Parents and teachers are often concerned about two things: First, how can we ensure that students will be adequately prepared for what faces them when they leave school? And second, with the apparent rise in the number of students with learning challenges, how can teachers manage to teach the full spectrum of students in their classes? Related to math, to complicate matters, parents can be sometimes fearful that their children will end up as math traumatized as they are. Inevitably, the fear seeps down from the adults to the students.
Math Anxiety Is Extremely Common
“Math anxiety: an intense lifelong fear of two trains approaching each other at speeds of 60 and 80 kph”
A research study from Spain showed that as many as 6 out of 10 university students present symptoms of math anxiety. Other research in the UK has shown that over half of adults can’t do basic math at an 11-year-old level. It goes on to say that in terms of employment, people with poor math skills are twice as likely to be unemployed as those without. Another study reports that 1/5th of adults cannot do basic fractions or percentages and many cannot even calculate a tip at a restaurant.
Talking About Our Fears
What is the solution to the fear of math? We can start talking about this fear with parents, our colleagues, and to ourselves. With teachers and parents, we can create time for discussions about this. We can ask, “What math experiences would you like your students to have?” Rarely will Waldorf parents say that they want their kids to plow through a long list of topics as quickly as possible. Then we can ask what it really means to have our students prepared for their future math studies and the “real world”.
How Does Math Relate To Us?
Waldorf starts off the introduction to math by asking a seemingly simple question, “What is the largest number in the universe?” My son (aged 5) came home from school and asked me the same question. I answered, “Well, erhmmm, it’s infinity.” He said, “No, one is the biggest because I am one.” Other responses discussed in class may be, “One is the biggest because without it there isn’t any 2, or 3, or even a million,” “One is the biggest because everything there is in one Universe,” or “One is the biggest because it can be any number it wants.”
All sorts of philosophical and mathematical truths become evident through just this “one” discussion. This gets students thinking in a whole new way about numbers, and how they relate to us and the world. Eventually, the children arrive at “I am one!” – they see how their bodies are shaped like the number one, they relate themselves to the vastness of the Universe, and realize at that point that they are co-creators.
Waldorf Teaches Math Using The Whole Body
Waldorf Education does not teach math in isolation of other subjects. It is part of a holistic learning approach, which connects the child’s inner self (that Waldorf’s founder Rudolf Steiner refers to as “will”) and body through muscle memory exercises. For the Class 1 child, Waldorf Math is really a kinesthetic or whole body learning experience.
By moving to math in the early grades, even before reading and writing, the child develops a proficiency much like a musician memorizing their scales. It is a slow and unhurried approach that does not push the child to count or read too early (which has been found to taint a child’s passion for learning). Once a child is moving to math, he or she may begin to use beans or glass beads to better understand the relationships that additions and subtractions make with the whole. Imaginative math fairy tales are told, where the children get to participate in solving the same word problems the main characters do. This allows for a real “living” math to develop within the children. When children begin writing, they begin with roman numerals. They integrate this lesson within their form drawing block.
Drawing Roman Numerals
Each number, 1-12, is a discussion involved in this deep intensity of imagination. Waldorf begins with Roman numerals and incorporates geometry into the discussion of each number, scribing freehand the relative polygons and stars. The children work to master each of the stars, crossing the vertical midline over and over again as they practice on large sheets of paper. Eventually, a particular star will stand out as the class favorite which tells the Class Teacher an immeasurable amount about the class itself. All of this happens in the first grade.
Math and Music
Math is also closely related and taught with music, furthering the important connection between a child’s body, and their understanding of numbers. As an adult, I know that the most lasting memories for me are always those with more than one sense being used. I still remember vividly walking by a jam factory near my house when I was a child on the way to school and counting the metal fence rungs while breathing in the delicious aromas of the jams.
Stanford Professor Jo Boaler says that students most effectively learn “math facts” working on problems that they enjoy, rather than through exercises and drills they fear. Speed pressure, timed testing and blind memorization damage children’s experience of math, she says. She finds that children who excel in math learn to develop “number sense,” which is much different from the memorization that is often stressed in school.
Problem Solving vs Memorization
And how do we generate enthusiasm for learning math and develop mathematical thinking? By carving out time in our classrooms for the students to have meaningful mathematical experiences. One math problem, which helps foster creative problem solving, is to find three numbers between 1 and ½ that multiply together to equal ½. This wonderful, open-ended puzzle encourages multiple solutions and is appropriate for a variety of ages.
Another problem is to discover a special relationship found with any circle and two inner tangent circles – specifically: how does the triangle which connects the three centers relate to the radii of the circles? A fascinating problem! The problem invites exploration, debate, and a depth of learning that we should all be striving for. Using art, colour and drawing geometric patterns and shapes further enhances the understanding and enjoyment of mathematic principals.
Math Can Be Very Imaginative
So from the start, children are aware of the significance of numbers and enter very deeply into them. When they have the imaginations of the numbers, they use their will to execute stars and polygons. They move their bodies through the math facts of all four processes (+ – / x) each day, and create personalities for each math function. Some children learn about Tessa Times, Mickey Minus, Penelope Plus and David Divide or other characters who are known by how they appear and act. For example, David Divide has a sword and always chops things up, sometimes in half or more. Children take part in music classes involving flute, voice, and lyre to illustrate the beauty of the voice of numbers. They use manipulatives (e.g. bean bags, chesnuts) to work through exciting math tales and classroom conundrums.
This multi-faceted learning approach continues into Class 2. Here is a Class 2 report summary of a math block lesson:
Column algorithms vertical addition 1, 10,100. By using the image of the chipmunks and their holes, rooms, and chambers to store and count the nuts, the children understood well by the end of this block. We practiced many sums and wrote some in our books. We worked the times tables in many different ways, always with rhythm: sticks, walking clapping bean bag throwing etc. We reviewed the 2 and learnt the 4, 8, and 11 times table. In circle we are doing lots of mid line work, expansion contraction, throwing and catching, and recently juggling! We have been walking squares, stars, and some eurythmy.
Class 2 Main Lesson Book Examples
A genuine love of math can only be enhanced by a practical approach in the mid to later grades. In the third grade curriculum, fractions are learned through cooking and building. At this stage, there is the introduction of the orchestral stringed instruments at that same time, which also leverages many math basics. Math is the key to participating in the music lessons. Math is everywhere. The sixth grader gets to experience this by working with the Fibonacci sequence and Euclidean to Platonic geometries. Waldorf Education seeks to help students develop and integrate math, music, building, movement, storytelling, and more all at once.
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