Thursday, November 8, 2012

Math Recalculated

One of the first posts I wrote for this blog was about math.  At the time, we were more or less "unschooling" math, and I was letting Bean engage in math play instead of doing structured work that moved along in a more or less orderly fashion.  At the time, I thought we would do that until it didn't work anymore.  About a month after I wrote that post, Bean stopped being willing to make colorful pictures out of the solutions to various types of equations; so I let her just do the problems themselves.  When she realized this was the same thing as just doing the problems in a workbook, she was no longer interested.

By this time in our lives as homeschoolers, we had been through enough cycles of smooth sailing, hitting brick walls, and starting over with something else that this was a familiar pattern and I had a fallback position for the next time this happened in any subject. I went back to The Book. My homeschooling bible that is, Home Learning Year by Year, by Rebecca Rupp. We were at the end of the third grade academic year, so I looked at Rupp's suggestions for fourth grade and saw that she suggested the Key To series for Fractions, Decimals, Geometry, and Measurement from Key Curriculum Press.  Each series covers one topic over four to eight workbooks, with each workbook representing about one grade level worth of work, and they are recommended for 4-12 graders. When I saw that each book was only four dollars, I had no problem ordering the entire Fraction series.  As soon as it was clear that Bean liked the style of this series and was willing to do the work, I ordered the entire series for each topic: Decimals, Geometry, Measurement, Metric Measurement, Percentages, and Algebra.  [I must note that the Algebra and Geometry series are not exactly the equivalent of high school level classes, but for upper elementary and middle school students, they are very serviceable for Pre-Algebra and introductory level Geometry.  The Geometry books do not include proofs and do not require any exposure to trigonometry.]

Armed with the Key To books, I outlined my plan for fourth grade last year, using Book 1 from the Key to Fractions, Decimals, Geometry and Measurement series.  I supplemented with the fourth grade Math Made Easy book for number theory, operations, and probability.  Math Made Easy is a workbook series published by DK, which is available from Amazon, and periodically Costco.  Intellectual snob that I am, it would be easy to overlook a workbook like this if it weren't effective.  It's not Singapore, Saxon, Right Start, or any other program popular with homeschoolers, and as such doesn't have conference cred, but Bean really likes the no nonsense layout and that aside from a few examples, there are no prescribed ways to do the work.  For kids who can figure out their own way from raw numbers to solutions and for parents who feel reasonably confident in guiding them there without a cheat sheet, these books are more than adequate - a fact our homeschool consultant has vetted more than once.

Last year, Bean was using all of these workbooks at the same time: Fractions one day, Geometry the next, etc.  She liked the variety, and that kept her interested and working, but the results were inconsistent.  By the end of the year, she had finished book one in most of the Key To books and was very confident with fractions and geometry, but she still didn't know most of the multiplication tables and was behind in her other computation skills (multi-number addition, subtraction, and division.) I knew the problem had more to do with application problem than a intellectual development.  That is, she was developmentally ready to do the work correctly, but wasn't applying her attention effectively.  If there was a developmental issue, that was it.  Because we were jumping around so much, the things she didn't find as interesting weren't sticking and she wasn't getting enough consistent practice.

So for fifth grade I decided to see if she was ready to approach math in a more disciplined way, tackling one topic at a time.  When I wrote up my plan for the year, I went through Home Learning Year by Year and looked at each math topic she outlined.  The subjects that are covered by Key To books are easy, Bean is doing the second book for each of those.  For number theory, probability, money problems, and word problems, I went through the fifth grade Math Made Easy table of contents and wrote down all the appropriate page numbers.  (By the way, Math Made Easy also covers fractions, but I like the way they are covered in the Key To books.  If Key Curriculum Press had books for operations, probability, and number theory, I would probably use those instead.)

This year, instead of jumping around, we are making the developmental leap of tackling one topic at a time.  So far this year, Bean has covered number theory and probability using Math Made Easy and she spent the entire month of October doing Key to Fractions Book Two.  She started Key to Decimals Book Two today, but between field trips for her California History class, Thanksgiving and open houses for kindergarten programs (yes, kindergarten; and yes, school - that's another blog post for another day) we won't scream through that book at the same speed with which she covered fractions.  So far so good, though Bean asks me at least once a week when we are getting back to Algebra.  My reply is that she can do it on her own any time she likes.  I'm not trying to hold her back; I know she has no trouble with algebra and will do it if she really wants to; I just want to make sure she masters the other elements of math that she is ready for but would ignore if left to her own devices.

After decimals, it's back to Math Made Easy for several months' worth of operations practice.  We'll finish up the year with Book 2 of Key to Measurement, Key to Metric Measurement, and Key to Geometry.  The Math Made Easy series ends with fifth grade, so I am on the lookout for a substitute to fill in the gaps around Book 3 for all of the Key To series.  I am considering the sixth grade Mathematical Reasoning book from Critical Thinking Company.  Hopefully by then Bean will have forgotten that she resented the presence of dot to dots in the first grade version of this book several years ago.

Our experience with math echoes our overall homeschool experience so far.  It kind of started as a mess after a disappointing school experience and took a few years to settle into a good routine.  Once we settled into a better routine and had a stable roster of resources, I was able to start setting goals (sometimes subconsciously) and start nudging Bean forward.