Math Inspirations Review

I love The Discovery Method from www.mathinspirations.com.  I'll admit, though, that when I first heard the idea, I thought, "That is ridiculous.  We have perfectly good ways of doing math that have been around for a long time.  Why make the kids figure them out on their own?"  However, as I learned more, I changed my mind.  Part of the reason was that this is completely organized and provides a system for making sure they learn to do every kind of math K-8 (I hope they expand to high school), which I had never seen a "Directed Discovery" method offer.  More than that, though, was a simple question they asked: "What does it mean to divide 2/3 by 4/5?"  I had to spend a while thinking about it before I realized, and now I'm sure I won't forget the algorithm for dividing by a fraction, because I understand what I'm really doing.  It was also tremendously exciting when I figured it out!  And I realized, I want my kids to have that same experience.  So I was sold.

This is going to be my official "curriculum" when my kids are old enough.  However, this is not really an EL-friendly curriculum.  Even EL kids are going to need quite a bit of logic and problem-solving ability, and my EL five year old is definitely not there yet.  Maybe some of yours are, but not mine.

Until about age 7 or 8, Emily Dyke, the founder of Math Inspirations, advocates nothing but games for math.  Some of her 100 games that you get with the course reinforce basic operations (addition, subtraction, multiplication, and division), so you will have some experience with those, but the main focus is on leaning the skills and mindset necessary for problem-solving.  My daughter and I are currently playing a variant on the commercial game "Mastermind" with our blocks.  One person hides three blocks; the other picks up groups of three and asks how many are right until they know which three are hidden.  It's been interesting to watch my daughter, who was not quite 5 when we started.  At first she had no idea what to do, so she would hide the blocks and I would guess while narrating my logic.  After a week or so she started guessing herself.  She'll still often get two blocks and then get really frustrated trying to find the third.  Or she'll get confused about what she really knows.   But she's definitely learning, and I can see how this and other games will prepare her for the curriculum.

I tried to do the first unit with her just for the purpose of the review.  She doesn't have the persistence necessary yet for the way this curriculum is set up, but here's how it went.  (The activity I did, while based on Emily Dyke's ideas, is not in the Basic Operations manual I own; I assume something similar is in the Number Sense book, but that one's not out yet.  So I feel that it's legitimate to share this.)

The curriculum is all about questions; the parent is basically never to tell the kid anything.  So we started with "What is a number?"  "It's how we count," was a perfectly good answer.  The next question is, "What is a digit?" and she has no idea.  (I don't use it often - oops.)  So I wrote some one-, two-, and three-digit numbers out and told her how many digits were in each.  Then we built those numbers with blocks.  Then I asked her to identify one digit, and she could do that.  But she couldn't articulate what a digit would tell her, which was the goal of the lesson.  She got frustrated and withdrew.  Like I said, she needs more problem-solving experience and maybe simply more maturity.

In general, the goal of the curriculum is to get a 10 year old to be able to work completely independently for about half an hour a day, and the parent comes and talks with them for fifteen minutes twice a week.  In addition, however, everyone in the family should be working on logic games or puzzles every day, so she recommends playing games daily as a family for about fifteen  minutes.  And younger kids or those new to the curriculum will need a lot more hands-on help.

For each concept, you start with defining terms, using something like my digit activity above.  The kid writes or dictates a definition, which you then compare with some definitions from math dictionaries to make sure all the important things are covered.  Then the final form of the definition is written in the child's Book of Math.  Then there are very concrete, hands-on story problems using the skill (like the ubiquitous "You have five candies and your grandma gives you four more; how many do you have now?").  The idea is for the kid model and solve the problem in some way.  The parent is not to explain how to model it, but if the kid is really stuck you can ask leading questions until they start trying something.  With little kids, you'd be sitting with them, but the goal is for them to eventually do this on their own.  When you work with them twice a week, your job is to say "Prove it" on a handful of problems they've done (anything you can see they've done wrong, of course, but also things they did right) so that they practice defending their ideas.

When the kid has solved a sufficient number (parent's discretion), they collect all their data (they need help with this) and look for patterns.  For example; Multiplying two teens always gets 100 plus the sum of the ones digits in the tens place plus the product of the ones digits in the ones place.  (That is a pattern I realized after playing algebra last week and it made me happy.)  They come up with a hypothesis of a rule they think will work in every case.  With younger kids, the parent pretends that they don't know this math, and there are cool exercises where the kid teaches the parent to help them craft their hypothesis.  Then they do more problems, doing each problem twice, once with modeling and once with the hypothesis, to make sure it always works.  Once it's solid, they write their new Theorem in their Book of Math.  You can also discuss other algorithms with them at this point, for comparison's sake, and they might incorporate other ideas.

It's a much slower process than just telling them the rule and then letting them practice applying it.  Each theorem might take weeks to develop.  And it requires a lot of persistence and logical thinking; they have to try many different things until one works, and it helps to be able to see patterns and manipulate them.  That's why my five year old can't do it.  But I love that it makes Directed Discovery into a concrete program, instead of the fuzzy "let them play and they'll learn things" that's all I've ever understood it to mean.  And since they spend at least half their time working on problems they have no idea how to do, they get a lot of confidence in solving unfamiliar problems.  And if they forget something and don't have their Book of Math handy, they know they can figure it out again; after all, they did it once already.

The training was excellent and worth the $120 I spent on it (it was on sale).  It really helped me understand how I can direct their discovery with questions and clear objectives.  I don't agree with everything Emily Dyke says (most obviously her stance on calculators), but it's a great resource.  It doesn't work with my little kids; persistence in the face of frustration and skills to solve difficult problems are not what we're working on with my five-and-under crowd in academic achievement.  But they are excellent skills that I will be investing in when they're actually elementary-school age, and I love how this curriculum teaches them.

So we're just playing blocks right now, a la Crewton Ramone, and we're starting problem-solving games with my oldest (she struggles with perfectionism and is easily frustrated, so we're taking it slowly).  When my kids are old enough to struggle with math, this is what we're going to do.  We'll identify the vocabulary and define it through logic puzzles, then act out story problems to learn how to do the problems.  We'll write our own rules for how to do math (I want to do this myself!) that we are much less likely to forget.  We will probably need to supplement or else be really good about the review games to get to mastery of basic things like the addends and multiplication tables, but other than that, I love this program.

Motherhood and MBTI

I love personality tests. They're just fun. Sometimes they are accurate or useful in some measure, but always they emphasize the fact that we are not all alike, we don't think alike, and we don't need to condemn or feel condemned by differences. And that is a very valuable reminder.

One popular assessment is the Meyer-Briggs Type Indicator, or MBTI. This divides people into 16 types, depending on where you fall on each of four scales: Extravert to Introvert (where you get energy, with others or alone), Sensor to Intuitive (whether you prefer concrete information or abstract ideas), Feeler to Thinker (making decisions more interpersonally or by objective standards), and Judger to Perceiver (needing closure vs always wanting more information). Check out 16personalities.com for a real breakdown of these dichotomies and the 16 possible outcomes from choosing one of each pair.

I'd tried MBTI before, but I could never accurately type myself (including on a professionally administered test) until I was a mom. Part of that may have been the book MotherStyles, which talks about type for moms and is a fabulous book because it shows how any type can be a good mother and all of them have struggles. It encourages moms not to compare but to enjoy their own strengths. Great advice for any mom, and we all need to be reminded of that sometimes.

But I think that a lot of figuring out my type as an adult had to do with making enough decisions on my own and running my own life enough to develop clear preferences. Meyer called this "maturation" and motherhood is certainly maturing me!

I grew up with and have always had a fabulous relationship with two parents who are nearly my type opposite: I'm an INTP and they are ISFJs. And society tends to reward ESFJ for females and ESTJ for males, which pushed me even more that direction. So it took a long time for me to realize that although I can use my Sensor and Feeler sides enough that the test came out neutral, and actually tested Judger as I scheduled my way through college, those aren't my native preferences.

As a mom, I find myself drawn to recharging alone and not doing too much, daydreaming and thinking about ideas, emphasizing independence and not wanting to be too drawn into people's lives, including my kids, and always leaving time for more research before a real final conclusion. INTPs are usually summarized as the absent-minded professor, and I don't have a problem with that. I love learning, including with my kids, and I struggle with the physical routines of cleaning and bathing and with the emotional drama and social requirements of raising kids.

What is interesting to me is how long it took my type to mature. I always thought it happened in childhood, but I didn't recognize my Intuitive nature until motherhood, and I still struggle to fully live my Thinker strengths. (My confusion over being a Perceiver was more due to misunderstanding the terms; once I realized that Perceivers can use schedules but don't want actual closure, always needing more research, I saw that I'd simply been mistaken.) I think my problem with Thinking is that I don't have a strong preference there, and since I've spent so much of my life being told to make decisions based on people's feelings, I am conflicted when I try to decide. Since Perceivers don't like final decisions anyway, it's tough!

One thing I have noticed is that when I rely on my weaker sides too much, I get stressed. If I'm trying to keep to a schedule and use my J side, I tend to overreact and not allow any changes, even when they'd be the right thing to do. When I'm caught between the right decision and one that makes people happy, I get paralyzed and can't decide at all. Too much concrete Sensor work and I tend to completely zone out, which can be disastrous with children. And after a morning at the park chatting with other moms, I put my kids in their rooms for a long nap so I can be alone. That has helped me identify which ones are my natural preferences and how I can guard against overreaction. After all, we all have to use our weaker sides, and we need to learn to do it reasonably.

How has motherhood taught you more about yourself?

Science "Observations"

It's a while before we'll actually start doing science experiments with my kids, but I have several books on hand for elementary science ideas and I glance through them now and then for fun. And I've come to a conclusion: most of what they suggest are not science "experiments." They're science "observations." Think about it: they have kids set an ice cube on a plate and see it melt, then teach them about the states of matter. And that's great... for an observation. It can spark interest and make information stick. It can be very fun and entertaining (does anyone else have fond memories of dissecting owl pellets?). But it's not an _experiment_.

This is a little tricky, because some science "experiments" done by professionals are observations. And if you want to call these little observations "experiments," that's perfectly fine. Really. Just don't, please don't, try to use observations to teach the scientific method.

We've all been there. We're watching ice melt, and this is Science, so we'll use the Scientific Method! Child, please make a hypothesis about what will happen to this ice.

The kid either already knows, and thus thinks, "This is stupid," or doesn't have any idea, and thus thinks, "I am stupid." (Yes, I'm oversimplifying hugely here, but this was my elementary school experience with science.)

Then, after forcing the child to guess, we assign a procedure, a recipe to follow, and ask the child to observe the results and draw conclusions. What's the difference between results and conclusions? Surprise: there isn't one in an observation! That's why you had so much trouble with this as a kid! This only exists in a real experiment!

So what is a real experiment? What's different about it from what I just described, which is what most of us did in science class? (I know I did, right up through undergraduate work in college - at least there, my recipe-following was part of a real experiment for a professor).

A real experiment starts with observation.

I put that as it's own paragraph so that you would reflect a little. _A real experiment starts with observation._ Do the observation on its own, for its own sake, without forcing it into the formula of the scientific method, where it was never meant to be. Observe, and then ask, "Why?"

That's the second step. Why does ice melt on a plate? What makes that happen?

Now, this is something you could easily look up without an experiment. But let's say you really want to figure it out yourself. _Now_ you can generate a hypothesis. Actually, generate a lot of hypotheses. All you can.

Maybe it's a reaction between ice and plates? Ice and air? Ice and light? Ice and time? Ice and temperature? What else could it be?

Now, pick one of these ideas and design a way to test it. Not a recipe - your own plan. Hour could you show it was true? More importantly, how could you show it was not true?

(As an aside, please, _please_ teach them that falsifying is the way to go. Science is about trying to disprove hypotheses. You want to try to show that it's not true. Your experimental design will be much better.)

So you hypothesize that ice melts because of something to do with plates. Well, if that's true, then ice next to the plate on some other surface won't melt. If it's not true, ice will melt anywhere. Let's set out lots of ice cubes next to each other on plates, paper plates, grass, concrete, sand, glass bowls, plastic dishes, everything we can find, and see what happens.

Results? They all melted. But some melted faster than others. Hmm...

Conclusion: it's not plates that makes ice melt. But different surfaces make ice melt differently. I wonder why...

And it starts all over again.

That's the scientific method. That's the beauty and the fun of science. Show it to your kids! Have fun with it! And please don't squeeze the life out of it by trying to teach it through observations. Observe, yes, as much as you can. And then do experiments to learn more. That's science.

Goal Days

Goal Days are something that, as far as I know, I came up with all on my own.  That's so rare, I just wanted to make a point of it.  Most of what I share on this blog is from much wiser people than myself, and I've just learned and implemented it.  But this is one thing that I believe I created for myself.  (I'm sure other people have done it as well, but I haven't read it anywhere.)

So, my great idea is: Goal Day parties!  This idea came about when my girls were begging for another holiday during a long drought of them and when I was trying to encourage my oldest to put her new reading skills to use in reading books.  I had an idea that I still love: whenever someone in our family achieves a goal that we've been working hard on, we will celebrate with a Goal Day party!  This will match our (low-key) family birthday parties: the Goal Day achiever gets to decide on what to have for dinner and request a special dessert, and they gain one gift (from the thrift store or homemade for the kids, or bought used online for us adults).  And it's a celebration!  We can have holidays whenever, regardless of the calender, for achieving!

We all love this idea.  It comes naturally, since when we achieve a goal we want to celebrate.  It's fun to make it a little more formal and to really make a big deal of the big achievements we've done.  So far we've celebrated crawling, swinging across the monkey bars independently, reading a whole book independently, and writing a short story.  The adults have not actually achieved a party yet, but we started this with our New Year's Resolutions and the adult resolutions take a little more time and effort than the kid ones.  We hope to get there soon, though.

This year we're each having a goal in each of four areas: Mental, Physical, Spiritual, and Emotional/Social.  At the Goal Day party, we date the goal we've achieved on the goal chart in the kitchen and then set a new goal in that area.  It keeps us motivated to always have goals and work on them.

Three Areas of Learning

I was listening to a podcast this week from the Circe Institute on "Igniting a Love of Learning."  (You can find the podcast here: https://www.circeinstitute.org/podcast/podcast-igniting-love-learning-your-students.)  The thing that struck me most was a comment one of the members of the podcast made about there being three types of learning we're trying to teach our kids:

1. Skills - handwriting, math computation, tying shoes, disagreeing appropriately
2. Information - dates, facts, pieces of poetry
3. Understanding - concepts, moral values

And these three need to be taught in different ways.  Unfortunately, the podcast didn't go into much detail about the different ways to teach each one, but it started me ruminating on the idea.

I don't have a problem using rewards or payment to teach skills.  I know some people do, and it's certainly not my go-to approach, but when a kid needs to learn a particular skill on my schedule (potty training, for instance), a reward can jump-start the process.

Skills take demonstration and lots of repetition.  It's a matter of drill.  It did say in the podcast that a moderate amount of drill, like 5-10 minutes, is better than half an hour or more.  I totally agree!  Drilling every single day for a short amount of time helps my kids a ton with their skills in math and phonics and other areas.

Information is taught by repetition, usually.  Creative repetition is nice, but it's not my strong suit.  But spaced repetition is the key to retaining information, as far as I understand it.  When my kids get bigger, I think we'll use something like Anki to retain information that's important.  (At some point, I have to figure out what is important; that's what this is waiting on, not some nebulous "older" age.)

And understanding, I believe, comes best through literature, conversation, and living.  That's why my teaching is heavy on reading and discussing with my kids.  All the homeschooling philosophies I enjoy, like the Robinson Curriculum and Charlotte Mason and Classical Education, are heavy on reading the classics.  This may be why.  Understanding is the most important, so it needs a lot of attention, without neglecting the other areas.

So my kids read and discuss classics.  We drill on important skills regularly, daily if possible for the most important ones.  And I really like the idea of a spaced repetition system for information; now I'm looking for what information to include!

Natural Cold Remedies for Kids

My darlings got a cold this week. Unfortunately, I have just learned that my go-to, foolproof cold remedy has eucalyptus in it, and eucalyptus is no longer considered safe for anyone under the age of 10! So what's a mommy to do?

Well, this mommy spent a scary amount of time on the internet looking up ideas, and then forced all kinds of concoctions on the darlings. Poor things. My poor husband, too; he didn't know what I would try next, and our house stank to high heaven.

The most popular remedy among the over-1 crowd was a teaspoon of honey mixed with a quarter teaspoon of cinnamon. The girls ate that happily twice a day. I don't know how much it helped, but the colds were of shorter duration and intensity than normal for them, and this may have contributed. Since they liked it so much, I would recommend it.

The one I saw results from was garlic in olive oil applied to the soles of the feet. I put that on at bedtime, and coughing and sneezing stopped for the night. They didn't wake up with stuffed up noses either. Their bedroom stunk and they found it weird, but it worked. The one night I only put it on the sicker one, her sister coughed a lot and woke up in worse condition. Evidence enough for me!

Minced garlic can burn the skin, so the olive oil is essential. The first time, I minced the garlic and mixed it with oil, then coated the foot with plain oil before putting on a light coat of oil-soaked garlic. When the baby got sick, I put the minced garlic in body-temperature oil and let it soak overnight, then applied just the oil to his skin.

The baby, of course, couldn't have honey. The garlic oil worked on his cough, but he got a sore throat and was miserable. So I mixed up a throat cure for him: 3 cloves minced garlic, 1 tablespoon fresh lemon juice, 1 tablespoon apple cider vinegar. Pour 1 cup boiling water over it, cover, and let steep until room temperature. I put it in a syringe and sprayed it toward the back of his throat every hour or two (about a half teaspoon at a time). He hated it, but he hates anything sprayed in his mouth. It did seem to work; the sore throat symptoms were gone in less than a day. And when I felt a sore throat coming on a few days later, I drank a cup and the pain went away. (It tastes like a weak salad vinaigrette; not exactly what you want in the morning, but not too horrible.)

So those worked. I tried all kinds of fever remedies on the baby (the older kids didn't get fevers), but none of them were successful. His fever succumbed to a night of pacing the floor with him in prayer, and divine intervention, I'm convinced. But the cold remedies, though stinky, were helpful.

A New Plan for the New Year

I want to focus more on my kids' physical development this year. I've denied the possibility of doing Doman style exercises because you need little bits of time all day, but being somewhat successful with Timmy has made me more confident. It has truly made us happier and more loving, he and I. And now I want to try the same thing with my girls.

I think I'll try to run through a set of activities before and after each time we eat, which is four times a day, plus one before bed. Nine times seems reasonable, and I won't be interrupting other things, since we always stop to eat.

Here are the things I'm aiming to do at each set:

Monkey bars (30 sec)
Low crawl to Mommy's room (30 sec)
1 set of 10 encyclopedic knowledge facts (15 sec)
Crawl to the front room and back (30 sec)
Read 5 words (15 sec)
Somersaults or log rolls on mom's bed (1 min)
Another set of EK facts (15 sec)
Demonstrate writing a letter of the alphabet (15 sec)
3 math facts (15 sec)
1 gymnastics move (30 sec)
Another EK set (15 sec)
Piano game (1 min)

So five and a half minutes before and after each meal. That should be doable and fun for all of us. Outside of this, I still want to practice running, read scriptures, do our computer learning, and do our Kimochis every day. Running should lead nicely into spending time outdoors, scriptures are usually first thing in the morning, and the computer is right before naps, so we just need a time for Kimochis. There's always more, of course, but that's a good start. We'll see how it goes.