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!

Buy All the Things

This is the last 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 Part 6: Do Over and Part 7: Finger on the Pulse.  The last "plus" isn't truly a "benefit" but it's one of the most fun ones to write about, so here we go:

• 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.

So here are some of the things I've spent money on instead of math textbooks:

• notebook paper
• ink pens
• new binders
• compasses and protractors
• a clock face stamp
• laminating sleeves
• dry erase markers
• dry erase crayons
• clipboards
• math quick-reference card

And here are some of the things I can imagine myself going overboard and using up the entire tax return purchasing in the future:

• more math-related read alouds (recently we've really been enjoying Sir Cumference books from the library, but I'm thinking we might want to own them)
• more math manipulatives
• subscription to MathAntics.com
• our own copy of Math on the Level
• Life of Fred books
• some new board games that would be particularly relevant to upcoming math concepts
• logical problem solving activities
• lots more fun math stuff!

From Homeschool Ryan Gosling

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!

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.

Snuggle Number

So.  This has been a challenging week.  At some point I need to write a follow-up post to the very somber-toned ones I put up on Monday.  But right now I feel more like keeping it light and sharing something fun!

A couple of days ago on Instagram a friend shared a picture of her kids playing a game called Snuggle Number.  I asked her for the scoop and she sent me to this blog post (I am in love with the blog title, too!).  I had been thinking about making and laminating some hundreds charts to use with the kids as another thing they could write on with their dry erase markers and this took up just enough room to fill up the blank space at the bottom, so, on it went.

All you need is a chart like this (which you could easily create by hand on scratch paper in moments) and a 10-sided die or a deck of playing cards, minus the face cards and jokers (count the Aces as 1 and the 10's as 0).  Roll the die or draw a card, then record that digit somewhere in the eleven slots on your game board (the original above is two-sided to allow for two games before the paper has to be tossed; my board below is simplified for little learners and since it is dry-erase is already reusable).  The goal is to get as close to the "target" number as you can in each row.  My board includes spaces for the kids to write the difference between their number and the target number and to add the total because I felt like they might need a little more structure to understand the gameplay.  More thorough discussion of the rules is on the blog above.

Want a copy?

Here is a copy of Snuggle Number only (half-page sized, so you could print two on a page)

Here is a copy of the whole thing I printed for my kiddos: addition chart, multiplication chart, hundreds chart and Snuggle Number (Note: For the number charts I used a special handwriting font which I don't think will show up via a Google Drive share, so the formatting will be a little different.)

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. ;-)

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.

Details on Demand

I'm determined to get in a post on some of the details of our experiment because my family has been asking about it.  It's a big question to answer, and there is a lot of "Teaching from Rest" intertwined in the process towards this plan.  But explaining Math on the Level will go a long way towards explaining what it is we are trying out.  As I said at the end of the last post, a friend recommended Math on the Level.  I had a chance to explore the idea on the website, on the Yahoo support group and by looking through her copy of the curriculum.

Math on the Level (MotL) is a complete pre-K through pre-algebra math program developed by a homeschool mom.  Instead of thinking of math in grade levels, she lists all of the topics that a student would need to cover through eighth grade (or in order to be ready for algebra).  The topics are organized into four categories - Operations, Geometry & Measurement, Fractions and Money & Decimals.  Within a category, the topics are organized approximately by complexity.  You, as the mom, can choose which topic you'd like to teach next.  There is no set minimum or maximum to cover each year.  You teach what your child is developmentally ready to explore.  She recommends that you cover topics from each of the four core books each year.

The MotL curriculum packs come with a book called "Math Resources" which demonstrates use of graphs and other visuals and a book called "Math Adventures" which is loaded with ideas for learning math through everyday activities like cooking, shopping and (of course!!) board gaming. :-)  The MotL Record Keeping book explains the (genius) record-keeping method that helps moms/teachers keep track of what has been mastered and needs to be reviewed.  And finally, there is a teacher guide for each of the categories which includes detailed, thoroughly illustrated and very helpful explanations of each topic.  In the back of each category book are oodles of practice problems for each of the topics.

Mastery of a topic is assessed through personal interaction and discussion.  The paper-pencil work is saved for review.  That's where the genius record keeping method comes in handy.  Moms/teachers keep a paper copy or spreadsheet copy of the topics to be covered and mark those mastered by students.  Mastered topics are then copied to another list which is used for selecting five problems a day for students to complete to review previously mastered topics.

What makes this system particularly brilliant is that the author has detailed which more-complex topics replace earlier less-complex topics so that students do not need to continue to review more basic skills when those skills are incorporated into the more complex processes.  Here is a little snippet of the spreadsheet I'm developing for our family.

See the column labeled Rep/Drop?  That lets teachers know when they can drop review of this topic because it is replace by another or if can simply be dropped from the review rotation once mastered.  In the next post, I'll take time to explain the lists of topics for review and how I've been developing the 5-A-Day problems for our experiment!

The Slow Trickle of Math Change

From the beginning, we've use the Abeka Arithmetic series.  And honestly, the truth is that I really like it.  Full disclosure: I've only ever purchased and used the student (consumable) books and the answer key, so I really can't speak to the teachers' guides or how they recommend you teach a concept, what learning activities they suggest, etc. - I'm sure they are great.  For us, the ticket was that Abeka approaches each new concept in tiny baby steps.  That made it simple to give each kid a little five-minute briefing on what was new in the daily lesson and send them off to do it.

If you read reviews of Abeka's math program online the one thing you'll hear again and again on the "con" side is that there are too many problems.  Too much review.  The benefit is that there is plenty of opportunity for more practice if needed.  But it also means the potential need to fight against your complete-all-the-problems-on-the-page obsession, should you happen to have one.  (In my case this wasn't a "perfectionist" or OCD thing.  It was a fear thing.  What if we don't?  What will happen?  Will they have what they need?  Will they be ready?)

One thing I've learned as a homeschool mom is that I may not (no, rather, I AM not) an expert in any subject area.  But I am an expert on my children.  Nobody knows my kids like I do.  And it's my job to use my expertise to their advantage.  This gave me the confidence to start tailoring their assignments a bit.  I started by not requiring them to do every problem in every section - do a few; do more only if you need more practice.  Then I got bold enough not to require them to do every section in the lesson  - why practice addition, subtraction and multiplication when you use all those skills when doing long division?

Then, last spring, as the homeschool machine got up and running again after a new baby arrived in February, I got a really radical idea.   I decided we didn't need to do all the lesson in the math book.  About a third of their lessons were "review" lessons - no new concept is taught.  This is good if you need to keep students up on their math skills for 170 days of instruction and don't have that many new concepts to teach.  But we were facing down summer and wanting to get math wrapped up!  As I said, Abeka is review-heavy within each lesson, so entire lessons devoted to review was kind of superfluous for us at that point.

In other subjects (like science and history) my theory has been to teach to the older kids and wrap in the little kids, counting whatever they pick up as a bonus.  Henry, my four year old, can tell you that some things Britain exported to the colonies were "tea, fancy dresses and fancy dishes".  Nevermind that he doesn't know what "Britain" or "exported" or "colonies" are - there's time for that later.

So why not follow the same strategy with math?  Sure, the other kids couldn't handle everything Luke was doing with fractions.  But could it hurt for them to sit in on a discussion or exploration of the concepts, glean what they could, and then practice at their own level?  Since Abeka is a consumable math program and the pages are perforated, I had debated tearing out all the pages from everyone's book and sorting them into topics so that I could teach everyone together on overlapping topics.  And then a friend said "You need to check out Math on the Level."