Math Concepts, Conceptualization vrs Memorization

Here is a short vid showing the wee ones doing a little math where you don't have to be there you can set it up walk away and come back and check it...then do more, walk away and check it. Math enrichment for them also means understanding what the powerful machines we have built are doing not just pushing buttons...I would be willing to bet that this six year old understands square root and what it means better than a lot of high school kids and even some college kids...

At this age just using a marker is fun in and of itself...the whole thing was a fun activity...took up about an hour of their day, it could have been shorter or longer depending how much fun they were having and how long their interest was held.

What you see here is a short part of it, but enough to give you the idea. I set up trays of blocks for them to count three different times...some days just one set is enough others times more or less...depending on their mood. Make it fun, not work...stress the concepts not the facts, mathematics is NOT computation. Remove the no from the lesson. If they give an incorrect response make them count again; tell them what they DO have not what they don't have, change the thinking from "wrong" to "acquiring more information."

Remember, it takes 18 exposures to get information back out again. We know that with one exposure the information is indeed stored but retrieval is hard, but after 18 exposures we can get more information from short term to mid term memory, and with more exposures we can move it into the long term memory and with yet more exposures we can make that information available for instant recall. Begin exposing your students to mathematical concepts EARLY. You will need to keep exposing them year after year for them to attain mastery and instant recall of things like addition and subtraction facts, multiplication, division and so fourth, but again you haven't taught them mathematics per se, just facts and computation skills which are how we do mathematics.

"Mathematics is a language plus reasoning." ~Richard Feynman

"Reality is consciousness, consciousness is expressed with language. Mathematics expresses reality numerically." ~me, standing on the shoulders of Terrence McKenna and John Paulos. Nanos gigantium humeris insidentes.

They have played with squares and rectangles before counting and building, here we begin introducing some symbols, later we will introduce more concepts and symbols so that we can write simple sentences like (3)(6)=18, 18÷6=3, 3x=18 and the symbols will make sense.

Same with building addends: 6+4=10, 6+x=10 will be simple and obvious and when explanations involving math terms like "additive inverse" are encountered they will also be understood even though they are cumbersome and oblique to most math students under the age of 12. I remember having 4 boys in 6th grade all bewildered, upset and offended by a set of problems like this:

5 + x = 14........x - 7 = 4

3x=24.............6x=24

3x + 5 = 20.......2x - 8 = 12

3x + 3 = 2x + 7 etc

It took about two sessions to clear all that up and get into negative expressions and I earned a couple hundred bucks in the process. (4 x $25 x 2) and people cannot understand why I find it all so ridiculous now...yet the parents and teachers both failed to explain it in a way they could grasp easily...and in the case of the parents some didn't even try, as soon as they see algebra they throw up their hands and say things like "well, I was never good at math so..." or "I get it but I can't explain it..." or "I don't remember any of that stuff even though I passed calculus with a B"....and are shocked when I tell them I failed calculus. FAILED IT. Not even close. Good thing I did. I can feel their pain and understand why it is they don't get it because I have the benefit of having been taught both ways. One way works and the other...uh, not so much.



These same kids play with 3rd power algebra, fractions, percentages and more. The ability to do all of that consists of countng to 9, being able to tell if something is same or different or not and being able to identify a rectangle.

More sample math lessons, tools and information are available at the house of math.

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Addends, Pythagoras and Math Fun

THIS IS A GREAT LESSON

The 36 minute vid requires a password and for 3 bucks (or 12 bucks for a year pass) it's worth it, if I do say so myself just for this vid alone. I just watched it again. It should really bring home certain points in the method and HOW you use blocks to reinforce the concepts. And that same password gets you onto pages with lots of worksheet PDF's and HOURS AND HOURS more video so you basically have no excuse for NOT using your manipulatives to teach math. All kinds of topics are covered and more all the time...

Here is a short clip from a tutoring session where we took it easy on a Friday afternoon and played...but it was serious play where we learned addends fooled with a triangle, learned lots of math concepts and worked toward mastery...of multiplication and addends using addends to count count by 6's and 7's well past 6x12 and 7x12.. All 45 addends and multiplication tables need to be mastered for instant recall...this will make all the other mathematics easier...and fun. In order to do that you need to make many, many impressions on the mind to build the nuero-pathway to that information. You'll see we go over 7+4 many times in this video...next time he comes back 7+4 be easier to recall and with a few more impressions it will be instant...like 2+2...all 45 need to be mastered.

This is a short segment of a lesson that's 36 minutes long at the house of math! It is a GREAT lesson if I do say so myself...you will enjoy it. Teachers will learn more about the lessons, students will get practice with understanding square root and what it means, we build one triangle, use a protractor, but mostly addends and their many and varied uses for making math EASY.

Check out the sample lessons at the house of math!

OR

You can burn it in there the old fashioned way, the way they do it at some learning centers with math worksheets and timed drills where the facts are repeated over and over again. This is effective BUT you may lose conceptual understanding and it compartmentalizes the information to the point where some students may have a hard time understanding how it all fits together, further you risk burning students out and creating a negative association with math...and just surveying the state of mathematics in this country how's that working out so far?

As you will see at the end of the full length video it's simple to tie it all together...and it's well past time for a different and fun approach.



Here is a little more from the lesson which actually happened before we shot the promo above...



If you want to see the full lesson, (you need a password). One of the things we did was count by 7's, and 6's well past 12 times, and I showed him how we could use addends to do it, we also fooled with a Pythagorean Triple and busted out a protractor to measure some angles...

Here is a two page test he did earlier in the week. Go here for a screencast covering these two pages. The screencast is titled Algebra Test. In the screencast they aren't sideways...

It amuses me no end that teachers and parents cannot understand how playing with blocks can lead to understanding mathematical concepts on such a profound level that 3rd degree polynomials eventually present "no problem." I am doing my best to remove the mystery and lay it as bare as possible...mostly for free. This system works, it's not an experiment it WORKS. It will make crappy math teachers into good math teachers and good math teachers into GREAT math teachers...it allows you to let your students see what the symbols mean. Therefore you can manipulate them...


http://www.crewtonramoneshouseofmath.com/


http://www.facebook.com/Crewton.Ramone

There are now hours of lessons, sample lessons pdfs for down load available with that same password. If you get materials through me you get a year pass to my sites if you already have materials or if you just want to see more, a start is 3 bucks, this gets you 60 days worth of time, for 12 bucks you get a year pass. You may need that much time just to get through the host of information available...and there's more going up every week.



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4 Year Old Factors Polynomials No Problem

Here is part of a longer video that you can find on the Sample Lessons Page. In it we see two little boys on a hot Hawaiian day playing algebra. You can see all the learning that takes place in this clip...they learn counting, addition, multiplication, factoring and algebra...and you can see it's fun and satisfying when they get it right.

God made it that way. Learning is fun. You can see when the endorphins go off by the expressions on their faces...you can hear the light bulbs going off in other videos with older students...ohhh, and ahhh, and "I get it now" are your verbal clues big smiles and clasped hands are physical clues.



Some day I would like to have a directors cut type session where I can pause the vids and talk over what's happening. The Mortensen Math methodology makes it easy for little kids to play math, it really does make math child's play...it's simple, once you understand the basic concepts. It's so simple some think it's magic, it's not magic: it's mathematics...and all we are doing is counting.

Too cheap to spend 3 bucks on a password? Go here for a FREE one hour overview on how to teach math using manipulatives, specifically using Mortensen Math.

Crewton Ramone Overview of Mortensen Math

Here is one hour covering various topics in math using the Mortensen Method.


Mortensen Math Video: The Amazing World Of Mortensen Math. You Can Get Straight A's In Math.




Here is the text of the Youtube vid page:

Visualization through our manipulatives based curriculum, is the means of translating intimidating equations to simple communication. Your children can get straight A's in math. We have 30 years of experience. VISUALIZING MATH IS THE KEY.

THE MISSION OF MORTENSEN MATH is to CHANGE the way students are taught. To help any student become an ACHIEVER, a BELIEVER in herself and himself. THE DIFFERENCE MORTENSEN MATH CAN MAKE: Students leave the "system" WITH THEIR DIGNITY INTACT. Students receive the GIFT of CHOICE. No one need be held back by a lack of confidence in math skills, causing avoidance of careers based on FEAR of math. Students now have the FREEDOM OF CHOICE based on their STRENGTHS in math to become Economists, Engineers, Robotics Developers, Astronauts, Scientists, TEACHERS, or even President!

VIEW MANY MORE Mortensen Math, JazzMath, iLuvMath.com Videos/Tutorials: http://vidgrids.com/mortensen-math

Visit Ben Rogers, Master Trainer, Teacher, Tutor for over 20 years using Mortensen Math on Maui HI and around the world:
http://www.crewtonramoneshouseofmath.com

Contact Us:
Toll Free USA: 800+4plus4=8! [800-475-8748]
Email Customer Svc: iLuvMath.Q@gmx.com
Web: http://www.mortensenmathdirect.com
Under Construction: MathNetwork.com, JazzMathChannel.com

Copyright 1981-2012 VJMCO, Mortensen Math World Headquarters, now iLuvMath, in Association with ReaL Love Song Media, Hollywood Ca

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Sample Lessons For Manipulative Math

Lola, Ruby and Opra help teach ALGEBRA.

Here is a bright 9 yr old girl, doing what most wouldn't consider math for 9 year olds and yet it's easy and fun with a little help from Lola, Ruby and Opra. As you will see we did a whole lot more than "just" factor

x² + 9x + 18

we also did some reduction of algebraic fractions and simple evaluations for x. Sounds complicated but this 9 year old never had any idea that it was hard...



The whole video is 21 minutes long and can be found along with some other exciting and fun vids here.

You can view them for as little as 3 bucks, which is what a two month password costs...or a year pass for 12 bucks...right now there are lots of math VIDEOS on that page alone lasting several hours. Everything from building tens to complex algebra...the page also contains links to a secret screencast page that has several more hours of vids on everything from percentages to 3rd and 4th power algebra, all presented in a way that even little kids can understand. All with one password. That same password unlocks pdf downloads too, including First Grade Math Worksheets, Fractions Worksheets and more.

If it works for them it will work for you...if you are a teacher or homeschooler or struggling student. I'm getting very good feed back...

Or you could spend 20 bucks on a crappy DVD filled with mindless entertainment...or a really overpriced (but delicious) sugar filled coffee drink for 3 bucks...if you get the small size. Feed your mind instead. And then you can feed the minds of others...of course there is a ton of FREE STUFF, pages and pages worth here on this blog and at Crewton Ramone's House of Math.

People on FaceBook ought to like this FaceBook page, you often get sneak peaks at video before they go onto the password protected pages, contests for free passwords and more...

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Crewton Ramone Expounds on The Math Methodology

Short screencast on using the methodology to teach a student math. The method is basically the same, get the basics down so then you can focus on problems, which are often one in the same...they can't do the basics so fractions and algebra are "hard" because they don't understand that math is just counting and fractions and algebra are just counting...and if you can multiply you can count fast and suddenly the math is EASY.

Use algebra to teach the basics like addends and multiplication, use fractions to teach multiplication...compound teaching makes things go faster. The student gets practice of basics like addends and multiplication WHILE they learn other math concepts like fractions and algebra...this is a simple screencast stay tuned for video of some sessions with him where he gets busted texting in my class...the full vid is here.

Addends Past 10

Here is a simple part of a lesson where we worked on addends with a 11 year old...he does math that is much more "advanced" by some standards but we know all math is, is counting so addends and algebra aren't much different on the "hardness" scale. Same goes for multiplication...the idea is to attain mastery in basic counting...addition, subtraction, multiplication and division.

The concept is simple: numbers are made up of other numbers. Here we practice the single digit combinations past ten...what you will find with any student of the mathematics is their knowledge has some gaps or holes in it. So occasionally it's good to go through and fill in some of the holes and gaps with fun practice.

Note that this is quite different from just memorizing facts or formula...they learn to figure out the formulas themselves, and if they forget the facts they have algorithms or tools to figure out the answers quickly for themselves if it is not part of their instant recall memory...and the more you practice the better the chance of it getting into the instant recall memory.

Adding some symbols to go along with the blocks certainly doesn't hurt anything. Notice it's just for keeping track and that he doesn't write out all the combinations, the blocks give a quick visual for that, especially with the colors for added instant recognition...we also did subtraction which is basically going "backwards and forwards."

If I have 15 and take away 8 I am left with 7 which is just the addend. You can also each them to just add 2 which is the 10 compliment for 8 to the 5 for a total of 7, or you could take five out of the 8 which leaves 3 and know that the 10 compliment for 3 is 7 or (leaste preferred) you could count backwards from 15, 8 places...students HATE the number line for a reason. It is ineffectual and can be confusing even when presented well. Knowing all 45 addends with emphasis on 9's and 10's will solve many problems later, in fact you won't just solve them you will avoid them altogether. I have had countless students who were failing algebra come to me unable to do simple addition and subtraction in their heads without aid of fingers or toes, not to mention multiplication...these addends lead to multiplication which makes all the math easy because it allows you to count very, very quickly....

Parents always ask me why don't you just cover the blocks why does it have to be a math bag (and why go to all the trouble to decorate the bag)? BECAUSE IT'S FUN. WHAT'S MORE FUN? COVERING THE BLOCKS WITH A PIECE OF PAPER OR GETTING INSIDE YOUR VERY OWN MATH BAG? Seriously: some adults are a sad shadow of the bright, fun loving, energetic, curious, infinitely inquisitive children they used to be.

Here as you can see is a youtube vid, with apologies to all my public school teacher friends who have to go home to view it. It's just a short (less than 3 min) vid where the unknown mathematician shows he knows some of the combinations without looking, without blocks or symbols (or fingers) just his imagination.



Find me on Facebook or Youtube. I'm told there are benefits to subscribing to youtube because sometimes I put videos up and then go back and un-list them as I put them on password protected pages. BTW lots more video has been added to the password protected pages...

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Autistic Integers

Here is the result of several lessons with factoring and integers presented in various manners:

It looks easy, but it took a long way to get here. You can see part of the journey as well as lessons on factoring negative expressions which is part of what I used to teach her to master her integers here at the house of math.

Of course in order to see that page you'll need a password. Passwords are cheap.

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Meet The Parents.

Here is a collection of Vids from the 70's, 80's and 90's...I got "involved" in 1990...

It's always interesting to see the what happened before. We have been higher than we are now and we have been lower...I plan to take it at leaste as high and as far as it has been in the past.

For those with really short attention spans or who are pressed for time here's 90 seconds:



Here we are going back in time:



Look how far we have come. Back in the day these vids were hard to make and expensive. Cameras and editing cost thousands. Now you can get a computer camera and other equipment all for less than $1000.00



Here is Jerry going over some simple problems using basic operations pieces that are no longer manufactured by anybody...one day we will revive them...the idea is not to spend so much time building the problem you lose sight of the concepts, getting out even 16 unites to build a square takes too long. These problems are whipped together quickly because he has the pieces handy and they are "stuck together"...meantime you can also draw them but make no mistake starting out in the concrete makes all the difference.



Also take a look at this promo vid from the 90's.

Find us on Face Book and be sure to go to the house of math for more on math, how to present it with manipulatives and make it fun.

Multiplication Math Town

Playing and having fun does several things. One of them is giving the child a positive feeling around numbers and math. I have more than a few students who fear math, or hate it. They come to me and have fun and I do my best to break that pattern but then they go back to school and the old pattern runs them over.  Just had a student tell me that she panicked when she took a recent test even though she knew everything on it and had even done some of the problems before...more than once.


"I don't know it was weird, I knew it all and I still froze up and got scared again."  These patterns are powerful and hard to break. Now imagine how much worse it is to NOT know everything and have those feelings...the point is if they feel good about math the learning comes easier. Math should be fun. When it's fun taking a test is just showing off.

Feynman said, "Math is a language plus reasoning." That reasoning leads to critical thinking. 

 So for about half of the lesson we built tens. We did subtraction and then although she always asks for it, we did just about no algebra and she didn't write a single symbol. We worked on counting and then we worked on counting fast which we call multiplication.

 As she built each tower she had to count it. Sometimes she just followed my lead other times she counted on her own...

 The town starts shaping up and she tells stories about each building and what happens there as we go.

 As we play the town gets built and rebuilt and changes...every time we knocked something down on purpose or by accident we counted it all over again...with lots of laughter.

 Just keep playing and adding stuff and pretty soon it starts to look pretty cool.

 Fine motor skills are further refined, counting and playing go together. We are doing multiplication ON a table but we aren't doing multiplication tables.  I was asked about math flash cards or multiplication flash cards and I said, "yes, they are great but not yet!"  When they have their facts close to mastered, they are familiar with for example 2's and 3's, and when you ask them what's 3 x 5 and it's almost on the tip of their tongues THEN flash cards. Using them as a a tool to teach math especially with young ones can lead to some very big misconceptions like the symbols 3 x 3 turn into the symbol 9!! I saw this over and over again during my travels. The kids had no conception that it meant three 3s. Here it's visually obvious as Maria Montessori used to say.

EVERYTHING gets counted, the tens the hundreds, we add, we subtract but mostly we have fun. It's math enrichment, so it should be an enriching experience, not drudgery. Especially when they are little or pre-teen...

Here is a 10  min screencast covering the pics you see above and more:



Find us on Face Book and be sure to go to the house of math for more on other topics.