Base Ten Blocks and Math Anxiety.

I have seen students whose confidence is so shaken by calculus or algebra that adding small numbers is no longer certain....the reptilian brain kicks in even basic operations become difficult...too much stress or anxiety and you can literally do about two things: fight or flee. This is why in martial arts you fight calmly and better yet with no conscious mind....otherwise the reptile kicks in and you can't remember what to do even if you have practiced for certain situations 1000 times.

I remember a student who was excellent in the dojo...got his belts easily etc. Went to his first competition and got his ass kicked by another guy who was considered less skilled...because he panicked and by his own admission "forgot everything." I have also heard of stories where guys get in street fights and lose with guys who are untrained because of the same reason.

What does this have to do with math and base ten blocks? PLENTY.

It's the EXACT same thing when a student with test anxiety is tested on subject matter with which they would otherwise be completely conversant and familiar...but get an "F" because during the test they can't think.

I remember a student who I worked with coming back with an "F" on material we both knew he knew:

"What was I thinking!" he exclaimed looking at one answer that should have been obvious and to which he wrote a completely wrong answer.
"You weren't thinking."
"Gee, thanks..."
"I'm not criticizing you...you couldn't think..."

And I then went on to explain what happened, and for that hour we did no math but talked about how to handle test anxiety and math anxiety and did some breathing exercises...explaining the flight or flight syndrome so they understand that what's happening is not only normal but HARD WIRED IN for SURVIVAL removes the "I'm stupid" thoughts, allows them to recognize it when it starts to occur and nip in the bud and deal with it instead of letting it run away with their their thought and emotions.

This student went on to pass his class with quite a few 100's something for which I'm famous, (check these vids out) and his parents gave me a hefty tip at the end of the year...he might have gotten an "A" if he hadn't started of with so many scores under 40...lol...and that's another thing too many parents wait till the kid is failing before they "breakdown" and get help. 

This also why the emphasis is on having FUN and playing: so the reptilian brain never gets a chance to kick in and your child's attitude and associations with math are pleasant and positive. As they get older math anxiety is avoided altogether because they understand math and the relationships and how it all goes together...and the symbols are easily decoded and understood.

Base ten blocks make math easy. There are silly people who think base 10 blocks will lead to "block dependency" where the kids can't do math without the blocks. Ludicrous. My blog and website are proof positive that this couldn't be further from the truth. Do any of the kids on that testimonial page get to bring blocks with them to public school when they take the test? Of course not.

Are DBoyz doing algebra and multiplication in their heads without blocks?  Of course they are. Your kids can too...and I can teach you how to do it yourself: check out this parent/teacher training page.

"Soon" (a very relative term at the house of math) there will be an audio course and more on the training page...here is a transcript of the beginning:

Well Hello! and welcome to Crewton Ramone’s 6 Disc -- probably 7 Disc, Audio Program--there is a bonus disc there with a guided Meditation--but what I want to do here over the course of this audio program is get you to understand that anybody can teach math the way I teach math, that YOU CAN use base 10 manipulatives to make math fun and easy, whoever your students are and whatever your mathematical background is; whether you had a good experience or a bad experience, whether you're male or female, you're a homeschoolers, you’re a teacher, a parent that has a kid in public school and you just want to able to help with math or give them “enrichment” this audio program is for you.

Now, specifically the target market that I’m looking for are the people with young children-- if this describes you then you are definitely in the right place. If you are a parent that has young children, definitely children under the age of 12, under the age of 8 better than that under the age 6 even better than that. Well let's say you have a student in--I don’t know if they are in grade school or middle school or high school...wherever they are this audio program is for you and if you have decided that you want to try and help your student or help your child understand mathematics then you are in the right place.

Now in order to do this I want you to be able to use these tools to their best effect, you just need to have some basic understanding, understand some principles and concepts, and you too can teach mathematics, you too can do what I do -- so many would say, "oh you are a genius" or "you are this or that", "oh--you are teacher: you’ve been doing it for 20 years" - "oh you’ve been..." {etc, etc}

Okay, when I was doing this and was two or three years in, people were like, "Wow! I can’t believe you’ve only been doing this for two or three years!", Okay? The idea is Jerry Mortensen had the same problem, everybody was like "Oh! Jerry is special he created the programs...of course", "Maria Montessori she is special because she created the -- Mario Montessori -- whoever it is, right?" -- they all have a crowd following that says, “you can do it but I can’t”...”you are special", "you are different” and what we are trying to do, and Jerry especially, but myself included, is trying to make you understand that you can do it also.


This blog and website is about removing excuses. There was a time when you spent 500 bucks and you got a kit and there were 4 hours of video. TOTAL. That's it. Watch these vids and now you are on your own. Not anymore.

If you wanted more training you could fly to Idaho once or twice a year...IF they were having a training: there hasn't been a training there for years now.

More PT Training.

26Sept14 10am HST

You were invited. Next one is NEXT Friday, the 26th, 10am HST more teacher training. All you need is the google vid chat plug in installed...a set of blocks, and 20 bucks.


Here is how it works..very simple. Contact me Paypal me 20.00. When you contact me I will send you the paypal info. You need gmail vid chat NOT SKYPE. You might also look into ooVoo, I've done some fun meetings there unrelated to the house of math. But for now gmail vid chat is fast and easy...just install the plug in and you are good to go, then add me to your circles or email me and I'll add you. THEN a little before ten you will get a call or invite.

DON'T try to do it if you don't have high speed internet...shut down everything else...you should have a browser running with one window...shut down all your other programs. Especially word processors and for those with Macs "preview"...have a set of blocks and something to take notes on...a white board is nice but not needed. The blocks are NOT optional. You will hear it over and over again in the vids get your hands on the blocks, math is not a spectator sport, contrary to the way you and I learned it.

2 more hours up on the teacher training page and another hour up on Raymond's page...learn to use your base ten blocks.

I have been told over and over again that just one or two of my password protected pages are are worth the price of an annual password...and the with more than 5 hours of training now on the Parent Teacher Training Page still available for 15 bucks that page is more than worth it. Look forward to a password protected pre-calc page soon.

Base Ten Blocks Make AP Calc EZ Too

I was working with an AP calc student. They are just getting started. As usual the student did not see the relationships between what we had done before and the formulas he was getting. When I showed him these side by side with a brief explanation the tell tale "OHHHHHH!" was exclaimed (the light bulb going on / the rush of endorphins when you understand something) and he said, "well, that's easy then."  Base ten blocks give a solid foundation so that when we get to this point many obstacles to understanding have already been mastered and are not issues.  Understanding square numbers and square root for example and trig which is basically the study of how triangles work is made plain using base ten blocks...no one ever explained to me in highs chool that math was a language and how all those formulas were basically saying the same thing and how and when to apply them. It was basically just memorize this, this and this...and I never got the relationships between them until years later.

Desmos.

This student comes once in a blue moon. If he came on a regular basis I wouldn't have to hit him over the head with it as it were and he would see that we are just finding the slope of a line, as well as see Pythagoras not only in distance formula but in the basic trig identity too.  In the last formula we talked about h being more than just h it's the distance  between the a and a+h expressed using economy of symbol.  (The thick black line below the red lines in the last pic below.)

He might also see our old friend from the doughnut factory and playing with ordered pairs rise over run for rate and slope and the "m" in y = mx + b or as he will now see it f(x) = mx + b where m = dy/dx....but all these triangles do go together....and it's pretty easy to see that even the complicated looking formula with a's and h's and stuff isn't so hard after all. The basics are covered on vids and on password protected pages like this. Look for Water tank, doughnut factory constant rate problems.

Then tangent lines and secant lines are no problem either and with a little more explanation of economy of symbol and that y = f(x) and how we just labeled the points with letters, the anxiety subsides rather rapidly and learning can take place. It's hard to learn anything while in flight or fight response.  We have proven this time and time again. It's pretty obvious that the secant and the tangent lines are going to need different formulas. Average slope between those two points is going to be less accurate the further the points are from each other and more accurate the closer those to points are together.  His online textbook actually had some cool gifs and animations that really helped explain things.  That link goes to a page that has an animation on the bottom give it a few seconds to load.

Now this and the formulas that came with aren't thought of as hard anymore and we can play and fool around with the concepts. If I want to know the distance between those points of course I use distance formula, if I want to know the slope of that line then I need to know dy/dx but now instead of just x and y, I have x and f(x) or in this case the points are labeled [a, f(a)] and [a+h, f(a+h)] but it's really just x and y...and secant and tangent and limits and intervals are all just language to describe what's going on here. But what if I don't want an average? What if I don't want the "as a crow flies" answer but the actual length of that curved line? Well I need more math and this guy named Newton came along and gave us more math, we call it calculus.

We can also find the tangent line to point P or any point along the curve.  Tangent Line = Instantaneous Rate of Change = Derivative.  That line would be "outside" the curve not under it....speaking generally.

Some more explanations and drawing make the general concepts understood. Here we can see the curve being analyzed a little further. See the triangle shaping up in the corner there?

We are going to use symbols to describe that triangle and the part we are interested in is the hypotenuse, but in order to find the hypotenuse which is the average slope of the curve between those two points we need to know the sides which are the changes or distances between  x and y.  

Secant line = Average Rate of Change = Slope. Simple.

 Add more information and it looks more complicated but actually there is MORE understanding taking place, not less...but you don't want to come in at the end...or in the middle which I find is where most text books start, instead of starting at the beginning.  I can also usually find the "holes" in the students mathematics that are making it hard.  Sometimes those holes go all the way back to not understanding division or fractions. Lots of times a review of triangles and Pythagoras is in order.

 Now I've added labels for the axis and put more info in blue the tan line and the secant line and the basic formula for it, the axis of symmetry is the dotted line and we can see that the tan line and secant line are not the same thing so we will need different formulas to describe them.

At last it becomes absolutely clear that we are just playing with triangles and those fancy formulas are just talking about the sides of the triangle...and all of this is in very general terms we are just playing with concepts. Next we will add numbers instead of just having the distance between a and a +h we'll have numbers that tell us what (where) a is and how far it is to a + h.  We'll get an quadratic expression  that describes the curve and from that we do lots of math. We can also find the area under that curve between a and a+h and we can be quite exact about it.    But that's a lesson for another day...and the blocks will come in really handy here too. Because how are we going to do that? By making and summing up rectangles...

Meantime we talked about limits and derivatives and how tan and secant lines differ and how to think about things in general and specific terms depending on the symbols.  We  talked about the power rule a lot and the chain rule a little bit and I showed him how the power rule works and what it means.

Going from f '(x²) = 2x and f '(x³) = 3x² isn't hard but the WHY of it can be. Then a little more discussion of dy/dx and d/dx and time was up...

Base Ten Blocks For A Real Head Start

Base ten blocks really do make math easy and fun. If you spend even just a few minutes looking around my website and this blog, you will find videos of little kids learning big math...and having fun while doing it. Base ten blocks make it visually obvious and fun for students of all ages. The younger the better.

Here is a group of kids playing math. Do they look engaged to you? Which one is the problem child?  Which one is considered the genius child? In this pic you can't tell. These students are all around 10 years old.



Get them started off right by using base ten blocks. Here are a couple of students that by now I'm sure you recognize. People are of course amazed at their ability to do math in their heads, thus disproving the thinking that base ten blocks somehow lead to block dependency where they won't be able to do math without having the blocks in hand and other ridiculous ideas.  In fact, I got the job teaching the kids you see above because these two were doing multiplication in their heads in a health food store (calculating simple stuff like if it costs $2.73 per pound and I buy 6 pounds of it how much does it cost?) and one thing led to another.



"This is back when I didn't know what anything was..." one of them remarked upon seeing this vid after not seeing it for a long time. Note how when they are young like this, how it looks is important in answering the question, "are they same?" This persists into adulthood and certainly into the teen years...2 + 1 = 3 does NOT look same because of the color of the blocks and on one side there is only one block and on the other two blocks...but in total number it is the same, and this is quickly understood. "The equals sign never lies" is an important math concept. Concept based math teaching with manipulatives speeds and eases the whole process. Very soon (a couple of years) and they are doing math like this.  Everybody is so impressed. They think it's EASY because it is.

Meantime many students have lost track of what the symbol equals even means and somehow come up with the "the answer is" instead of same as...this one understanding has, I have been told directly by older students, made a huge difference in algebra, pre-calc, and trig, and of course calculus. Anyone will tell you x + 5 = 8 doesn't look same, but that statement says it is...IF x = 3. I was also reminded of how much things get lost and confused working with a AP calculus student...because math gets so segmented and compartmentalized they fail to see relationships.

Here is the "whole thing" for those of you interested. This lesson is also on the sample lessons page (I think) along with many hours more video of sample lessons with base ten blocks. These are actual unrehearsed lessons not scripted demonstrations: practice not theory. If you want theory I have about 3 hours of it up now on the parent teacher training page...with more to come. There's some short free stuff there now for you to check out if you want to get a better idea of the theory behind the method. And there are posts like this to help you understand more about the method and posts like this to help you get started using base ten blocks.



So of course now doing algebra like this is no big deal and neither one of them is even 10 yet. I keep telling them as they get older it's less impressive which is why this is funny on a lot of levels. It's kind of an inside joke. You can see him looking at the picture and being very careful to get it right...he looks at the picture YOU see the symbols.



If you have older kids or students, base ten blocks make math visually obvious for them too, the blocks level the playing field because they speak to all learning styles. Whether male or female, visual, kinesthetic, or auditory learners, ALL benefit from the use of base ten blocks. And  younger really is better. So I made this to help get them started off right. Combine with this blog and website and your kids won't have to worry about common core mathematics, because they'll know math not just have some stuff memorized and jumping through the silly hoops on tests showing work or "number sense" won't be hard at all...all they may see the absurdity of it all.

I have a goofy little base ten block book I wrote that people have found useful for the younger crowd. If you have a copy please go leave a comment on this page. There was a spurt of comments when I first built the page but now they have trickled off. Add yours. Good, bad or indifferent.

"I have to tell you that when I first started to watch your videos I cried....after learning it myself in school (haha) then teaching my three daughters algebra using Saxon, Math U See and things from the Teaching Company, I never really had any idea of what I was doing. Watching the videos of you made everything make sense!!! I'm sure that this is a labor of love for you but I just wanted to say thank you! It is much appreciated." ~HS, Ohio, USA.

Having traveled the USA doing seminars I can tell you this was not an uncommon response when people finally understood a math concept and faced their math demons...usually revolving around algebra but sometimes with much simpler things like why invert and multiply--something most teachers have no idea how to explain and end up saying "just memorize it..."  Avoid the problems in the first place it's never too late to break the cycle, start off with my book if you have young children.

Here is what it looks like when you give a young kid a head start with base ten manipulatives. YOU can do this too.