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"...it 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: http://crewtonramoneshouseofmath.blogspot.com/ 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. http://investigations.terc.edu/index.cfm
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:
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 again...it 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.