Family Math

I promised that I would give you a glimpse of what family math looks like around here.  I know folks are wondering "Is this method sustainable?  Will you really be able to cover all of the things you need to cover for a range of different ages and abilities of children in a whole-group setting?"  So here is the answer: "I don't know!"

I really haven't done this long enough to know if there are cases where this model will prove more challenging.  But I have definitely seen many beautiful aspects of this approach.  Let me share with you a few anecdotes and then a few observations.

Examples:

• We did a review of the concept of place value using play money - hundreds, tens and ones - over the course of a few days.  The children practiced exchanging between hundreds and tens and between tens and ones.  We experimented with what happens when you add, subtract or divide a three digit number, and which order (hundreds, tens, ones vs. ones, tens, hundreds) makes the most sense for each process.  My ten, nine, eight and six year olds were all in participation.  The older three have definitely mastered the concepts of regrouping and their application to the three operations we examined.  The six year old showed a clear understanding of place value, but not as great a fluency with "regrouping" and didn't apply it to the operations.  That's OK.  She's learned some and become familiar with the concept.  She'll have plenty more exposure to it in future.
• I realized that, though my six-year-old can tell time fairly well, she was having trouble taking into consideration the movement of the hour hand as the minute hand makes its way around the entire clock face.  I planned to take a moment during math time to talk about this with her, but since the older children were sitting nearby, the conversation turned into a discussion of percentages and proportions with the older children when one of them said,  "So, if the minute hand has gone 25% of the way around the clock, then the hour hand should have also moved 25% of the way between two numbers ..."  This reminded us why it is that we refer to times as "a quarter past" or "a quarter til" and we also talked about the reason (historically) that the minute hand is larger than the hour hand.  We also discussed that situations like this illustrate the usefulness of percentages, because they allow us to make comparisons between the parts of two different-sized things.
• We are now studying Geometry.  Sometimes we read one of the Sir Cumference books.  All of the children (except the baby who still takes a morning nap) sit and listen as I read.  We have also done some hands-on activities.  The oldest four participate and the younger two (ages 4 and 3) go back and forth between being engaged and doing their own thing nearby.  For example, as we explored perimeter and area, we used Blokus pieces to make rectangles of different sizes and to calculate the perimeter and area in the pretend units of a Blokus (B) and a square Blokus (B²).

Thoughts:

• In pretty much every other subject, my approach has been to teach the older kids and let the younger ones listen in and glean whatever they are able.  Why not math?  It can't hurt, right?
• If math is a conversation, then each person can engage at the level to which he is able.  Older children can bring more complex ideas to the table and younger ones can pick up on the simpler aspects of what we're learning.  Math really isn't as compartmentalized as we tend to think - there is so much overlap and interconnectedness.  And making connections between previous learning and current learning is a huge piece of what education is all about.
• Math as a conversation easily overflows to other times of the day (like lunchtime) because we've all been a part of the discussion, not just Mama and one kid.
• When other children are getting a concept and one is not ... Do I stay on that topic and approach it from a different angle to see if I can make it clear?  Do I determine that that one child just isn't developmentally ready, and move on, figuring that she'll grasp it later on another pass when she is ready?  Do I find a chunk of time to work individually with her on that topic?  From where I sit right now, it seems like any of the above would be a viable option.  I know how to track what has been mastered and what hasn't.  So if not everyone is on top of a concept, it doesn't have to stop us from moving forward and doing the next thing as a group.

Have you ever explored math in a multi-age group?  What worked for you?  What did you like or dislike about that approach?  In reading over the descriptions above, what questions come to mind?  What is concerning about that approach?  What is attractive about it?  I'd love to hear your thoughts!

Finger on the Pulse

This is the seventh part in a series based on this cost/benefit analysis.  Here you can find Part 1:Scoping out the Sequence, Part 2: Making the Grade, Part 3: Unscheduling, Part 4: Why DIY?, Part 5: Race to the Finish and Part 6: Do Over.  Next I want to talk about this "plus" for us in letting go of our math textbooks:

• I have a better handle on the actual, individual progress of each child and I can individualize practice not only to the specific topics each child needs to review, but to the frequency with which each needs to review.

I talked here a little bit about the spreadsheet that I use to track what the kids have learned and what we still need to cover and here about how I track what each kid needs to review and with what frequency.  (And, because I haven't mentioned it in a while, I want to reiterate that none of this was an original idea for me.  It is entirely based on the Math on the Level concept.)  So my intention here is not to re-explain the mechanics of the process, but just to share what I'm enjoying about it!

We already discussed here and here how having a separate system for keeping track of mastery and review enables me to un-link record keeping from the textbook scope and sequence.  And I wrote here about why I like being able to make up the problems myself.  All of that is facilitated and made possible by having a closer eye on individual progress.

In a textbook, topics are reviewed at some recurring schedule.  I haven't been observant enough to figure out what the schedule is.  Probably more complex things are review more frequently, because it seems like there are multi-digit addition, subtraction, multiplication and division problems on most every page.  But it was commonly the case that I'd skip over massive amounts of review material on each page in the textbook, either because I didn't think my child needed to do so many problems in one day, or because I didn't think they needed to review that topic again so soon.  The spreadsheets help me to make informed choices, not just hazy guestimates.

Also, at a certain point, I realized that we could make our review more efficient by thinking about all the processes that go into a problem.  For example, in completing a multi-digit long-division problem, you are:

• dividing, obviously, but also ...
• multiplying
• subtracting
• regrouping/borrowing/carrying or whatever you are supposed to call those strategies these days
• using place value concepts
• comparing numbers
• rounding
• estimating
• possibly dealing with remainders, decimals, repeating decimals, fractions and/or dollars and cents

Add another layer by putting it in the context of a word problem and you could be ...

• averaging
• converting between units of measurement
• dealing with percentages or rates
• reducing large fractions
• calculating measures of sides or angles in geometry
• and probably lots more I haven't thought of!

So, give a long division (or other multi-process) problem and check off review of lots of concepts.  In the reverse, however, if a child continues to struggle with long division (or another complex-process problem) break it into pieces to determine where the difficulty may occur.

In a couple of cases, I've realized that I could add something to the review line-up that a child hadn't officially come across in her textbook because she grasped the concept.  In another case, I realized that even though a child had moved through a concept in her math book (and had completed problems accurately), she didn't grasp the concept well enough to be able to work confidently with it on her own.  I wanted to drop back and explore/experiment with it more before putting it back in the review rotation.

Another big "win" was in tracking (by color-coding) the difference between "needed to go back and correct this" (in yellow) and "needed help knowing how to do this" (in red).  In my mind, a student who can find and fix his own errors has a different place for growth than a student who needs help completing the problem.  The first one may need encouragement to work accurately, but he grasps the concept.  The second student may need that concept moved from review back to something we can investigate further.

Finally, I am hoping (though this is completely untested as my oldest is only ten) that this system will help us to know when a student is ready for algebra.  Between the beginnings of math discussion to the completion of pre-algebra, there are 146 concepts that need to be covered.  Of course, part of preparedness for algebra is a developmental maturity.  But seeing how we are progressing towards mastery of the concepts and how strong the understanding is retained through review should (I hope!) give us some clues in that direction.

Oh, and did I ever mention that I love spreadsheets?  Yea, that's just an added personality-match bonus for me.  A friend told me yesterday that she and her brother joke about spreadsheets being their "love language".  If that is a thing, then I think it might just be one of my things!

Do Over

This is the sixth part in a series based on this cost/benefit analysis.  Here you can find Part 1:Scoping out the Sequence, Part 2: Making the Grade, Part 3: Unscheduling, Part 4: Why DIY? and Part 5: Race to the Finish.  Next I want to talk about this "plus" for us in letting go of our math textbooks:

• A LOT less time spent explaining work and correcting (and re-correcting) work.

I want to say up front that what I'm comparing here isn't really, purely, textbooks vs. no textbooks.  What I'm comparing is the way we used to do math vs. the way we do math now.

Before:

"Math" every day was sitting with one kid at a time and explaining to him what to do on his math assignment.  It went something like this:

"See, they're showing you that in order to divide by a fraction, you just flip it upside down and then  multiply.  Does that make sense?  Here, try this one.  Exactly! Good!  Got the idea?  OK, so you are going to do these five problems about that.  And then how about if you do one of these ... and one of these ... one from each of these sections ... and a word problem and, sure you can do all the Roman numerals.  OK, go get your sister and tell her it's her turn."

So, basically, it was like math, minus all of the best parts of math.  There was no exploration.  No wonder.  No awe.  No lightbulb moments.  No connecting the concepts.  No conversation.  Like a Dementor had kissed our homeschool math.

Maybe we can get into all that some day, I'd tell myself.  Some day when I didn't have to spend 15-20 minutes x 4 kids just telling them what they had to do on their worksheet for the day.  Someday when I wasn't exhausted by all of the exertion of the "management" of six other people while I tried to spend an hour meeting with each of the least destructive ones individually.

And what about quiet work time in the afternoon?  It went something like this,

"Good, all of your Roman numerals are correct.  Oooh, sorry, your long division problem is wrong, so you'll have to do that over.  Stop grumbling; math is supposed to be challenging.  And, oh, wait.  Yikes!  You weren't supposed to flip BOTH of the fractions upside down.  Only the second one.  Oh dear.  I guess I didn't really explain that very well.  OK, maybe I can go over this with you tonight and you can do all these over tomorrow along with tomorrow's math."

Good fun, right??  Can you tell why the kids and I all dreaded math?

Now, all of the exploration of new concepts happens together in a group.  There is still some "people management" - there always will be - but usually the oldest four are engaged (they are either hands-on or answering with their dry erase "slates") and the younger two are coloring, which is their version of "doing math".  And quiet work time?  Sure, they still get problems wrong.  And there are still corrections to be made.  But not as many because:

1. They are only doing review work - not work on new concepts.
2. There are only five problems.
3. There is only one problem per topic, so no more discovering that they've done eight problems in a row wrong because they didn't understand one concept.

I've gotten some questions about what "family math" looks like these days.  I promise to write a post on that when I'm finished with this series (almost done!) but I have to say up front: we've been doing this less than two months!  I can tell you what it looks like so far, though, for what it's worth.

Race to the Finish

This is the fifth part in a series based on this cost/benefit analysis.  Here you can find Part 1:Scoping out the Sequence, Part 2: Making the Grade, Part 3: Unscheduling and Part 4: Why DIY?.  Next I want to talk about this "plus" for us in letting go of our math textbooks:

• I'm not bound up by a need to "finish" a purchased curriculum,  or "get  my money's worth"; no need to weed through and pick out which parts of a lesson to do.

Yes, I have hang-ups.  Yes, I have first-born perfectionist tendencies (though you wouldn't know it to look at my house!).  Yes, it somewhat bothers me to purchase something and then leave it incomplete (more on that in a moment).  But that's not really the pivotal factor in this benefit for us.

We all want to make sure we cover our bases in teaching our kids any subject, but especially one as central (in our world, at least) and developmentally sequential as math.  How does one make sure she covers all the stuff she's "supposed" to cover?  Well, the simplest way to achieve that is to let someone else (usually someone who has a lot more background in the subject) do the research and planning.  You purchase a textbook.  When you've covered all the things in that book, then you move on to the next one.

Sure, you can take a textbook and pull it apart and mix it all up and use it differently.  But unless you are committed to finishing everything in that book, you need some other system for keeping track of what has been covered and/or criteria for deciding what should be covered and what should be omitted or saved for later.

As I mentioned above, it does somewhat bother me that we've got these half-used textbooks on the shelf.  But I got myself into that situation on purpose.  I wanted to experiment ... but I wanted to experiment with a safety net.  I figured that if we tried this system for a couple of months and it didn't work, we'd just pick up our textbooks again.  I also figured that I wanted a few months to test the theory before convention came around (for us that's June) and I needed to decide whether or not to purchase new textbooks for next year.

At this point, I am so enjoying what we've been doing here that I don't see myself wanting to go back to the textbooks.  In fact, I've been letting the kids use up the pages doing "school" with each other in their free time.  I thought that perhaps they would come in handy in case I was in a pinch and I needed something quick to pull out and give the kids to do.  Here's why that hasn't been an inviting option (yet):

• There are tons of problems on a page.  Deciding what to have the kids do takes some work in and of itself.
• If I'm there and I don't have 5-A-Days prepared, I can just put some problems up on the whiteboard, everyone can do them on their dry erase "slates" and we're done.  (If I really want to, I can even open up the spreadsheet and track as we go.)
• For days when I am going to be out (such as to appointments with the orthopaedist!) there have been so many things I've wanted the kids to have more time to do that it isn't a problem to leave them with other activities, like snuggle number!

So, in summary, the real benefit behind not having to "finish" a textbook stems from the fact that we've un-linked progress tracking from textbook scope and sequence.  We keep track of what we've learned, mastered and practiced elsewhere, so we are free to use or not use whatever we want from the textbook - and many other sources as well!

Why DIY?

This is the fourth part in a series based on this cost/benefit analysis.  Here you can find Part 1:Scoping out the Sequence, Part 2: Making the Grade and Part 3: Unscheduling.  Next I want to talk about this "plus" for us in letting go of our math textbooks:

• I get to create the lessons and activities myself.

I've said this before many times, but I want to stress again that this series isn't meant to be an objective argument against the use of textbooks, or textbooks for math.  It is simply an exploration of why that choice has "fallen for me in pleasant places".  So if you read the above "pro" for going without textbooks and you think "Why on earth would anyone want to create things from scratch when they could be purchased already done?" then by all means, purchase them ready-made and don't give it a second thought!

I have a dear friend who is constantly knitting things for her children.  One Christmas she made her boys really cool real-looking "chainmail" with yarn!  She makes baby gifts (several for us!) and all kinds of other wonderful, cozy homemade treasures.  For the longest time I felt intimidated.  I saw all of the things she was doing and I thought to myself, "This is what good, dedicated mothers do - they knit.  Knitting is such an essential homemaking skill and it is frugal and it is such a wonderful, productive kind of busy.  If I was a good mother, I would do this, too."

I did try learning to knit, but I wasn't very good at it (maybe just because I didn't give it much of an effort) and I was disappointed in myself.  I thought, "My friend is so diligent and has so much good will power and self-control.  Why don't I have that?  Why don't I make the time to do this important thing?"  And then you know what I realized?  She doesn't knit because she's convinced it is a morally superior way to nurture her family or because she has the self control to "do hard things".  (She would probably laugh out loud if she knew that's what I was thinking.)  She knits because she likes to knit.  She knits because it quiets her soul.  She knits because that is where she finds peace and relaxation.  She knits for the joy of knitting!

And that, my friends, is why I love to make up my children's math work myself.  Please hear me. When I say "love" that is exactly what I mean.  I don't mean "I feel frugal," I don't mean "I feel diligent" and I don't mean "I feel educationally superior" I mean "I just like doing it".  When the children are in bed and I sit down with a stack of fresh notebook paper and a spreadsheet (just another thing that I love, because I'm a dork like that) it isn't a duty thing.  It just clicks with how I am wired.

The other day, I needed to make an activity for my six year old in sequencing numbers.  She's been working on place value to the hundreds, so I was going to ask her to order these numbers from least to greatest:

102
201
101

But just for fun, I also included

½

This isn't something most first graders would come across in their math books.  But she has been having fun with fractions recently.  At Sunday lunch she was given two cookies.  She carefully bit off half of a cookie and then held them both up together and said "Now I have a mixed number!"  I knew she could handle ordering a fraction in with whole numbers, and she loved it!  It just stirred my soul to get to make those choices myself.

Have you ever bought a used item of furniture or clothing with great plans to pull it apart and remake it just the way you wanted to suit your particular purposes?  And then at some point, did you come to the realization that using the bits and pieces of the pre-made item had actually become more complicated than scrapping it all and starting from scratch?  Well, that's how it was for me with textbooks.  Even after I had made changes in how we did math, I tried using textbook pages (because I still have four half-used consumable textbooks that are sitting on the shelf).  I was surprised at how hard it was to find one page with five problems that fit what each kid most needed to review.  Making the problems myself was just quicker and easier.

And, just to make sure you don't leave this post saying, "She is so good and diligent.  If only I could be a dutiful mother like her" (pardon me while I laugh myself to tears) I want to assure you that it's not all that complicated.  First, it's only five problems a day per kid.  And secondly, remember, I have  a handy spreadsheet (which I did not create myself) that helps me to pick what kind of problems to make.  It might sound intimidating to just make up five math problems.  But what if I said "Write down a three digit subtraction problem that requires borrowing."  You could do that, right?  That's all there is to my job.  It's just that I love doing it!

For me, it was a huge relief to drop slogging through pages of a pre-made textbook and instead much more energizing to make the problems yourself.  So what's the take-away?  The take-away for you is to know how you "tick" and to understand that using that as one of the factors in choosing how to homeschool isn't selfish or lazy - it's just a smart use of limited resources!

For more encouragement on the freedom to choose the method(s) of schooling that works for you, definitely read Teaching from Rest or check out Julie Bogart (founder of Bravewriter) Scoping about the "divide" between structured and unstructured learning.

And just for fun, head on over here and check out Mystie Winkler's page on your Homeschooling Personality Type.  You know what mine says?  Here are some relevant snippets:

The ENFJ ... loves to put together a plan just right for her family. 

• Strengths: mentoring, teaching, relationship-investment activities like read-alouds and family vacations
• Struggles: people-pleasing, her own intensity, anxiety and inner conflict
• Style: whatever she feels allows for the best development of her children; she will prefer an eclectic approach that follows her gut.

I don't believe that personality tests are perfect or that they dictate choices.  But it was pretty fun reading through that list and identifying some of my friends and their gifts and loves and seeing that there is so much variety in how we each are wired and how we homeschool.  That's a good thing, guys!!

I don't knit, but she does.  To each her own!

Unscheduling

This is the third part in a series based on this cost/benefit analysis.  Here you can find Part 1:Scoping out the Sequence and Part 2: Making the Grade.  Next I want to talk about this "plus" for us in letting go of our math textbooks:

• I can school without the parameters of a "school year" or a "work week".

Textbooks are designed to be used by schools and to meet the needs of a school schedule. And so they should be; this is not a criticism.  They generally plan for students to have 32-36 weeks of lessons and to complete lessons five days a week.  They intersperse new material and review material to round out the appropriate amount of assignments needed.  But couldn't a family use a textbook and still choose their own schedule?  Absolutely.  Here are some of the ways I've adapted our various subjects to fit with our own schedule.

• Our on-line History program has 32 topics with 5 "lessons" per topic (4 lessons and a test).  We do the test along with the fourth lesson so that we have four days of history instead of five per week.
• Our Latin textbook has 32 chapters of material, but interspersed along the way are review chapters.  Sometimes we skip the review chapters or sprinkle the review material in with other chapters.  Also, we often don't have a chance to complete all of the activities per chapter since we don't school 5 days a week.
• Our Math textbooks contain 170 lessons each.  In some grade levels, the textbook authors expect you to have a test (in a book you purchase separately) either every 5 or every 10 lessons (presumably every Friday or every other Friday).  I've never used the test materials and we've been skipping over those lessons that are only review with no new material presented.

So yes, you can use textbooks and make them work on most any schedule.  In other words, if I were trying to compile an objective list of reasons why one ought not to use textbooks, this one wouldn't really fit.  And even in a list of my own personal cost/benefit analysis, perhaps it would be more accurate to say that it was a secondary benefit rather than a driving cause.

See, in my imagination, our school culture would look something like this.  We would be a home where learning was part of the normal activity of the household.  We would study a variety of topics and read a variety of things.  We would wholeheartedly engage with what was in front of us, explore further if we wanted to, read extra, do some more problem solving or spend another day on it if needed.  And, when we had a need or an opportunity for a break, we would take it.  And when we had refreshed ourselves through a break, we would get back to the business of learning whatever was next.

And yes, this is doable with a textbook.  But when (for other reasons as well) we moved to going without the math textbooks, a wonderful benefit was realized in terms of the increased freedom to break when we need to and begin again when we are ready (which, at this point, has mostly included sick-days and broken arms!).  Perhaps, in the final analysis, this "benefit" speaks more to my own personal hang-ups over loose-ends and tidy finishes than to any objective characteristics of textbooks.  But if what we're doing is an individual cost/benefit analysis, personal hang-ups carry weight, too!

Making the Grade

This is the second part in a series based on this cost/benefit analysis.  Here you can find Part 1: Scoping out the Sequence.  Next I want to talk about this "plus" for us in letting go of our math textbooks:

• I can school without the restraints of grade level and (related) comparing my children to other children around the same age.

As I mentioned here, I was stopped dead in my tracks by this quote from Andrew Kern of the CiRCE Institute:

 To what level has my child mastered this skill?  And what is next?  Nothing else matters.

We are only a couple of weeks into this experiment, but already I am thankful for the release of focus on grade level and what each child "should" be doing or "should" have covered at this point.  In some cases, I have been astonished to realize that younger children were perfectly capable of grappling with concepts I intended only for older siblings.

Other times I realized that, though a child had successfully completed problems on a given topic many times, she didn't really understand the concept and I was thankful to have another pass at it as we learned as a family.  In one case, I decided to simply make a note of a concept that I felt she wasn't ready for (though she had completed many such problems in her current and previous math book) and come back to it later.

If we discuss a concept as a group and someone is not developmentally ready to comprehend it, then there isn't really anything that can be done at that point to force them to "get" it.  In fact, (as I have witnessed before) "forcing" the issue is what leads to my strong math thinkers "hating math".  Sure, if you work within the outlines of a grade level, you can control at what age you present the material to a child.  But you still can't control the age at which they master it.  

I can't quite predict how this will play out long-term.  To what extent - especially within the context of our culture - is it realistic to push aside concepts of "grade level" and move forward based on my children's developmental preparedness only?  If one of our students doesn't make it through calculus by age 18 does that mean this approach is flawed ... or that that child wasn't developmentally ready for the material and wouldn't have been ready under any system of instruction?

Perhaps my comfort and confidence with this approach will have a lot to do with whether I perceive my children to be getting "ahead" or "behind".  If this method primarily enables the younger ones to explore and master concepts they normally wouldn't have encountered so "early", then perhaps I will feel confident in our choice ... and less so if it leads to mastering concepts "later".  Hmmm ... that would be ironic, wouldn't it?

Scoping Out the Sequence

Back here I gave a rough outline of my cost/benefit analysis of going without textbooks (at least in math).  Since I've gotten some questions about the the reason behind them, I'd like to do a brief post expanding on each of the items I mentioned as "pros" for us.

• I'm not constrained to a particular scope and sequence (order of topics) and can order them based on learning opportunities, whole-family instruction and the developmental abilities of each child.

I want to stress (again) that there isn't anything wrong with purchasing curriculum with a scope and sequence or following one.  As mothers, our resources are limited.  It is not a cop-out to choose materials that take some of the work off of our plates!  However, at this point in the life of our family, the scope and sequence in our textbooks felt more like a restraint than a help.

As I looked through the children's textbooks (grades 6, 5, 3 and 1), I realized that there was a great deal of overlap in topics - at varying degrees of complexity, but related to the same general ideas.  However, these topics were not presented in the same order in each grade.  My first impulse was to tear all of the pages out of each of the (consumable) books, rearrange them by topic and use binder clips to clip together all of the pages that fell under the same general concept.  The problem with that idea was that since I'd be teaching the topics out of order (according to each individual textbook) and since an Abeka math page is about 25-40% work on the current topic and 60-75% review, the children would potentially be assigned "review" problems for concepts they had not yet learned.

Sure, I could create a system for keeping track of what each kid had already learned and then assign or skip over review problems accordingly.  But if I am going to keep track of those details and have that close of a handle on who needs to review what, the limited options offered on each math page actually become more of a restraint than a boon.  More on this when we talk about ...

• I get to create the lessons and activities myself.

A Very Simple Schedule

At the beginning of the week, I felt a moment of crisis because I knew that I needed to spend more one-on-one time with my new reader and my struggling reader.  The schedule already felt packed and scary and the thought of adding one more thing was daunting (to put it mildly).  Monday evening, I attended Part 2 of the Focus and Align class at the Read Aloud Revival and the beginnings of some ideas began to percolate.  We had two hard, rough days, followed by two good, smooth encouraging days, followed by one more hard, low, rough day (as viewed from my internal perspective, only).  And here, in retrospect, is what I think has settled out to be our new schedule*:

• Breakfast (sometimes while listening to a recorded book or story)
• Morning Chores, Joseph (1) to nap
• Read the Bible
• Talk about Math
• Talk about Language
• Meet one-on-one with Luke (10) and Robyn (6) to practice reading skills
  Emma (9) and Ruth (8) take turns doing things with Henry (4) and Hazel (3)
• Lunch
• Quick Straightening, Hazel (3) and Joseph (1) to naps
• Quiet Work Time (Math 5-A-Days, Latin and some silent reading)
  On Tuesdays this is replaced by "Latin Class" with another family
• Play Outside
• Final Clean-up
• History (on-line course the kids do as a group) while Mama fixes dinner

That's it.  That is all we can do in a day.  And some days we don't accomplish all of that.  If you look closely, you'll probably notice things that aren't included.  I bet your list wouldn't be even a third of the things that are on my mind.  But I'm setting that aside for right now.  Let tomorrow worry about itself.  This is what we can do right now.

* We do school Monday-Thursday.  Fridays are for laundry, housework and maybe projects.

The Next Thing

One of the things that I have recently found to be a crushing burden of homeschool (for me, for now) is the feeling of needing to "finish" something in a given time.  I fear that if I don't finish it, my kids will be "behind".  I fear that if I don't finish it, I will have wasted the money I invested in it.  I fear that if I don't finish it, I'll miss out on that break I was hoping to take when it is all done.

For some (and even for me, in other phases of life) the structure is helpful.  It's nice to have someone else plan out what a year's worth of work includes, how much to review when and what should be included in a day of work or practice.  It feels very tidy to have five days worth of activity and begin again on Monday.  When we are able to get it done, it brings a sense of completion and closure.  But those days are getting much fewer and farther between.

Perhaps I'm less able to accomplish something that would be good to accomplish.  Perhaps the new pressures and constraints of life at this moment are revealing "shoulds" that never should have been "shoulds" and I am now releasing myself from them.  But whatever the case (and in some ways, it really doesn't matter) there is only this: what can we - at this stage, with this present grouping of children and this present, tired mama - accomplish in one day?  That is it.  What has God given us to do on this day?  Let's do it.  Let tomorrow worry about itself.

And what if we get to the end of the day and it wasn't all done?  Then not all of those things were things God meant for us to do today.  Yes, maybe there was time wasted.  Maybe we could have been more efficient.  But on this day, at this moment, whatever the causes, the task is still the same - trust to the Lord what wasn't accomplished and wake up tomorrow to start on the next thing.

As much as possible, I have moved away from organizing our subjects such that they must be done on a daily or weekly schedule in order to "work".  I've tried to avoid setting up things such that if we miss a day we are "behind" and have to try to cram two days worth of work into one (or three into two).  Instead it has worked much better for us if Mama has a general sense of the next thing(s) she'd like to teach or work on with the children.  When we come to school time, we do the next thing.  And if we don't get to it, it is tomorrow's next thing.

Didn't read a chapter of our read aloud book?  It will still be there tomorrow.  Talked about place value but they didn't fully "get" the concept?  Talk about it some more tomorrow; try another approach.  Time to start school but not all the morning chores aren't complete? They can wait until the next slot of time for getting a little work done.  (Or, do a little more housework and some school things can wait until later.)

The only way to make this system a reality has been, as much as possible, to unchain activities from each other so that each piece can move forward (or not!) independently.  Since our math discussion and written practice are no longer directly linked, we can do one without the other, if needed, on any given day.  Since the children's Five-A-Days are all things that we have already covered and they are just reviewing, we can take more time than I expected to work on our current concept without interfering with the Five-A-Day work I picked for them.  Or, conversely, if we didn't get a chance to complete the Five-A-Days, they can wait for the next day and our morning math conversations can keep happening.

This week, my oldest was only able to finish three out of the five problems on his Five-A-Day one afternoon.  Rather than requiring him to "catch up" on those two and do five new ones the next day, I simply took those two problems, added three more and they were his Five-A-Day for the next day.  If we've determined that five problems in a day is what we can manage, then why plan to do seven?  There will always be more good things to discuss and practice.  What do we gain by "doubling up"?  What are we racing against?  More and more, for us, the answer is: nothing!

Note: The two subjects that still "need" to fall into a weekly pattern are History and Latin.  And for now, I'm going to let them stay that way.  I'm not at all convinced that Latin is something all homeschoolers must do, but I have a degree in Latin and, quite frankly, it's something I love to teach.  Plus, our pastor's wife and her two youngest come over on Tuesday afternoons to do Latin with us, which is a big plus in the be-with-people category (perhaps even more for Mama than for the kids!).  We began three years ago with Song School Latin and are now working through the Latin for Children series.  We are on Primer B out of C, so after next year we'll reevaluate what to do next.

Though it is not absolutely essential, our history program works best done in five-lesson-a-week rotations because every five lessons covers one topic.  I absolutely love the Veritas Press History for many reasons.  Content-wise, it covers history, including Church History, map skills and lots of historical context.  Each era of history has its own song which helps the children to have a mental framework for the order and relationship of historical events, as well as some key dates.  Another plus is that it is on-line, very interactive, and the kids can do it on their own (mostly) while I watch and listen from the kitchen as I make dinner.

Why No Textbooks?

(Note: What follows is a discussion of why I am experimenting with not using textbooks, not an argument for why anyone should not use textbooks.  See here also.)

I once read an article in Reader's Digest about how to decide whether to do a task yourself or pay someone to do it.  For example, is it a more economical use of your time to mow the lawn yourself, or to hire someone else to do it?  Part of the calculation had to do with your own income level and/or hourly wage.  If you divide your annual salary by the number of hours you work per year and that figure is larger than the cost per hour to hire someone to mow your lawn, hire out the job because your time is more valuably spent elsewhere.

But, thankfully, that was only a part of the equation.  Another part (I wish I could find the article, because I'm sure there was more) was to consider what you enjoy.  In other words, the personal "perk" you get from performing a task yourself is also a factor in the "value" equation.  If mowing the lawn is something you really enjoy, or you prefer doing it yourself because you are particular about how it is done, or the satisfaction you get from doing it yourself and saving the money is a "plus" in your energy category, then this may outweigh the basic dollars per hour calculation above.

The same is true with mom-energy, even if we don't have an actual paycheck calculation.  Matt has a degree in economics and he is always reminding me of "implicit cost".  In other words, I may be able to find kids' jeans cheaper at a thrift store ... if I don't mind making several trips, if I don't mind weeding through rows of clothes, if can find the sizes I need and if I check them thoroughly for stains.  But if I walk into Kohl's and grab the pairs I need in the sizes I need and walk out ten minutes later, that may be worth the extra (and it might not be that much extra) cost, because time is money.  And stress is costly!

This applies to hundreds of areas of life.  Why do you choose to ... breastfeed or not, use cloth diapers or not, make your own bread or not, paint rooms yourself or not, even (yes, I'm saying it) homeschool or not?  At the end of the day, it isn't a simple right/wrong decision.  And it isn't only a money decision.  It's a broader cost-benefit analysis.  You may not think of it that way consciously, but it is.

One person uses cloth diapers because the things on the "plus" side (whichever things those might be fore her) outweigh the things on the "minus" side.  Reusing something for multiple children gives such a feeling of satisfaction that it outweighs the not-so-bad (to her) job of rinsing dirty diapers.  For another, the the cost of disposables is small (with relation to her household income) and is well worth it compared to the fact that cloth diapers make mommy the only person in the household who is qualified to change and dispose of diapers.

So when I consider going without textbooks, it isn't really a consideration of "right" and "wrong".  It's not even about "good", "better" and "best" (more about that in another post).  It's really about the cost-benefit analysis for our family and, more specifically, for me personally.

Here's a sketch of the "cost" of going without textbooks ...

• No ready-made material on hand (more time and brainpower needed to make things by hand)
• Missing out on the colorful, professional layouts
• More responsibility rests on me to choose (i.e. research and decide on) the scope and sequence (not just within the year, but from one year to another)

But here are (on my balance sheet) are the benefits of dropping textbooks ...

• I'm not constrained to a particular scope and sequence (order of topics) and can order them based on learning opportunities, whole-family instruction and the developmental abilities of each child.
• I can school without the restraints of grade level and (related) comparing my children to other children around the same age.
• I can school without the parameters of a "school year" or a "work week".
• I get to create the lessons and activities myself.
• I'm not bound up by a need to "finish" a purchased curriculum,  or "get  my money's worth"; no need to weed through and pick out which parts of a lesson to do.
• A LOT less time spent explaining work and correcting (and re-correcting) work.
• I have a better handle on the actual, individual progress of each child and I can individualize practice not only to the specific topics each child needs to review, but to the frequency with which each needs to review.
• I don't have to pay for textbooks.  But this almost doesn't count, because there is no doubt that I'll find other ways to spend the money on our homeschooling ... some of them probably made necessary by this approach.

As I read over these, I realize that each one could use some explaining.  Actually, each one could probably use its own blog post.  So for now I'll leave it as it is and come back and retro-link each one as I have a chance to write on it elsewhere. [done!]  As you read over this list, you may realize that some things in the "cost" category would be huge costs for you.  And maybe some of the things in the "benefits" category don't seem like much of a benefit (or would even qualify as a "cost" for you).  This would be one of those areas where knowing yourself and making decisions accordingly will be of great benefit to you and to your family!

Textbooks and Training Wheels

I wrote the very first post for this blog (with the same graphic) early one Monday morning before the kids were up.  I had a crazy plan.  I had been talking to my dad and my brother some about it.  And I wanted to start documenting it from the beginning.  So I started the blog.  I meant to talk about the training wheels analogy at some point.  And I meant to talk about why I would think about going without textbooks.  And then life kinda happened.  And this whole journey churned up a lot of other thoughts to process that ended up as blog posts.  So, here I am again, back to the start to finish what I began.  What does this blog have to do with training wheels?

We had our first homebirth with the birth of our fourth baby.  While part of me thought "I wish I had done it this way all along!" another part of me wondered if I really would have been up for that.  Perhaps, in God's providence, it was the right thing for me to have a few babies in the hospital before coming across the idea of homebirth.  I feel the same way about going without textbooks.  I haven't even finally decided if this will work for us.  But I feel pretty sure that it wouldn't have worked for me from the beginning (though I am sure that there are plenty of moms out there who take off sans-textbook from the word go).  I needed time to get my balance, so to speak, and, honestly, to mature a little bit.  That is why I use the analogy of training wheels.  I'm glad I learned to homeschool with textbooks.  Now I'd like to try without and see if we can enjoy and manage the freedom (and risk!).

However, I want to be very clear that I didn't choose that analogy because I wanted to set no-textbooks as superior to or more sophisticated than using textbooks.  I don't even see it as something that all homeschooling moms are or should be working towards.  It was just that on that Monday morning, our new experiment felt to me like taking the training wheels of my bike for the first time.  Exhilarating ... yet terrifying!

So many times as I read through Teaching from Rest, I felt like Sarah Mackenzie had reached into my own brain, scooped out my half-formed thoughts and composed them into eloquent, coherent sentences.  Here's one example that applies to this discussion:

Whether or not you purchase open-and-go curriculum doesn't really matter.  You can pretty much forget all the heated discussions about whether you are caving in to school-at-home if you use traditional workbooks or a straight-from-the-box curriculum.  I know successful homeschooling families who use textbooks and successful homeschooling families who eschew them.  I don't think that's a relevant debate to be having if you want to teach from rest and become happy, content, peaceful and effective homeschooling moms.

If I have one point to argue about using textbooks, it isn't that you should or shouldn't.  It's just that you don't have to.  I don't yet  know which camp I will land in.  As this point, I think it likely we'll use textbooks for some subjects and not for others.  But either way, this experiment has been worth it, because I now know that I can decide based on what works best for us!

DIY Math on the Level

As much as I have raved about Math on the Level (and I DO love what I know of it and WOULD recommend it if anyone was considering it) I haven't actually purchased a copy of the material.  I have looked over a friend's copy of the material, read everything there is to read on the website and taken a few webinars with the author.  But at the moment, part of our "experiment" is testing out a kind of a home-grown version of a Math-on-the-Level-like system.

From what I know (and chime in if you know better than I do) here are the essential things Math on the Level offers:

1. What to Teach - Math on the Level clearly outlines and describes what your children need to understand and what skills they need to master in order to be ready for Algebra.
2. How to Teach - Math on the Level books are full of very detailed explanations of each topic and lots and lots of good ideas about how to teach math and specific suggestions about how to help your children encounter individual topics, especially in "living math" ways.
3. How to Assess - The primary means of assessment is in face-to-face interaction with your student as you teach the lesson.  The material also includes many, many practice problems (and answers) for each topic so that you will have plenty of options for making up their Five-A-Days.  Also, the record keeping system (either by spreadsheet or paper/pencil) enables you to know what has been mastered and what needs review.

At this point, my working theory is that I have resources available to accomplish all three of these these things.

1. What to Teach - Using a combination of the table of contents to the math textbooks my kids have used in the past (because I still have the answer keys), the Mathematics Common Core lists and the Math on the Level list, I've put together my own list of topics.  (It's basically the same as the Math on the Level list, with a few additions/modifications.)
2. How to Teach - This is the part I love best and that I most appreciate having the freedom to do on my own.  However (ironically?) it's also the part where I feel the most insecurity.  If I purchase my own copy of Math on the Level, it will be mostly for this reason - because I want to make sure that I teach each concept completely and thoroughly.  We've also been making use of Math Antics and  Kahn Academy to help us out with the how-to-explain-this aspect.
3. How to Assess - I love the Math on the Level method.  I've basically adopted that method by use of a free spreadsheet I found on-line (which saved some time, but could be easily made from scratch by someone who had some basic knowledge of spreadsheets).  I already believe strongly in assessment by conversation (even in math) and am liking the new method of only five practice problems a day just to ensure that skills stay sharp.  Also, since I have teacher answer keys from all of the children's past Abeka textbooks, I have an enormous supply of practice problems (and answers).  And, of course, the Internet (including  Math Antics and  Kahn Academy) contains abundant resources for practice.  Of course, the benefit of the Math on the Level practice problems is that they are arranged and indexed by topic making it much easier to grab just what you need.

So, will this DIY method work?  Or will I end up purchasing a (used?) copy of Math on the Level?  Or, will I throw my hands in the air and just order everyone an Abeka textbooks for next year?  Stay tuned to find out.  Or, watch paint dry.  Either way, should keep you on the edge of your seat and provide great family entertainment. ;-)

Flu and Freedom

After Hazel's surgery, Matt got the flu.  And then he kindly shared it with each of us in turn.  I thought I had the worst of it Saturday, Sunday and Monday.  I was wrong.  Tuesday was so bad I had to ask Matt to stay home from work.  Yesterday I was just barely well enough to be the grown-up in charge.  And it was a wonderful day.  Not in every way.  But in some ways of good, long-term importance.

Sarah Mackenzie, author of Teaching from Rest also has a blog and a podcast.  (See ... that's why I didn't want to read her book.  What kind of normal mother of six children can do those things?  Plus in her blog pictures, she looks perky.  And showered.  Clearly she is in super-woman territory and I don't fit in that category.  But I digress ...).  The same friend who finally convinced me to read Teaching from Rest has also been "pestering" (and I use that term in the nicest possible way) me to check out Sarah's podcast.  There is a members-only side of the site that includes author events, extra resources and what she calls "Master Classes".

So, because I was stuck in bed and needed encouragement even more than I needed physical healing (which is saying a lot) I decided to take the plunge.  After all, I am forever grateful that I finally gave in and read Teaching from Rest.  So the chances were good this friend knows me well enough to know what will bless my soul.  I took a Master Class she recommended (and was also taking) called "Focus and Align" and it was UH-mazing.

Sarah led us through several steps in considering our particular family, our gifts, what works for us and what is important to us.  For example, in one of the exercises, Sarah asked us to imagine that our children were sitting down to a meal with friends some 20 years from now and someone asks "So, you were homeschooled. What was that like?"  What words do I hope will come to mind?  What are the things that I most want my children to remember as their experience of childhood and homeschool?

These activities helped to take me beyond the ground-level focus on "math" and "handwriting" and more towards the goals, practices and atmosphere of my home.  We then used this thinking and exploration to create our family "Rule of Six" - six things that are foundational to our family and which we hope to do every day.  Here is how ours turned out.  (And below it are two other prettier versions from my Sarah Mackenzie-pushing friend that she fancied up for me!)

I completed this activity Tuesday evening.  By Wednesday, when I was on my own again with all the kiddos, somehow, "homeschool" seemed more manageable.  If these were the six most important things to do every day, in big, broad brush strokes, then I could adapt them to something I could do from the bed as well.  In fact, we opened our homeschool day by talking about our new "Rule of Six".  The kids were excited.  Tonight at dinner we talked about what we did yesterday and today that involved each item on the list.  It may seem like a small thing, but it reminded this Mama that good, important and grace-infused things are happening right here, every day.  Even on flu days.

P.S. Our assignment was to make up our own Rule of Six and share it on social media, tagged #RARruleof6.  If you want to see what other folks have come up with, check out that hashtag.  What is so beautiful is that they are all different!  There is not one "expert version".  We are each the experts on our own homes and our own children!

Details on Demand - Part 2

In my first Details on Demand post I talked about how a friend suggested Math on the Level and what an amazing discovery that was.  However, the post was getting long, time was getting short and, to be honest, my spreadsheet wasn't finished yet.  Now that I've got a completed spreadsheet under my belt (that's an odd mental image, isn't it?) and a little more time, here's the rest of the summary overview of our new system.

In the last post, I shared an image of the main/first page of our spreadsheet:

This worksheet lists all the concepts to be tacked before Algebra.  The X's on the right simply indicate mastery - concepts that are ready for review.  However, I also have separate worksheets for each child.

Each child's individual worksheet enables me to track not only what concepts they need to review, but how often they need to review them, when they have recently reviewed that topic and how they fared with it.  Here's a sample of Luke's worksheet.

"Max intended" lists how frequently I'd like Luke to practice this concept.  Because I'm just getting my feet wet (and because Luke has a ton to review ... this is only about half of his list) I've put most everything at 21 days (once every three weeks).  However, he had a little difficulty with #76 Converting Between Customary Units, so I upgraded that to a once-a-week (7 days) review.  The blue column shows how many days have passed since the last practice and the column to the right of that displays *** if the topic is up for review.

As I assign new problems, I put in the date to the right.  The gray column tracks the most recent time that topic was covered.  I took this screen snip after assigning Luke 5-A-Days for 2/3/16 but before updating the spreadsheet to show how well he did so that you could see the ones assigned for a particular day.  Even though he only does five problems per day, one problem can review multiple concepts.  For example, I was able to ask one question that addressed both #10 and #11 and another question that addressed both #7 and #129 (Comparing Fractions).

Problems given on previous days and already checked have been color coded.  Green means he got it correct.  Yellow indicates a problem he missed, but was able to correct without any help.  Red (not shown here) indicates he had trouble and needed help.  More than one red and I'll reassess whether this is really a concept that belongs in the "mastered, ready for review" group.

For comparison, here's Robyn's personal worksheet.

While the screen snip from Luke's page showed only a portion of his review concepts, this is everything for Robyn.  A much smaller list.  And so a much more frequent rotation.

Another day I'll go into more detail about why this system is so great for us.  And I know I've just dropped a blizzard of new blog posts on folks, so feel free to take a few days to sift through it all.  It may be that long before I get back to adding anything new because my next project is to get the Language spreadsheet up and running.  Enjoy your weekend!

P.S. There is a Youtube Video giving more detail about how to use this spreadsheet narrated by the person who created it (a Math on the Level homeschool mom).  It won't be of much use/interest to you, unless you are thinking of personally adopting this kind of system.  Otherwise the summary above is sufficient.