Several years ago I was involved in what has been called “The Math Wars”. Alpine School District had quit teaching the times tables, long division, and some other basic math skills, to children under the promise that a constructivist (ie. children need to construct their own knowledge) approach to math would deepen their skills. This was an abominable failure. Even at BYU where 2 math education professors got permission (by someone over the math department’s dead body) to teach a class of honors calculus to freshmen with this method. The result was a disaster. Honors calculus students measuring Dixie Cups with rulers while regular students were learning how to integrate. Predictably to everyone but those 2 professors teaching the constructivist class, their students scored below all 17 sections of non-honors calculus on the final exam. Their final defeat? Blame it on the test writer who had been creating the same test from the same objectives for years.

Unfortunately, with adoption of Common Core, the state of Utah took a bad idea that parents in Alpine School District hated, and decided to spread the love around the state. As parents slowly wake up to the horrors of constructivist math and wonder what happened to their child’s love of math, there will begin a new revolt that will bring tens of thousands of angry parents raining down on the heads of the state leadership.

Don’t believe me? Consider how upset a parent is when their child goes off to college with straight A’s in math and winds up in remedial math. At last look, UVU has a 70% remediation rate for incoming freshmen in math. In fact, it’s so bad, they don’t just have remedial math classes at UVU, they have a remedial math DEPARTMENT. SLCC has roughly the same percentage of remediation. That’s a pathetic waste of taxpayer dollars that when tens of thousands of students arrive they can’t do high school math and need remediation, and before someone suggests it’s because young people are arriving after serving LDS missions and have simply forgotten how to do math, that’s been examined and it’s a trivial reduction in the percentage.

Let me illustrate with a video. I recently sat down with an anonymous but very involved person in the Utah education arena, and reviewed a few books. Interactive math, Saxon math, and the Utah State Office of Education’s (USOE) own home grown math book. Watch the horror show demonstrating these textbooks and then read below.

http://youtu.be/FdgGqVq-akg

Here’s what the state shows on their RIMS database for schools and districts to pick textbooks from. I’ll start with Saxon.

Saxon math-Recommended **Limited**

“Evaluation: Textbook review for Saxon Algebra I. Overall, the program matches the Utah Core Standards for Algebra 57.75%. The following is a breakdown of the evaluation by individual Utah Core Standards for Algebra I: …(removed specific line items for space…read it on the site)

This program does not develop concepts for deep understanding. It provides few examples and the flow of the program is missing, very disjointed.“

If you didn’t watch the video, you’re missing out. Saxon is full of examples while the other programs have NONE.

This isn’t the first time I’ve witnessed a hit job on Saxon math (link 2). Saxon was developed by an Air Force Engineer turned educator and a few years ago when I evaluated the top 10 scoring schools in Utah for math on standardized exams, 7 of the 10 schools were using Saxon. It’s a great program that builds skills and depth of understanding. It’s the type of math most of us grew up on and that we can look in the textbook and remember how to do a problem and help our children. In short, it shows how to do a problem, explains the concept, and gives students an opportunity to practice what they learned so they can obtain mastery over the knowledge.

**Contrasted with…**

Interactive Math-Recommended **Primary**

“Evaluation:

This non-traditional text approaches the study of mathematics through student-centered exploration and meaningful tasks.Teachers would begin the lesson by presenting the task for the day, and students and teachers would work on the tasks together as they develop their mathematical understanding of the topics.The format of this text encourages active learning of mathematics.Each unit in this text has a central problem or theme and focuses on several branches of mathematics including algebra, geometry, probability, graphing, statistics, and trigonometry using an integrated approach.

This text covers more than 80% of the 2012 Utah State Core Standards for Secondary I or Secondary I Honors.

Lessons consist of single-page individual or group tasks without traditional mathematical instruction or explanations.Mathematics is learned through the culture and practice that is developed within the classroom as students work on the various tasks.

Although topics are not easily~recognized by lesson titles, this text includes an index of mathematical ideas which makes it easier to find particular ideas. Problem sets are minimal but build depth of understanding. A nice glossary is included at the end of the text.”

Remember from the video above, Interactive math has declared the most important purpose of their book is to make math fun!!!

There is no line-by-line evaluation of the shortcomings of Interactive Math as there is with Saxon. It’s pathetically obvious from looking through the book that it’s devoid of content and yet the reviewer, obviously a disciple of religious constructivism, announces this text will produce “depth of understanding” from minimal problem sets. This comic is worth 1,000 words.

Finally we come to the third book, the USOE’s own creation which is similar to Interactive Math and it’s constructivist approach.

Open Education Math – The Mathematics Vision Project- Recommended **Primary**

This “textbook,” *and I use that term very loosely* since there is no instruction or examples, was also given a rating of “Recommended Primary” by the USOE. *Convenient that you can rate your own product*… It was developed by 5 school teachers, who as far as I know have no prior experience in writing textbooks, at least 3 of which are known constructivists, 2 from Alpine School District.

“Evaluation:The OER Secondary I textbook is designed to be an online textbook that may or may not be printed. The textboook will allow for future updates and improvements as well as teacher customization. The first edition of this online text addresses the first third of the 2012 Utah Core Standards for Secondary I Mathematics. The content of the text is accurate andrepresents the current research in mathematics. Each lesson begins with a task to help students develop an understanding of the core concepts to be learned. Teachers may need professional development to teach using tasks. There are extensive instructions and teacher notes to guide the teacher to teach each task. Some of the tasks have a lot of reading which may be challenging for ESL students. ~ The homework has three sections. The Ready section has problems that will help the student for upcoming concepts. The Set section contains practice problems for what is being developed in the current lesson. The Go section has problems that help students review concepts learned previously. The homework sets are not long and tedious so students can focus on what is being taught. ~ The Getting Ready Unit reviews ideas from previous courses that begin to connect the content that will be taught in Secondary I. This section may help during the transition to the~new core. ~ Each lesson begins with a task to help students develop an understanding of the core concepts to be learned. Teachers may need professional development to teach using tasks. There are extensive instructions to guide the teacher to teach each task. Many of the tasks have a lot of reading which may be challenging for ESL students. There are no materials at this time to address special educaiton students and ESL students. ~There is an extensive section for parents that includes online resources such as the Kahn Academy videos and worked out examples of procedural problems. ~ ~This book would require that teachers allow time for students to think and have a lot of discussion in the classroom.“

Wait a minute…this book relies on the Khan Academy videos to teach procedures? That’s convenient. Lets write a textbook and say, “we just want depth of learning, you go somewhere else to learn HOW to do math.”

Require teachers to allow time for a lot of discussion? What if those students actually want to learn math and not have their peers discussing what they ate for lunch?

Now the big lie. Current research says there are NO studies that support constructivism. Dr. Jim Milgram, Stanford math professor who has been and may still currently be the only educator invited to serve on NASA’s advisory board, noted that if constructivist math were a success, NASA would be looking for students that went through that pedagogy. The fact is, BYU’s math education professors’ failure is typical of constructivist programs.

There is only one conclusion. Following the USOE’s math recommendations will kill STEM (science, technology, engineering, and math) initiatives. All you business leaders and technology oriented professionals supporting Common Core are going to be in for a rude awakening as this machine destroys love of math, destroys math skills, and destroys any edge Utah has for technology…unless…

Utah must drop Common Core and restore local control. The USOE is hell-bent on constructivism and unless there is a major personnel change at the USOE, it’s going to rest on the shoulders of parents to take their children’s education into their own hands (literally), and leave those who can’t get the support at home to drown in fuzzy math.

In 2006 or so, Brett Moulding, state curriculum director at the USOE invited me to his office to ask a simple question. “Oak, you’re a parent who is very involved in your children’s education. How can we replicate that to other parents?”

“Easy,” I replied. “Just implement Investigations math statewide and you’ll have all the parental involvement you can handle.”

True story. I just had no idea they were going to take my suggestion literally. Parents, you may seriously want to consider The Great Escape…Homeschooling.

Wow Oak, That video is simply devastating!

Great job!

Here is a Blog Post I recently wrote to give further depth to the Math Issue: http://jennyhatch.com/2013/04/30/uncommon-lore-the-original-saxon-math-curriculum-math-a-firm-foundation-to-build-a-homeschool-on/

And this past week I have been chatting with a Common Core Math Curriculum writer in the Comment Section of a site called Math Recap in a post dedicated to testing common core for Math Specialists: http://www.mathrecap.com/skip-fennell-math-specialists-get-ready-now-common-core-assessments-are-coming/

The conversation has been illuminating, to say the least.

Jenny Hatch

http://WWW.JennyHatch.com

Cedar City Mom

The problem I see with the article title and conclusion is this:

There is a huge difference between encouraging science/technology/math/engineering and what is known as STEM.

The difference is that encouragement can be individual, flexible, tailored, and mostly free, whereas STEM is an increasingly government-funded and -mandated program or focus. See where the funding comes from at http://www.stemreports.com/wp-content/uploads/2012/04/Screen-shot-2012-04-29-at-9.52.56-AM.png

It’s the difference between being on board with Cap and Trade versus being careful with my personal resources (i.e. not letting the car idle very long, keeping the windows closed on days the furnace is on, etc.)

Furthermore, I’m increasingly convinced that our main focus should be something other than science fields. I think our situation is currently similar to the one in John Adam’s time, when he said, “The science of government it is my duty to study, more than all other sciences; the arts of legislation and administration and negotiation ought to take the place of, indeed exclude, in a manner, all other arts. I must study politics and war, that our sons may have liberty to study mathematics and philosophy. Our sons ought to study mathematics and philosophy, geography, natural history and naval architecture, navigation, commerce and agriculture in order to give their children a right to study painting, poetry, music, architecture, statuary, tapestry and porcelain.”

As a nation, we’ve lost our knowledge of correct government, legislation, and administration, as well as natural rights and the source it’s all based on. The latter is where our focus should start.

This book looks to be the one used in the non-college-bound sequence, for those who are not actively pursuing the harder academic road in math and science to get into college. Is that how Alpine uses it now?

The critic says this is a standard Common Core book introduction — but if the book has been used in Alpine District for a year, it’s too old to have a Common Core basis.

What’s the reality here? What is shown suggests a great lack of knowledge about what goes on in actual classrooms.

Ed, Interactive Math has been used in Alpine School District since about 2000. This textbook has been on the state’s primary approved list for probably that long. I campaigned Brenda Hales at the USOE and Patti Harrington the former State Superintendent to remove Investigations, Connected, and Interactive math programs from their primary approved list because they are so weak. They removed Investigations and Connected math back in 2007 or 2008, but never did remove Interactive. This was actually the first time I saw an Interactive math textbook. In the past, they were individual magazine size booklets that would span the year. It is my belief that Alpine still uses Interactive math, and is emboldened by the state’s constructivist approach so they will continue to do so and damage the future for tens of thousands of students.

Oh, and no, this is not the non-college bound sequence. It’s “approved primary” for the regular Common Core sequence. Further, it shouldn’t be used for ANY students.

Good point Rhonda. My article was addressed primarily to the Utah business community and legislators who view STEM as the encouragement of science, tech, engineering, and math, and aren’t even aware of a national agenda. I hope they will wake up and see Common Core for what it is, and also quit supporting the USOE’s implementation of it which is going to hurt the Utah economy if not corrected soon.

Our clinics Cognitive Tutors, utilize Saxton Math EXCLUSIVELY when providing private services for kids in public schools who have fallen through the cracks via USOE’s non validated math instruction methods. Common Core has resulted in tripling our staff of in home tutors the past 8 months. As proud as we are for getting it right, we would prefer that USOE did their tax payer funded jobs.

Very sad news Oak.

funny, I’ve seen way more students need tutoring with Saxon than I have with other programs

I am a homeschooler and that was not our experience. Our child who used Saxon tested out of most of his math courses at a rigorous college. He is now a CPA.

You should check out the thriving tutoring and supplement business in Alpine School District, and it appears at Dr. Thompson’s clinic above. Saxon is used to remediate the students who have suffered through constructivist curriculum and teachers.

After teaching it this year, I’d have to say I can NOT recommend Saxon math. Love that it reviews so often, and they do have very good examples. But in doing that they have sacrificed deep understanding. I’d actually be fine with Saxon if they put lessons in an order that made more sense instead of jumping all over the place. It looked like a good curriculum until I actually taught it. I suppose Saxon could also work okay if I had 2 hours every day for math. But we get 50 minutes, not 2 hours.

I also taught the state designed book this year for Secondary One (Mathematics Vision Project). We start with a more exploratory task and then they get the procedures and examples as part of their notes. It’s not simply “story problems” but something that requires more depth. And there is a LOT of math in those problems that you are dismissing. Things that we do with the students and have them write out. It’s not just a bunch of story fluff. And I do supplement with other things. If they need something more traditional for reference I actually have old Saxon books in the room they they will occasionally look at :) Saxon is good for that. Good for clear examples. Not good for retention or deeper understanding of concepts.

I love the changes I’ve seen in the standards to Common Core. I also really like that Utah has adopted an integrated path. Instead of just one year of algebra, one year geometry, etc., we get to see better how they all tie together.

Sounds like you should visit a charter school where they use Saxon Misty. That way you can see how they teach Saxon, achieve deeper understanding and retention, and do it in less than 1 hour a day.

The USOE book is a joke. There are no examples, there’s no practice problems, there’s no way for parents to work with their children by reviewing a mathematical concept,…it’s just not a textbook. It’s a problem set, and weak at that. It’s also got indoctrination in it.

https://www.utahnsagainstcommoncore.com/reigniting-the-math-wars-over-the-death-of-calculus/

Interesting video I found that compares math instruction around the world.

http://www.youtube.com/watch?v=CHoXRvGTtAQ

The “Japan uses constructivism” argument has been debunked Misty.

http://www.cs.nyu.edu/faculty/siegel/siegel.pdf

There are no studies that support constructivism as a pedagogy.

http://www.oaknorton.com/mathupdates/20080903.cfm

For a non-educator with an extensive education, this material remains difficult to understand. However, it seems that constructivist math presents a story problem and requires that the student guess what it is he is supposed to be learning. The individual or collective then must guess how to solve the problem.

As they have not received any instruction and have not seen any examples, students must work with each other to see if they can collectively come up with a solution (i.e. reinvent the wheel over and over again). I have a basic problem with the collectivist approach to anything. I have no problem with helping children learn to critically think; I do have a problem with teaching children what to think. I also have a problem with spending the whole school day teaching them to think, but neglecting to really teach the fundamentals.

In addition, we know that children who grow up in a strong, nurturing core family have life skills far in excess of those who are left to their own devices through abuse, neglect or abandonment. Constructivist math seems to me to be another way to abuse, neglect or abandon children to their own devices when they need to learn important principles that will help them get a good job and be successful in life.

Another point is that homeschooling (or private school) might be the solution short-term, but when it comes to high school graduation or taking the SAT or ACT, students will be tested in these examinations based on Common Core content. If this content is not included in homeschooling or private school, for the vast majority, your children will not score well on these tests, they may be barred from high school graduation or from attending college and restricted for life to lower income vocations.

Is this what we want for our children?

I home-schooled my oldest daughter since kindergarten. In 9th grade, we used Euclid’s Elements, a book over 2000 years old, for geometry class. We used traditional college algebra and trigonometry textbooks for her other classes. She has a 4.0 in her first year in college and will be taking Calculus and Chemistry her sophomore year after acing her Precalculus class. When the Precal class got one of their tests back late in the semester, after comparing grades another student complained, “Home school students have all the advantages!”

Is that feeling of possessing an inferior high school education what you want for your children in public school?