## Is Your Child Being Used As A Guinea Pig In School?

By Greg L | 28 January 2008 | Prince William County | 76 Comments

*Guest Post By “Raging Redneck”:*

If you live in Prince William County and send your child to public school, the answer is unfortunately, yes. Believe it or not, PWCS has implemented the controversial math program called TERC Investigations in Number, Data and Space, a radical program that has been widely criticized and shown to be inadequate in teaching children the basics of math.

In a nutshell, “Math Investigations” tosses out the time-tested and reliable system of teaching children simple algorithms. For those of you who don’t recall what an algorithm is, this is the way you learned to add, subtract, multiply and divide. Instead, this “fuzzy math” relies more on exploration and discovery and ultimately the overuse of calculators. See this youtube video for a better explanation, and you won’t believe your eyes:

You can read recent articles about the program and sign an online petition at pwcteachmathright.com. Over 750 residents have signed so far. Be sure to read the heartbreaking comments hundreds have left. Here are just a few:

“My daughter has reverted from knowing math facts, to solving each problem by counting her fingers since we moved here.”

“My third grade son is being left behind in math because of this program.”

“Don’t experiment with my child!”

Several sources report that by the fifth grade, children taught with the “Math Investigations” curriculum have fallen behind by two years! Despite its demonstrated deficiencies and criticism from noted professors, education experts and parents, the PWC School Board seems to be taking an entrenched position regarding its continued use. They argue that discontinuing Math Investigations would skew the results of its evaluation and therefore its use must continue until it is proven to be failing our children. They also cite that millions of dollars have been spent on the program so far. The county has spent millions of dollars on a lousy math curriculum, and we can’t discontinue it because we sunk so much money on it and haven’t yet assembled enough statistics to prove how bad it is failing our children. Are you kidding me?

Unbelievably, our kids are being used as guinea pigs. The next school board meeting is February 6. You might want to attend.

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### 76 Comments

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Thank God for homeschooling! Saxon math is the way to go.

Heaven help the kids! Mine were in school during the 60s when the “new math” was introduced. Tom Lehrer’s song was spawned during those years. For some reason it was felt that kids should be able to work in “base 8″, which Lehrer called “the same as base 10 is you’re missing two fingers”.

Night classes for parents were flooded, and in the end nobody understood anything, including the teachers. My two oldest never recovered fully from this side trip into “educational experimenting”. Textbook issuers are the only ones benefitting from something like this.

..”base 10 IF you’re”

The Federal laws governing protection of human subjects in research would not let PWC parents be given a survey without adequate notification of their rights, but these same laws permit public schools to do any experiment to school children in the name of curriculum development without telling parents anything. My daughter suffered through what sounds like a similar experiment, called STEM, while we lived in Ohio. The school told me that parents were not permitted access to the experimental materials or to know anything about it. I urge PWC parents to demand an explanation of what is being done to their children, insist on seeing the classroom procedures and materials, evidence that the experiment will not harm their children, and what procedures are in place to determine whether any harm did occur and how it will be corrected.

Investigations does not sound like anything I would like teaching or learning. However…and it is a big however….I have all the confidence and respect in the world for Mrs. Carol Knight, mathematics supervisor, Prince William County Schools. I know Carol Knight both professionally and personally and she is a fine person and excellent teacher. She highly endorses this program and would not do so unless she firmly believed in its value.

Without seeing the program and working with it I will have to rely on her word because of my confidence in her.

This is the sort of “feel good” quackery you’d expect to find in San Fran or New York, not here in Virginia. Let’s return to the basics. I don’t know what the school board was thinking when they approved this. A simple google search shows this curriculum has failed everywhere its been tried.

I’ve been waiting, just waiting for BVBL to pick up on this.

Math Investigations doesn’t teach things the “old fashioned” way by memorizing rote mathematics facts. Let’s not mince words here. When opponents of Investigations talk about the removal of time-tested algorithms from the curriculum, let’s use the right words. These aren’t algorithms like you’d have in algebra or calculus. These are tables of facts to memorized.

Cognitive research has actually shown that the part of the brain used for memorizing these math facts is completely separate from the part of the brain used to do higher level mathematical problem solving. In other words, memorizing you times tables works the wrong muscle for future mathematics ability.

Investigations attempts to get students to understand more than just the rote number. It’s one thing to know that 2+2=4. It’s quite another to be able to put into words why this is true (and trust me, “it just is” is an unacceptable answer). This time of mathematical reasoning ability, developed at a young age, has been show to IMPROVE overall mathematics performance. Math Investigations is also in line with the standards put forth by the National Council of Teachers of Mathematics.

Overuse of calculators? Why not! Does a carpenter eschew the use of a power tool because that’s not the way it was done in the old days? Does a doctor dismiss modern diagnostic tools because a stethoscope was all his professional ancestors needed? Let’s be realistic. Once you learn and understand the basic concepts (something Math Investigations *does* teach despite the rhetoric), what difference does it make if you are adding 2-digit numbers, 3-digit numbers, or 10-digit numbers on paper? What good does page after page of repetitive drill and kill exercises really do? From the cognitive research? No much. More to the point, how many of you in the daily exercise of your lives are called upon to do complex division without the aid of a computer or calculator? Investigations recognizes this change and focuses more on developing math awareness and in-depth understanding rather than cute parlor tricks (”Look, my little Susie can divide a 10-digit number by a 3-digit number using only paper and pencil”).

I would suggest that those who are truly interested in the issue take the time to learn about it before passing judgement based on a YouTube video and an unsourced blog post (”Several sources report that by fifth grade…” how about citing some of those sources?).

Gee turn, I seem to recall the “algorithm” method serving me just fine during my learning of higher math (particularly college calculus and calculus based physics). I am glad I learned the old way. Oh…and by having to depend on a calculator creates a technological paralysis. What if a calculator is not available? What then oh wise one!?!

Turn, check your own facts before YOU spout off!

Dr. Wilfred Schmid at Harvard said of the TERC program (Investigations Math):

“A TERC teacher doesn’t explain, and a TERC teacher doesn’t teach! I don’t want to be misunderstood: group learning and discovery learning are parts of the tool chest of every accomplished teacher, but it is folly to turn these techniques into an ideology. If we mathematicians had to re-discover mathematics on our own, we would not get very far! And indeed, TERC does not get very far. By the end of fifth grade, TERC students have fallen roughly two years behind where they should be.”

I don’t need your stupid “cognitive research” to tell me it’s pathetic that a fifth grader doesn’t know what five times five is without consulting a calculator. By the sound of you, I imagine you are a part of PWCS. God help us all!

Turn PW Blue,

Your tactic of arguing how things “should be” in an ideal world ignores the failure such ideas have in the real world. This seems to be a theme with socialists.

Public school is not the correct place to be pushing the bleeding edge of new sociological or cognitive theories. Such experiments should be performed in private schools on YOUR OWN CHILDREN.

Anyhow, yet more data to reinforce the high value of homeschooling.

I’m with Slick and the Patriot. When a Harvard professor indicates it is a bad program - it is most assuredly a bad program.

Luckily, my children were in Accelerated Math and not taught using the TERC system.

I will, however, be signing the petition.

I just watched the whole video….WHAT A NIGHTMARE! The amount of steps involved to solve those simple problems was totally inefficient! Additionally, you gotta love the statement “when the problems get cumbersome, just use your calculator” (or something like that). RIDICULOUS! Again, thank God for homeschooling!

Turn,

I won’t get into the back and forth of the cognitive-rote memorization-calculator argument. I will just say that this program is a huge failure to my child. There are different learning styles and Math Investigations focuses only on their specific method (which some children do excel at). However, the implementation in PWC is only that approach. Teachers are NOT ALLOWED to teach any other way. So for the child that is having problems with this approach or is challenged with the intuitive approach: are not learning, are getting extremely frustrated with math, and will be at a huge disadvantage in Middle School and beyond. This is a big issue that other school districts have found to have hurt their children after years of use. And now the School Board wants to wait and see test scores. Walts has spent millions on this program and will defend it to the final failed child.

Oh…and this program must have been developed by the same people that brought our society “NEW AGE PARENTING”. We all know how well that is working right? Right!

Krusty said on 28 Jan 2008 at 2:58 pm:

Heaven help the kids! Mine were in school during the 60s when the “new math” was introduced.

A subject we both agree on totally. My kids were in school too when the “new math” was introduced. Another folly.

The Patriot (Got E-Verify?) said on 28 Jan 2008 at 3:47 pm:

What if a calculator is not available? What then oh wise one!?!

You will have to count your fingers and toes like the “investigations” calls for.

Despite its demonstrated deficiencies and criticism from noted professors, education experts and parents, the PWC School Board seems to be taking an entrenched position regarding its continued use. This is one of the reasons this countries public education system failing. Anyone with kids in middle school should seriously be thinking HOMESCHOOLING!

If you want to know more about the program, why not contact the math department at Prince William County Schools and ask to have a demontration for concerned citizens. It seems to me like an awful lot of people here have no first hand, or even second hand knowledge of the program and yet have some mighty strong opinions.

I know a lot more about Carol Knight and her level of expertise and professionalism than I do about some Harvard professor who is probably publishing to keep from perishing and hasn’t taught a class in 15 years. Mrs. Knight would not recommend a program without thoroughly checking it out and believing that it was in the best interests of children for their mathematical futures.

Mrs. Knight is a professional educator. And all you with opinions based on not ever seeing the program would be professional ____????????

Top scientists and mathamaticians are speaking out against the

TERC Investigations in Number, Data and Space program.

http://www.mathematicallycorrect.com/nychold.htm

Here is an overview of the program and downloadable software if you are so inclined to go further into it’s inner workings:

http://www.fierworks.net/education/terc4teachers/01starthere.html

dolph,

How many of Carol Knight’s children are being taught using this method?

The new programs, many without student texts, are based on a “constructivist” teaching philosophy, which discourages teachers from teaching mathematical rules and procedures. Instead, teachers guide students, through group activities, to their own “discovery” of personal solutions. Students are encouraged to seek help from each other, rather than from the teacher.

dolph:

Dr. Wilfred Schmid at Harvard is a *research* mathematician, not a children’s math educator. He does not research pedagogy or children’s cognition.

I’m with you. Carol Knight (and the staff of PWCS math department) would never intentionally want to hamper our children’s ability to learn mathematics nor would they choose a program that did not have significant research and confidence behind it. Yes, it is different from the way we all learned. But the way we learned was failing us as well (look at US math scores, the number of US students pursing advanced work in mathematics, and the number of US students pursuing careers in math-related fields–all are pathetic).

My third grader the other night had the following question as part of her MI homework:

Which is greater 9 X 6 or 5 X 9? Explain your answer.

Under the “old” way, she would have the memorized facts that 9 X 6 = 54 and 5 X 9 = 45. Quick and simple, she knows 9 X 6 is greater because 54 is greater than 45.

But that’s not really the crux of the question. It’s the explanation. That’s what gets lost in the diatribe against MI. It’s *understanding* more than just a series of numbers is tables. It’s developing number sense and being able to use the vocabulary of math.

Under MI, though, she had to dig deeper than just the rote answer. Here’s the answer she came up with:

9 X 6 is the same as 6 x 9. That means there are 6 sets of 9 things (54 things). 5 X 9 means there are 5 sets of 9 things (45 things). There is one less set in 5 X 9, so 6 X 9 is greater.

OK, so her answer seems long and convoluted. But let’s look at what she did. In addition to doing the multiplication part she also did some set theory (pretty big concept in computer programming) and demonstrated the transitive property of equations (9 X 6 = 6 X 9) without realizing it.

Which answer will develop her mathematically reasoning ability better? Which answer will serve her better down the road when it comes to mathematical problem solving?

When we give kids a paragraph to read and then ask them questions to see if they understand what they’ve read, do we ask them how many words there were? Do we ask how many sentences? No, we ask for context. What was the reading about. Under Math Investigations, that’s what is happening with math. What is the problem about? What is your understanding of what the numbers mean.

I think most of us don’t get it because we never *got* math. In polls of adults, it’s not uncommon to find that a majority say they never liked math, never understood math, or they were never good at math. Math Investigations is trying to reverse that trend. Make math understandable. Make math something to think about versus something to memorize and spit back without knowing WHY.

But hey, I’ll take the word of an armchair commentator over a professional educator any day of the week, right?

My daughter had “whole math” where everything was related to multiculturalism. Students were expected to get into groups and teach themselves. The teachers loved it because they made a lot of money providing private tutoring after hours. This whole math came out of California, natch.

Math isn’t about “context”. Math is right or wrong. 2+2 is always equal to 4 and no amount of “context” about it is going to change it. I “got” math. It was ok subject but reason most people hate it is it’s right or wrong status. There is no partial credit for math. Either you got 4 for problem of 2+2 or you didn’t. At Higher levels of math in High School, it tends to get ugly and large problem is we continue to teach kids math they don’t need to know. If a kid shows massive issues in Algebra 2, move him to a course of learning how to apply the math he knows in real world situations like balancing a checkbook and calculating which item is cheaper. 12oz for 2 bucks or 16oz for 2.50?

Answer to your kids homework assignment Turn PW Blue is simple:

“9×6=54 and 5X9=45 therefore 9X6 is greater”. There is no further explanation is required. Any teacher who marked that question wrong after one sentence should be fired. As for your third grader learning “set theory” which according to you is massive part of programming. somehow I missed that part of computer Science classes

Of course, Turn PW Blue is giving standard liberal response of there is people out there smarter then you on this subject so you need to shut up and listen to these professional “educators” (whatever a “professional educator” is)

Everything is going to depend on how well the third graders do on the SOL tests this spring. The current crop of third graders are the first wave of Math Investigation students to face the SOL (other than schools that we piloting the program.)

Turn,

I have a degree in corporate finance. All I took was math for the better part of 4 years. I GET IT! IT DOESN’T WORK!!! And thanks for insulting all of us concerned parents by calling us armchair commentators.

Turn PW Blue proves an important point: Leftists cannot grasp facts very well. LOL

“You can’t take three from two, two is less than three, so you look at the four in the eights place. Now that’s really four eights so you make it three eights, regroup, and you change the eight to eight ones which you add to the two to make one-two base eight which is ten base ten and you take away three that’s seven . . .”

“Which is greater 9 X 6 or 5 X 9? Explain your answer.”

The 9’s are common so drop them. 6 > 5, bingo! Don’t need to know the result. There’s many ways to skin a cat.

I think the way they’ve taught math since the Pyramids have been built is just fine. I don’t want to drive over a bridge that has been built with any “new math”.

just my $0.02.

Time for the blow and brag-a-thon to begin. Most parents went to school so therefore they know better than professional educators. Let’s see, what is a professional educator? Someone who has been trained to educate others and whose profession it is to do so.

Turn PW Blue,

Thanks for that explanation. The example you used covered several objectives. My only disagreement would be…whispering….commutative property of multiplication;) Right now, kids don’t have any better understanding of math than they did 20 years ago.

MND,

Do you mean Carol Knight’s personal children? None. They are grown. I don’t know how many children are involved in the program. No clue.

Have fun. Multiply and divide in Base 2 (or 8 or 16)! Increase your brain-bandwidth.

I just can’t imagine going through life NOT knowing my math facts instantly. Can you? I’m so thankful that my teachers and parents INSISTED I learn them. There are admirable aspects about Math Investigations that do help with deeper understanding. But, children need to be held to a standard of mastering basic facts.

Anonymous @ 9:10

I totally agree with you about how critical it is to know math facts. I just cannot imagine not knowing them. I think also think deeper mathematical understanding is critical, especially to meet the challenges of the future.

The math needed when I was a kid really is pretty useless today.

When I think about all that long division I did as a kid….arrgghhh.

Not all mathematics is exact. Estimation and approximations are every bit as useful as exact answers in the real world.

The numerate adult will be one who not only knows basic math facts but also can think in math.

Dolph,

I’m sorry my friend but estimations and approximations are NOT as useful….nowhere near as useful as exact answers!!!! You must be a desk jockey. What planet are you living on? Can you imagine a carpenter building a house on “approximations”? How bout a NASA scientist? Oh well, it doesn’t matter if you land the space shuttle in Florida or Georgia, just so long as its somewhere in the SE US!!! Your thinking has been polluted by the trendy and misguided relativism theorists. Some things are more valuable than others…always have been, always will. And 2+2 is always 4, not somewhere between 3 and 5.

Ah Slick,

Literal minded are we? Yes, measuring for houses and landing space shuttles demand precision. However, many math applications deal with trends, approximations, estimations, and other inexact types of responses such as greater than and less than. 1 + 1 = 2 is an absolute (in base 10) and all folks young and old need to know basic facts. To not know them is to be innumerate and illiterate. It is like knowing English. Knowing English and having command of basic math is empowering.

Students, both children and adults ones, have a difficult time when asked to come up with quantitative answers that are not exact. These are much needed skills and ones that should not be shrugged off. It all depends on what you are doing whether exact or approximate are needed.

I absolutely do not know what you mean about my thinking being polluted by trendy and misguided relatism theorists. What does that mean in English?

I was actually sort of shooting from the hip….having spent a career dealing with quantitative matters.

Slick said on 28 Jan 2008 at 9:32 pm:

And 2+2 is always 4, not somewhere between 3 and 5.

RIGHT ON!

TERC Math Investigations has been brought to PWC because high school students have great difficulty with algebra and other higher level math courses. Graduation requirements are mandating that students pass the higher level math courses. So, blame has fallen to the elementary schools for not teaching children to “think mathematically.” Math Investigations is

a hope that more students will “get math.” MI does not “go for mastery” and teachers are not supposed to be concerned when their students “don’t get it.” MI is supposed to be on-going. If a student doesn’t get it now, don’t worry, the topic will come around again.

I don’t think MI is going to be “the answer” to our algebra woes. Some students will get algebra and many won’t. But, at least with the old methods people could perform basic arithmetic without looking like an idiot.

Silence idiots! Dolph has spoken. She knows the school teacher, and says that the Harvard professor knows nothing. Case closed. Go back to whatever you were doing. What, did you think this was an open forum or something?

Mrs. Knight is the Supervisor of Mathematics for Prince William County. Archie, my opinion is just as valid as yours. However, I am willing to admit I have no first hand knowledge of the program in question, therefore I will not judge it.

I have read and listened to many meatheads over the years who sit and ivory towers and tell everyone else how to do things. Most of them couldn’t find their arses with both hands. I really have very little respect for those who yodel from that ivory tower.

Interesting that I have gotten under your skin. Is it math education or in general, because I am not an archie?

es_la_vey,

I completely agree with you, I went pretty far into the math mix (Calc 3, differential equations, boolean algebra, etc…) and the one thing I did find in the whole mess is that their is “more than one way to skin a cat” and the other thing that I experienced is that if you dont use it, you loose it. I think “fuzzy math” may be a novel approach to teaching mathematics, but I’m not into education so I’m not learned on the subject of teaching children.

I’ll have to bring this subject up in my debates with my Father, being a teacher for over 40 years he should have some input on the subject.

I like the comment about the pyramids I figure we should all go back to playing around with the abacus! Do they still use those in class these days? I remember having one as a kid.

Josh,

Totally agree about more than one way to skin a cat and if you don’t use it you lose it. (and I have lost a lot)

I am not sure if this program is fuzzy or not. It depends on who you ask. People have been fighting over calculator use for the past 30 plus years. I have read that back in the day, the issue was over whether to allow erasers or not. It was thought that erasers enabled students.

I do think it is important that people realize that todays students are not being groomed to be calculators of math (performing mathematical computations) like they were 100 years ago. Today’s students will use mathematics to make decisions and predictions and to follow trends and flows…..and all sorts of things I have probably never thought of.

Why is it that so many people feel it is perfectly ok to say, I am horrible at math or I cannot do math? Would they be as comfortable saying I cannot read and write? I think not!

Differential equations is a mean course! I chickened out….just didn’t have that old Davy Crockett spirit there with that one.

It seems that what the program lacks is that it ignores the fact that all systems have some level of wrote memorization (i.e. fundamentals). Memorizing addition, subtraction, multiplication and division tables might be boring, but the discussion that can be had once every student has the fundamentals mastered is much more interesting and more fun.

This approach is like trying to play a game of chess with a child without explaining how the pieces move. The game will not be interesting or fun because it will seem arbitrary.

Children have an amazing capacity to memorize even what they don’t fully understand. Unfortunately it doesn’t always work the other way. If they don’t have some foundation, it will be unlikely that they induce an answer out of thin air. You are basically asking them to reinvent math on their own.

A good math teacher can teach an algorithm then provide an application or present a problem and propose an algorithm to solve the problem. Either method works, but nothing can make the student succeed if they think that 2 + 2 = 5.

It seems to me that this new Superintendent is trying very hard to break something that wasn’t broken until he took over. In 2005 the Prince William County system was the best in the state, though not the most expensive. Almost ALL schools were already accredited, and many had been so for 5-6 years (prior to 2005). SOL scores were high, many schools well above the mean (and that includes MATH scores). My own daughter had already been recruited by colleges when she was a Freshman in High School (2003), and she was on a Math/Science path and had won the BDHS (HIGH SCHOOL) mathematics award as an 8th grader. We had an outstanding school system here, and I’m speaking from the perspective of a parent that kept a VERY close eye on it throughout the years that my children were in it.

Would you try to teach a child to read without first having them memorize the alphabet? Would you have a student just try to figure out the letter sounds on their own or do you make them memorize them? When you are learning the basics of any subject, there is some part of it that must just be memorized. You’ll never write a sonet without first learning the alphabet and basic phonics and you can’t move on to higher math without first learning (aka memorizing) the basics.

The part of this that is just so insulting to me is the fact that parents are not being listened to. Who knows their child best? Who is sitting at home helping their child struggle with this subject? Teachers may be experts in their subject, but parents are the experts when it comes to their kids. When did this county become and educational dictatorship?

I feel like we are all on an episode of “Are you smarter than a 5th grader?”, but instead of Jeff Foxworthy we have Milt Johns. You should not need to take a course to help your elementary school student finish their 1st grade math homework.

BTW, whoever said Saxon math was the way to go, you are soooooo right. While it is used my a lot of homeschoolers, it is available for classroom use as well. In fact, it is what they use in Fairfax schools.

http://investigations.terc.edu/

It’s not new

just new to the US

Remember when all the crazys wanted to change to the metric system

thank god that didn’t happen

“Higher level thinking” not something to debate on this blog

Keep your head in the sand and talk out your ___

Anonimom

I like your analogy. The TERC methods are so cumbersome that it is so hard not to make a mistakek somewhere. And, the messiness of children adds to the possibilities of careless mistakes. So, papers are scored by rubrics that give partial credit for 78 + 34 = 111. If you show your method you can get partial credit. When do we say sorry Johnny. Wrong is wrong. Checking student work is extremely time consuming. Students work far fewer problems and get far less opportunity for becoming fast and fluent at working basic arithmetic problems. That is not a good platform to build on for future advanced math.

anonimom…I am an advocate of Saxon math! I said it was the way to go…because it is! Your comments are right on. When I was growing up….we didn’t use calculators (unless we were computing things such as in trig./geometry). We had to show our work, but it was using the normal algorithms. I did really well in math (and I liked it alot) and so did MOST of my classmates. Post high school, I went on and took college algebra, college calculus, college calculus based physics, biomechanics, etc….all using the fundamentals I learned the old school way. This new age crap is just that…crap. It is just a way for professional educators to “blame” everyone but themselves and the parents for helping their children learn properly. It is also a way to sell new textbooks. GET BACK TO BASICS. This is just like all of those diet programs that don’t work. The bottom-line is…you have to eat right and exercise (you know the basics)…plain and simple…period.

Anonymous @ 7:31 am:

Now those sound like valid criticisms of any curriculum. It also sounds like you have had some first hand experience with the program.

My objection here has been how many people have had the lemming, me too, approach.

Patriot,

Not sure about what kind of math you took there. If you even had a calculator to use for trig functions it would have been post 1970. Post 1970 you would have taken some sort of dreadful new math. It was all the rage. It wasn’t until the 80’s that actual new math was pushed aside for a hybrid math that was part old and part new. I am not even sure it had a name.

It really sounds like you don’t like educators at all. If you had such positive math experiences, didn’t any of your teachers get any of the credit for making you like it so much?

dolph, thanks for the whispered correction. It is, indeed, the commutative property she demonstrated without knowing it.

I think the part that is so frustrating for people about MI is that we’ve never really thought about what math means. We made it mechanical. And it is to an extent. 2+2 is always equal to four. MI *does* teach that. It’s just that instead of simply taking it as a universal truth because the paper says so, MI asks the students to show and experience how 2+2=4. If may be through a picture with two apples on one side and two apples on the other. At the end of the day, they’ve learned 2 + 2 = 4, but that now has *meaning* beyond just numbers on a sheet. Deriving meaning and context arms students with the tools to make broader application of what they’ve learned. As a 3rd Grader, my daughter is learning multiplication. She started by skip counting (ie., 5, 10, 15, 20, 25, 30…and so on) to get answers. Yes, she probably could have memorized that 1 x 5 = 5, 2 x 5 = 10, and so on. But by skip counting she conceptually understandings what multiplication is doing whereas simple memorization would have given her a correct answer without any meaning.

Someone said earlier that traditional math is like memorizing the alphabet. The metaphor is wrong. The parallel in math would be memorizing numbers and what they symbolize. Simply being able to write 5 + 5 = 10 doesn’t mean that I understand that 5 items plus 5 items will give me 10 items.

Advanced understanding of math is required when you hit the tougher math courses like geometry, algebra, trig, and calculus. Simply knowing how to put numbers together to get an answer isn’t enough.

Let me give you an example. The following equation is CORRECT: 1 + 1 = 10

I hear the gasps now as fingers fly across the keyboard saying “look, he even admits that being close is good enough! What are we teaching.” What’s missing from the equation above is the context. In binary math, 1 + 1 = 10 (10 is the representation of 2 in a binary (Base 2) system), but you’d need to understand the system and the context, not just the numbers on the page.

Dolph, I grew up in the 70’s and 80’s. And yes, I did have a “scientific” calculator for trig./geometry. No, I did not have any “new” math. I applaud MY instructors for keeping the old methods and not allowing us to use calculators for most of the math courses (except those I specified). Educators must stick to the basics. Educators must demand parent participation. Unfortuneately, once the NEW AGE PARENTING came about (after I had graduated high-school…thank God), the classrooms seemed to start falling apart as well as the materials and methodology.

Patriot,

A mere youngster aren’t you? If you took your high school and college level math courses in the 80’s then you did escape the worst of new math. Lucky.

I got bitten by it because I went to a high school where no new math was taught and ended up in a college course that was totally new math. It was horrifying and to say I didn’t do well is an understatement.

Somewhere I think there is a balance. Let’s not use the word ‘new math’ because it could actually mean anything. I think the most important thing is to look at what kinds of math tasks the working population will be using and what skills are needed for various jobs. 100 years ago huge populations of persons who could do calculations were needed. They are no longer needed, so we change our emphasis as we prepare young people for future job markets.

I certainly do not think that the SOL objectives specify what is needed. How many years could you live without knowing how to make a stem-and-leaf plot or calculate the surface area of a pyramid? Most of us, a life time.

The biggest problem is, the math folks themselves haven’t yet agreed on what is best practice. They probably never will. If the supposed experts cannot agree, how can anyone else hope to.

Turn PW Blue,

I think you ought to get a special reward from the PW math dept for giving such great examples.

How does your daughter’s third grade teacher feel about teaching Investigations? Does she feel it is worthwhile and that his/her kids are learning?

My concern with many of these programs that start out in elementary school, and that is where they must start, is that many elementary teachers are most uncomfortable with mathematics in general. This sets up a situation where you have people who lack math concept understanding teaching it to young kids…and you see where I am going with this.

I would be more comfortable with programs like this if there were math specialists in every elementary school each and every day.

Sooooo, if you are from Harvard and running for president, we don’t want you because you are from Harvard but if you are from Harvard and want to teach our children math we should listen.

LOL - at One Voice.

It has been said that those who can, do, and those who can’t teach. Well something I have also observed is that those who won’t, complain.

How about we try something completely different and say that in the spirit of compromise we have our teachers KEEP teaching the way math has been taught since Christ was a Corporal and incorporate this new way to learn as ANOTHER way to do come about the same answer.

The question was posed, “What if there is no calculator.” I agree with your logic, but you have to take it one step further. If NASA was going to go to the moon, would you trust the scientist who did the math in his head, or used some sort of aid (calculator, slide rule, mainframe computer)?

Oldie but appropriate:

Last week I purchased a burger at Burger King for $1.58. The counter girl took my $2. I was digging for my change when I pulled 8 cents from my pocket and gave it to her. She stood there, holding the nickel and 3 pennies, while looking at the screen on her register. I sensed her discomfort and tried to tell her to just give me two quarters, but she hailed the manager for help. While he tried to explain the transaction to her, she stood there and cried.

Why do I tell you this?

Because of the evolution in teaching math since the 1950s:

Teaching Math In 1950

A logger sells a truckload of lumber for $100. His cost of production is 4/5 of the price. What is his profit?

Teaching Math In 1960

A logger sells a truckload of lumber for $100. His cost of production is 4/5 of the price, or $80. What is his profit?

Teaching Math In 1970

A logger sells a truckload of lumber for $100. His cost of production is $80. Did he make a profit?

Teaching Math In 1980

A logger sells a truckload of lumber for $100. His cost of production is $80 and his profit is $20. Your assignment: Underline the number 20.

Teaching Math In 1990

A logger cuts down a beautiful forest because he is selfish and inconsiderate and cares nothing for the habitat of animals or the preservation of our woodlands. He does this so he can make a profit of $20. What do you think of this way of making a living? Topic for class participation after answering the question: How did the birds and squirrels feel as the logger cut down their homes? (There are no wrong answers.)

Teaching Math In 2008

Un hachero vende una carretada de madera para $100. El costo de la produccisn es $80.

John Light,

LMAO!!!!!!

This is a huge wart on the part of the school board and especially on the part of Superintendent Walts for rushing this program in. They piloted it for only one year which was a big mistake. Of course the county admin. math department was supportive of it! Their brand new boss brought the program with him and was determined to get it through. What choice did they have with a new superintendent who was cleaning house in the central office after decades of Dr. Kelley? Do you want to keep your math department job and promote my superdeduper new math program or hit the highway?

And now the school system has no way to back up their claims that this math program works. They have an internet filled with thousands and thousands of parents saying that it stinks and stories of states who’ve spent millions only to have to throw the entire program out the window.

Why didn’t they have a longer pilot program so they could substantiate their claims that it will help test scores? That would have helped shut up the critics and provided a foundation to assure parents. I could be a believer because I get the concept of the program. That is I could be a believer if I saw results, but now I just see a mess.

The sad thing is we’ll probably never know whether the program works or not because the school system was so stupid with the way they approached it. There is a reason new drugs are tested for several years before they are released into the market, although I don’t advocate testing Math investigations on mice.

The SOLs will probably be terrible, and the pubblic will be outraged. They’ll tar and feather the school board, who will fire Dr. Walts and bring in some other bird brain who coincidentally will bring another whacked out math program with him and we’ll start the whole mess all over again. The PWC taxpayers will pick up the bill just like they’re picking up the bill to build walls in all those 1970’s schools that were built when open concept classrooms were “brilliant, creative, and going to revolutionize educating our children”….sound familiar?

I guess there really is something to homeschooling.

John, NICE! I disagree with your 1980 line item though. That certainly did not apply at my school. Now as far as the scientist is concerned, I would expect professionals to use references, books, tables, computers, calculators, etc. Students should learn the fundamentals without these…when they become pros then they can use them. Kind of like a new pilot should learn to fly with manual instruments and then can transition to computer assisted instruments after learning the basics.

The Patriot - No, I agree wtih you 100%, but just trying to make the point that there are more than one way to skin a cat, but without the BASICS, children are being cheated.

I have to admit, I had a pretty good education (Old Keene Mill Elementary, Washington Irving Intermediate, and West Springfield High School) growing up, too bad I did not clue in to take my birthday off yesterday as it was a teacher workday and the boys were home Guess I just will never learn - lol

inon,

I did a google on mr Walts. He came to us via Greece NY. Guess what math program they used up there…yup TERC! It set off a huge battle which the press donned the “NY math war”. As far as I know they are still duking it out there. So let me get this right, our illustrious superintendent threw an incendiary bomb in his last position via MI then leaves under a cloud of legal problems and comes here and starts the same thing all over???? WOW! I’ll keep researching.

Dolph,

i thought boolean algebra was far more painful that DE, after taking a bunch of calc DE was pretty smooth sailing, what’s even more painful is that I switched major’s to justice studies after deciding not to be an engineer so the math was pretty useless, although I did enjoy it

I know nothing of TERC outside of what has been mentioned here. I googled the term and it didn’t seem to be too favorable as a teaching method.

I loved the wikipedia entry…

http://en.wikipedia.org/wiki/Investigations_in_Numbers%2C_Data%2C_and_Space

Josh:

I figure we should all go back to playing around with the abacus! Do they still use those in class these days? I remember having one as a kid.You’re not that old, are ya? I think the abacus has become a glorified back massager.

But I have a beautiful slide rule (circa 1963).

Thanks for reminding me. I’ll have to see what that can bring on eBay.

Josh,

I hated abstract algebra the worst. That was painful.

Slick,

Will you provide those links to Dr. Walts please? He also brought a few EEOC suits that our school board didn’t know about. Oh and did we mention wire tapping the Greece, NY school board room? I heard some rumblings about that also. The guy who did that supposedly came to PW with him.

Turn PW Blue @ 11:18

1 + 1 = 10 as an equation, is INCORRECT in both base-ten and binary.

One plus one equals ten. That’s just wrong no matter how you slice it. You don’t use the word “plus” in binary unless you write out the entire algorythm like trying to figure out that 1,0 represents the numeral 2.

You might get away with saying 1&1=3, since one, one is the binary representation of the number three. But, as an equation, 1+1 has absolutely no meaning in the binary system. As a matter of fact, just putting in “1″ has no meaning, it would be “01.” Binary - “bi” - “two” spaces.

Try this: 0,1 + 0,1 = 1,0 that is the closest you can get to representing the base-ten numeral 2 in a binary fashion using arithmatic operators.

The Patriot (Got E-Verify?) said on 29 Jan 2008 at 11:39 am

In reference to your earlier post, I used a slide rule for high school chemistry. Does that date me? I didn’t see a calculator until college.

John Light, your 1:15 post is one for the ages. I nominate it for post of the year!

Dolph

I had forgotten the wiretapping story. I thought it was in the papers right after Dr. Walts came on. Does anyone remember the details?

jfk, thank you…glad you liked.

es-la-ley Jan 29 at 7:21 - Please let me know what you find out on e-bay about slide rules. I have a few beauties (ivory, I believe) plus a circular one in a very worn leather case that my late husband used in the 40s. - He also bought the first Hewlett-Packard “computer” for a (for us at the time) stratospherically high price. - Maybe there’s a market for the old sliders.

Slide rules - ahhhh, the memories. I remember in my classroom having one that went the entire length of the chalk board and we actually got to use it when we would demonstrate how we solved our math problems. This was in elementary school, of course. By high school calculators were the rage (my parents would not let me get one for fear I would use it as a crutch) but you could still find the slide rules in use.

dolph:

My daughter’s teaching seems to be OK with MI. He (yes, he) is a little concerned about SOLs because the pacing and sequencing in MI doesn’t match 1:1 with the Virginia SOLs, though he thinks his students will be fine. When I talked to him about the whole program, he was positive and said he saw some great things coming out of his students. From other teachers I’ve talked to, the one thing they say they really could use is more inservice training. I think a lot of the concern raised by parents and echoed by some teachers stems from the very issue you raise. By and large elementary school teachers fall into that group that says “I was never really a math person” yet they are being asked to teach the foundations for our future math whizzes. The “old way” was comfortable for them because it was familiar and doesn’t require being able to answer the tougher questions.

Old way:

Teacher: 5×6=30

Student: Why?

Teacher: Because it is. Next…

MI Way:

Teacher: How can we figure what 5 x 6 is? What does 5×6 mean? and so on…

The TERC program recommends a two-week pre-service for teachers new to MI. PWCS requires just a day and half. If there is any place that criticism can be aimed, it is at the lack of training and preparation provided to the teachers who have to implement this program.

The teachers have had days of training and that was part of the big cost of this program.

And the old way didn’t just say 5 x 6 = 30.

The old way showed 5 blocks of 6 or 6 groups of 5. The problem with MI is that is never seems to go past those blocks.

These kids will not be able to do long division like 765 divided by 43…that should concern parents. Instead they will subtract out groups of 43 until they come up with enough subtracted 43s to come close to 765. Then they add up all those little groups of 43 that they subtracted and get the answer and a remainder, if applicable. It takes a whole page to do one lousy problem and with the multiple subtractions and additions (far more than the normal method and things are not neatly lined up), there are far more opportunities for math errors there leading to an incorrect answer. I can imagine what will happen with the SOLs.

I’m not completely knocking MI because it may have its good points, but when I haven’t found a single teacher that likes it, that makes me worried. Perhaps they are worried about the SOLs because if these kids mess up, the teacher’s neck is on the line. Notice how many third grade teachers are complaining. That is because they know exactly what knowledge is required to pass that test and they realized the kids coming out of last year’s 2nd grade MI experiment aren’t cutting it and they won’t be ready for spring SOLs. Maybe MI is great for long term math learning but we have the problem that SOLs are mandatory now. And they are a law, so unless we change the law, we shouldn’t start tinkering around with math reforms that won’t help these kids pass the tests that they must pass. Personally I absolutely hate that we teach to the test, but until the law changes, it seems to be a mistake to to risk every school in the county failing to make AYP just to prove a point. Almost half of our schools couldn’t cut it this year and it will only get harder next year.

Our reputation will have gone from World Class Education to Third World Education.

Anon

You are completely right. The third grade teachers are very concerned. Poor scores on the math portion of the SOL can push a school onto the failing list. Sanctions against the school would make life miseable for all those who work at that school. And, of course the property values in that school’s boundary will also take a hit.