The Christopherus Curriculum – Mathematics
The following is a rough outline of how our math curriculum unfolds over the years, through the grades. As of writing, we have only gotten through 5th grade so there will, undoubtedly, be some changes! You can see as well that we have put seventh and eighth grade together – this is in part to leave ample flexibility for those students who are advanced in their work in math as well as to meet the needs of those who are struggling.
In general, I advise people to not hold their children back in math. Whereas one might have very good reasons for wishing to wait in, for instance, science or language arts (i.e. the child is not mature enough to deal with the content), math is rather different. However, like all of the Waldorf curriculum, the way math progresses is not arbitrary in any way. It is carefully crafted to meet the needs of the developing child. And so I advise parents that if they need to move ahead more quickly with their child that they should try to stick to advanced work within the topics which are within that grades’ curriculum.
Games are a very good way to challenge fast students – and inspire sticky ones. Joyful Movement (see our Bookstore) has a number of math games in it and throughout our curriculum we give ideas, instruction and resources for you to engage your child actively in mathematics.
As with most topics in our curriculum, we tend to go rather slowly at first and then really put on steam. Our goal is academic excellence to the full extent that each child is capable of. Please click here to read a blog article by Donna on academic excellence
We bring this up here because it seems that Waldorf education does not have the reputation for rigor in the sciences and in math that it should. There are a number of reasons for this (including an abundance of teachers who come from an arts background who feel insecure teaching math and science). One area that we are concerned about is the practice of telling stories for math lessons beyond the earliest grades. We question whether this undermines the need for children to grapple with abstract thoughts as they pass their ninth birthdays.
And so, though we certainly start out with stories, by 3rd grade we have, for the most part, ceased providing stories in our curriculum for math. Instead, as third grade is utterly concerned with practical work (see our 3rd Grade Curriculum), the work itself, the hands-on measuring of wood, rows for carrots and so on, carries the lesson material. And because we are homeschoolers, this is easy – we can do while children in classroom often have to rely on stories or models. By 4th grade, we feel strongly that children have no need for stories – they need, instead, to be grappling with the math itself, the concepts and ways of thinking demanded by mathematics. This is not what is done in many Waldorf schools nor by other Waldorf curriculum providers such as Live Ed who continue to use stories to explain mathematical concepts to children.
Obviously, we do not simply provide dry concepts which need to be learned by rote and worked with only by pencil and paper! Our Christopherus Curriculum is lively and exciting, speaking to the whole child. Thus, throughout all 8 grades, we provide a wealth of ideas and strategies to bring math to your child in a living way. Ideas include hands-on work (music notation and quilting in fourth grade to support learning fractions for instance); games; movement; real life business math; cooking; and artistic exploration with geometry and the properties of numbers and operations.
Quality of Numbers 1 through 12; Four Processes, addition, subtraction, multiplication and division. How these four work together. Math squirrels, not the usual tired Waldorf math gnomes! Counting forward and backward to at least 100. First multiplication tables. [Part of our Full First Grade Curriculum]
Further work with the four processes up to several-step addition, division, multiplication and subtraction. Moving from horizontal to vertical operations. Mental math (number journeys). Place value and carrying and borrowing (re-grouping). Odd and even. Ability to count into the thousands. Further work with multiplication tables. [Part of our Full Second Grade Curriculum].
Consolidation and deepening of work from last year, especially with regard to several-step carrying and borrowing. Main subject for the year – experiential measurement, carried across the curriculum in handwork, crafts, cooking, building and farming as well as Native American stories. Time and money. Use of zeroes and very large numbers. Number journeys as well as word problems. Estimation and rounding off. Basic graphing (weather data). [Part of our Full Third Grade Curriculum]
Catching any weaknesses a student might have involving the four processes. Long division. Breaking down large multiplication problems. Square numbers, factoring and prime numbers. Estimation, comparison and rounding off. Number journeys and word problems. Math vocabulary. Charts and graphs. Area and perimeter. Measurement problems (Key To math workbooks included). Introduction to fractions (Key To workbooks included). (Map skills during geography.) [Available separately: Fourth Grade Mathematics]
Long division. Math of ancient civilizations. Further work with fractions and measurement. Decimals. More on area. Mixed numbers. Complex mental math and word problems. Free hand geometry. (Map skills during geography.)Note: many fifth graders will find plenty of challenge and support from our fourth grade mathematics resources, sold in the Christopherus Bookstore.
Fractions, decimals and percentages. Business math (interest, commission, taxes, profit and loss. The three uses of money – gift, loan, purchase). Negative numbers. Metric system (for Americans). Geometric constructions and deductive geometry. Ratio. First steps in algebra. (Use of scale in mapping.)
Seventh and Eighth Grade
More on fractions, percentages and decimals. Geometric proofs (Pythagorean theorem, volume, area, Platonic solids). Powers and square roots. First steps in algebra. Biographies of mathematicians, a sense of the historical development of math (8th grade). Binary system and introduction to computers (8th grade). Statistics and graphing. Accounting. Proportion and the Golden Mean and the Fibonacci series. Algebra.