Tuesday, August 15, 2017

Word Triggers For Learning The State Capitals

Over Christmas break, way back in December, my eldest wanted to finish memorizing all the capitals of the United States.  I told her we could absolutely weave that into her Winter Break Homeschool activities.  We would not, however, be using the rote memorization approach that they had been applying at her charter school.  Rather, we would use a "trigger word to story" memorization device.  I'm happy to report that not only did she learn the remaining 30 state capitals within 5 days, but she has retained them over the past 6 months!

How to learn, how to acquire information, how to build knowledge, and how to apply wisdom are often lacking in an education system.  Many times the student is left to their own devices to figure out ways of doing these things.  Within our homeschool we actively seek out a variety of ways to get stuff into our heads (See our homeschool Charter, VII.Tactics of Exerevno Academy.5).  It is hoped that by doing this, each of our girls will find multiple ways that work for them so that when they, as adults, have to learn something, they can do it on their own, both effectively and efficiently.
The funnier the association the better

As shared, the technique we explored together for her states was "trigger word to story." I have no idea what the formal name is for this approach, but it is the technique of seeing a word in something and building a story out of it that clues you into the answer you want to recall.  It is a simple two step process.

First, I asked my daughter to look at the state name and blurt out the first word that came to mind.  For example, when she saw Nebraska she said "Ask".

Second, I challenged her to build a story that links "ask" to Lincoln, the president.  She shared with me that when she did the debate module at school, she was told the history of the Lincoln Douglas debates.  She then continued on with something like, "and he would ask a lot of questions."

Viola! That's it, when she sees Nebraska, she triggers with "ask a" recalling that Lincoln asks a lot of questions.

Below are 20 of the associations she built. The key point is that the trigger word and story had to resonate with her, not me. My context, my knowledge, my background, etc. would build associations that didn't/wouldn't naturally fit her recall.  For example, she got stuck on Oregon, so I offered that I see Oreo and that is a cookie sandwich, and that she could instead have a Salami sandwich (for Salem). Nope, that didn't work so after some poking and prodding, she came to one that she still hasn't forgotten but doesn't work for me at all ... something about "Sailing"

After we built her list, when she would recall the capitals, she would regal me with the story each time, thus further burning her association into her mind.  Some of her associations were funny, some were crude, and some made no sense to me ... but that didn't matter, they made sense to her and she remembered.

Examples from my daughter:

Alaska - Whats the best month to visit the coldest state? Jeau Know? June, No?
Arizona - Prisoner of Azkaban/Arizona? The Phoenix
California    - Sack Ra Men Toe (I don't get this one at all!!)
Colorado - Where does a DOe live? In the Den of Fur (Den-of-fur, Denver)
Idaho - "I da ho" No you're not, you're a boy, see (Boy-see, Boise)
Illinois - There is no Ill in Spring Field (notice the rhyme)
Iowa         - "I owe a" "these monies"  des monies Des Moines
Kansas - Where is the Kan Of Sauce? At the Top! (Top-E ka)
Michigan - Mich gets rich by land Singing
Minnesota - Mickey was jealous because Minnie had lunch with Paul
Montana - Hanna Montana? No Helena Montana!
Nebraska     - Aska lotta questions? Lincoln debates
North Dakota - Dakota is a good business woman with Mark, Bis-Mark (friends of hers)
Ohio - Oh, Hi!!! O.... What Columbus said when he first came to America
Oregon - Or, go Sailin (Or, go is from Oregon)
Texas - Austin likes to Text (Austin is a friend of hers)
Utah - "ahhhh" from the Salt Lake bath (ahhh comes from U ---tahhhhhh)
Washington - Must being washing tons of clothes for Olympians
Wisconsin - W is on in? Because of his Mad Eye Son
Wyoming    - Why you, Ming? Because of my friend shy Ann

Tuesday, August 1, 2017

Discovering Math Tricks, Secrets, and Facts To Really Learn Algebra Mathematical Principles

"Dy, quick, what is 5 times 484,682?"
[about 1 second later]
"2,4,2,3,4,1,0 ....  that's an easy one dad ... give me toughie"

I love these kinds of interactions with my 9 year old daughter.   It allows her to show off her abilities, add to her confidence, flex her mental muscle, and work on her mental math skills.  But how did she know the answer so quick?  By applying a simple math fact*.

Cool as this is, what is more powerful and important is that an awesome mathematical fact (like the one she applied here) provides a vector for learning bigger, more important Mathematical principles.

To explain this more plainly, let's look at the math fact that Dy used.  You may have already figured it out, based on the way I wrote her response.

Here is the math fact she used:
5 times any rational whole number is simply that number divided by 2, times 10 (which is simply tacking on a zero if the starting number is even)

So, for her I made the problem easy.  First, I led off with "5 times".  At that point, Dy triggered into her 5 times facts.  Then I gave her a number that she could divide by 2 in her mind easily, simply going down the line of the even digits that made up the number 484,682.  So, she retained that number in her mind (a good mental exercise in its own right) and spoke out the result of dividing each digit by 2.  So, 4 ÷ 2 = 2, 8 ÷ 2 = 4, 4 ÷ 2 = 2, 6 ÷ 2 = 3, 8 ÷ 2 = 4, 2 ÷ 2 = 1, and times 10 so 0. So, 2423410.

She knows this fact now, which is cool.... and maybe during some test for college, a problem will come up with a 5 times in it and her speed will be helped if she recalls this fact .... but the real cool part is that in "discovering" this fact and how it works, she has nicely teed up algebra.

Here is the flow of her discoveries.

First, I challenged her to demonstrate her ability to multiply anything by 10 as I gave her a series of numbers (2, 4, 42, 544, 18, 20, 8, 532934, ....), which she did like a champ. Then I asked her to describe for me all the ways she could think of to write the number 10. I prompted her with "Like, 20 ÷ 2, or 10 x 1"  She paused, thought about it, and blurted "100 ÷ 10".  Awesomesauce! I kept poking her to produce more, and then she shared "2 x 5." Ahaha!  The one I wanted.

Second, I asked her to write down "4 x 10", which she did.  Then I asked her to replace the 10 with her example of the 10 equivalent, 2 x 5.  This resulted in "4 x 2 x 5."  We then explored multiplying in different orders, and to her amazement it always worked.  4 x 2 is 8 and 8 x 5 is 40, etc.

Third, I asked her if she could re-write 10 but with addition.  She wrote down 3 + 7.  I asked her to replace her 10, in her 4 x 10, with her 3 + 7,  which resulted in her writing 4 x 3 + 7.  I then asked her to solve, which yielded 19! (4x3=12, 12 + 7 = 19).  "Dad, that doesn't work." "No baby, it doesn't. The order you do this, the operation, matters."  We then launched into a nice discussion of order of operations, parenthesis, etc. for 30 minutes. :)

Fourth, I then asked her to go back to her original equation, 4 x 10 and write it out.
"4 x 10 = 40".  Next, I had her replace the 10 with her 2 x 5 version.  She wrote, "4 x 2 x 5 = 40".  Good.  Now I asked her "well, let's do the 4 x 5 first of the 4 x 2 x 5, since the order doesn't matter."  "That would be 20 then dad, so we have 20 x 2"  Me: "Well, that's interesting because 20 is half of 40, so that that makes total sense."

"Using this stuff, Dy, here is something that pops out that I'd like you to think about.   For any number that you multiply by 5, you could simply multiply it by 10 and cut it in half .... or cut it in half first and then multiply it by 10."  It wasn't instant that she understood it, but after 3 examples, she knew the trick.  After 10 examples, she was convinced. Trick learned.

Fifth, "Dy, let's replace the 40 with 20 x 2"  4 x 2 x 5 = 2 x 20  "Dy, do you see that both sides has the 2?  Does the equation work if we simply pull the 2 out?" It sure does.  

Sixth, "Let's re-write our equation but instead of writing the 2, let's replace it with a star"  Dy then writes out 4 x ☆ x 5 = ☆ x 20.  "I wonder if we can replace that star with anything?" Dy then starts trying numbers out.  2 works of course.  3 works.  How about 10.  Wow, she finds that everything works.  Neato!

Seventh, "We could always simply pull out that ☆ and it would be true right?" Dy then erases the star and sees 4 x x 5 = 20.  Big smile on her face.

A couple of wonderful hours with my little girl, and she now has an amazing foundation start with Algebra.

[Sidebar *: Early in this post, I used the phrase math fact.  I am using the word fact here because my wife hates when I call it a trick.  She likes to point out that it isn't a trick, just an application of some facts.  She is, of course, right (aren't they always! ;)  but many kids like to have secrets or tricks, and calling it a math secret could make your kid even more interested)]