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!

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!

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.

Day 7: Failure or Flexibility?

Because I stayed up (too) late the night before working on the math spreadsheet ... and because the person I was sleeping next to spent the night dealing with fever and chills, I was a tired, tired girl in the morning.  I hadn't made any Five-A-Days for the kids. So, here was the true test.  Our experiment met its first big trial-by-fire.

I do have a tendency to procrastinate.  Sometimes I choose not to work because the work seems overwhelming.  But sometimes I choose "fun" work (like getting a spreadsheet up and running) over less fun work (like writing out Five-A-Day questions).  The night before I was telling myself I'd get up early and do them before the children woke up (which I have done several times over the course of this experiment).  When that didn't happen, I told myself I'd find a time somewhere to fit them in during the morning, since the kids didn't have to do them until the afternoon.

The result was that everybody had Math 5-A-Days, but nobody had any language.  So, was this a failure of the system (or a proof that I don't have the character qualities for a system like this)?  In hindsight, I truly think not.

First, the night before, what I had spent about three hours doing was setting up the review-topics section of the spreadsheet for each individual kid.  Yes, this was fun (for me).  But just because I'm enjoying my work doesn't necessarily prove I'm being lazy, selfish, weak or [insert other pejorative character trait].  This was good work that needed to be done.  And it was one-time kinda work.  Maintaining the spreadsheet on a daily basis will take moments, compared to the hours the initial set-up process took.  (Good thing I enjoy that kinda work, right?)

Secondly, because the math spreadsheet was fully up and running, and the language one wasn't (still isn't) it gave me a great chance to compare the process of making 5-A-Days with and without a fully functional spreadsheet!  Getting math set up was fun and easy - look down the list of topics that need review, pick a few and make questions to fit.  Language, on the other hand, was daunting (and so never got done) because it was more of a mental effort.  Not as much of the planning was laid out for me.

So, in the end, I think Day 7 was a great success.  We did morning school smoothly.  And I had a chance to see what a great resource and tool the spreadsheet is!  Gives me even more motivation to get another (others?) up and functional!!

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!