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.
Math was never my favorite subject as a child. I remember sitting in my second grade class while the teacher taught us to tell time. I didn’t understand it and I was terrified that she would call on me. I didn’t ask for help because I didn’t want anyone to know that I didn’t understand. I had the feeling I just wasn’t good at math. Now math might not be one of my natural strengths, but there isn’t any reason why I couldn’t have learned to feel strong and confident while receiving an excellent math education. I know many homeschool teachers are scared to teach math to their children. Maybe they also had hard schoolroom math experiences. Maybe they still don’t feel very comfortable with math topics. Maybe they forgot so much they’re worried they won’t know what to teach. Most of all? I think moms don’t want their children to have an aversion to learning math. They don’t want to pass on a math phobia. They want their child to get a solid math education without it being painful.
Even if you didn’t enjoy math growing up you can still love teaching it. And your child can have a completely different experience than you did. I love teaching math at home. And the way I teach it is nothing like the way I was taught in school.
I want to zero in today on what holistic learning looks like in first grade math lessons. For an overview of the essentials of first grade please see this post and to read more about the first grade math main lesson blocks please see here and here.
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:
- Work towards moving and speaking at the same time
- Introduction to the quality of numbers
- Develop a sense of number and a sense of the relationships of numbers
- Learn to count with fluency up to 100 and back
- Learn skip counting (or rhythmic counting) by 2s, 3s, 4s, 5s, 10s, and 11s
- Introduction to the four processes (addition, subtraction, multiplication, and division)
- Learn the math facts up to 20
- Form drawing and introduction to freehand geometry
- 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:
- Developing a sense of the beauty of mathematics
- Experience with active arithmetic (kinesthetic learning)
- Developing a sense of number
- Developing a sense of the relationships of numbers
- Mechanical skills in writing numbers, counting, four processes (operations), and skip counting
- 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. See this post for ideas on how to incorporate active math in circle. 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.
What does a math lesson look like when WORKing WITH THE WHOLE CHILd?
Begin each lesson and each new topic with activity. Get the whole body involved in experiencing math through games, movement, and rhythm. You could:
- Toss a beanbag while you count
- Play hopscotch
- Jump rope
- Recite a verse
- Skip while counting by fives
Then teach something new through the feelings or imagination. You could:
- Tell a story with the four processes using animals, gnomes, or fairies
- Act out a little number-journey together - be a squirrel family gathering acorns
Take what you’ve learned and work with the intellect. You could:
- Review and practice topics from the day before and previously
- Use manipulatives to solve four processes problems
- Write problems in your main lesson book and illustrate them
SCHEDULE FOR FIRST GRADE MATH
I recommend 12 weeks of main lesson divided into 3 blocks (often October, January, and April work well). The first main lesson should focus mainly on numbers themselves - what they are and how they’re expressed in the world (Quality of Numbers). The next two blocks should focus on the four processes (Arithmetic).
Finally, 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.
Making Math Meaningful by Jamie York is an excellent overview of the Waldorf math curriculum for grades 1-4. The opening chapters on how to teach math effectively and avoid math phobia are priceless. The curriculum and objectives for each grade and main lesson block are given in detail but the particulars on how to bring the subject to life (with games, verses, art, stories, and so on) are left up to the teacher.
Active Math in Circle is a useful post on incorporating math into circle time.
Lavender’s Blue First Grade is a complete Waldorf-inspired curriculum with a uniquely strong math program. It includes detailed instructions for teaching math, fully planned out main lesson blocks with illustrations, active math for the year (with all the verses on audio), and original stories for a beautiful and strong start in math! Click here to learn more and purchase.