There has been some discussion within the Waldorf homeschooling community about when (or if) to add in a mainstream math program as supplementary practice for the Waldorf homeschooled child. Homeschooling mothers often worry about daily practice in areas like math, especially if you live in a state where taking standardized tests or the possibility of your child attending public or private school is in the near future. Here are a few of my thoughts and experiences about the mainstream programs folks are using and a few thoughts as to *how* to use some of these resources. Mathematics in Waldorf Education has a developmental approach and often mainstream math programs do not share this same view so I think it behooves discussion and consideration in regards to how to add practice of math into the homeschool day. I have included Making Math Meaningful and Math By Hand in this discussion, as I think they could be used no matter how one homeschools and these guides, while based in Waldorf Education, also seem to have an understanding of what is going in math education in all realms.
Grades One and Two: I have seen Waldorf homeschooling parents use a mainstream math program in these grades, particularly if they were afraid they were going to have to put their child into public school at some point, or if they held allegiance to a particular math program (usually I see this in families who feel very loyal to Singapore or sometimes RightStart math from other homeschooling experiences). However, I honestly don’t think you need a supplemental math program for these early grades where number sense is being developed. Daily practice that you make up, along with the math blocks, should really be enough at this stage in my opinion so long as you are diligent with practice. If you need a guide to this, please let me recommend Jamie York’s “Making Math Meaningful” for grades one through five (blue cover) and also the book “Games For Math” by Peggy Kaye. If you really feel as if you need “something else” in this stage, Math By Hand is a Waldorf-compatible resource that has some lovely hands-on kits to help you bring math in a visual way with certain activities and stories. Math By Hand runs first through fourth grades.
Grade Three: For Grade Three, several different Waldorf curriculum providers recommend the use of the “Key To….” books on the market to supplement the math blocks. The “Key To” books focus on one particular area – such as four books about measurement, four books about fractions, etc. This often works well within the framework of Waldorf math since it focuses on one topic at a time. Some families start the first fraction book of the “Key To” series in third grade and see how far they get. I think you could do this several different ways depending upon your child’s needs. Some start the “Key To Measurement” series at the beginning of third grade and work through most of the books in the third grade (one of the books is about volume, which really is more of a later middle school topic developmentally in Waldorf Education). Some parents do the measurement block/blocks first and then do however many of the measurement books they can get through in the second half of third grade and carry on into fourth grade. I like to do more practice with conversion of measurement in fourth grade so I personally don’t mind using some material from these books in fourth grade if I need a source of practice problems, but I don’t think you need these books in third grade either if you are diligent about practice.
Fourth grade in Waldorf Education sees a review of everything covered so far, along with a concerted effort to work with times tables in cross stitching and other projects, long division practice and fractions. Fractions correspond to the children themselves who are now nearing the end of or past the nine year change and can see the differences between themselves and others; there may be splitting of groups from the whole of the student population (fractions!). Some parents use the “Key To Fraction” series here. Again, this may carry on into fifth grade depending upon what point you start them during the year. Some families are still using a traditional all –around math program if they started in the earlier grades or if they have a student that they consider to be having a harder time, they may start a “traditional” math program for extra math practice in fourth or fifth grade. Saxon, with its spiral approach and yes, a bit slower approach then some other programs on the market, seems to be a favorite for this – I would just warn you to look at it! It is VERY different than the developmental approach of Waldorf and the scattering of topics from day to day in the spiral approach doesn’t work for every child. I like the visual approach of “Math By Hand” for some of the topics in fourth grade as well. In general, however, most families I speak with seem to wait until middle school for this step into a more formal math program.
Fifth grade is a great review of everything up until this point. The metric system should be introduced if it has not already (or the English system if you started with measurement in metric), and decimals. Tori Finser has several sentences about “Decimal Island” in his work, and I love that image to draw from in this grade. The approach to supplemental math often looks similar to what I wrote about in the fourth grade section. Here is a post by Waldorf School teacher Meredith about using mainstream math resources for grades 4 and up that might be of interest here.
Sixth grade: The general challenge of many of these supplemental programs is that they often don’t follow the developmental approach of Waldorf Education. There are reasons WHY fractions are in fourth, as I briefly mentioned, and decimals are in fifth and percentages are in sixth grade. However, sixth grade with its introduction of business math and the conversion of fractions, decimals and percentages, plus the constant review of most basic arithmetic, makes it an easy time to add in a mainstream program that reviews everything covered up to this point in addition to the regular sixth grade math blocks of geometry, percentages and business math. Most families I know consider “Making Math Meaningful” or “Saxon Math” at this point as daily supplemental work to the math blocks presented. I personally like Rod and Staff, a Christian program, for thorough review in sixth and seventh grades as a source of practice problems – not as a replacement for Waldorf math blocks nor a replacement for our own movement in math and looking at math in art and nature. Rod and Staff works by topic with review of previous topics in each lesson (but smaller review compared to the spiral approach of Saxon). This is not a blanket endorsement, and different children need different things. Please look at it and decide if it resonates with you or not if you decide you need a source of practice problems. These mainstream resources are not at all “waldorf” by any means. There are also “Key To” books about percentages could be used during this year, and the “Key To Geometry” series.
Seventh grade includes work in reviewing and working with everything up to this point, more complex geometry, area, an introduction to algebra and much more. I think “Making Math Meaningful” (the middle school overview book with the purple cover) is a go to resource for what to cover, and again, supplemental mainstream program choices I hear families using include the “Key To” series in geometry, metric system and algebra or the use of Making Math Meaningful (the student workbook) or Saxon Math. I personally still like Rod and Staff for sixth and seventh grades.
Eighth grade sees work with platonic solids, computers, stereometry, loci and more. Some families are expanding into either prealgebra or algebra at this point. Jamie York has an entire post regarding when to place algebra here and the pressure that is filtering down to the schools. The sequence I see used quite a bit is either Saxon Math for supplemental practice, Making Math Meaningful’s eighth grade or yes, even a full-blown pre-algebra or algebra program. What I am hearing from non-Waldorf homeschoolers is the push to do algebra in this grade in order to move into calculus in twelfth grade.
Please do remember this is a discussion about SUPPLEMENTAL, daily practice – not the math blocks themselves, and also doesn’t take into account the daily math practice we get in movement nor the mental math practice we do daily as part of Waldorf homeschooling.
I would love to hear from you, and if/how you use mainstream math resources in addition to your math blocks, or your feelings about pre-algebra versus algebra in eighth grade in order to get to calculus by twelfth grade.