Problem Solving With Hero Zero.

Here is a short video that might change the way you look at equations and your understanding of the equals sign. =

This symbols never lies.  = means same. Here is what many consider a novel approach to problem solving. Hero zero makes an appearance and over time problem solving this way will be second nature. You job is to get them to understand equals means SAME and introduce the concept of hero zero and sometimes same is NOT visually obvious and we have to get help from our hero zero.

In the problem 5x + 16 = 4x +12 we are going to end up with NOTHING on one side. We have a symbol for nothing ZERO.

We start off with a low degree of difficulty like this:

3x + 2 = 2x + 6

then

5x + 16 = 4x +12

then

2x - 3 = x + 5

a few more and these kinds of problems won't be scary at all.



Find out more about the best ways to use your base ten blocks at Crewton Ramone's house of math.

Get my book on subtraction, Crewton Ramone's Supremely Simple Subtraction it also covers the basics of this kind of problem solving. These concepts can be taught to and understood by even very young students. Hopefully you begin to see how it all goes together...check out this what's under the cup video and you can see problem solving introduced in the most basic way with what's under the cup. When we bust out hero zero we have moved down the road a little. But 5 + x = 10 and 8 + x = 10 and 3 + x = 8 are great ways to start with the CONCEPT of making same and then finding same on both sides is a natural progression. Moving from whats under the cup to seeing 8 + x = 10 = 8 + 2 therefore x must be two is just another more complicated way of playing what's under the cup, but to kids who have played what's under the cup at an early age the symbols make sense because they have SEEN what the symbols represent from an early age.


"Sometimes it is useful to know how large your zero is." ~Anon

"The hardest arithmetic to master is that which enables us to count our blessings." ~Eric Hoffer, Reflections On The Human Condition

Algebra and Base Ten Blocks, What's under the cup?

Introduce Algebra right away.

 Just playing with blocks as I have said many times teaches a lot of math. This child likes playing with my boys much more than she likes playing with me alone. Wouldn't you rather play in your sandbox with friends, it's much more fun...

Here we introduce algebra concepts without even trying. We are just playing. The idea here is simple PLAY! You can play with anybody anywhere...all you need is a set of blocks for each participant, and away you go!


At this point with the student they rarely even need to see the symbols and we say 6 plus what is 14...or we can tell a story, we have 14 people but only six cookies how many more cookies do we need? When they do see the symbols the symbols make sense.

Basically it's controlled chaos...but playing math doesn't have to be orderly and silent. I'd argue more learning takes place at this age playing and being rambunctious than sitting with a worksheet in silence...MUCH MORE.



Then here is a quick video with a variation on the theme...which instead of teaching addends and algebra, will teach multiplication and division...



A very simple variation on the theme. Here we can learn addends, multiplication and some algebra too. And we learn how to ask and answer questions mathematically, soon we will relate them to the symbols.

3x = 15 for example, We could skip count the 3's. The sound effects just make it that much more FUN.

These kids are separated by half an ocean and half a continent...video tutoring can give you child an actual head start, or give you as a parent an idea of how easy it is to get started...get a few lessons and then do it on your own...so many parents tell me they don't know how to play math or make it fun because they have absolutely no experience with math being fun. I can show you how and give you a few tips and pointers. Or you could just get a password and you can watch the vids on Rayond's Page and others...there are tons of sample lessons (that page has over 10 hours of video on it) and that's just for starters. The idea is GET STARTED.  Don't be overwhelmed, just take a bite at a time. Here is another bite basically the same thing just a slight bit more emphasis on introducing a 4 year old to problem solving. Rarely too early to start, but often too late.

People are amusing because a few years ago before I got all this together the excuse was, "now that I have blocks there's nothing to show me what to do", or "not enough material to get going with" that excuse has been removed...parent/teacher training is also coming soon. there was a time when the sum total of training was 5 VHS tapes with about 10 hours total of instruction on 5 topics. Very rudimentary. Other than that you had to fly to a training in Idaho...people are actually asking for that kind of live training again. Eventually it could happen. Meantime...

Crewton Ramone Strikes Again! Sarah.

Here is another testimonial. Sarah has hit a goal and removed a block to her progress. She passed her Compass Test.  This is kind of a big deal. Keep in mind when I met her she had no high school math credits.



Also keep in mind that her family swears up and down that this was a "normal" kid until she was three and she had a round of shots. When she was a baby/toddler she was happy and talkative and liked to draw and play with pencils.  Her mother says she was actually a little advanced because she was drawing not just scribbling and she started talking "early." (Sarah is quite an amazing artist.)  She got her shots and within days became quiet and withdrawn and for quite didn't play with pencils anymore and stopped talking altogether. The hubris filled medical profession coached by pharma has told her that her daughter had Autism all along she just didn't realize it. This is because her doctors know the child better than the parents.  In dealing with Autistic kids I have heard this story many more times than once...

I have also had to deal with schools and teachers that once they applied the Autism label limited what the students were allowed to do "for their own good"...in Sarah's case it was math. I will say her mother deserves quite a bit of credit for standing up for her daughter and getting her into some math classes.  She wants her daughter to be self sufficient. "I'm not always going to be around."



I can not take full credit for her progress because she has teachers and aides that now work with her too. I will say that when I first met her we started at square one...addends, adding numbers and multiplication.  There are still some holes I intend to go back and refill like fractions, ratios, money and problem solving.

I thought that once she passed this test which was the goal for which I was hired that we would be done but Sarah called me herself and asked me if I would do more tutoring with her even though she had passed the test. 

I have to admit that when her mom explained her goals I was among the ones with reservations, some of the school administrators flat out laughed at her,  I didn't go that far, I figured "we'll see." But I was not as optimistic as I should have been. I thought I was just being realistic. I have also been taught another valuable lesson.

Sarah has risen to the occasion. I like working with her because it increases my teaching skills as I figure out how to get her to discover some concepts on her own and how to get her to understand some of the things they teach her in school where she can mimic the algorithm but doesn't really understand what she is doing. She is beginning to understand and "know" the math not just memorize long enough to take the test which I see too many students who are not autistic doing.

I will take credit for this though because I know for a fact she would never have gotten it the traditional way...just like a lot of "normal" kids don't.



I prefer enrichment students and students who are already good at math and want to learn more. I also don't care to get put in a niche where I only work with autistic students; however, I am happy to do video tutoring with students who need help. Scheduling might prove interesting depending on your time zone but I think you find my rate of $40.00 per student quite reasonable. It's not about the money, it's about the math.

Sarah has her own page at the house of math. There are many vids there you can't find anywhere else. I put up quite a few lessons and will add more as well as a link to this post. I was wanting to to film more but sometimes this adds a dimension that is disturbing to the process. There is quite a bit there...it will take a few seconds for all the vids to load.

The idea is you learn how to help your own kids not pay me...you can get a password for 5 bucks.  I also have more video sitting on my hard drive that needs to get edited and added so check back and refresh the page there as I add more in the coming year.  I was working on a book, Crewton Ramone's Completely Cool Curious Counters' Kindergarten Compendium which took quite a bit of my time, but I was sill tutoring and making vids, they just didn't get loaded up to youtube and are sitting on my hard drive. Get the book and read it to your young child autistic or not, repeatedly.

New improved version I added an "r" to the title.

Quick Lesson Inverse Functions

You need more than one example but this is a quick 3 and a half minute lesson on how to find the inverse of a function.



In this case what is the inverse of

y = -4x² + 2 ?

Due to my math experience I looked at the multiple choice answers and knew which one it had to be...however due to my carelessness when I tried to show him why I got the wrong answer because I left off a negative when I copied down the problem. We did the problem more than once and this vid shows the last time we did it.

Two principals here:

One: NEVER TRUST THE TEACHER.

Two: You aren't wrong you are just getting more information.

Too many parents (and some teachers) are afraid to work with their kids because they might get it wrong and be embarrassed or what have you. Just get to work and see if you can get the answers...sometimes it's good to get the answer first and then look at the problem. I have had more than one student say it's easy when you know the answer. That's true and then with the thought this is easy you can see how to solve the problem and you know where you are going.

Another thing with some multiple choice tests: you can see answers that reflect common mistakes or misunderstandings of concepts that would lead you to pick the wrong answer. Talk about them. Talk about why they would put that answer as a choice on the test. This often helps deepen understanding.

Now in order to learn how to do these it requires more than on 3 and a half minute video. They can get the rule "just switch the variables and solve" but they will forget the rule in just a few weeks...

You need at leaste three examples of which this would be one of the last ones. They should have also spent some time understanding the basic concepts of Hero Zero and No Fun Get Back To One. (HZ & NFGBT1)

Here is the first example I showed this particular student:

y = x² therefore the inverse would be y = ± √x

First we "swap" the variables: x = y² which is the same as y² = x and solve (NFGBT1) by "square rooting" both sides: y = ± √x

Then you just make them slightly more complex: y = x² + 1 etc...

Then you get two thumbs up because they "get it."


"Example isn't another way to teach, it is the only way to teach." ~AE

More at the house of math.