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!

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!

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.

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. ;-)

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

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!

Day 3: "Slates"

The only new thing yesterday were the "slates" I made for the kids so they could be more hands-on participants in the lessons I was doing with them in the morning.  I printed some handwriting sheets and grids on cardstock paper and laminated them.  I ordered some washable dry-erase crayons and washable dry-erase markers (both Crayola products) and the whole system has been a huge success.  Unforeseen bonus: when I give the kids a break from school, most of them stay at the school table and draw so they are all available and ready when we get started again!

When I was a school teacher, my students used dry-erase markers and boards.  I wonder now if all the parents secretly hated me for it.  It is impossible to get those stains out of clothing!  Even the dust from erasing stains permanently!  I had read reviews of these washable options and they seemed less than glowing.  However, we thought both products were amazing.  The only thing I can figure is that Crayola has changed the product recently, or perhaps people were looking for something substantial enough to write on a big board for students to see.  They are probably not dark/thick enough for that.

I know I still haven't gotten into much of a discussion of all those things I promised to tackle.  In my mind there is a "chronology" of thought progression that makes sense.  Getting it all in written form - that's another thing!  Soon, I hope!