Unfortunately, those who work within the public education still insist that 2 + 2 = 5 or any other number, providing the student understands why their answer is correct, regardless if the math proofs states that 2 + 2 = 4.

In the comment section, below is a typical defense of defending the fuzzy math curriculum, and the reasons why it is not necessary to form a solid foundation in math.

“The only way to get kids learning mathematics is to make sure they get the questions.

Teaching students abstract procedures to find answers to questions they don’t understand is useless. Algorithms work for students with enough aptitude and/or experience to make sense of them. Those students integrate the algorithm into a conceptual web that involves estimation, mental mathematics, and algebraic reasoning. The rest of the students (the majority in many public schools;—especially jr. high and younger) try to memorize more and more complicated and abstract strategies. These students struggle with application of the algorithm in problem solving situations and will except absurd answers from an algorithm or from a calculator! Furthermore, any math teacher with significant experience knows that it is easy to teach efficient algorithmic procedures to students with strong conceptual understanding. It is conceptual understanding that is lacking when they get to university not long division algorithms.

There are no sure-fire routes to universal mathematical literacy and numeracy. But the strategies in the new curriculum involving sense-making, estimation, mental math, and personal strategies are more beneficial to our students, communities, and economy than trying in vain to teach everyone long division.”
http://www.cbc.ca/news/canada/story/2011/09/21/new-math-paper.html

We no longer have to wonder why our grade 12 graduates are taking remedial math in post-secondary, and can’t do the simple arithmetic calculations, without the need of hiring someone to do it.

I never knew teaching my child the most efficient methods, and in part memorization, practice leads to inefficient and poor math skills, as the above comment to the CBC article. Isn’t he crackers, and I would not want to hire him or even relied on him to work around the house, Conceptual understanding comes after a firm foundation as well as the all important element fluency.

I suspect the commenter is a teacher, and my kid would have a great time correcting the mistakes that this teacher would make, to the delight of the other students.And she would be sent to the office, being perceived as a behavioural problem.. Thankfully, the local math and science teachers in the high school, know that fluency as well as a solid foundation leads to a solid grounding in numeracy as well as a deep understanding. It has been a hot topic down my way, since the word slope has become a banned word in grade 10 mathematics and below. The teachers have visions of extensive remediation in grade 11 and grade 12 math, in order to understand the sciences in physics, chemistry and in sciences where there is an element of math. Slope, another important concept being discarded, without a thought how will the students pass the public exams.

As it is now, the local high school is focused on the remediation of writing skills, skills that should have been taught in grade school, and now next year, math remediation will be added. I can hear the whispers of Khan Academy, as a short term solution, while trying to figure out a way to get rid of the latest changes to the math curriculum, without losing their jobs in the process.

It’s intriguing that “experts”  routinely say this sort of thing without pushback from real math people.  There should be a public hue and cry.  Tinhis is positively dangerous.  Good for the cbc for actually publishing the Frontier info; bad on them that nobody was there to ridicule and expose this quackery.

I spent some time the other night tutoring a young man in a college welding apprenticeship course.  He was working on some review early in the text; grade seven level fractions.  He had a calculator.  But he could not come up with the LCD   with multiples of 8.  He took three tries to get 4*8.  He is a very bright lad, and he can succeed.  But I told him he had a lot of work to do to overcome the witchcraft that passes for school math.

Here’s what the educrat said, quoted by the CBC:

“Within our curriculum, direct instruction has its place and so does discovery and problem solving,” said Simone Gareau, the ministry’s executive director of student achievement and supports.

She cautioned against thinking that the old-fashioned way of multiplying numbers is always the best approach.

“If you do the old-fashioned algorithm, 32 x 48, where students have to carry over and put in a zero to hold the spot ... students can learn to do that by rote, but it doesn’t necessarily mean they understand,” she said.

“What we’re aiming for is that deep understanding. Once they have that in place, they can move to the traditional algorithm if that’s a strategy that works for them.”

Of course they “won’t necessarily understand”.  Unless they learn all the incremental steps and concepts, with practice, that are antecedent to the “traditional algorithm”. 

All learn differently?  And Oceania has always been at war with Eurasia.

CBC NEEDS MORE FUNDING FOR PRUFFREDRS:

I noticed I failed to adequately proof my comment above on “experts.  No excuse especially with the preview option.

What is the CBC’s excuse for this, on the same page as the Frontier report article:

“
Does “new math” add up in Saskatchewan?

Children are being taught math differently these days. “New math.” Critic Michael Zwaagstra says the changes have made what used to be simple equations far too complex.

Simone Gareau is the executive director of student

acheivment

and supports. She says the “new math” helps form a deeper understanding, and that there is still a place for traditional…

This is a case where “those who forget the past are condemned…”  NOT to repeat it.

According to Orwell,

” As a language, Newspeak applies different meanings to things and actions by referring only to the end to be achieved, not the means of achieving it”

His protagonist, Winston Smith, is employed burning the past and its real meanings in “the memory hole”

“... an editor revising historical records to concord the past to the contemporary party line orthodoxy?that changes daily?and deletes the official existence of people identified as unpersons.”

The result is that words and concepts take on meanings determined by the party leaders.  Nobody either knows or cares what really happened or what is really true.  They can be thrown into a blind rage against those who challenge current “newspeak” 

The creators of the past, or rebels in the present (thought criminals) are made into “unpersons”.

Or in our case, “non-educators”

The work of SQE is vital, not just with respect to public schooling, but to the whole enterprise of cultural and historical memory.

“Who controls the past, controls the future”.

If you’re not horrified by the comments of Simone Gareau, you don’t have a soul.

I suspect there is no push back, because it would be a waste of time to inform them that they are wrong. I found it really difficult, to understand where they are coming from, because their premise is based on illogic thought. Math is pure logic, and it is why I find math easy to understand, because it is based on logic. I cannot argue with people, who insist that math can be learned from an illogic base, in the same way I cannot debate with people who insist in cutting the grass with a pair of scissors. Exaggeration, but life is filled with illogic stances, but the beauty of math, logic reigns supreme.

A paper - “Generations of even well-educated adults are under the delusion that mathematics is difficult, and that mathematicians must therefore be very clever. In this talk I will explode this myth and show that mathematics is in fact easy, and moreover that mathematics is precisely ?that
which is easy? for an appropriate sense of ?easy?. We will take ?easy? to mean ?attainable by logical thought processes?. As a corollary, or a converse, or a contrapositive or something, we will discuss the importance of illogical thought processes in non-mathematical life and the fact that life is thus difficult. Hence or otherwise we will deduce that mathematics is not life, nor can it nor should it
be.1”

http://cheng.staff.shef.ac.uk/illogic/illogic-web.pdf

A science fair project last year, my youngest with a little help from me, reduced a mathematical theory to the simple action of counting. Any 10 year old could understand the theory, and learned in the process that math is easy. What I thought would be a sure gold project, and even a honourable mentioned, turned out to be a silver. Too bad, because as told by my youngest, the ordinary math teachers who were the judges, and not university math profs, kept running to my child’s project for clarification on other projects dealing with the same math theory. To everyone’s dismay, including the other students, my child should have place first in the math division for the sole reason of making math easy, and not at all complicated. Any math professor would appreciate the true simplicity of my child’s math project, base on the logic why the theory is correct in the first place. And be impressed that she knew the theory inside and outside, along with the proofs that were reduced to simple counting. The project that won, had the series of proofs, which anyone can do, using complicated language that sent the judges running to my child’s project for clarification.

“You might be wanting to point out a flaw in my argument already: if maths is easy, why does
anyone find it hard? Well, this isn?t the fault of the mathematics. If someone finds maths hard it?s probably because nobody told them it was supposed to be easy. And I?m not just being facetious. (That is, I?m not just being facetious.) If you look at something the wrong way up, it?s bound to be harder. If you look at something the wrong way round as well, then it?ll be even harder. If
you then think you have to learn how to stand on your head and look in a mirror at the same time, it?s no wonder that you give up and go and study English literature instead. There are as many ways to make things difficult as there are to make them easy, and we can be sure that a whole ton of them have been applied to mathematics. If someone finds maths hard it might also be because nobody told them what it was for ? a fork is rather hard to use as a knife. It?s also rather hard to use if you?re trying to eat a sandwich. Or a bowl of soup. Or a packet of maltesers…......”
http://cheng.staff.shef.ac.uk/illogic/illogic-web.pdf

Excellent post Nancy!  I absolutely agree!  I loved math (still do) for the very reason that it is so logical.  I also loved that the more I did the easier it became. The thing is, did math help develop my logic or did my logic help me in math?  Chicken or the egg? I tend to think it’s the latter and I’ll tell you why.

In 1980 when i was in the third grade the teachers went on strike.  Luckily for me (even though I didn’t think so at the time) my grandma was a retired school teacher so I spent my days with her.  She was as traditional as you could get and she was very good.  I don’t remember struggling in school before grade 3 but I definitely never struggled afterward. 

Charles I totally agree on Orwell and Newspeak, I mean really that’s what edubabble is.  No wonder kids can’t think for themselves and have no common sense these days.

Last Thursday my son came home from school and said “Mr. X believes in Global Warming.  We had to watch 24 hrs of Reality at school today and he told us if we want good info to go to David Suzuki or Greenpeace websites.  Hmmmmm.  I visited the teacher the following day and asked him if he was planning to show the other side.  He asked me what I meant and I said are you planning to show them The Great Global Warming Swindle, he looked shocked and said No!  I asked him why not and he told me the science was settled. Ummm no it’s not.  In the end we had to agree to disagree. I don’t mind that they watched it but I couldn’t understand why you wouldn’t show both sides and let the kids, armed with facts, make up their own mind.  It could have been a great lesson but instead just ended up being a waste of 45 mins of class time.  Don’t even get me started on wasted class time.  He’s in grade 7 and their big science experiment was to go on a long nature walk and take a picture of a tree.  I’m pretty sure I did that with him when he was 2!  When I was in grade 7 I was using bunson burners and disecting frogs and learning in depth about the solar system.  No wonder they’re bored!

Stairway to Math helped me so much last year.  It seriously was a godsend and so is this site.  Thank you!

Oops I meant to say the former.  Proofing is not my strong point

Seriously, in grade 7 taking a picture of a school? Unbelievable, and thankfully in my corner of the world the science is pretty good, but not the math. And the teachers present both sides of the on going debates such as climate change. When my child was in grade 7, she was winning gold in the local and regional science fairs. And in class, at least they were exploring the world of biology as well as the earth sciences, and actual give the students a good grounding for grade 8 and grade 9 sciences.

By the way, the foundation in math, as well as the fluency gives way to the logic. One can’t teach logic, without having a firm foundation to spring from. In today’s lousy math in classrooms, it is done backwards, where logic is taught first, and the word logic has been replace by critical thinking. And more importantly, there is no need to have a firm foundation in math, and hence it is why 52 % of the adult population has low numeracy skills and the achievement in math of students, is pathetic, and the educrats should be hanging their heads in shame, and not defending their stances. I once had a very heated discussion with an educrat over it, and the curriculum went from really bad to really the worst kind.

The only lucky thing was the class of 95 (my child’s class), who never benefited from the last changes, and that class will be the last one to do calculus and trig the old way, from the old text books of the late 1980s, and curriculum written by teachers whose degrees are in math. Today the math teachers at the local school worried what they will do, and when I heard, my first thoughts remedial courses in the maths, english and sciences for anyone entering post-secondary.

Sorry, I really should read word to word.

What I meant to say is, Seriously, in grade 7 taking a picture of a tree?

No worries Nancy, really when it comes right down to it what’s the difference, they’re both lame.  Honest to god i have never, NEVER thought of myself as a homeschooler but it’s tempting.  It’s not entirely the school’s fault they were a K-5 until the school board in their infinate wisdom decided to make the 3 schoosl in all our surrounding neighborhoods all K-8 which I supported in the beginning.  Once I saw it play out that changed. Hey everyone makes mistakes, who knew?  I guess I would have hoped the people that took on this big shift, you know the people at the top.  That’s not how it works though, it’s decided at the top of this huge bureaucracy and everyone else has to just deal. They’re so removed.

This is why I don’t get why good teachers would be against charter schools.  Charter schools also give teachers choice.  Choice is a good thing.

They are missing out on the jr. high experience.  There’s no art room, or lab or band room (or instruments) or cafeteria or home ec room or industrial arts.  how do you make a school that barely held all the elementary kids and add jr. high.  Jr. high is not just desks.  It’s ridiculous.  What was i thinking.  I guess I thought they’d bring in portables for classrooms (like they used to do in the good old days) and convert the other space to labs and artrooms and stuff. Guess not.

I feel like i’m ranting but COMMMONNNA I’m so tired of paying for nothing.  Imagine if the amount the gov’t spent on your child for education (and i use that term loosely) was in your hands, for you to decide…....it’s big money and i bet i would make the best choice.  Just sayin….I would ...and so would the majority of parents out there!

We’re one election away from making it happen in AB.  It will happen.  WRP believes in attaching the money to the child, privately run publicly funded education.  I still have hope!  Lots of hope, Education is #1 with everyone I know.  It’s a crisis and people are waking up in this province(with a little hlep from me i’m not gonna lie) .  It can’t come soon enough!

Why don’t our governments of education get real experts in subject areas to write curricula?  So many of these educrats/experts have B Ed’s and M Ed’s.  What subjects did they study to get these degrees?  To date I’ve never seen any post secondary math, so they have no real knowledge of math; yet they’re touted as experts by the media, and never asked by the media about their backgrounds.  The public falls for this every time.  I just don’t get it.

I wish I could turned back the clock, and homeschool. Perhaps I could have started something, but more than likely I would have been branded with some type of label, in my rural concern. Yesterday, was filled with interesting news regarding local education. A junior high, from grade 7 to grade 9 located about 55 kms away, was once a full K to 8 school. During the last 15 years, on again and off again discussions on closing down the school. Meanwhile during the last 15 years, reports of mould and other nasty air toxins have surfaced from time to time concerning the junior high. About 20 years, a decision was made to close surrounding community high schools, including the junior high and have the students be transported to the local urban centre that sits in the centre, within a 25 mile radius or so. The urban high school changed to a senior high school, the junior high school change from a K to 8 school to a 7 to 9 school, a number of school closures, and virtually all students will be bused.

A lot of money has been spent, in the millions where the schools are full capacity, and well over capacity. The junior high has added grade 10, because the urban high school can no longer handle the number of senior high students. And now, the junior high may very well close for extensive renovations due to mould problems. The urban high school cannot take the students, including the grade 10 students, and the rumor is that the students of the junior 7 to grade 10, will be bused to more rural communities, including the one that I live in.

The monies in bus transportation would be huge, considering the distances are about 45 kms to 60 kms. The more rural schools including the local schools where my child attends, are smaller schools that has all the bells and whistles, such as science labs, gyms, computer labs, but are limited to what courses and activities are offered, compared to the junior high and the urban high school of the more urban locales. And now the junior high has mould problems, and the school board is in a pickle of their own making, decisions made years ago without thinking of the future outcomes.

The word on the street, is that none of the rural communities want to take on the extra students for various reasons. The more rural schools may have more capacity for students, but no one wants class sizes increasing to 35 +, like the more urban schools are experiencing, and have been experiencing for the last 15 years. Like I said before, the more rural schools are smaller, compact that has a key advantage, that teachers get to know their students very well, since most of them live within the local communities. One of the outcomes, less skipping, more time to work with students who are failing, and more time to raise achievement for all students. One of the reasons, why I did not choose homeschooling years ago, but with all the knowledge I have acquired, if I could turned back the clock, I would homeschooled my child until she was well-versed in the 3 Rs, The crappy curriculum and instruction is the biggest reason, and the secondary reason is the policy decisions being made, spending tax dollars on questionable policies such as the junior high that should have been closed down for a spell years ago to take care of the mould problems, instead of closing down schools.

The spending of tax dollars and how it is spent within the provincial education systems, I believe is the engine that is driving choice to the forefront. It is the only outcome, in a system that is closed to outsiders, as well as being unaccountable for their actions.

Bev, you asked “Why don?t our governments of education get real experts in subject areas to write curricula.”

From the handful of english and math profs that I spoken to over the years, apparently they are not experts regarding the education of children. More important to have that education degree, than the necessary subject knowledge. The science curriculum fares better, but it is heavily influenced by the progressive philosophy and all its dogma.

Yes, I feel the same way about home schooling, Nancy.  My children got an excellent start in Asia, but once back here, they languished in school.  My son’s an engineer, but speaks no other language (although French was ‘taught’ in public school and high school).  He was reading Tolkien at age seven, but his love for good literature didn’t expand here.  My daughter listened to me a little more, and rounded herself out with languages and sciences (chemistry) at the post secondary level.  Even though my children are fairly well educated, they have gaping holes in their knowledge.  All the money spent on education, and this is what we get :-(

Regarding the topic of educrats not being experts in the fields they’re researching and or writing curricula for:  I’ll reiterate that I wish the media would do their jobs properly(especially CBC) and question exactly what you stated, Nancy above…  Perhaps the general public would begin connecting the dots and catch on to why children aren’t learning!

Charles,about Simone Garreau`s statement,horrified;not that it`s anything new-education malpractice.

Bev,“I don`t understand,why doesn`t the MOE get curriculum experts”?Oh God,I asked myself that question for years ,I can`t imagine how many years Malkin and Doretta asked themselves those questions,logic and a desire for every child to learn with a research based curriculum isn`t on the agenda,it`s just politics and banter at MOE offices.

I learned one thing the hard way by visiting the cognitive research departments and the teacher prep departments at OISE,Keith Stanovich`s stomping ground,the departments are completely disconnected and there is a turf war.The research department will say,of course we should be using explicit systematic synthetic phonics and phonemic awareness instruction as a precursor for optimal results in teaching kids to read and spell but “the building is divided”.
The teacher preparation arm doesn`t worry about curriculum and best practice,they just ignore the whole thing and they don`t train teachers to teach Reading.
Critical Thinking has replaced the acquisition of real knowledge in teaching students to read and spell as well as teaching children to do foundational arithmetic.
The emperor has no clothes.

Good morning!

I’m going to wade into the conversation knowing that I won’t be back to my computer into later this evening. I do this a little reluctantly because I prefer to have some time during the day to actually participate in the conversation, even if it’s only during a recess break or over the lunch hour.

I’ll preface my remarks by saying that I totally respect the the thinking on this that says it’s better to teach kids directly what we already know to be true. That’s how I began my teaching career, and that is how I was taught myself.

The fact of the matter for me is that I didn’t really begin to “learn” math and get excited about math until I realized that my foundational understanding was lacking. Unfortunately, I was 25 years old at the time, and I was already teaching math to grade eight students.

My main point in the conversation is going to be that math instruction, especially at the very youngest of ages, deeps to resonate with the development of children.

My 2 and a half year old son knows that 1+1=2; his older brother taught him that. The “problem” is (and it’s not a major problem) is that he has no idea what a one is, let alone a 2! He’ll grow into the “math fact”, I’m sure, but that is no reason why he shouldn’t be given lots of opportunity to explore with tons of concretes and manipulatives.

I think that there comes a time when math facts need to be directly taught, but I would argue that this needs to come after exploration of the basic concepts have taken place.

We can make it look like kids “know” math by having them memorize a bunch of formulae and algorithms, but they really remain empty procedures unless we have the chance to explore them, play with them and make some discoveries of our own with them.

I’m not suggesting that everything we know about math needs to be rediscovered by every student in every classroom; I am arguing, however, that much, much more room for discovery needs to be given, especially at the earliest stages of development. I believe that this will ensure greater foundational understanding and more “aha’s” as students move into more abstract forms of math.

Going back to the original post, and with all due respect, the sky is not always blue (according to my 4 year old, it is black right now). In fact, its “blueness” is the result of something other than the sky itself. The sky doesn’t rise in the east. In fact the sun doesn’t rise or set at all. I will admit that 2+2=5, though!

Stephen,you`ve been brainwashed by the new math textbook.Go to U.C.C. and see how they teach math.

Oh yes,look at the numeracy scores in the province.

Stephen, many moons ago I read several articles, that math sense was developed first, before speech.
Even animals have a sense of rudimentary counting sense, according to the articles. It made sense to me, because my children at the age of 2, knew the difference between one cookie and two cookies. Could have been the Sesame Street programs, watching the songs of counting, and more than likely it was. It was not until my youngest came around, and her speech delay, the subsequent testing, that counting was used as a tactic to get my child to respond. During testing, between 16 to 18 months, it was discovered she knew the difference between 1, 2, 3, 4, and 5 was a little hazy. She could not picked out the actual number, but she clearly knew how many 4 was or 2 was. The testing took longer than usual, because they were trying to figure out why she was not talking. Today, she would be diagnosed with a speech delay, and dyslexia.

That said, my youngest entered school, knowing how to subtract and add using the numbers between 0 to 10, Everything was fine, until grade 1 and the horrid math curriculum and instruction. Very quickly she became confuse, and lost the ability to add and subtract with ease at school, but not at home, when it came to cookies, and things that matter to her. One could say that it was the dyslexia, but at that time the word dyslexia was not on my mind. All I knew, she was difficulty in a lot of areas, that are signs of a learning disability. Math curriculum and instruction, was the first area that I focused on, because it was the first time ever that I had to confront the school, defend my parent ability, as well as my child’s abilities to their pronouncements on developmentally slow, and a whole host of adjectives, describing slow. The first teacher-parent interview in grade 1, my focus was on math, among other learning issues.

The math curriculum is horrid, and elementary teachers do not have a solid foundation in arithmetic. Nor are the elementary teachers trained properly in teachers’ college. Discovery learning can be a curse if not done properly, especially in the early stages. Throw in the developmental stages, and the knowledge that a teacher has in this area, as well as math knowledge, no one has to wonder why math achievement is dismal.

” “This study reinforces the idea that math knowledge is incremental, and without a good foundation, a student won’t do well because the math gets more complex,” Geary said. “The kids that can go back and forth easily and quickly in translating numerals, the number five, for example, into quantities and in breaking complex problems into smaller parts had a very good head start.”

The researchers also found that first graders who understood the number line and how to place numbers on the line and who knew some basic facts showed faster growth in math skills than their counterparts over the next five years. However, the researchers found that these early math skills had no impact on future reading ability.”
http://www.sciencedaily.com/releases/2011/07/110711131605.htm

Funny thing, the first teacher-parent interview, I said the number line was very important, and is a much easier way for children to add and subtract. Not according to the so-called math experts that hail from teachers’ faculties, and not according to the pedagogy taught to the teachers. Discovery learning in math is a curse, because children do not developed a firm foundation, major confusion and a result, children are unable to learn advance arithmetic with ease, in areas of fractions, square roots, and so forth.

I believe number sense is innate. Here is a small study exploring it.
“Humans have an intuitive sense of number that allows them, for example, to readily identify which of two containers has more objects without counting. This ability is present at birth, and gradually improves throughout childhood. Although it’s easier to compare quantities if the amounts differ greatly (such as 30 versus 15 objects), greater precision is needed when comparing items that are much closer in number. When this ability is measured during the school age years, it correlates with mathematics achievement. However, it has been unclear until now whether this intuitive ability actually serves as a foundation for school-age math abilities.”
http://www.sciencedaily.com/releases/2011/09/110914171751.htm

My child had good number sense prior to entry into school. It was destroy by the math instruction and curriculum. Repairing it was relatively easy, but first she had to unlearn the fuzzy math. As I discovered, I had to have a deep knowledge of arithmetic, in order to unlearn math, and than re-teach her. Good thing that I had a solid foundation in arithmetic, it made the job much easier,

Nancy, I’ve come to appreciate very much your story and the references that you use to illustrate it.

I agree that discovery learning, if not approached properly and with the right balance of student exploration and teacher intervention and instruction, can be a nightmare and place some students further behind.

I’ve learned that there are some kids who will succeed no matter what method you use, but most are dependant on teacher knowledge, confidence and planning.

I see discovery learning not so much as a theory, but as a description of what happens when anyone really learns.

To your point, there are many teachers teaching math at the elementary level who are not comfortable in the deep understanding that we are trying to foster. And we need to address that. A discovery learning approach, as you know, is not a synonym for a “free-for-all”. In fact, much of the professional learning in mathematics education across the province now focuses on teaching educators how to properly plan, execute and assess learning that combines time for exploration as well as time for direct teaching. A good math lesson is a very carefully devised thing!

I think that the effort to make discovery language an integral part of our math teaching is important. Just learning the algorithms and the “facts” should never be a fall-back position, but a natural extension of the learning process.

Joanne, interesting that you think that I’ve been overly influenced by the new math textbook. Those that know me will know that I’ve fought against over-reliance on any math textbook.

I’m not sure if there is a specific that you are referencing.

I’ve always prided myself on having a strong math program. I’ve been pleased with the results over the years.

I hope that I haven’t been brainwashed by anything or anyone. That would be very unfortunate, but I suppose I wouldn’t be the best judge of whether that were true or not.