More on Math Facts

I had to use a tutorial to figure out
how to sew linings on three
little flower girl dresses

Maybe you'd like to paint your bathroom cabinets, sew a baby quilt, or learn how to make one of those snazzy Nutella spiral breads. Most likely your first step will be to search Pinterest for a tutorial.

Not long ago I wrote an introductory post about learning math facts. As I mentioned, some kids master math facts almost effortlessly. But for others, more work is required - both from them, and from their parents and/or teachers.  What I've wanted to do for some time is write a tutorial for teaching these kids addition and multiplication facts.

But writing any kind of tutorial is time-consuming. And with the first part of 2017 filled with wedding preparations for two of our kids, free time has been in short supply.

Happily, I've found an excellent addition math facts tutorial written by Kate Snow, a homeschool mom who has a math ed background.   "Everything You Need to Know to Teach Your Child the Addition Facts" is the best explanation I've seen of an approach that introduces and teaches addition in a common-sense, logical manner.

More than any other strategy, pay attention to step 1 - "Break it Up." Instead of expecting your child to learn all the math facts at once, teach +1 and practice those facts. Then teach +2. Then work on numbers that add up to 10. And so on.

Here let me add a couple of tools that will augment this. Print out a blank addition table like this one. Fill out the chart - but color code the various sets of facts by writing the numbers with colored pencils or markers. For example, the +1 and +2 problems could be blue and the "adding to 10" facts could be red.

Then, mark the facts that your child has mastered by shading those facts in. If he already knows +1 and +2, let him shade over all those boxes. Phew! Instantly the amount of facts she needs to learn looks less daunting! Each time he conquers a new set of facts, color in the boxes.

Next, make a set of triangle flashcards - with a twist. The twist is that you will use the same color code for these facts as you used on the chart. As you use these cards to drill, they will remind your child of the strategy for solving. I used manilla file folders for a set of sturdy flashcards that stood up through many children. Here's one *tutorial* for making triangle flashcards for multiplication and division facts. (I prefer mine to have rounded edges instead of the sharp ones shown here.) Of course, addition/subtraction cards are made in the same way. Just remember to color code them.

Mrs. Snow has numerous other helpful articles and resources. Check our "A Parent's Guide to the Most Useful Addition Strategies."   You might want to sign up for Kate's weekly newsletter, too. If you do, you'll get these three articles:
Should I Change My Homeschool Math Curriculum?
What to do When Your Homeschooler HATES Math
How to Teach Your Kids to Read Math (and Be More Independent, Too!)

Hurray! Now I can continue working on getting my family ready for wedding #1 this weekend in Texas!

When Learning is Hard

On my design board
Suppose, for example, you have a high schooler who tells you that stoichiometry makes no sense and must be done by voodoo, but you, who happen to have a degree in chemistry, think stoichiometry makes complete sense, so you proceed to tell him how very simple it is, not to mention fun. It's like Sudoku! Or Kenken! you tell him exuberantly. Until you remember that for some strange reason he takes no pleasure in math puzzles either. And then you seem to recall, neither fairly or accurately, that none of his seven older siblings had difficulty with stoichiometry, so what's his problem, anyway?

Yes - something along these lines was going on in my head last week as I worked with a bewildered son who did make some comparison between stoichiometry and voodoo. And I might have said something about how simple it really is.

At that point it became clear I needed to step back and reevaluate. Was the problem a lack of effort on his part? Well, yes, to some extent. But not entirely. (And his father spent some time addressing this!) But as I reflected, I realized I had done a poor job teaching this and some other chemistry concepts, flying through material which seems so obvious to me. So instead of pressing on, we backtracked to the point at which my son had become confused and spent a couple of days working through foundational material.

Phew. I think it's starting to come together now for him. Though yes, he still needs to apply himself thoroughly to conquer this subject for which he holds little love.

Why am I telling this story?

Because similar scenarios happen routinely in homeschools. Sometimes kids inhale knowledge and rapidly move on to the next level. Other times you watch a child go over the same material day after day, and you wonder if he will ever catch on. I had one child who learned to read before he was four and another who needed a year of intensive phonics at age eight to help him break the code.

When a child struggles to learn, there can be all sorts of reasons, including these:
- Maybe he just needs a bit more time or maturity
- Maybe he's not working hard enough
- Maybe he has some kind of processing difficulty
- Maybe the teacher did an inadequate job teaching the material in the first place
- Or maybe there is some combination of several of these

If one of your children is struggling with math facts, chemistry, reading, spelling, or something else, pause and reevaluate. Do some analysis and try to discern what is going on. Sometimes you can put the difficult material on hold for a while. Often my beginning readers would hit a plateau and need to park at a certain place for a while. Rather than hurrying through their reading program, I'd just find reading material on that level for a while without trying to introduce anything new.

Frequently, though, you'll need to try to figure out what is causing a roadblock. In the case of my son and chemistry, I had to find out the point at which he had gotten lost. After going back to that spot and making sure he understood some concepts from a previous chapter, he was ready to move forward. If you have a child struggling with math, often you can best help by finding a different way to present the material.

I have some suggestions (and some helpful links) specifically about teaching math facts for a future post, but here's one final thought about learning difficulties.

Struggle is a natural part of learning. Some kids struggle more than others, but all of them will butt their heads against some part of their academics. Yes, you as a parent, whether or not you are homeschooling, need to take measures to figure out exactly what issues are involved. But beyond that, remember that struggle isn't all negative.  Because as Mystie Winkler so wonderfully writes, "Math is Character Building"

Struggle, in fact, is often the best soil for a young person's growth and maturity.  My son who had the most difficulty learning to read? Having to work harder than his siblings to overcome his dyslexia produced the fruit of self-discipline, perseverance, and a work ethic that pays off time and again. (He's about to graduate from from college with a triple major and this summer will join the accounting office of a major corporation.)  So when your children struggle, don't panic but take a deep breath, give thanks for this opportunity, and make plans to move forward!

Just the Facts, Ma'am!

Did you know there's a controversy about how children should learn basic math facts? Some say kids should learn addition and multiplication tables through repetitive drill. Others feel they will absorb this information by osmosis as they solve problems. And still others think the answer lies somewhere betwixt these two.

Here's the part everyone agrees on: all kids need to (eventually) learn basic addition and multiplication facts.

Here's what folks disagree about: WHEN and HOW and TO WHAT EXTENT this should happen.

Math wars rage between progressives who favor "discovery learning" and  "arithmetical fundamentalists" (don't you love that!) who see a good bit of value in repetition and, yes, drill. 

Stanford math education professor Jo Boaler, author of a paper called "Fluency without Fear," argues for a deemphasis on memorization and drill:
While research shows that knowledge of math facts is important, Boaler said the best way for students to know math facts is by using them regularly and developing understanding of numerical relations. Memorization, speed and test pressure can be damaging, she added. (Learn Math Without Fear)
Others disagree with this idea.
One critic of the [Canadian] government’s adoption of “discovery-based learning,” Ken Porteous, a retired engineering professor, put it bluntly: “There is nothing to discover. The tried and true methods of addition, subtraction, multiplication and division work just fine as they have for centuries. There is no benefit and in fact a huge downside to students being asked to discover other methods of performing these operations and picking the one which they like. This just leads to confusion which ultimately translates into frustration, a strong dislike for mathematics and a desire to drop out of any form of mathematics course at the earliest opportunity.”  (Math Wars)

Which philosophy do I subscribe to? Both, actually. Of course I want my children to "develop understanding of numerical relations," and thus my young children spent a good bit of time in math play. Messing around with Cuisinaire rods, for example, helps develop a sense that 5+3=8 without hardly thinking about it. They just knew that a yellow rod and a light green one are the same length as a brown rod. And playing math games with preschoolers and primary aged children also goes a long way towards painless acquisition of math facts.

BUT - drill with triangle flashcards, wrap-ups, and Calculadder sheets, and even computer games was also an essential part of each one of my children's early math education.

Because no matter which approach you (or your child's school) takes, the reality is that by about fourth grade, children who don't have their facts mastered start falling behind. Counting on fingers may be just fine for first graders, but by the time kids are doing long-division, that won't cut it. And no, calculators aren't the answer. Kids need enough proficiency with arithmetic to determine if their calculators answers are even in the ballpark.  (And did you know that calculators are banned from certain sections of college admission tests and even from a number of college math courses including many calc classes?)

Some kids absorb math facts very readily and need little drill. For others, learning the addition and multiplication tables is painful! I've had children who feel into both categories. Recently I've had questions from a couple of moms about what to do when a child struggles more than his peers.

So, as time allows, I'm planning to write about teaching math facts using teams (math families), tools, and tricks.

In the meanwhile, you might want to take a look at this article on the Living Math website.

Job's Tears - longest WIP ever

Long, long ago, back when I had only three children, I started a quilt called Job's Tears. It was a beautiful pattern, but for many reasons, I was unable to bring it to completion. (Like six more children! And all those curves made this pattern an overly ambitious design for this young quilter.) So the completed patches and the remaining fabric languished in a plastic container for a decade. And another. And half of another.

Fast forward to a new phase of life. While those nine children still give me plenty to do, time for sewing is happening once more. So this summer out from the box came this quilt which I wanted to finish for a Christmas gift.

The fabrics are unlike those being sold today. In general, I'm moving in a more modern direction, but I still like the vintage feel of these. It was hard to find border and binding fabrics that would look right, though! Even the colors being produced these days are different from those 25 years ago.

So I finished up the blocks, added some borders, worked and reworked those wedges for the corners, and then quilted it using my new Juki TL 2010-q. That new machine makes quilting large quilts so much easier! I even tried a feather border pattern in the outer white border.

About the time I was putting the finishing touches on this quilt, I happened to be reading through the book of Job. This has always been a difficult book of the Bible for me. As a younger woman I found it hard to get past the fact that all of Job's ten children were killed. All his CHILDREN! ALL his children! I'd think, even as I made my way through to the end. In more recent years I read with a growing frustration at the "advice" from Job's three older friends.

For some reason this time it was different. First, maybe because I happened to be reading a different translation than normal, or just because I'm older, I noticed and loved the poetry. But more than that, the theme of the book shouted: God is GOD! This message shows through Job himself, through the words of his young friend, Elihu, and then most especially through God's response to Job. Yes, indeed! God is God! (And I am not!) I may not always understand His ways, but I know He is sovereign and His ways are good and righteous!

Finally, tonight I found a song called "God is God" by Stephen Curtis Chapman which beautifully expresses this truth. HE is God! All praise be to Him!

And more jackets!

Before Christmas I put up a few pictures of the first two quilted jackets I made for our oldest grandgirls. It was a rush to the finish, but I did complete the last two just in time to turn my sewing room back into a bedroom before the onslaught of children, grands, and dogs arrived.

Here's the one I made for Jenny, our little red-headed orange lover:

Toddler Eliza adores animals of all kinds. So this is what I designed for her:

Both front panels are big-stitch quilted, which goes oh so fast! Eliza's animals are paper pieced. Here's one up-close:

Phew! I think I'm done with quilted jackets for a while. Maybe until we have some more little people join the family?


"Hitherto hath the Lord helped us."  

         - I Samuel 7:12

Christmas Eve hike
 Front row: Faith with Eliza, Annie, Amanda, Kara (Bunter), Paul.
Back row: Collin, Laurel, Ben VW, Kristen, Ben, me, Tim, Andrew with Jenny,
We're missing Peter, Esther, and Jon.

As we put a wrap on 2016, this verse is the refrain of my heart. As all years, this one has included plenty of joys mixed with some trials and sorrows. On balance, this year has had more joys than difficulties, but even in years that the opposite is true, this verse is every bit as true.

Here are some of the ways the Lord has helped us in the past year.

Kristen and Ben VW
Joy and Love

At the start of the year, neither Andrew nor Kristen had yet met the ones they would give their hearts to, but now at the end of this year they stand on the brink of marriage to these two future spouses. How we give thanks for Esther and Ben, who love the Lord, the church, and Andrew (Esther) and Kristen (Ben)!

Andrew and Esther

Changes, changes

Jonathan graduated from IU and took a job as a software developer with Amazon in Seattle in May. He's setting in there, but was able to spend Thanksgiving week with us in Indiana, a time for which we are thankful.

We sent another daughter off to Purdue this fall, and here again we have so much to be thankful for. The Lord has given Amanda and Faith a wonderful, solid church family in Lafayette, and they are both growing and having a place to serve others. Both are enjoying their studies and grateful for the opportunity to be at Purdue.

Travels, travels, and more travels

Snow in March in Kentucky!
We've been on the move this year more than usual. In April, Tim and I and the youngest two boys spent a weekend in Red River Gorge.

In July we took the four youngest offspring to North Carolina for a wonderful time white water rafting on the Nantahala River and hiking in the Smokies.
A screaming good time!

Andrew and Jenny  during our camping trip
August found our clan gathering at Chain O'Lakes Stare Park in northern Indiana for a group camping weekend. We're hoping to make this an annual event.

And in September. Kristen and I made the trip of a lifetime as we spent a week exploring the Andes Mountains in Peru. We fell in love with the Peruvian people (who didn't mind that we spoke only a smattering of Spanish), and we were thrilled to be able to mountain bike from 14000 ft. to 9000 ft., hike around Macchu Pichu, attend church in a little village, and buy textiles just about everywhere we went.

An Ever Elastic Household Size

Most days there are just four people running around our home. It's quite a change from the days when we had eight or nine children at home! But then - whoosh - some or all descend for a weekend or a holiday - and it's super lively around here again!

Our family is growing through births and marriages these days, and we've found ourselves scrambling to come up with enough beds to house everyone. We had 16 folks living here during much of the Christmas holidays, filling our seven bedrooms and more. So Tim built a "Cupboard Under the Stairs" a la the one of Harry Potter fame. Hopefully ours is a bit cozier. (Paul has plans to turn it into his algebra study center.)

I've been adjusting to teaching only two students and working hard to give them solid instruction but also plenty of latitude so they will continue to grow in independence and competency.


No, we haven't found any fountains of perpetual youth. And I can't exactly say either Tim or I are feeling any younger. But it has been a year where we were blessed with more opportunities to work with the young people of our church, and that has been a real joy!  

Cycling and ... Running (?!)

In October Ben and I participated in a lovely 20 mile bike ride on the new Milwaukee Trail (Lawrence County, IN) "Howl at the Moon" event.

But I've been doing less cycling this year than in past ones because this I took up jogging after something like a 26 year hiatus. I now go slower than I thought it was humanly possible to go and still have both feet in the air. But I tell myself that's ok; at least I'm giving it a go.
After the Reindeer Romp
One of us looks worse for the wear

Peter and I ran in our first event together in December. He ran 8K at a 5 something pace. I was almost twice as slow, running a 5K at a 10:11/mile pace. Peter won the whole thing. I finished third in my old-lady category. Haha! It was a hoot!


It's been a good year here, too. As a self-employed contractor, we never take God's provision of work for granted.

Loss and Trials, too

Of course, all has not been fun family times and endless delight. We've also experienced sickness and the sad results of sin.

Tim's mother, Sally, went to be with the Lord in May. She's struggled with declining health for some time now, and had been longing for heaven.

But in these hard times, too, or even especially, the Lord's help has been ever present. While I can't write about all that has taken place this year, I can publicly give thanks for His mercies which are sufficient.

The New Year

As Charles Spurgeon says, though, hitherto doesn't just look backward.
But the word also points forward. For when a man gets up to a certain mark and writes "hitherto," he is not yet at the end, there is still a distance to be traversed. More trials, more joys; more temptations, more triumphs; more prayers, more answers; more toils, more strength; more fights, more victories; and then come sickness, old age, disease, death. (Morning and Evening, Dec. 29)

What will 2017 bring?

We know a few things this new year should bring, Lord willing. We're planning for a wedding in March and one in May. In July Peter plans to move to Minneapolis to take a corporate job as an accountant. Kristen will move to Atlanta after her marriage, and then we will have children in five states. So much change will certainly be coming. But beyond these expected events, we know little. I'm so thankful that as I look to the unknown future, I have the past year, and in fact decades of past years, of memories of God's faithfulness to recall.

Yes, hitherto hath the Lord helped us, and He will continue to help in the days to come.

Double Happiness!

We have happy, happy news! In the next few months our family will have the joy of celebrating TWO weddings!

In March Andrew will wed the lovely Esther!

Andrew and Esther met through mutual friends, and sparks flew almost immediately.  They've been keeping the airlines busy traveling between Dayton and Texas.

Andrew made Esther's engagement ring which involved designing it, having a wax mold 3D printed, and then the gold cast from that. There were some difficulties and delays along the way, but isn't the finished product lovely?

We're all super excited to travel to Texas during spring break to celebrate Andrew and Esther's wedding!

Good things come in pairs, right?

Here's our second happy couple.

In May Kristen will become the wife of Ben V.W. (Or V-Dubs as some in our family are starting to call him as a way to distinguish this Ben from our youngest son.)  Ben is a native Georgian who works just outside Atlanta as a civil engineer. To make life even more interesting, both Kristen and Ben have lively puppies. (Who have yet to meet.)

Tim and I couldn't be any happier for God's wonderful gift of Esther for Andrew and Ben for Kristen!