Posts Tagged ‘constructivism’

Someone sent me a link to this graph which comes from pg. 74 of a PARCC document and shows exactly what’s happening in public education. 89% of high school math instructors believe their students are ready for college level work, yet only 26% of college instructors think they are ready. What’s the disconnect here? Are high school math teachers in a bubble thinking they’ve imparted “higher order thinking skills” through constructivism but reality is otherwise?

Most universities have remedial math courses for students who have had difficulty getting to university math levels. However, few universities have remedial math DEPARTMENTS. UVU is one such university that has been forced to do this because of the low quality math skills of students who arrive at the university.

For years the Utah State Department of Education has maintained that the high remedial math class percentage at UVU is the result of returning missionaries who haven’t had math for a period of 2-3 years and then need help getting back up to speed. This is a myth which can now be fully corrected.

UVU generated the following information after a request by Dr. David Wright, math professor at BYU, and Senator Margaret Dayton.

Click to enlarge

This chart shows that these remediation rates (as high as 72% in the past few years) are for first time college students. Many people who go on missions squeeze in a semester or two before they leave, and when they return from their mission they are no longer counted as a first time college student. The percentage of students prepared for college level algebra, is a pitiful 16-24%. How can this be? Constructivist math promoted by BYU’s Math Education department has made the rounds of all the surrounding school districts and it’s killing us. There has not been a single study showing constructivist math programs as effective. Yet we continue doing this injustice to our children making them non-competitive with the rest of the world. When will our schools change? They won’t until school board members quit listening to the so-called “expert” educators within their districts and from schools of education. It’s obvious these folks don’t value actual scientific facts or else they would drop these programs and just use something that works like Singapore math.

If you assumed this was Alpine School District in Utah, it’s not, but it’s the same old story. We’ve just saved $26,000 by not having the study done.  This news report is about Anchorage School District in Alaska which has jumped into constructivist math with the “Everyday Math” program (named thus because it was designed to frustrate parents and children every day). The “A-ha” moment of this article is right here. In all my years of studying this issue, I never saw this insidious angle.

Both Comeau and Nees say that they’ve heard complaints about the “Everyday Math” program from parents, who say that the method is so different from what they learned in school, that some parents aren’t able to help their children with their homework.

“When you have [the traditional method] on the board, and [the “everyday math” method] on the board, and the parent’s trying to do it the traditional way, [the student] is going to stop listening to Mom and Dad, and Mom and Dad can’t help them,” Nees said.

“Mom and Dad don’t know how to do it this way, so I will only listen to my teachers from now on.” Hmmm, where have I heard something like that before? Oh, that’s right, BYU’s Education department national consultant, John Goodlad.

Public education has served as a check on the power of parents, and this is another powerful reason for maintaining it.”
– John Goodlad, Developing Democratic Character in the Young, pg. 165

“Most youth still hold the same values of their parents… if we do not alter this pattern, if we don’t resocialize, our system will decay.”
– John Goodlad, Schooling for the Future, Issue #9, 1971

Parents do not own their children. They have no ‘natural right’ to control their education fully.”
– John Goodlad / Developing Democratic Character in the Young, pg. 164

Every child in America entering school at the age of five is insane because he comes to school with certain allegiances to our founding fathers, toward our elected officials, toward his parents, toward a belief in a supernatural being, and toward the sovereignty of this nation as a separate entity. It’s up to you as teachers to make all these sick children well – by creating the international child of the future.
-Dr. Chester M. Pierce, Harvard Professor of Education and Psychiatry, in an address to the Childhood International Education Seminar in 1973

It is a very real possibility that Mr. Goodlad and all these other educators have embraced constructivist math not only for the social engineering aspects, but because it’s another barrier between parent and child. Parents don’t know how to do this method of math, so they may figure that it will serve to separate the parents a little further from their children and get children to believe that their teacher at school is the source of knowledge they should turn to. Why? Here’s what other prominent national educators have taught.

Every child in America entering school at the age of five is insane because he comes to school with certain allegiances to our founding fathers, toward our elected officials, toward his parents, toward a belief in a supernatural being, and toward the sovereignty of this nation as a separate entity. It’s up to you as teachers to make all these sick children well – by creating the international child of the future.
-Dr. Chester M. Pierce, Harvard Professor of Education and Psychiatry, in an address to the Childhood International Education Seminar in 1973

Education should aim at destroying free will so that after pupils are thus schooled they will be incapable throughout the rest of their lives of thinking or acting otherwise than as their school masters would have wished …
-Bertrand Russell, quoting Gottlieb Fichte the head of psychology that influenced Hegel and others.

I have never before understood this issue in this way. If you are new to fuzzy math, or even for a quick refresher, I strongly encourage you to watch these videos and read my comments below. (Update, looks like the video on the news report has been taken down now. You can still read the story though.),0,7214623.story


One final note, when the lady in the video above says that when students learn this way studies show they do better, that is utterly false. There are no studies that support constructivist math as a superior method of teaching. To the contrary, they have been shown as failures.

Here’s meteorologist M.J. McDermott to explain this bizarre lattice method along with a stinging rebuke of Everyday math and Investigations math (the parental-separator of choice for Alpine School District). This video is 15 minutes, but she explains the lattice method after a couple minutes. I strongly encourage you to keep watching though, as she will explain fuzzy division, and then share an astounding quote at the 10 minute mark from the Everyday Math textbook telling teachers that mastery isn’t important.

At the end she holds up a couple of Singapore math workbooks to help your children learn math and I also endorse the Singapore Primary math workbooks which you can get at

Post note: Just to be clear, this is not an endorsement of Jump math. I think the jury is out on it and things I’ve read since this post indicate it may have some issues to resolve, but it does appear to be worth looking into.

I received an email Wednesday concerning an article appearing in the New York Times blog ( on a program called JUMP Math asking what I thought about it. In reading the article, I came away very impressed but naturally skeptical. As a critic of bad math programs for some time I thought “is this some dumb fad claiming success off bad studies or what?” Then Thursday I got 2 more emails from people asking about JUMP math and one of them referencing the article. I decided to look up the company online and see what they were about. (be sure to read that article)

JUMP stands for “Junior Undiscovered Math Prodigy” and if the article above proves correct, may replace Singapore math as my favorite math program. After browsing around for a bit and looking at some of their curriculum materials online, I had a couple questions and thought I’d call the company. The curriculum people weren’t picking up so I dialed the CEO directly. I was surprised he answered and we had a very pleasant chat. After we agreed that the constructivist approach to teaching math didn’t work, I obtained my first level of comfort with him and their product. I mentioned that I didn’t see the times tables being introduced in their 2nd grade materials (though the samples online weren’t by any means comprehensive) and so he asked their curriculum folks about it and they said they do skip counting and arrays in grade 2 and then are deeply involved in multiplication in grade 3.

What attracts me to their material is that they break down all the steps of solving a problem to minute levels and practice individual concepts to mastery. There’s no lame spiraling where “if you don’t get a concept now, don’t worry, we’ll cover it again later” nonsense. They teach for mastery and they seem to succeed at it pretty well based on the studies and evidence they have. One study is under peer review right now and sounds like when it’s released will show a big improvement over whatever it was compared to (though I wouldn’t be as impressed if it’s being contrasted to TERC because then the improvement would be a given – That will lend more credibility to it on a scientific basis, but they do have a number of testimonials on their site and video stories from teachers. Funny enough, this one caught my eye…

“JUMP math is pedagogically sound and ensures success in all students. I finally see the ‘aha’ when students to this program. They find it motivating, beg to do more math and are challenged without being frustrated. [It] is the antithesis of ‘fuzzy math’.”
– Vancouver Teacher

All I needed was that last sentence.

So here’s another interesting thing. The company is a charity. The founder was a mathematician, playwright, and author, and he designed this program after tutoring children in math and being frustrated with the way math was being taught. His belief (and mine as well) is that everyone can learn math if it’s taught properly. JUMP was designed as a remedial product to break down math to each individual fragment of a problem to help students who were struggling understand why each tiny step worked. In the process, he created a program that appears to really level the playing field between the top and bottom levels of math ability and bring them all up to speed on doing math well. He authored the book, “The Myth of Ability.”

This sounds very promising. They are a charity instead of a for-profit publisher so materials are quite cheap and hopefully there is no “must publish something new” cycle of insanity. There isn’t a textbook for students, but just workbooks they take home and they run about $11 and if you purchase 20 or more, you get a 40% discount. That’s dirt cheap. The teacher guide is either a free pdf book to download, or can be purchased for about $80 or 90 if you want a hard copy.

The workbooks, which you can see samples from online, are very visual, which is another parallel to Singapore math ( I’ve been a fan of Singapore math for a long time and for good reason. They have the top results in the world from their Primary Math series, and their workbooks are fun and engaging. They also arguably have the world’s best word problems for children to wrestle with. I don’t know what JUMP math has in that area at this point.

They don’t have a Kindergarten series because this was designed as a remediation program so a kindergarten series was not needed, but they are considering a senior Kindergarten program. I’d be in favor of dropping Kindergarten to save money and then using a program like this to start students out with a good foundation in grade 1, and let parents teach children what they need to know for Kindergarten.

If you are with a school and want to get a set of all their books, you can order a special sample pack of 16 books for just $100 (2 workbooks for each grade 1-8). See here for details:

They do have books available for sale on Amazon to check it out but just realize they are in Canada and use the metric system and haven’t converted to U.S. coins and measures, though that’s easily supplemented.

This appears to have the possibility of being a breakthrough program. They are working on expanding their grade offerings though at the moment they are working on an adult remediation program to help adults that are looking to return to school but need some extra help in math. Then they will probably be doing grades 9-12 as high school teachers are asking for those resources to round out the entire curriculum.

With these kinds of prices (under $14 for the 2 student workbooks for the year after discounts for a classroom) and a free pdf teacher’s guide, I think a lot of schools would be interested in checking this out. When they receive funding they are planning to do a U.S. edition that matches the Common Core standards, though if their current program was sufficiently close, we should definitely be investigating it for what areas it would need supplementation and then pilot it in a couple areas. They do have training available to use the program and they are looking at doing it online for teachers so that’s another cost saving benefit. All in all, I’m impressed with what I see so far and will definitely be interested in further news out of this organization.

Last week on the Rod Arquette show, a Judy Park (??? not sure of last name) from the state office of education spoke with Rod concerning the release of the latest PISA scores ( which help show math, reading, and science ability rankings from around the world. The United States was down the list a ways for math and was behind such powerhouse nations as Liechtenstein, Estonia, Iceland, Slovenia, Poland, and Luxembourg (aside from the obvious ones like China and Singapore). We did pull ahead of Qatar and Tunisia thankfully. 🙂 Among the claims made by Judy were the following:

-Utah is above national average in math benchmarking as evidenced by NAEP (National Assessment of Educational Progress) scores
-The new Common Core standards are something to get excited about and will help the states do better in math

The first one has already been dis-proven a couple years back when Dr. David Wright at BYU showed that since Utah has an over 80% white population, it artificially raises our state average when compared to states that have a much higher minority percentage (minorities tend to score less on standardized tests). He was able to show that when comparing whites to whites, Utah actually ranked 37th and 39th at 4th and 8th grade respectively. This was based on 2005 NAEP data and I would assume nothing has changed since then. This is comparing apples to apples. Utah is NOT above national average.

As for NAEP’s qualifications as a test, several years ago Dr. John Hoven compared U.S. NAEP test questions to those of the world class math leaders. Here are two of his main points from his article (

  • “My point is simple: There is a chasm of difference in expectations between NAEP and the problems used by world-class mathematics leaders. We expect too little from our children, and by lowering our expectations we lower their incentive to achieve.”
  • “NAEP classifies its problems as “easy,” “medium,” or “hard.” I benchmarked the “hard” 8th grade problems, examining NAEP’s highest level of expectation for 8th grade math. Most of these “hard” 8th grade problems are at the level of Singapore’s grade 5 – or lower.”

Now for Judy’s second point on the Common Core standards.

Just a few short years ago, a number of people went through an incredibly difficult process to get the state of Utah to raise it’s math standards. Nobody at the state office or state school board wanted to change from standards that were rated by the Fordham Foundation at a ‘D’ level, and the US Chamber of Commerce rated them a ‘C’.  The state board also rejected the notion of just adopting California’s ‘A’ rated standards on the basis that this is Utah and we are somehow unique and different than California so we need our own math standards. No matter that that would have saved us a lot of time and money…

After a lot of work by a lot of legislators, educators, and citizens, Utah capitulated and went through the rewrite process. Upon review, they garnered an ‘A-‘ from the Fordham Foundation. They were pretty good, though still subpar to countries like Singapore that have fewer standards so they can spend more time mastering those concepts. The trite phrase “a mile wide and an inch deep” was referred to repeatedly by educators and board members in this state, but nobody would admit it was indicative of Utah’s current standards that weighed in around 60-70 topics per grade level giving teachers only 2-3 days to cover a topic.  In Singapore, they have an average of 9 days to delve into a topic, master it, and then build on it without having to repeat concepts over and over. This chart illustrates time spent per standard. The area of the rectangles roughly match.

Utah Standards


So now the Obama administration sets in motion the Common Core standards. States were offered bribe money to “Race to the Top” and be one of the first to adopt. Most states jumped right on the bandwagon including Utah which somehow overcame the difficulty of their prior position that Utah is unique and doesn’t need or want something developed by someone out of our state. Some mathematicians look at the standards and say they’re pretty good. Others are not so excited. What’s the difference? One see the path of the agenda, the other sees a carrot (bribe).

“How can the State Boards of Education make decisions when they haven’t even read the standards? Many state’s Board Members had never been initiated into what was in these documents.  What were the policy issues coming out of these documents and whether these analyses truly were in a sense legitimate academic analysis…These are very serious issues about what self- government means at the state and local government level.”–Sandra Stotsky,  professor in the Department of Education Reform at the University of Arkansas, and holds the 21st Century Chair in Teacher Quality.

The real danger comes in this way. National standards lead to national tests to ensure the standards are followed. Those are followed by a national curriculum to ensure students are ready for the tests. That is followed by tracking teachers and giving them an incentive to have their students progress well. That means teachers and students are tracked in a national database. That opens the door to the government indoctrinating in the classroom through test questions, curriculum, and teacher merit pay based on how well their students test ACCORDING TO TESTS WRITTEN BY THE GOVERNMENT. This is extraordinarily dangerous to our freedom and future. Teachers teach to the test. If the assessments are geared toward social justice, constructivist style questions, it will further the deliberate dumbing down of American students in preparation for a government mandated future.

Here’s the kicker. Someone recently posted a quote on Save Alpine School District .com from John Goodlad’s book Developing Democratic Character in the Young (pp. 161) as saying “the current demand for unprecedented levels of academic achievement is getting in the way of [our] humanistic purposes.”

This is all part of the plan of the progressive educators like Goodlad and Noddings. They don’t care about academic performance. Their emphasis is on creating democratic citizens that are fully enculturated into a social and political democracy. You may think schooling is non-partisan and non-political, but in this same book’s preface you will find Goodlad in disagreement stating, “Schooling is a practical, political affair.” They know their purpose and it is not academic excellence. It is the subjugation of a nation by turning them into obedient little automatons. This is why Goodlad had Marxist revolutionary Bill Ayers speak as the keynote speaker in Goodlad’s NNER conference in October 2010.

How important is math to America? We aren’t competing against China anymore, we’re competing against the top students in China. Until Utah’s education system and legislature take this seriously, we’ll continue to slide all the while touting how great we are doing for the amount of money we’re spending. I’ve got news for you Utah, plenty of other countries spend less money than Utah and outperform us. Why? Real standards and real curriculum. It’s time to pilot Singapore math in Utah and replicate the success of Benchmark Charter School in Arizona where 94% of all students say math is their favorite class and they prove it by being the top scoring school in the state.

I came across this web page recently while doing some research on John Dewey and John Goodlad. Both men are cut from the same progressive, humanist cloth, and this page tells the incredible tale of how various education and government organizations are intimately tied together.  If you do a search for John Goodlad’s name, you will discover that in 1968 he was involved in moving forward a plan for national curriculum centers. In the 1980’s, Mr. Goodlad would be hired by BYU to help them form the Public School Partnership that created the framework for the 5 surrounding school districts to be heavily influenced by the philosophies Goodlad and his cohorts espoused…one of which is constructivism.

Confused? Not if you like reform math. Found on the TERC website comes this nonsense:

“In reality, no one can teach mathematics. Effective teachers are those who can stimulate students to learn mathematics. Educational research offers compelling evidence that students learn mathematics well only when they construct their own mathematical understanding (MSEB and National Research Council 1989, 58).”

Although it is tragic when I get stories like this expressing the frustration of a parent over how constructivism has destroyed a child’s love for math, it is not unexpected.  I have received many of these over the years but I believe this is a good time for middle and upper math constructivism to get the boot.

“Mr. [name removed]–I know that my son [name] has already spoken to you regarding
his grade.  Now I am coming to you as a parent.  Perhaps if you were able to
show us why he lost so many points on the “student taught” assignment or if
you had given him some way to make up for the lost points…I am so
frustrated as a parent.  I watched him put in many hours on your class.  I
watched as he and my husband had to go online to find out how to do things
because my son hadn’t been TAUGHT how to do them and had no textbook.  I
know the frustration that both my husband (a PhD and also an educator like
yourself) and my son felt over the lack of basic instruction that occurred
in the classroom.  I watched as my own father, also a PhD and a math
teacher, struggled to help [son] with assignments.  His assessment was
always that [son] has not been TAUGHT basic fundamentals.  I suppose that
you have to give him the grade that his points equal, but I assure you that
this is not over.  I am tired of watching the math program at Lone Peak High School, and all of Alpine
School District, be a joke.  And I guess you have lit a fire in me that has
long been waiting for a match.  I am sure we will meet as some future point.
A crusade has begun…”

Donna C.

Follow-up email about how this teacher “teaches”.

“My understanding is that he gives the assignment, without instruction and without a textbook to give any guidance.  Then the student is supposed to “figure it out”….the intention is to “go over it in class” but my son says they usually don’t have time.  What are they doing with their time?  I have no idea. “