Here you will see students as young as 4 and 5 years old doing algebra and "advanced" math, without ever knowing it's supposed to be hard.
You are invited to learn how to use this method...

Wednesday, April 25, 2012

TERC = Lame and ineffectual way to teach math.

Here is an interesting thread from Facebook that I got involved with briefly you might enjoy reading it.  

DJ: wrote: I found this woman several years ago when looking for help retaining algebra. Math Education: An Inconvenient Truth M.J. McDermott is speaking about the current state of math education, as a private citizen . KCPQ does not endorse this video.


KB: This is fascinating. How could any group of mathematics teachers agree to the TERC Investigations method? Cluster problems = cluster f***. No one would as they grew up even bother to calculate a problem. Can you imagine going to the grocery store and trying to figure out which size can of tomatoes was the better buy in your head? Hahahaha I loved the part where the teacher's manual says that it's just too hard to teach kids how to do division and that they're better off really using a calculator because it would take too long to teach them! OMG Have you ever seen this Crewton?  

Crewton Ramone: Yep. Deliberate dumbing down. Notice her explanations of the standard algorithms are not exactly sterling, nor does she make it clear what is going on...but she is correct that TERC sucks ass. (Comment got 2 likes)  

KB: Hey at least she spoke out. Besides she's not the genius you are. She's just the weather lady. *lmao*  

DJ I tried to find this since. This is exactly what happened to me. I hate them.

 KR: this video alone should convince people to homeschool their kids.  

SSK: Ok. My daughter's school adopted this "Investigations" math program this year and I have to say I hate it. I also have friends who teach at the school and they hate it as well. When you hear the kids try and explain it, or read the manual, you are thinking WTF? At the beginning of the year, I and my son were having to re-teach the concepts at home. But as everyone has discovered how confusing it is, and so many teachers and parents have complained, they are using it less. It won't last long. Good example of consumer preferences making a shitty product go away. I think the premise is that there are many ways to learn a math concept, and some kids don't get traditional forms. I'm not certain of their research and development, don't care, don't like it.

 SSK: Myself and my son...

 KB: The TERC method she showed I can't imagine how anyone could do even grocery store math in their head with it.  

Crewton Ramone: I have to write a bit of a dissertation on this and I will make a blog post out of it. This is blog post week for me I have lots of math vids piled up for crewton ramones blog of math and even a couple for math genius making. Please allow me to use this thread in my blogpost. IF you would like your name withheld or your comments withheld let me know.  

SSK: I would have to see your blog before I could decide. Debbie who is "them" that you hate?  

Crewton Ramone: First off it is amusing to me how many "scientists" can't do math. And when I say math I mean statistics and critical thinking using computation. I have seen this with biologists, meteorologists, botanists etc. They took the math required and then promptly forgot it because for the most part our math instruction has become a meaningless dance where most participants can't see how it applies to their field of study memorize whatever the fuck it is long enough to pass the test and then forget it. I just heard this recently from a student that was in Calc II which was a requirement for him becoming a doctor why do I need to learn this? I want to be a Pediatrician.

 "Oh I dunno, maybe so when the pharma companies use stats to lie about the effects of mercury on child development you can look at the study and see the bullshit?

Would that be helpful?"


"Now let's take the integrate sin⁵...which I will admit does little more than test your ability to follow complex rules; however, it will as we proceed force you to think critically and make you pick and choose formulae and when to apply them."

I also have heard it from a more than a few "math moms" (parents of my students) one of whom actually had a Masters in Mathematics. Here is a cut and paste from an email:

"By the way I have a masters degree in maths but dont ask me any question b/c i don't remember any thing which i learned. :)"

This is not uncommon. At all.

TERC would be great as an adjunct, that is in addition to or as a preamble to learning the "standard algorithms"...if you watch her do the multiplication you can actually see where the rules come from, same with division you are actually keeping track of subtraction with division...which is why there are quotes to the effect that you can do ALL mathematics with just addition and subtraction, it just takes longer. Mathematics when it comes to computation is just counting, multiplication is counting very quickly, summation (using that goofy sigma symbol) quicker than that.

BUT mathematics is not just computation, computation is what we use to do mathematics. And mastering basic operations that is addition subtraction multiplication and division is indeed laborious and time consuming AND NOT OPTIONAL.

As with all languages earlier is better.

The human mind goes through development stages. A two year old can barely reason...a seven year old can, but even then reasoning must be developed. And sure there are outliers on the bell curve but over all the bulk of two year olds have almost no reasoning skills which is why I am always amused at parents who try to reason with kids that age, just because they have developed some language. At the early stages of development repetition is quite normal as evidenced by the child's ability to sing a song 1000 times over and over again and never tire of it, they can watch a video over and over again or a TV show. This is the time to introduce the memorization of addends and multiplication facts and the algorithms for their effective use. If they can memorize nursery rhymes why not certain formulae too? Simple things like 1/2bh=a or a² + b² = c² or the quadratic equation...which is every bit as fun as "Barney is a dinosaur...." Or "Sunny day chasing the clouds away..."

I'm not saying instead of to be clear I'm saying in addition to, right along with...math is fun for little kids. The way you teach basic operations that is addition, subtraction, multiplication and division is with endless repetition. You don't just teach multiplication in 4th grade and be done with it. It should start early and be repeated YEAR AFTER YEAR. Further it can't be "just memorize this multiplication table" has to be fun, involve play, songs movement, writing, drawing etc.

I can't stress enough that play is the primary way children learn. Here is a simple story about teaching two bright little boys to count by sevens: (stay tuned)  

Crewton Ramone: Crewton Ramone's Blog of Math  

KB: My g/f the doctor has to ask me to do math problems for her. I've seen masters prepared pharmacists not be able to do drug calculations for IV titration. I will never forget the time I called the pharmacy department to have a pharmacist double check my calculations for a heavy duty drug that had to be administered in micrograms per kg per minute and he flat out said, "I'm gonna have to go with what you've got because I can't do that calculation".

DJ: Teacher told mom I just wasn't trying in math, as I was a pretty good student otherwise. I've felt I had a math learning disability for decades. Who knows?  

SSK: Interesting, Crewton. I am a speech pathologist and I work with disabled preschoolers. I agree, learning must be fun and I use play therapy we well. I did the same with my own children, except with language. I taught them sign language at 9 months. They each had a vocabulary of 50+ words by 12 months, and they were fully conversational by 18 months. Just so you know, I am not defending TERC. However, I do not believe it is part of some conspiracy to dumb down math. You have to understand, these curriculum programs are sold much like pharmaceuticals. The reps come and explain their research and devel. as well as their field tests and success, etc. School districts decide what to adopt (buy) from year to year.  

SSK: Of course they are going to make it sound wonderful, they want the sale. Perhaps our school district chose it because we have a diverse population, I don't know. Teachers and parents here were quick to see it's problems, and move away from it.
RA: ur right SSK, sold just like drugs. 4 some reason people were never taught how 2 break things down to understand them. when i was early n school i noticed that lots of students didn't want 2 take time 2 learn the procedure 4 getting the answer 2 a problem ---they wanted to memorize the answer & can't do that 4 there r infinite problems w/ infinite answers. U MUST LEARN 2 REASON LEARN THE PROCEDURES.

  KB: The whole idea is to force the child (especially with math) to preform cumbersome and unpleasant regimented operations. How many times have you watched a child be scolded for figuring out math by a different and I might add more organic method? My father was a mathematic whiz and he saw all kinds of problems with the taught methods, he had his own. He could do calculations in his head that most people can't do on paper. He was horribly frustrated watching my brother and myself be castigated in school for using better methods he showed us at home or ones which we thought up ourselves. The whole point of their exercises is conditioning. You WILL do what you are told even if it doesn't make sense, no matter whether you like it or not, you will preform. End of story. You cannot deviate from the plan.

Now if a child had done this in the Soviet Union they would have been plucked out of the normal classes and fast tracked to advanced mathematics, chemistry and physics just like their kids who twirled and danced around were sent off to ballet and gymnastics school or if they plinked around on the piano pretty good at age 3 they went to music conservatory. Now I'm not supporting the dogmatic development of talent as you saw in the USSR or in the current People's Republic of China but it does go to show the depth of talent. For every concert pianist on the circuit they've produced there are 100's more who are just about as good. Where they are anomalies in the West, they're a dime a dozen in those systems. We're wasting a lot of talent by making everyone the same.

Why should the kid good at certain times be forced to spend inordinate amounts of time at things they neither like nor enjoy? Why do we make people learn subjects just long enough to pass a class and then later in life they remember nothing of it, not even people with masters level math degrees? It's insane.  

GH: Absolutely true. As I posted in your other thread, we need to get away from the Machine, as bad as it was to start it's completely atavistic at this point. Forcing kids into the public school system is like tossing them into a meat grinder and hoping they'll miss the whirling blades.  

SSK: KB, when was the last time you saw a child scolded in school for finding the right answer in the wrong way? From what you describe, I would think Investigations would be your cup of tea since it embraces the idea that there are many ways to solve a problem and allows many forms of operation. For my own daughter it did not work as she was shown 4 different ways to do long division. She picked up bits a pieces of each, put them together, and it did not make sense. I have dedicated the last 20 years of my professional career working with special needs kids in the public schools. My 3 children attend public school. I will be leaving this thread now. Have fun bashing.  

KB: My nephew experienced the same thing in Huntington public schools. Same scenario of finding the answers by alternative methods and being told he can't do it that way. My brother took him out of school and put him in private Christian school by third grade which ended up being a mistake because he ended up further behind than he would have been in the public school. If my brother and his wife didn't both have to work they would have chosen to home school. It just wasn't an option for them.

Crewton Ramone: I don't see them scolded but I see kids get marked wrong even though they got the right answer because they didn't do it "the teacher's way." And often that way is the hardest most confusing way possible. I use manipulatives to teach addends, then use those addends to teach multiplication. The process ends in cross multiplication for two digits which is just a faster way of doing the same standard algorithm she talks about in the video with proper verbiage understanding you are multiplying tens in the tens places... Lets take the example of 7's because they don't repeat their pattern until you have added ten times. Other numbers have an easy pattern you can see after just five such as 6:

 6/36/66/96 etc

So the emphasis can be on the first five and then repeat the pattern...and at the house of math we learn the "tables" out to 20 not just 9 or 12. First we sing songs, and whisper count and listen to patterns and count by ones, then we use addends for seven it goes like this: Once you understand numbers are made up of other numbers and all numbers want to be ten un less they are tens the they want to be hundreds, unless they are hundreds because then they want to be thousands....etc.

7 plus 7, the 7 takes 3 from the 7 and we get one 10 and 4, 14
add another 7, 4 takes 6 out of the 7 two 10s and 1, 21
add another 7, easy 1 + 7, 28
add another 7, 8 takes 2 out of 7, 5 left: three 10s and 5, 35
add another 7, 5 takes 5 out of 7, 2 left: four 10s and 2, 42
add another 7, easy 2 + 7, 49, we stop to observe 49 is square
add another 7, 9 takes 1 out of 7, six left: 56
add another 7, 6 takes 4 out of 7, three left: 63
add another 7, 3 wants 7 and gets it! 70.

Now they have all ten and can start is a long process but it gives the child an algorithm for adding them all up and not just memorizing a string of digits. The lesson is repeated MANY times in may different ways. As the months go by more understanding is added and we are covering many math concepts besides multiplication.

Nobody wants to do multiplication over and over again by the time they are in high school. As young children repetition is natural but as they get older it is not unless it is music. My two little boys have done this many times and we hadn't done it for a while but now it's easier than before and when they watched a multiplication rock video "Lucky Seven Sampson" I could see it made a lot more sense to them. Especially when he gets past ten and they could see 7 x 13 was indeed 70 plus 21...I could literally see them getting more out of a vid they had seen many times because they had done the work of adding one seven at a time.

They are well on their way to having instant recall when asked what is 7 x 4 they can say 28 just as easily as they can say 2 x 2 is 4. It takes lots of time but multiplication IS THE CRUCIAL MILESTONE in the mathematics because it allows us to count very, very quickly and see and discover factors and patterns in algebra, fractions, and percentages and more. Once single digit multiplication is mastered moving up to numbers like 6 x 16 is easy it's just 60 + 36 = 96, then 13 x 13 is also easy because we have manipulatives where they can see it is

100 + 30 + 30 + 9 = 100 + 60 + 9 = 169

and the standard algorithm works and they can see it works and WHY it works. The next step is just doing it all at once and keeping track of tens.

Two Digit (Cross) Multilpication With Crewton Ramone

I was going to make comments and add more but just formatting this and changing the names to protect te innocent took a lot of time perhaps I will work on this post more in the future but don't count on it...the thread continued after this too...needles to say base 10 blocks are better.

Wednesday, April 18, 2012

Crewton Ramone Playing With Polar Coordinates.

The concepts themselves are simple.

You should be able to see how many of the things the young student would normally learn in grade school apply to a high school lesson. Sadly most students don't make the connection or have forgotten the previous lessons and don't see how they apply. So for the younger students we start off with a lesson that's easy and fun and we can make a bit of a game of it...once this is digested and mastered we add a little more covering the same ground and a bit more and then the same ground and a bit more and and so on...until the unit circle is filled in. But we start with just a few points and add more each time.

All we are doing is decoding a point on a plane. ( 6 ,  π/2 ) for example means get a six block and point it to the π/2. Notice the little boy has to be taught where to start from (the origin) and what the symbols mean. On the second lesson he will "get it" more and the third more than that.

Counting by 1/12, 1/6, 1/4, 1/3 and 1/2 are handy skills to when we first start out we can count out a few of the easier ones and get more and more complex each time we come back to visit the concept.  And we can see 3/6 = 1/2 from a very different perspective than fooling with pieces of a pie even though we are fooling with pieces of pi. Fractions teach multiplication too.

Many teachers don't know what is going to be taught in high school or have forgotten so they fail to prepare the young students for what comes and never make any attempt to show the younger students what they can expect when they get older. Teaching math has become so compartmentalized that students get lost going from what compartment to another. I often see this in the text books themselves chapter to chapter these is no thread or common theme except that it's all math. I often as how do they teach addition and subtraction and integers as three separate and distinct lessons? How do you teach multiplication without teaching factors and division...?

Why not use the so called higher math to teach the basic operations instead of thinking you have to know the basic operations first?

We can do many lessons on "same" or the concept of same...π/2 = 90º and π/6 + π/6 + π/6 = 3π/6 which is same as π/2 which is the same as 90º's not hard and can be fun.  Rather than give them a circle like that to memorize why not have them build the circle themselves? They can fill in more and more information with each lesson. Dividing by two is important to be able to do here...and you'd be surprised at how many "ah-ha" moments can be created whe they find out that 1/2 of π/2 is π/4 and 1/2 of 90º is 45º...then 1/2 of π/6 is π/12 and all kinds of wheels turn when you mention division is just multiplication by the inverse... π ÷ 2 = π x 1/2 = π/2 and if you look closely that first set of symbols should make you go, "of course." It's right there in that division symbol: ÷ put one over the other.

Counting in degrees is also EASY and converting back and forth and how to do so should be discovered by the students so they make up their own rules (which will become the formula most are given to memorize and then forget).  Once they have made up a formula for going from radians to degrees a lesson on converting from polar coordinates to Cartesian coordinates or rectangular coordinates would be in order. Most of the time they get all of this at once in one chapter. Confusion ensues.

Also I note a lesson on polar coordinates is often not introduced until high school, then they see it ONCE and they may not see it again until college. One exposure is insufficient to learn ANYTHING. Then they will become confused when they begin teaching vectors and spherical geometry because the text books assume they know this much because it should have been covered in high school. It was, once, and then it was forgotten. Anybody besides me see the problems here?

Monday, April 16, 2012

Algebra its many uses.

I have said it before, algebra is just generic math. It has many uses for teaching math at various levels. Here is the same exact problem with two very different students:

Note how it is nicely color coded but this is NOT sufficient, even the drawing is not sufficient many reading this may still not "get it" completely. I found as I traveled the USA that the only time we got 100% comprehension in workshops was when everybody had blocks or manipulatives. If you only have symbols or drawings some people get lost. They have to be able to get there hands on it. Now we can start off with manipulatives and then stop sing them over time but the concrete is ALWAYS where you start off. And one or two examples does not cut it it takes MANY before you can move to drawings only and then symbols only and this process often takes months and years.

Here is vid one with an older student:

Here is a much younger student doing the same exact problem notice it takes much longer and more patience with the younger child:

Note the difference in emphasis between the students. The older student's focus is the distributive theory of multiplication in preparation for problems that have negative coefficients. The younger student is learning to count up things that are SAME and as you can see because the x² are not the same shape even though they are color coded the same he has a bit of trouble and because the x are different color again he has a bit of trouble...but he can see what he is doing and it makes sense. Later more understanding can be added. Meantime adding up and counting in algebra isn't scary or hard and it's kind of fun this is enhanced because he knows older kids do this stuff and I tell him some of them find it scary and hard and he thinks I'm teasing him...but then they met some students that assured them that this isn't how they were taught in school and indeed algebra can be quite scary and hard.

Look for a future post where I go into a little more detail on adding layers of understanding. Hopefully I will remember to link it here.

Now some people comment that having the little kids do algebra shames the older students. Only if they have poor self esteem brought about by poor parenting skills. My students know that the point of showing them that little kids can do it is not to shame them but to emphasize that algebra is so EASY it is child's play. Even advanced algebra is no big deal, just more counting. And that if a little kid can get it they can get it. And so can YOU.

Algebra can be quite useful for teaching basic operations, that is addition, subtraction, multiplication AND division. As can be seen with the younger students they get experience with adding or combining like terms and counting as well as multiplication when the factors are positive and combining like terms that are negative and positive as well as multiplication when they have negative factors or coefficients. Further how do you teach multiplication without teaching at the same time.

This is a lot more fun than memorizing multiplication tables or doing endless worksheets on addition or multiplication...yes they need practice and LOTS of repetition but don't turn it into drudgery. Be careful with worksheets. I tell my students as with sports you don't throw the ball a few times and become a pro you throw the ball a many times a day for many days and you still will need practice. That's why in textbooks you often see the problem sets labeled practice.

Here is another video with young students where I use algebra to teach counting skills like multiplication and addition:

And more "higher algebra" for the same purpose:

If you want to see the negatives you need a password.

Also people say I don't put enough posts up on my blog. That may be. But i can tell you that I post on my math page over on facebook everyday. If you want a steady stream of vids and math etc like this page:

Also you may want to do some searches with crewton ramone in them because there are now MANY videos showing how to use algebra to teach math. Too many teach algebra all by itself as a subject unto itself thus adding to the confusion by cutting the mathematics up into too many segments that seem unrelated to each other.

Monday, April 2, 2012

Crewton Ramone's Completely Cool Curious Counters' Kindergarten Compendium

Crewton Ramone

My book has been taking up quite a bit of my time lately but I am happy to report it is just about complete. You are no able to download a PDF off my will of course need a password to do so and you will note it is officially Copyrighted so take it easy with the file sharing...and don't let me catch you trying to sell it for money unless you are an affiliate. I actually sent it in the the US Copyright Office. Now that doesn't mean I don't want you to share it. I do. And I have seen quite a bit about various artists who have gone the creative commons route and basically given their work away for free or for a donation and have forgone DRM of any kind. That's my plan. I'm not even going to attempt it. I know plenty of people will be willing to pay for it once they see it...and I know people will copy it. If you want to see more books like this some of you have better pay for it. It cost me quite a bit in time and money to get this thing done they way I wanted it done. I expect you will be pleased with the result. If you have comments I'd love to hear them.

I added an apostrophe after the S in "Counters" Crewton Ramone's Completely Cool Curious Counters' Kindergarten Compendium hopefully I catch a few other details like that before it hits the presses...

I expect people will share it. I also expect some people will get the PDF and really want to get a book or pay for a version that can go on their favorite E-reader. Like Kindle, iPad, Sony's E-Reader or Nook or what have you. It seems to me if you have an iPad or other tablet the PDF should be good enough.

The plan is to have it available on Smashwords which will push it to several formats, plain ol' regular PDF, a PDF with lots of hyperlinks to vids and web pages and of course an actual Hardcover Children's book. Right now the PDF is done.

I really want the hardcover book to stay around 10 bucks but that may or may not be realistic. As you can see it's full color and full color and lots of graphics adds to the cost of printing. I have a couple ideas for "pre-editions" that will hopefully pay for a run of hard cover books.

So I have quite a ways to go. I will probably start off with a soft cover pamphlet type where you take a 8 1/2 x 11 and fold it in half hit it with a stapler and there you are.

There is nothing like taking a book to bed, and although the concept is on it's way to being obsolete we are not there yet and I think kids will enjoy the rhymes and bright colors this book contains.

Here you see where I take a short digression into the concept of square roots, but mostly it is a book on addends and addition at the very end I introduce the concept of multiplication by two. It really is a book for 5 year olds (and under) and the idea is to have it be a bedtime story book that gets read over and over again like "Cat In The Hat" or your favorite Richard Scary sons ask for the same books over and over again, why not teach them math while you are at it?

In this case you are just teaching them to using addends. I also throw in some simple problem solving along the way and by the end of it we are ready for a problem where we add into the thousands.

This page uses symbols but most of the pages have the blocks on them in full color as you can see. The concepts are simple and any little kid will get it especially if you read 30 or 40 times (or more) over a couple of years...I know little kids who have "The King, The Mice, And The Cheese" memorized. Might as well memorize some math facts too...but up until now there hasn't been a book like this where they can SEE the numbers.

I will also make a screen cast where I point out what I had in mind when I made this book and how you might use it to best effect, and I will also point out a few things you might want to emphasize to your child. Also I would like to point out that older students will also enjoy this book because with our public school system the way it is the concepts in this book may be considered appropriate for students who are older. Perhaps much older.

I know I was supposed to work more on my website, especially the fractions page but this book kind of took on a life of it's own so I went with it. I am pleased with the result and think it will be worth the five or ten bucks it takes to get yourself a copy in whatever form you like best.

The Password Protected PDF's Page
costs 5 bucks to get into. Once you have a Password you not only get this book for down load but a bunch of other PDF's and videos you won't find anywhere else. Hopefully this is just h beginning of the books. Supremely Simple Subtraction is partially finished and so is a coloring book and a few other things. Plus I have an endless amount of ideas for the many and varied topics that make up the mathematics, in such a fashion that they make sense and people can see how it all ties together to make up the beautiful language in which the universe is written. 

UPDATE: some of you just want the book, go HERE, scroll down and you can get the book all by itself, no password required for just $2.99.