Math Lessons for Elementary Grades

Today I read a book entitled Math Lessons for Elementary Grades. Its author is Dorothy Harrer and it is published by the Association of Waldorf Schools of North America (AWSNA). It’s a short little book of 131 pages. After an excerpt from Rudolph Steiner (The founder of Waldorf education) and an introductory chapter on teaching arithmetic in general, the remaining chapters and the bulk of the book are dedicated to sharing mathematics lessons from grades one through six.

I am adding a new section to my posts called The Lowdown. This section will be just the highlights or just a summary of the blog given in a list from 1-10. Given my blog entries tend to be verbose (though clear I hope!), I wanted to give you, the reader, an option of just getting a quick snapshot for when you don’t have the time to read a whole entry. Say no more here it is:

The Lowdown

First let me say that I absolutely want to re-read this book in order to actually do the problems presented in the book. Being a teacher, I know how important it is to actually do the problems you are presenting to your students so you can see what sorts of questions or problems they might have. It is also wonderful to challenge yourself to do every problem more than one way (like hopefully you ask of your students).

General ideas to keep in mind
Children who are weak in math should have extra time to do movement exercises that include counting forward and backwards, moving a staff around the body, walking and running. Why?

“What lies at the root of arithmetic is consciously willed movement, the sense of movement (and it) will have the effect of bringing the child’s arithmetical powers to life.”

When phrasing math problems, do say  ”I have 7, how much must I take away to get 3?” Don’t say “What remains over if I take 4 from 7? In the first example you are dealing with concrete things: what you have and what you need to get. This sort of thinking is easier for children to access. In the second example, the phrasing is abstract, making the problem more challenging to access.

Since multiplication is just repeated addition, they could and should be taught together. Not only that, but the the author claims it is much more efficient to teach all four processes at the same time without lingering too long over explanations and then just move into practicing all four. In this way I suppose, children are more likely to see the relationships between numbers and their functions, a skill which tends to be lacking for many students.

Children, especially 6-7 year olds are quite imaginative and active. As a teacher, you should reach the child using these same ideas. Use pictorial lessons for helping students access their thinking powers and rhythmic activity for memory. Dramatic acting out also helps set things to memory.

1st grade- Lessons include rhymes for numbers, shapes, a Gnomes and Jewels math story and pictorial representations of the four processes (+,-,x,/) using gnomes.
2nd grade- Story to introduce factors, active arithmetic for learning about even and odd, fill in the blank stories with math problems, a game where kids act out characters such as “Treasure Hunter,” stories for various times tables, skip counting rhythm exercises and pattern making.
3rd grade- Story about math in our lives, finding patterns in number tables, practice in written and oral skip counting, measurement stories discussing liquid and dry measurements, weights and time.
4th grade- Story introducing carrying and borrowing, traditional algorithms, area measurements, fraction tree, four processes with fractions, expanding fractions, active studies in squares, ten as a helper number, order of operations.
5th grade- History of numbers, story Pythagoras,  square, triangular and oblong numbers, chart of equivalent fractions, extend and reduce fractions, “secret” divisor, manipulating numbers when dividing and multiplying fractions, decimal practice, fraction to decimal conversion list for memorization.
6th grade- Convert fractions to decimals, percents, mills, interest, principals, rates (of loans, rent and fares) , time, simple and compound interest, commission (retail & wholesale), net proceeds, special sales & discounts, taxes (city, state and federal and why we have them), ratio equivalents

I am so impressed with what Waldorf students must be doing in 6th grade math. I didn’t learn most of this stuff until much later and some of it like rates of payment, interest and loans I don’t remember ever being taught in school….though I do remember they were problems I couldn’t do on some of the tests I took. Although I don’t agree with all of Rudolph Steiner’s philosophies, it is apparent from this book that the teaching content and methods within this book are written to be developmentally appropriate. In constructivist teaching, a teacher is there to guide each student through their own process of learning. Put another way, the teacher helps students construct their own learning as opposed to telling them what to do and often how to do it. I may have to do a whole blog on constructivism given there is a lot of semantic disagreement among educators and critics.