All Students Can Learn Mathematics At a High Level

Our country has a problem with math. Too many people say they are no good at it, were never any good at it, and never will be any good at it. One study, done by Marilyn Burns of Math Solutions, suggested that about 2/3 of American adults have some kind of math phobia. (Math: An American Phobia, Math Solutions, 1998). I’ve seen this phenomenon first hand. When I tell someone I am the Elementary Mathematics Specialist for the Utah State Office of Education I get mostly negative responses. They range from, “I’m sorry…” to “Oh, I’ve never been good at math.”

There is also a wide spread belief that the ability to learn math is somehow innate. Some people are math people, others are not. The result is many students don’t learn mathematics because they don’t believe they can, because their parents don’t believe they can, and because their teachers don’t believe they can. Educational research is replete with studies on how teacher attitudes effect student achievement.

It is far past time to change these attitudes and beliefs. Part of any vision for mathematics teaching and learning in Utah must include the fact that all students can learn mathematics at a high level. That assertion is not wishful thinking nor empty rhetoric. It is based on research (see, for example, Adding it Up: Helping Children Learn Mathematics, National Research Council, 2001). It is attainable if the conditions, structures, and policies in mathematics education necessary for success exist.

This blog will be focused on those conditions, structures, and policies for the remainder of this school year. These ideas are taken from Principles to Actions: Ensuring Mathematical Success for All published by the National Council of Teachers of Mathematics (NCTM) in 2014. Readers are encouraged to obtain a copy of the book from NCTM and to participate in the Principles to Actions course in the Utah Professional Learning Series. The next course begins in January. Registration is free and will be available soon at The course is only open to Utah educators.

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Revised Utah Core State Standards in Elementary Mathematics

One more announcement before the big first post of the New Era of Elementary Mathematics Newsletter Blogging Renaissance:

The Utah Core State Standards in Elementary Mathematics have been under a revision process for the last year. They have now been released for a 90-day review. Go to for more information and to give your feedback. There will be five public review meetings held in the next two months, as follows:

Core Standards Review Public Meetings

October 7, 2015
Utah State Office of Education
Board Room
250 East 500 South
Salt Lake City, Utah 84114
Time: 6:30 p.m. – 7:30 p.m.

October 22, 2015
The Grandview Learning Center
1591 Jordan Avenue
Provo, Utah 84604
Time: 6:30 p.m. – 8 p.m.

November 12, 2015
Iron County School District
District Office Board Room
2077 West Royal Hunt Drive
Cedar City, Utah 84720
Time: 6:30 p.m. – 7:30 p.m.

November 19, 2015
Uintah School District
District Office Moon Room
635 West 200 South
Vernal, Utah 84078
Time: 6:30 p.m. – 7:30 p.m.

December 2, 2015
Box Elder School District
District Board Room
960 South Main
Brigham City, Utah 84302
Time: 6:30 p.m. – 8 p.m.

I hope you can make it to one of the meetings!

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Apology and Announcement

Apology: To those of you who followed this blog in the past: my abject and sincere apology. I have only posted once in the last 18 months. I got many comments from teachers in my travels around the state that they read the blog, they enjoyed the blog, and they learned from the blog. And then I disappeared. My duties at the office grew exponentially a year ago in August and I had to drop something. So, the blog went away. I am sorry. I missed writing it.

Announcement: I am restarting the blog! As of today. I am going to write shorter blog entries once a week instead of the long drawn out essays I used to write. I hope you will enjoy them and learn from them and even comment back to me once in a while.

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USOE Professional Learning Series

PLS+GraphicMany of you will (may?) remember that, at the end of the Utah Standards Academy last year we said the Core/Standards Academies were all over, done, never to appear again. While that is true, at least in terms of the four day experience in different locations around the state, we at the USOE have been hard at work designing what is a unique professional learning system for Utah.  Here is what it says on the Professional Learning Series page on our website:

“For 2015, we are transitioning to an online interface via Utah Education Network (UEN) for opportunities for teachers to engage in professional learning.  Interactive webinars, self-guided modules, and teacher-facilitated courses will be made available starting in May 2015. The 2015 Professional Learning Series will provide high quality instruction in English Language Arts, Mathematics, Science, Social Studies, Physical Education, World Languages, and Fine Arts throughout the year to complement and support the integration of the Utah Core Standards and to ensure that all Utah students are college and career ready.  Utah State Office of Education (USOE) and/or Southern Utah University (SUU) credit will be available for all formats.

The webinars, courses, and modules could be done independently, in professional learning communities, in district professional development sessions, and other professional learning settings.  The possibilities are endless.”

All the courses available for the summer semester are listed in a course catalog you can download here: .

Let me give you a heads-up about the elementary mathematics courses. They were developed by teachers who understand the Utah State Core Standards thoroughly, who are master teachers in their own right and are acknowledged as such in their districts or charter schools, and who have experience designing and conducting professional learning for elementary teachers. All of the courses are on-line. They are innovative in their design and are varied in their approach. Just to give you a flavor of what we are offering, here are the course titles:

Principles to Actions for teachers in grades K-12

Laying a Rigorous Foundation in K-1 Mathematics 

Extreme Math Makeover for 2nd Grade r

Laying the Groundwork for Fractions, Multiplication, and Division in 3rd Grade 

You Can Read, Write, and Speak Math (Grades 3-5) 

Using Technology to Teach in Math (Grades 3-5) 

Teaching Kids How to Think (Grades 3-5)

Bringing Math to Life Through Science (Grades 4-6) 

Understanding and Implementing the 5th Grade Mathematics Standards 

6th Grade Fractions: A Rational Approach 

What and How Do I Teach Math: Components of Math Lessons to Enhance Understanding (Grades K-6)

See the course catalog for more details and sign up for a course today!

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Guest Post – Follow-Up on Homework in Elementary Schools

After I published the post called “What About Homework” I got an e-mail from a friend who is a principal in Washington County in southeastern Utah. With his permission, I am posting his e-mail here, with emphasis added where needed.

“Very interesting that you should bring up the homework controversy as I read Visible Learning for Teachers by John Hattie (maybe you’re familiar with his work?) and he does list homework in his compilation of research.  If you’ve read him, you’ll know that his studies include an estimated 240 million students, but in order to reach “effect sizes” he uses over 161 studies of 100,000 students or more (so his results are quite believable).  So… an “effect size” of 0.40 is considered “worthwhile” (whether it’s an intervention or a program, etc.) and anything above 0.40 is even more worthwhile.  It’s a very interesting read to see all of our practices and how “effective” his analysis of research shows they are.  It’s been fascinating, actually.

Ok… that being said… you’d be interested to know how homework rates?  In high school the effect size is 0.50…. so it’s worthwhile, actually pretty good.  But in elementary…not so good.  The effect size is -0.08…. That’s negative 8 hundredths!   That means it does more harm than even close to being good.  That made me wonder.  We haven’t changed much at our school, but we’ve discussed this research including the homework. Homework Monster

I just thought I’d pass that along.

Kelly Mitchell
Principal, Washington Elementary”

Thanks, Kelly. That ought to give us something to think about.

Homework Monster downloaded from
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What About Homework?

Back when I was a youngster, lo, these many years ago, homework was the bane of my existence. In fact, I tell people, truthfully, that I only did homework for two classes in high school – Trigonometry and Medieval Literature. That I graduated at all is a miracle. That I got college scholarships is even more of a mystery. Now I believe that homework itself is a mystery. At least in elementary school.

How much homework is too much? Should we send homework at all? What kind of work should be homework? Should there be policies regarding homework in elementary schools? See what I mean? Mysteries. When I talked with the LEA (Local Education Agency – that is fancy talk for school districts and charter schools) mathematics supervisors a few months ago it became clear that most LEAs haven’t thought a lot about homework policies or practices for quite a while.

The research on homework is an extremely mixed bag. In the Winter 2012 edition of the Harvard Graduate School of Education magazine Ed. the following quote appears, “As Cathy Vatterott, the author of Rethinking Homework, points out, ‘Homework has generated enough research so that a study can be found to support almost any position, as long as conflicting studies are ignored.’ ”

The same article quotes Alfie Kohn, the author of The Homework Myth, as saying “The fact that there isn’t anything close to unanimity among experts belies the widespread assumption that homework helps.” Mr. Kohn believes strongly that schools should never assign homework.

However, in the same article, Howard Gardner, a professor in the Harvard Graduate School of Education says, ““America and Americans lurch between too little homework in many of our schools to an excess of homework in our most competitive environments — Li’l Abner vs. Tiger Mother,” he says. “Neither approach makes sense. Homework should build on what happens in class, consolidating skills and helping students to answer new questions.”

Educational Leadership, the journal of the Association for Supervision and Curriculum Development, notes the following recommendations for homework:

Research provides strong evidence that, when used appropriately, homework benefits student achievement. To make sure that homework is appropriate, teachers and principals should follow these guidelines:

  • Assign purposeful homework. Legitimate purposes for homework include practicing a skill or process that students can do independently but not fluently, elaborating on information that has been addressed in class to deepen students’ knowledge, and providing opportunities for students to explore topics of their own interest. Teachers should never assign homework that introduces a new skill or asks students to practice concepts they still find difficult to understand.
  • Design homework to maximize the chances that students will complete it. For example, ensure that homework is at the appropriate level of difficulty. Students should be able to complete homework assignments independently with relatively high success rates, but they should still find the assignments challenging enough to be interesting.
  • Involve parents in appropriate ways (for example, as a sounding board to help students summarize what they learned from the homework) without requiring parents to act as teachers or to police students’ homework completion. If parents feel they must teach their children a concept the homework, at least in the younger grades, is probably not appropriate.
  • Carefully monitor the amount of homework assigned so that it is appropriate to students’ age levels and does not take too much time away from other home activities. The authors note that many research studies recommend the “10 minutes times the grade” rule. In other words, in first grade all homework combined should not take more than 10 minutes per night. In second grade the time allowed could raise to 20 minutes, and so on. However, the studies also note that positive effects of homework in junior high top out at 90 minutes. More time spent on homework over that time limit actually had a negative effect on achievement. In high school the limit seems to be 1 1/2 to 2 hours a night, depending on the study.

The point here is that elementary teachers should be very careful with what they assign as homework and with how much homework they assign. Parents should be made aware of the purpose of the homework assignments, the length of time the student should spend, and what the expectations are. Parents should feel free to call a halt to homework assignments if their child is getting frustrated, spending an inordinate amount of time on homework, or obviously doesn’t understand what to do. Sending a note or an e-mail to the teacher is entirely appropriate in those cases and teachers should respond positively.

As well, there are many technological solutions to help solve the homework mystery. In Cache School District, for example, many elementary teachers use an app called Educreations on their iPads to record lessons. They then post them either on the Educreations website or on their teacher blogs. I saw an outstanding example of that approach last October while visiting McKenzie Sorensen’s  fifth grade class at Summit Elementary in Smithfield. Here is my description of the event:

Ms. Sorensen was using her iPad and Educreations to teach long division with decimals. Her iPad  was connected to the projector and she was not only recording her voice but was using the iPad as a kind of smart board. She was writing on the iPad as she taught. She also recorded student comments, their answers to questions, and so on. Mr. Pugmire, the principal, was standing right next to me and told me she would post that lesson on her blog that night so students could refer back to it, so that those who missed class could see and hear what happened, and so that parents could understand what their students were doing and help them with their homework. It was a good thing, too, because she was teaching division with decimals in a mathematically correct and conceptual way, very different from how most of us were taught. Instead of just telling the students to move the decimal point she emphasized that they were changing the place value of the digits in both the divisor and the dividend by multiplying them by a power of ten. She stressed that they could have done the problem without changing the place value, but doing so made the problem easier to do because they didn’t have to worry about keeping track of the decimal point.  They were also able to preserve place value, which doesn’t often happen in long division.

Other teachers in Cache record short messages for parents and/or students about what they taught that day and how they taught it. Such messages can help parents understand the strategies and teaching methods they use to help students understand concepts.

Other teachers I have talked to record a short video on their smart phone at the end of the day and explain the homework for that night. They post that on their website and parents know to check for it. Others simply send an e-mail message. Others direct the parents to websites such as LearnZillion that have short videos made by master teachers explaining mathematical concepts. Jordan District, for example, has linked both the Utah Core Standards and their textbook to LearnZillion videos. Many textbook publishers also have websites for parents that can help. Contact your LEA to see if their adopted textbook has such a site.

So, to recap. The research isn’t clear about whether homework in the elementary grades has any correlation to student achievement. One researcher, Duke University Professor Harris Cooper, found that for elementary school students, “the average correlation between time spent on homework and achievement … hovered around zero.” So some elementary schools are eliminating homework other than nightly reading and citing research to do so. Still, it is hard in an era of “raise the bar” academic standards to think about forgoing homework altogether. Those elementary schools that do give homework should think very carefully about the recommendations given above. It is hard to justify homework outside of the given recommendations.

By the way, I am not endorsing Educreations. There are other apps like Doceri and Explain Everything that do the same thing. They are called interactive white board or screencasting apps. Happy mathematics learning to all!

Sources: Illustration from the same source. 

Marzano, Robert J. and Pickering, Debra J. “Special Topic: The Case for and Against Homework. Educational Leadership. March 2007, Volume 64, Number 6, Pages 74-79 Accessed 5/28/2014 at

Cooper, Harris. “Does Homework Improve Academic Achievement? If So, How Much is Best?” Accessed 5/29/2014 at

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Association of State Supervisors of Mathematics

A few weeks ago I attended the annual meeting of the Association of State Supervisors of Education (ASSM), followed by the annual conference of the National Council of Supervisors of Mathematics (NCSM). These were amazing meetings and I learned a great deal. At the ASSM meeting, I, with my colleagues who lead mathematics in other states, heard from the likes of Steve Leinwand, Cathy Seeley, Phil Daro, Dan Meyer, Tim Kanold, Linda Gojak, Bill McCallum, Uri Treisman, and so on. These are some of the brightest minds in our field. I learned a great deal. I, with many of my colleagues, also tweeted a great deal. Tweeting is my way of taking notes at these meetings. I found an application called Storify ( that allows the user to insert tweets, videos, blog posts, and so on and put them into a story format. I decided to do that with the tweets from the ASSM meeting. If you would like a small sample of what was discussed and the powerful ideas that were presented at ASSM go here:

Dan Meyer also wrote about his presentation at ASSM in his blog. I’m sure he didn’t develop the whole idea just for us. However, his presentation called “The Future of Textbooks, If There Is a Future for Textbooks” was really thought provoking. Taking digital textbooks out of airplane mode was his main theme. If they don’t do anything a smartphone in airplane mode would do, if they don’t connect to anything else, then they are just a textbook.

More later.

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