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.

Saturday, October 6, 2012

Learner's Permit

I was standing behind the steering wheel of a 32 foot sailboat, supposedly in control of the vessel with three strangers on board, fighting back nausea, trying to figure out which way the wind was blowing and whether that was right, left, starboard, and whether the boat was close hauled, broad reach, or just up a creek.  Clearly I had no paddle, which I was far more used to, and no rudder, like the 27 foot boat I had sailed with a fair amount of competence the month before.

One of the strangers, the instructor I had just met two hours before, was shouting at me to get control and find my heading before we heeled or keeled or did something else equally liable to land me in the Pacific.  I took a deep breath, fought back the urge to either throw myself overboard or hurl my breakfast onto the smug father and son duo would had flown in from Phoenix specifically for this class and adjusted the wheel.

As the boat settled, I saw with crystal clarity how Bean feels when faced with a workbook page asking her to delineate the parts of speech in a sentence.  I realized that what started out as a whim might be the best thing I had done for our homeschooling in a long time.

I hadn't really planned to learn how to sail at all.  As I flipped through the parks and rec catalog, looking for summer classes for the kids, I happened to notice a basic sailing class for adults and thought it might be a fun way for me to fit in some exercise.  The fact that the class counted toward certification to be a bareboat skipper was a bonus.  Having an official piece of paper with my name on it might be gratuitous, but it never gets old.

Taking a sailing class is a continuation of a theme that I've noticed since I was about 35: I relearn something that I did poorly as a kid.  Usually, I associate some degree of trauma with whatever I'm re-learning.  When I was nine I picked knitting as one of my 4H projects for the year, but after my first few wonky inches of a scarf, the co-leader of our club suggested I better pick another project quickly since the county fair was only six months away.  (The other co-leader was my father, and since I wasn't doing anything related to horticulture or animal husbandry, I'm not sure he even knew about my ill-fated attempt at the fiber arts.) At 35, I taught myself the knit stitch using a book and the purl stitch using YouTube and proceeded to knit non-stop until Boo was born, at which point, I realized it would take more than an online video for me to figure out how to knit around a nursing baby and keep up with then 5 year old Bean.  I know some mothers who manage to knit through all sorts of hell and high water, but I was not gifted with their dexterity.

I did figure out to hire a babysitter and squeeze in math and science classes after Boo was born.  I had always planned on being a doctor until a particularly nasty run-in with physics class my sophomore year of high school.  This and related disasters of adolescence pretty much upended my life at the time and led me firmly down a book-lined path of liberal arts and away from labs and numbers.  Taking pre-calculus, biology, and chemistry at the local community college has not yet steered me back to med school, but it was cathartic and gave me extra confidence when it came to working with Bean on math and science.

My childhood encounters with sailing were fleeting and far less traumatic.  The summer I was fourteen, the only thing I did on my family's summer vacation besides sit in the back seat and listen to Tears for Fears until the batteries on my Walkman were drained was take two classes on a lake somewhere in Michigan (the vacationland of the midwest) in a boat barely big enough for myself and the instructor.  I found it thrilling and confusing, not quite grasping the relationship between where I wanted to go, the wind, and the direction we actually sailed.  Later that summer or maybe the next, I spent a week with my father, his best friend and the friend's eight year old son on a boat.  This was as thrilling as it sounds - complete with sea-sick-enhanced food poisoning contracted from fried fish and screaming fights with my father over whatever world-shattering thing we fought about in those days. (I wish I could go back and tell my teenage self that I wouldn't even remember all the small tragedies in 25 years.  I'm sure I would fight bitterly with myself and not believe a word of it.) I have always remembered the boat as a sailboat, but after my second sailing class this summer, I began to wonder if it had really been a power boat, because nothing seemed familiar.

Sailing is not knitting or math.  It is physically demanding as well as mentally challenging.  Sailing has its own language and it's own locale that is completely different from anything in my day to day life.  From the minute I step on the dock, I am in different world.

More than anything else in my adult life, learning to sail has reminded me what it's like to be a freshly scrubbed, raw human being trying to learn the business of life and learning
 from scratch.  It calls to mind the Buddhist concept of "beginner's mind." It's easy to lose that feeling under our daily and yearly accumulation of experience and knowledge. It's even easier for me to forget that Bean and Boo are still in the very early stages of hunting and gathering their way to fully formed human beings.  But when I am learning something unfamiliar in a vast environment that has its own dangerous power, forever reminding me how bumbling and inexperienced I am, it renews my perspective as a parent and gives me reserves of empathy when my children are in a tight spot, gripping their steering wheel and unsure which way the winds are blowing and what to do next.

Thursday, August 23, 2012

Summer Stretch

Whew! We made it.  When Bean paddled into the harbor just before noon today, her two-day stand up paddleboard (SUP) class ended.  A full summer's worth of eight weeks of classes ended as she paddled under the bridge that signals the border between the calm waters of the north harbor and the choppier waters near the entrance to the bay.  Dr. Yap and I looked at each other.  She did it!  She went at least as far as  the busy lower harbor, and maybe out into the open waters of the Pacific Ocean.

When I left her this morning, after zipping her into the now well-broken-in wetsuit, she wasn't entirely sure she would be willing to brave the swell outside the harbor.  Yesterday, when she and I went out together, she went half way under the harbor bridge and decided that was far enough.  Last week, during kayak camp at the same facility, Bean adamantly refused to participate on the day her class headed into the bay in tandem sit-on top kayaks.  She was not convinced her instructors would fully prepared her class of 8-12 year olds to handle the waves, since they spent the first day entirely in the safety of the harbor. Besides, after all the warnings that sit-on top kayaks were less stable than their spray-skirted brethren, she wasn't about to get in one with an unpredictable almost-stranger, let alone navigate it to the ocean.

Honestly, Dr. Yap are weren't sure Bean would make it through her full summer of classes at all.  The first week, a modern dance camp with her regular instructor but in an unfamiliar facility was every bit as intense as it was billed.  The four day camp was situated on the banks of a river, surrounded by sycamores, the one tree to which Bean is allergic, and took place the week after a strenuous trip to Chicago.  She started out tired on day one and after five hours of social interaction and dancing, she was exhausted. On day three, I got the call I often expect, but rarely get.  Bean stood up in the middle of the afternoon session and insisted that she had to go home right now.  Fortunately, she and the instructor worked out a way for her to stay and participate before I even got Boo to the car.  After the second call, telling me they would see me at the end of the day, I stood in the kitchen, knowing exactly what had happened:  Bean wasn't feeling her best, the afternoon session was not her favorite dance style, and suddenly she just couldn't take it anymore.  In her Asperger's mind, she wasn't allowed to excuse herself or take a break on the side, she couldn't see a way out and couldn't break the rules, so she exploded.

The next class was a Boogie Board class, one Sunday afternoon at one of our favorite local beaches, with instructors who taught a bevy of native California kids how to read the waves for signs of rip current, then sent them into the surf under their watchful eyes.  It sounds like a fun, light-hearted class that could be a formality for kids growing up in sight of the Pacific. But for a kid who has been swimming confidently for less than a year, it was fraught with anxiety.  The morning was filled with growls and feet stomping directed towards Dr. Yap and I, who were guilty of being far too willing to shell out money for these classes and of giving her the responsibility of deciding which classes she was ready for.  Clearly, if we had been less able to pay the park district fees and more restrictive with her choices, her life would have been easier.

Our life would be easier too, if we had to decided to keep the activities to a minimum and let the summer unfold without schedules or planning.  Once upon a time, in the early days of homeschooling, we did that.  Our first summer, we continued to homeschool as I continually tried to figure out what, how, and when we should work on what.  But sometime during the foggy mornings of July, I followed Dr. Yap's suggestion and looked online to see what summer offerings were still available at a local private school known for their excellent summer program.  Circus Yoga!  If ever a week-long class had Bean's name written all over it, that did.  Once she made sure it would only last a few hours each day, she was willing.  It turned out to be a great experience.  The class size was smallish, the people friendly, the school way more organized than any local private school we'd encountered.  Maybe one more week?  Mask Making with a former staffer at Jim Henson's studio?  Yes!

The next year, we knew to look at the course schedule as soon as it was posted in March and Bean picked four weeks of half day classes that would break up the summer of continued homeschooling.  After the first week, which did not go off without a hitch when her original class was cancelled due to low enrollment and she suddenly found herself in a Nature Art class, the classes at the private school were once again a hit.  It was a way for her to be at a school, without actually going to school; a chance for her to socialize with other kids, without expecting her to be around them for a whole day; an opportunity for her work with new adults each week in science, cooking, and animation classes.

If last year's summer classes offered a nice diversion, this year's slate was a stretch. Besides dance camp, and all the ocean sports,  Bean took three Lego robotics classes, a Lego architecture class, cooking, and  a web design class at the private school.  For five weeks, she had to be somewhere every day, renewing friendships from previous years, navigating the playground and lunchtime when she stayed full days, and admitting that she hated being the only 9 year old girl in a robotics class full of 12 year old boys with enough time for me to switch her to a different session instead of refusing to attend or exploding in an unexpected temper tantrum.  It wasn't always easy, but she did it.  We made it.  She stretched herself way beyond her previous boundaries, taking on far more activities and challenges than she normally does during the school year.  She learned a lot of things she was excited about, but not always in the exact way she would have liked.

Will this translate into smoother homeschool days? I don't know. But I do know that we're paying for two extra dance classes this fall and that I'll be spending three afternoons driving across town to the dance studio.  And I've bookmarked the full-week circus day camp on the other side of town for next summer.  We never know what we're capable until summer comes, we get a break from our normal routine, the days get longer, and we stretch outside of our usual pace and schedule.

Yesterday, I asked Bean what her favorite activities were.  The answer, a particular Lego robotics class with a great group of kids and stand up paddling.  When Dr. Yap and I met her on the dock, we learned that she had made it into the open ocean, out of safe harbor, saw a sea otter snacking on a crab, and never planned on doing that again.  But she didn't refuse to try it, as two of the kids did, and she didn't exclaim to us that she hated it and was made to do it, as two other kids did to their waiting moms.  She did it willingly, skillfully, and bravely, if fearfully.

Thursday, August 16, 2012


Over the last two and a half years, our homeschool schedule has evolved to a pretty nice sweet spot.  We still tweak things here and there, but overall all, I would say we've settled in to a nice routine.

For a long time, I tried various ways to schedule our homeschool time and plan Bean's work.  The first idea that worked well was to come up with a standard school time and stick to it.  We start as close to 9 AM as we can and almost always finish by 11 AM.  This works nicely for both Bean and I since we're morning people and our brains are freshest after my second cup of coffee and before her lunchtime carb fix. We both also like the predictability and structure of having a set time for school.  I plan whatever I need to get done for the day in the afternoon, and Bean knows she has that time coming up to do whatever she wants.

As we added and subtracted things from the overall lesson plan each year, I struggled to figure out how much and what to do each day and to figure out how often to do each subject.  In order to avoid resolving this, I weighted each subject, from math to health, equally and had what I thought of as a scrolling schedule.  I listed the next assignment for each subject and we just went down the list, covering whatever seemed like the right amount in a day.  Gradually, it became clear that we could do about six things in a morning.

Soon after we officially started Fourth Grade last fall, I finally admitted that language arts and math should get top billing in the schedule and show up each day.  It helped that we finally settled on workable curricula for each of those subjects.  Once we had work we didn't mind looking at, it was a lot easier to commit to doing them every day.  We alternate language arts and math with other subjects, covering six things total every day.  I try to arrange the day with a nice rhythm, alternating tasks that require more writing or brain energy on Bean's part with those that are more passive.  I also try to make sure there's some variety: world history one day US history on another; music and art happen on different days as well.

Foreign language ended up anchoring every day until I realized that as often as not, we were too tired/hungry to do it when it came around and it was getting passed over in favor of lunch with a (usually unfilled) promise to do it in the afternoon.  Now, Bean starts her day with Rosetta Stone.  I used to specify which language she was to work on each day in attempt at keep her progress even, but often as not, all she wanted to do was Dutch. Or she wanted to do Arabic on the day I had planned to do French.  I reasoned that since foreign language was entirely optional at this age as far as the state was concerned, she could do whatever language she wanted each day as long as she was doing one.

My latest tweak is moving to what I think of as a modified block schedule.  Instead of assigning subjects to specific days, I gave each group of subjects a letter A through D (since Bean usually attends a homeschool class one morning a week, we only homeschool four days and this works out nicely with the amount of subjects we cover.) Until I read about the block schedule used by a local private school, we would do geography on Monday, art on Tuesday, etc.  If we missed a Monday for a sick or Dr. Yap homeday, we missed geography that week.  After a while this got confusing with my lesson planning and the lack of continuity was leading to a lack of enthusiasm for some things.  Now, we just start with the next letter day in the schedule.  For example, if we take Monday off for Labor Day (also known as an extra Mommy homeday in these parts) and Tuesday is an "A" day, we finish the week on a "C" day and start the next week on a "D" day.

So here's what our schedule will look like when we officially start Fifth grade in two weeks:

A Day

  • Rosetta Stone I record the chosen language after the fact.
  • Read aloud from Fifth Grade Literature list We're finishing up the Chronicles of Narnia and one of us cannot wait to finish that and start the Adventures of Tom Sawyer.
  • Language Arts 1-2 pages from the Critical Thinking Co.'s Language Smarts D (This is technically a third grade book, but it's large and we're slow and it's totally appropriate for Bean.)
  • Geography Bean is finishing up a States workbook - it's taken us a year, but we've made it to South Carolina; then switching to topics from What Your Fifth Grader Should Know and Color Yourself Smart: Geography - I hate the title, but it really is a great series.
  • Math Topics vary throughout the year, but we mostly use the Key to...Series.
  • US History Westward expansion, the Civil and Reconstruction. Oh my.
B Day
  • Rosetta Stone
  • Read aloud
  • Language Arts
  • Literature topics We're starting with an introduction to Shakespeare (Midsummer Night's Dream) and then do some poetry.
  • Math
  • Latin This is Bean's request, but I think it's a great idea.  I don't consider Latin a foreign language, I think it's a great foundation for many things: building vocabulary, spelling, understanding medical and scientific terms, critical thinking.
C Day
  • Rosetta Stone
  • Read aloud
  • Language Arts
  • Science We'll do some reading in the physical and natural sciences, but this year I'm trying a lot of hands on kits, preferably those that do not require "common" household items that I never seem to have on hand.
  • Math
  • World History We're covering the rise of Western civilizations, starting with a peek at what happened in the millennia between Lucy walking out of Ethiopia and the pharaohs building giant monuments to themselves in the Nile Delta.  After that, we will run through Ancient Egypt, Greece, and Rome, with as much of a side trip into Mesopotamia and Byzantium as I can muster, but these aren't the most resource-rich areas, in terms of curriculum.
D Day
  • Rosetta Stone
  • Read aloud
  • Language Arts
  • Study Skills A dreaded but important subject, since she isn't naturally building these over time in school and many of them don't come naturally to Bean. We're using the excitingly-titled Study Skills for Early School Success.
  • Math 
  • Music We're reading through the music theory and history in What Your Fifth Grader Should Know, listening to music and occasionally using Simply Music's piano instruction.  
One noticeable absence from this schedule is art.  I have come to the end of what I can teach or facilitate in terms of art theory and practice.  Bean continues to produce all manner of art on her own, and I will keep exposing her to art and art history, but I want to outsource art instruction.  I was hoping to start her in private or small-group lessons with a wonderful woman nearby, but that was before Bean decided to take three dance classes and a homeschool gymnastics class.  On the plus side, I never have to worry about PE.