at all as a subject until first grade and the introduction is deep and slow with a focus on the quality of numbers and feeling the rhythms of counting in the body. But then all four arithmetic operations are introduced and practiced together (because they are related to each other), they are presented for conceptual understanding rather than simple rote learning (although learning the facts is definitely emphasized), and there is also an introduction to freehand geometry, a pretty advanced topic!
Here’s a list of the typical objectives for first grade math the Waldorf way:
1. Work towards moving and speaking at the same time
2. Introduction to the quality of numbers
3. Develop a sense of number and a sense of the relationships of numbers
4. Learn to count with fluency up to 100 and back
5. Learn skip counting (or rhythmic counting) by 2s, 3s, 4s, 5s, 10s, and 11s
6. Introduction to the four processes (addition, subtraction, multiplication, and division)
7. Learn the math facts up to 20
8. Form drawing and introduction to freehand geometry
9. Learn to write the numbers up to 100 (and roman numerals up to XII).
You can see these aren’t all facts or quantifiable skills. In our culture we tend to have a mechanical view of learning the skills of math and reading, when in fact the mechanical aspects of these skills are just one (important) part of a bigger holistic picture. So what is the bigger holistic picture of teaching mathematics? I think in first grade we want to focus in these areas:
1. Developing a sense of the beauty of mathematics.
2. Experience with active arithmetic (kinesthetic learning).
3. Developing a sense of number.
4. Developing a sense of the relationships of numbers.
5. Mechanical skills in writing numbers, counting, four processes (operations), and skip counting.
6. Developing a sense of balance (form drawing and freehand geometry).
How is this all accomplished? Let’s look at a few of the objectives for first grade math and how they could be taught holistically.
How do you teach counting and skip counting? You can work with movement and rhythm, using your body to march, skip, gallop, walk, stomp, clap, toss beanbags, etc. as you speak. You can work with imagination, pretending that you are crossing a stream on stepping stones or chopping wood with an axe. You can work with verse and poetry (for example with the Strange Family verse).
How do you teach the four processes? You can start with an imaginative story to show the ways that numbers can be related to each other. You can use characters in your story to represent each process and present it in a rich way, drawing on temperament, verse, and real problems that must be solved. You can work with manipulatives including fingers, acorns, or counting stones to make each problem very concrete, visual, and kinesthetic. You can draw the problems as well using little pictures before moving into the more abstract with dots and then numbers and symbols. You can move into practicing math facts and multiplication tables using movement and rhythm once the concepts are understood. You can keep the four processes in the holistic realm by learning not just the mechanics and not just the facts, but also learning how the processes are related, how they undo each other, how the amazing patterns in numbers and shapes translate into these relationships.
How do you teach writing the numbers? You can start by understanding the numbers as a larger construct than just their forms - you can feel the numbers in your body and in rhythms of music and poetry, count them on your fingers and with many objects, notice them expressed all around in the natural and physical world. You can learn the Roman numerals as an extension of counting on the fingers. You can learn the arabic numerals as form drawings, special symbols that communicate the numbers to others. You can practice writing numbers in all sorts of kinesthetic ways such as drawing them in the sand, walking the forms, drawing them large on the chalkboard, tracing them on each other’s backs, modeling them with beeswax, as well as writing on paper.
If I could say anything about teaching first grade math from a Waldorf perspective it’s this: Build a capacity for learning mathematics, a sense of beauty and awe for how numbers are expressed in the world, a deep understanding of numbers and their relationships…..and the skills will be a natural extension of all this, just icing on the cake.