I stumbled across another misinformed, incorrect video purporting to show how “frightening” the common core standards are.

The mathematical issues brought up in this video are the same as the issues I address in many of the other posts about Misunderstanding the Common Core. Please read those. But, here are some new thoughts that this video created in me.

Thought #1 – The anti-common core movement really likes to pick on the idea of subtraction! I wonder why? There must be hundreds of other standards and yet, apparently, only subtraction brings up these emotionally charged challenges to the common core standards. Are we to think that if subtraction is “frightening” then all other standards are “frightening as well?” Is that good thinking?

However, as I have tried to explain in the other posts, the method of subtraction shown in this video is not bad! The lady in the video shows how 43 – 13 is computed. First, 3 – 3 is zero…write a zero below the 3’s. Then, 4 – 1 is 3…write a 3 below the 4 and 1. The answer is 30. Done.

The so-called common core method to subtract is a method related to counting back change. It is a method where one counts back, starting at 13, to 43.  Thirteen plus 2 is fifteen. Fifteen plus 5 is 20. Twenty plus 10 is 30. Thirty plus 10 is 40. Forty plus 3 is 43. Note, we counted back 30 units. Therefore, 43 – 13 = 30. No big deal.

Thought #2 – Even though I have no problem with the “counting back change” method as ONE POSSIBLE method to subtract 43 -13 = 30, this is not the “common core way” as reported in this video. I challenge any reader to show where, in the actual common core standards document, it says that subtraction must be done in this way or any particular way! In fact, I find the following standard:

4nbt 1

To say that the common core standards require one method of subtraction over another is just not true.

Thought #3 – Just because a person doesn’t understand something does not mean this is a bad thing! I think that the lack of mathematical content knowledge of the general population in the US is a big reason for the so called “frightening” aspects of the standards. As I have tried to explain in all of these posts, there is nothing frightening about the standards! Rather than to react to something that one doesn’t know much about, I challenge everyone to become more aware of the standards. Read them. Ask questions. Study. Then if you have a legitimate, well-reasoned concern, then certainly engage in a respectful discussion about the issue!

This sounds like something we could all learn to do in other areas of our lives as well…






Here we go again! I just saw the following on Facebook:


What was wrong with the old way? Before I answer…IT”S NOT THE OLD WAY! It’s just A WAY! If you want to read much about misunderstanding the common core, consider the other posts with a title “Misunderstanding the Common Core Parts I-IX”. I will reiterate, recap, and re-explain for anyone new to this blog.

When we subtract as shown at the bottom of the image, 568 – 293 = 275, there is a lot going on in terms of understanding the algorithm. Understanding the algorithm is what allows us to be efficient and accurate in computing by hand. Which brings us to an interesting issue: most people would use a calculator to do this!

Suppose you were going to attempt to compute 568 – 293 in your head. Or, suppose you were estimating. You might start with 568 – 200 = 368 just to get the thinking started. You might estimate/round 293 and say it is nearly 300 so 568 – 300 is about 268. Here’s my point…the most important digits are the digits in the 100’s place not the 1’s place! It is much more natural to start with the 100’s place than with the 1’s place as is traditionally done.

Let’s get back to it…once we think 568 – 200 = 368, the next thing to think about is the 10’s place. Let’s subtract 90 more. 368 – 90….hmmmmm…well…368 – 60 would be 308….hmmm…10 more…308 – 10 = 298….hmmm…20 more…298 – 20 = 278. It’s hard to do in writing but what I am trying to convey is that when people think about computations mentally, they might first focus on easier computations…subtracting 60, then 10, then 20 is much easier to do in my head that subtraction all 90 all at once.

So, we have subtracted 568 – 290 so far and have arrived at 278. Now subtract 3 more…278 – 3 = 275. There  you go! 568 – 293 = 275!

It would happen much faster in my head in reality than it seems when you read through everything that is happening in my head. Here it is in one, smaller space:

568 – 293….well, 568-200 = 368….now 368 – 90 is 368 – 60 = 308 and 308 – 10 = 298 and 298-20 = 278. Finally, 278 – 3 = 275…done…and fast!

What’s wrong with the old way? Nothing! What’s wrong with thinking, focusing on place value, mental math, understanding algorithms, and number sense? Nothing!

Here is the bottom line to me when it comes to this particular image. When we try to explain our thinking and show all the details of doing a simple subtraction problem, it might look convoluted and confusing. When we really think about how things work and try to understand the structure of the algorithm, it can make perfect sense!

One more thought…at the bottom of the image, we see this…

common core x part 2

People look and say…wow, look how easy that was compared to that new, crazy math that my kids are coming home with! Yea, right! There is so much missing that many 3rd graders would not understand!

Likely, people would start on the right and find that 8 – 3 = 5. Fine.

Next, people would look at the 10’s place…6 – 9…hmmm…you can’t take 9 from 6! Sometimes kids see this and their brains tell them to think about 9 – 6 and they put 3 in the 10’s place! But we know, you have to “borrow” from the 100’s place and actually subtract 16 – 9 = 7 (note…I am ignoring place value here since that is the traditional thing to do).

Finally, move to the 100’s place. Remember we borrowed 1 (ignoring place value and meaning) from the 5 to make it 4. So, 4 – 2 = 2 so put a 2 in the 100’s place.

There is so much going on here that a 3rd grader has to figure out. The creator of this image chooses to omit it in order to present a stark contrast from “the old way” to the “common core way.”

Making sense of mathematics (in this case 3rd grade subtraction) as I have tried to do in this blog post is not crazy…it is not new….it is just MATH!*


*Credit to Dr. Ted Coe!


Quote  —  Posted: September 18, 2015 in Teaching and Learning Philosophy
Tags: , ,

I am one of the most conservative political persons you can imagine and as such I have been quite frustrated with those that are aligned with me politically and the closed-minded stance that they have taken to the Common Core standards. From Conservative political candidates for president to politically active Conservative individuals, many have exhibited their ignorance (defined as: one with a lack of knowledge or information) in many instances. Therefore, it was refreshing to learn that the Lutheran Church Missouri Synod, of which I am an active member, formally published a document recently that demonstrated a positive and accurate reaction to the CCSS from a Conservative Christian perspective. Here are some of the important points made in “Should Lutheran Schools Consider Adopting the Common Core State Standards?”

  1. Lutheran schools have a rich heritage and long standing commitment to academic excellence that is rooted in the Christ-centered mission that flows from the Lutheran Confessions. The Common Core State Standards may serve as a tool that enhances curriculum development. They could provide additional guidelines upon which the rigorous programs of study for our students could be designed. The rigor is not the product of the CCSS standards alone; rather, is connected with the instructional process provided by Lutheran educators.
  2. The Common Core State Standards suggest a set of high-quality academic expectations that all students should master by the end of each grade level. They propose consistent grade-level learning goals for all students and inform parents about learning outcomes, thereby making it easier for parents to collaborate with teachers in helping their children achieve success.
  3. The Common Core State Standards are not a curriculum. (emphasis added) A curriculum includes what, when and how subjects are taught and what materials to use. These matters are not dictated by the Common Core State Standards. For Lutheran schools, these elements will continue to be determined by individual schools, working to meet the needs of their students.
  4. The Common Core State Standards represent a fundamental shift in the teaching and learning process. They establish clear, measurable goals for students that assist teachers in making instructional decisions. They place emphasis on creativity, critical and analytical thinking and application to curriculum content. They may serve to assist our schools in guiding the way that instruction takes place in each classroom while allowing the school to develop its own unique curriculum content.
  5. The Association of Christian Schools International (ASCI), Christian Schools International (CSI) and The National Catholic Educational Association (NCEA) support the move toward the Common Core State Standards. The reason? – Its focus on rigor, relevance, best practices, and college and career readiness.
  6. Ultimately, Lutheran schools will determine independently which standards to follow. The process of that discovery must remain true to The Lutheran Church—Missouri Synod’s (LCMS) Christ-centered mission: to provide a solid, Christian education developed with standards that drive instruction so that every child can be reached with an effective education – one that centers on the LCMS faith. The Common Core State Standards may be considered a tool that would allow LCMS schools to more fully prepare its students for service and witness to Christ and the world.

What I find the most reassuring about this document is that if one will take an honest look at the standards themselves with an open mind to assessing their quality removed from the political process and scheming that many see how powerful and helpful they are!

Trey Cox, Ph.D.

The following article was written by Dr. Jo Boaler:

Jo Boaler is a professor of mathematics education at Stanford University, co-founder of http://www.youcubed.org, and author of What’s Math Got To Do With It: How Teachers and Parents can Transform Mathematics Learning and Inspire Success. (Penguin, 2015)



Memorizers are the lowest achievers and other Common Core math surprises

In this Feb. 12, 2015 photo, Yamarko Brown, age 12, works on math problems as part of a trial run of a new state assessment test at Annapolis Middle School in Annapolis, Md. The new test, which is scheduled to go into use March 2, 2015, is linked to the Common Core standards, which Maryland adopted in 2010 under the federal No Child Left Behind law, and serves as criteria for students in math and reading.

In this Feb. 12, 2015 photo, Yamarko Brown, age 12, works on math problems as part of a trial run of a new state assessment test at Annapolis Middle School in Annapolis, Md. The new test, which is scheduled to go into use March 2, 2015, is linked to the Common Core standards, which Maryland adopted in 2010 under the federal No Child Left Behind law, and serves as criteria for students in math and reading. 

It’s time to debunk the myths about who is good in math, and Common Core state standards move us toward this worthy goal. Mathematics and technology leaders support the standards because they are rooted in the new brain and learning sciences.

All children are different in their thinking, strength and interests. Mathematics classes of the past decade have valued one type of math learner, one who can memorize well and calculate fast.

Yet data from the 13 million students who took PISA tests showed that the lowest achieving students worldwide were those who used a memorization strategy – those who thought of math as a set of methods to remember and who approached math by trying to memorize steps. The highest achieving students were those who thought of math as a set of connected, big ideas.

The U.S. has more memorizers than most other countries in the world. Perhaps not surprisingly as math teachers, driven by narrow state standards and tests, have valued those students over all others, communicating to many other students along the way – often girls – that they do not belong in math class.

The fact that we have valued one type of learner and given others the idea they cannot do math is part of the reason for the widespread math failure and dislike in the U.S.

Brain science tells us that the students who are better memorizers do not have more math “ability” or potential but we continue to value the faster memorizers over those who think slowly, deeply and creatively – the students we need for our scientific and technological future. The past decade has produced a generation of students who are procedurally competent but cannot think their way out of a box. This is a problem.

Mathematics is a broad and multidimensional subject. Real mathematics is about inquiry, communication, connections, and visual ideas. We don’t need students to calculate quickly in math. We need students who can ask good questions, map out pathways, reason about complex solutions, set up models and communicate in different forms. All of these ways of working are encouraged by the Common Core.

Technology leaders are publically arguing that calculation is not math, and that math is a much broader subject. Conrad Wolfram, one of the leaders of one of the world’s most important mathematics companies, Wolfram-Alpha, urges schools to stop emphasizing calculating and focus instead on problem solving, modeling, thinking, and reasoning as these are the mathematical abilities that students need in the workplace and their high tech lives. This broad, multidimensional mathematics is the math that engages many more learners and puts them on a pathway to life long success.

Part of the problem in the U.S. is the desperation of many parents to advance their children in math, pushing them to higher levels of math faster and sooner, somehow believing that a resume packed with advanced math courses will guarantee their future. Bill Jacob, a mathematics professor at the University of California, Santa Barbara, speaks openly about the dangers of students being pushed to higher levels of mathematics too soon. “I know it is hard to persuade parents that their students shouldn’t race to get calculus, but I really wish they wouldn’t. Too much content and depth is left out when they do.” said Jacob, who is not alone in saying that he would rather have students in his university mathematics courses that have breadth in their mathematical experiences than any additional Advanced Placement courses. Experts in England are giving the same advice to parents of high achieving students. Geoff Smith, chairman of the British and International Math Olympiads warns that accelerating children through the system is a “disaster” and a “mistake”. He, like me, recommends that high achieving students explore the mathematics they are learning in depth, instead of rushing forward.

Mathematics is not a subject that requires fast thinking. Award winning mathematicians talk about their slow, deep thinking in math. Fields Medal winning mathematician Laurent Schwartz wrote in his autobiography that he felt stupid in school because he was one of the slowest thinkers in math. Eventually he realized that speed was not important – “What is important is to deeply understand things and their relations to each other.  This is where intelligence lies. The fact of being quick or slow isn’t really relevant.”

Some school districts, such as San Francisco Unified, are trying to slow down the math experience, requiring that advanced students go deeper rather than faster. Students still reach calculus but the pathway to calculus consists of deep understanding rather than procedures and memorization. This is an important move. There is no harm in students being introduced to higher-level mathematics earlier, as long as the mathematics is enjoyable and ideas can be explored deeply. Third graders can be fascinated by the notion of infinity, or the fourth dimension, but they do not need a race through procedural presentations of mathematics.

New brain science tells us that no one is born with a math gift or a math brain and that all students can achieve in math with the right teaching and messages. The classrooms that produce high achieving students are those in which students work on deep, rich mathematics through tasks that they can take to any level they want. No one is told what level they can reach and no one is held back by narrow questions that limit students’ mathematical development and creativity.

Many people across the U.S. have gross misconceptions about mathematics learning, thinking that mathematics is a narrow subject of memorization and speed and that people who do not calculate fast or memorize well are not ‘math people’. We need to change the conversations about mathematics, communicating to all children that they can learn. We also need to change the way math is taught, valuing the different ways of thinking that are so important to the subject. Mathematics, itself, needs this and although change is hard, it should be embraced.

We need to broaden mathematics and open the doors of mathematics to all students. When we do this we will see many more creative, energized young people equipped to think quantitatively about our ever-changing world. We all need this.

Jo Boaler is a professor of mathematics education at Stanford University, co-founder of www.youcubed.org, and author of What’s Math Got To Do With It: How Teachers and Parents can Transform Mathematics Learning and Inspire Success. (Penguin, 2015)

This story was produced by The Hechinger Report, a nonprofit, independent news organization focused on inequality and innovation in education. Read more about Common Core.

“Five percent of the people think;
ten percent of the people think they think;
and the other eighty-five percent would rather die than think.”

-Thomas Edison

I don’t know exactly what Edison meant by this or how he determined the percentages, but the message, to me, is this: thinking is not what people do well!

On a recent Sunday news show, Texas governor Greg Abbott claims that the Common Core State Standards are bad because “it takes a teacher more than a minute to teach a student how to learn that 9+6=15”. He is referencing this video. Check it out.

Let’s think about this. How is this an argument against Common Core?

Is teaching a student how to think about 9+6 = 15 a bad thing? There is a difference between just doing 9+6 and thinking about 9+6. The Common Core Standards clearly have an emphasis on procedural fluency. Students should be able to determine that 9+6=15 quickly. But, how will such fluency happen? It will happen when students have a way of thinking about 9+6. Because it takes a minute to explain this thinking does not mean that it will take a student a minute to compute! Furthermore, the expectation is to push mental math…a good thing! For a student to flexibly be able to see 9+6 as equivalent to 10+5 is very good!

Governor Abbott does not have the opportunity to explain how he believes students should be taught that 9+6=15, but I will make a conjecture that he will argue that students should just memorize it. And in saying this, what would he mean by “just memorize it”? Perhaps something like this (and I embellish):

Teacher: “OK Johnny, this shape right here (9) is called the number 9 and this shape right here (6) which kind of looks like an upside-down 9 is called the number 6. And when you put this symbol in between this (9) and this (6) the answer is two shapes…a 1 which sits right next to a 5. So 9 + 6 = 15”
Johnny: “But why?”
Teacher: “Don’t ask why…just memorize it. Let me get the flashcards.”

We might as well do something like this:

Teacher: “OK Johnny, let me tell you something that I want you to memorize. If you take purple and add dog the answer is banana.
Johnny: “But why?”
Teacher: “Don’t ask why…just memorize it. Let me get the flashcards.”

The teacher in the video is just unpacking the mathematical thinking necessary for a student to make sense of what 9+6=15 means and how this fact might be memorized in a meaningful way. Certainly, we expect students to be able to respond to 9+6 in just a few seconds. This memorized fact will be retained when the mathematical reasoning and thinking, done by the student, allows the student to make meaning and make sense of the computation.

And by the way…this kind of thinking, to allow students to memorize basic math facts, has been around long before the Common Core Standards! This is not a Common Core thing…this is just good teaching.

Diane Briars, president of the National Council of Teachers of Mathematics, says this about the issue: “Teachers have used techniques like splitting a number into parts of 10 for addition–rather than straight memorization–since the 1950s at least, and the research showing its benefits goes back to the 1920s. It has long been best practice for early childhood math.”

I encourage everyone…please read the Common Core Standards and understand their purpose. Then, if you want to debate the issue of the federal government offering federal money tied to the implementation of these standards, great! If you want to debate standardized testing, its cost, its taking instructional time, its impact on the mental health of students, teachers, and parents, great! But please…do not conflate these issues. Standards are standards…teaching is teaching…curriculum is curriculum…testing is testing. My experience is, when people actually consider the Standards, the issue is not the Standards! When they see that students are expected to become effective problem solvers, mathematical thinkers, and fluent in computations, most agree that the Standards are not a problem.

When people try to show that the Standards (not the role of the feds, not standardized testing, etc.) are bad, it is clear that they are not really thinking…



There seems to be a common theme among the complaints about the Common Core Standards. Parents say, “that’s not the way I learned it…why not just do it the “old fashioned” way?”

Part of the reason is this: Because we are trying to prepare students for a new, modern world! Years ago, it was very important for people to become very accurate with paper and pencil computations. That’s just not the case anymore. Now, it is important that we take a balanced approach…a balance between computational fluency AND conceptual understanding AND the ability to apply mathematical ideas to solve real-world problems. This is exactly what the common core standards have as a major focus…a balanced approach!

Here is a question that we all should think about…how does a young learner develop computational fluency? Does it just happen magically? The following videos seek to answer the question in the context of addition algorithms, subtraction algorithms (videos made by Dr. Scott Adamson) and multiplication (video by Dr. Raj Shah).








Here is the latest (for me) bashing of the common core standards:


Again, the subject of the bashing is subtraction…I find it interesting that subtraction seems to be taking the biggest hit when it comes to common core bashing!


The blogger says, “Here is the insane method” they came up with to utterly confuse 4th graders about subtraction:”

Insane? Utterly confuse? I think not!

Consider this: Albert Einstein was born in 1879 and died in 1955. How old was he when he died? Think about it…then pay attention to how you thought about it…


Many adults think about this situation like this:

  • Starting with 1879, it takes 21 years to get to 1900.
  • Then, another 55 years takes us to 1955.
  • So, Einstein was 21 + 55 = 76 years old (or would have turned 76) in 1955.

This is the “counting up method” described in the textbook! This method seems SANE and UTTERLY sensible to me!

As I have explained in other posts (Part I, Part II, Part III, Part IV, Part V, Part VI), the main issue is how one thinks about subtraction. If one only thinks about subtraction as “take away” then their understanding is incomplete. We can also think about subtraction as a comparison…which is really what is happening here. We are comparing 1955 to 1879 to see how many years have elapsed. Furthermore, think about the method (yes, it is a method!) described early…first add 21 years…then add 55 years…and compare that method to the standard subtraction algorithm from a “take away” perspective.

CaptureWith the double borrowing, mistakes can be made. In addition, I am a fan of mental math…it can absolutely be a helpful and healthy thing to keep track of quantities mentally!

The goal…and who can really argue this…is for students to become fluent, flexible, and efficient with computations.

  • Fluent in a way similar to becoming fluent in a foreign language…comfort, ease, speed, and confidence are all hallmarks of fluency.
  • Flexible in the sense that a student will use an algorithm if necessary, use a counting up strategy if possible, or other strategies learned in school.
  • Efficient in the sense that a student will choose a strategy that is appropriate for the task at hand. For example, in the Einstein example, I argue that the counting up strategy is more efficient than the traditional algorithm…at least for those who have been trained to think that way!


Parent: I don’t understand why you won’t answer my son’s questions in class.

Teacher: This is the new common core teaching method. Students need to figure things out on their own.

Parent: I am unclear on the way you want my son to complete this homework assignment. Why can’t he just follow the traditional algorithm?

Teacher: We are using the new common core curriculum. This is how common core wants students to do that particular computation.

Parent/Teacher/Student: (with much frustration) &%!@# common core *&!!@($^ math *@##!$%^% stupid…


Parents, if you have had this kind of a conversation with a math teacher recently, I encourage you to challenge that teacher to explain the difference between common core STANDARDS, common core CURRICULUM, and common core TEACHING METHODS. 

The interesting thing is that one of these things is not like the others…STANDARDS! The common core STANDARDS are not like the others because the others don’t even exist!

The common core standards for mathematics include content standards for grades K-12…that is, what content should be taught. The content standards are written in such a way that mathematical ideas and understanding can be developed in a coherent, structured way through what they call “progressions.” For example, the ways in which students are to think about, make sense of, and ultimately compute multiplication problems are developed so that the way students are thinking in 3rd grade are extended to 4th grade, etc.

What the common core standards DO NOT do is tell teachers HOW to teach in order to provide the opportunity for students to master the standards. Nor do the common core standards provide curricular material to support the learning of the content standards.

In addition to the content standards, the common core includes Standards for Mathematical Practices.

  1. Make sense of problems and persevere in solving them.
  2. Reason abstractly and quantitatively.
  3. Construct viable arguments and critique the reasoning of others.
  4. Model with mathematics.
  5. Use appropriate tools strategically.
  6. Attend to precision.
  7. Look for and make use of structure.
  8. Look for and express regularity in repeated reasoning.

Will teachers need to find/create/adapt high quality curricular material to meet these standards? Will teachers have to think about their teaching practice and possibly adjust so that these practices can be developed? YES! 

The question is…so what DOES good teaching and learning look like (whether held to the common core standards or not)? 

I will try to capture the essence of this in the following vignette:

You open the door to the classroom and your initial reaction is shock.  It seems that chaos reigns as you notice students out of their seats as they talk with one another.  Furthermore, the desks are not neatly arranged in rows, but seem to be randomly clustered into small groups as the students use the desk tops for what appears to be some sort of technical equipment set-up.  Where is the teacher?  You are not sure.  Concerned with the outward appearance of this classroom, you enter the classroom to investigate.  You stop at the first group of students and try to figure out what is going on.  Quickly you realize that the topic of their conversations is highly technical.  They are discussing the result of an experiment where two tuning forks of different frequency are struck and the combined frequency is measured.  Would the frequency be the sum of the frequencies of the two tuning forks?  The difference?  Or some combination that will be difficult to determine?  They follow through with the experiment using a data collection device and a graphing calculator and the students begin to analyze the results.  They are discussing ideas and concepts foreign to you as they search for the beat pattern, calculate the period and frequency, determine the equation of the sinusoid which fits over the beat pattern, and ultimately discover the relationship between the frequency of the individual tuning forks and the combined frequency.  You ask one of the students, “why are you doing this?”  Annoyed by the interruption, she responds that they are trying to solve the problem at hand where, in the situation given, an old World War II mine needs to be deactivated.  This can only be accomplished by directing the proper sound frequency at the timing mechanism in the bomb in order to disable it.  You find it refreshing to see students motivated to solve a problem and notice that students are simultaneously using technology, paper and pencil calculations, and teamwork to find the solution to a problem that has obviously engaged the interest of the students.

You move on to the next group of students.  They are equally engaged in what appears to be a different problem.  You first notice that the students are huddled around a graphing calculator screen.  Suddenly, a shout of celebration is heard as students triumphantly give each other “high-fives”.  You get the attention of one of the students and ask what they are doing.  He explains that their team was given data related to the height of waves in the ocean during a particularly dangerous storm.  Their job was to create a scatter plot of the data and determine a sinusoidal regression model for this data so that they could calculate the period, frequency, and height of the waves at the moment in time a small touring vessel was capsized.  Given the manufacturers specifications of this vessel, the students would be able to determine if it was built to withstand such a storm or not.  This would aid in the investigation and eventual lawsuit brought by passengers of the vessel who believed that the vessel’s skipper used poor judgment in venturing out into the storm. 

Impressed by the level of engagement of the students, the high-level discussions that were taking place between students, and the interesting combination of technology and paper-and-pencil calculations that were taking place, you still have one more concern: where is the teacher?

You move on to the next group and find that they are working with tuning forks also.  Peering in to see what this group is discussing, you find that one of the members of the group seems to be asking questions.  “What would you know about the frequency if the period is 0.123 seconds?”  “Do you see a pattern when you consider the different combinations of two tuning forks and their resulting beat pattern?”  “Can you explain the difference between period and frequency?”  You realize that this is the instructor asking probing questions to the students to help them construct their own understanding of the mathematical concepts being explored.

Standing back to observe, as a whole, the classroom setting that initially brought disgust (nearly), you now feel joy (nearly) as you realize the high engagement of students as they study difficult math (and physics) concepts.  But the students seem to be enjoying it.  Could this really be a math classroom?  What curriculum development and implementation steps were employed by the instructor in this classroom to get to this point? 

The National Council of Teachers of Mathematics recently released a book (Principles to Actions: Ensuring Mathematical Success for All) describing the Mathematics Teaching Practices that “provide a framework for strengthening the teaching and learning of mathematics:

  1. Establish mathematics goals to focus learning.
  2. Implement tasks that promote reasoning and problem solving.
  3. Use and connect mathematical representations.
  4. Facilitate meaningful mathematical discourse.
  5. Pose purposeful questions.
  6. Build procedural fluency from conceptual understanding.
  7. Support productive struggle in learning mathematics.
  8. Elicit and use evidence of student learning.

Much support and patience is required as mathematics education is improved in the USA. Let’s all commit to making sense of the problem of mathematics education and then persevere in solving it!


Here we go again…another false statement about the “dumbing down” of American kids…about doing math in ways that seem foolish…about the “idiocy” of the Common Core Standards.

If you want to see the original post, go here: toprightnews.com/?p=3958

Most of what is discussed here has already been addressed in Parts I – IV. But I will use this post to highlight some of the issues and why I claim that folks like this (in this case, Jason DeWitt of Top Right News) are misrepresenting the Common Core Standards and that the root of the issue is their misunderstanding of the Common Core Standards.

Point #1 – The standards do NOT tell teachers/students how to do arithmetic

In the article, we see the following:

One student got tired of being dumbed-down by Common Core’s convoluted “standards” to do basic arithmetic.

“Standards” like how to add two numbers, which the student was told to do like THIS:

I challenge any reader to show me where in the Common Core Standards that students are told to “do basic arithmetic” in any specific way. Certainly, you will see standards that encourage students to make sense of mathematics…to understanding computational algorithms…to explain their thinking. Also, you will see standards that encourage computational fluency. What this is really an example of is how young learners might begin to make sense of the traditional algorithm for adding two numbers. Mathematics educators would NOT expect students to remain at this stage…rather, we expect students to develop computational fluency by thinking about the mathematics involved. Here is the example shown in this article:


I must be crystal clear…this is not an example of how students HAVE TO do this computation…this is an example of how a student MIGHT THINK about the computation.

Can we all agree that it is easier to do mental math that involve numbers like 20, 30, or 40? So a student might think…”26 is four less than 30…so let’s think about using the number 30.” Since  we are adding 4 to 26, we would have to subtract 4 from 17 in order to get an accurate result for the final sum. Instead of thinking about 26 + 17, think about 30 + 13…which is 43.

I challenge you to ask 10 adults how they might think about 26 + 17 mentally…some will do this method! Some will imagine the algorithm in their minds eye (6 + 7 = 13…carry the one…2 + 1 + 1 + 4…so 43). Some might take 17 up to 20 by adding 3…which means we would have to subtract 3 from 26 to get 23…therefore, 26+17 is the same as 23+20 = 43. Can we all agree that 23 + 20…or 30 + 13… are easier to do mentally than 26 + 17?

Point #2 – There is no such thing as “the common core way”

In the article, another example is given and the following statement is made:

So when he was given his next basic arithmetic assignment, to find the difference between 180 and 158 (180-158), this 5th grade student just did it his own way — the right way – 

Exactly…the student “did it his own way…” That’s what we want! We want students to make sense of the mathematics involved in these computations and to develop a fluent and efficient way to compute. While the article makes this statement as a way to diss the common core…I argue that this is exactly what the common core would encourage! As long as “his own way” was a way that makes sense to him and to others.

Ok…ok..I get it…the point of the article is that the student “stuck it to the common core man” by explaining how he found the answer…using one word…MATH! How cute…how clever…

Please…common core bashers…explain to me…what is so wrong with asking a student to explain his/her thinking? My hunch is this…you can’t do it so you don’t want your kids to do it. That is, you are uncomfortable explain your thinking so why should your kids have to explain their thinking? And if your kids are asked to explain their thinking and you don’t know how to help them do it, then there is something wrong with the assignment/teacher/standards/textbook/test/whatever.

Hmmm…mathematical thinking…not mathematical doing…mathematical thinking…

Kaye Stacey writes about mathematical thinking this way

The ability to think mathematically and to use mathematical thinking to solve problems is an important goal of schooling. In this respect, mathematical thinking will support science, technology, economic life and development in an economy. Increasingly, governments are recognising that economic well-being in a country is underpinned by strong levels of what has come to be called ‘mathematical literacy’ (PISA, 2006) in the population. 

Do we want students who can “use mathematical thinking to solve problems”? Do we want to encourage our kids to engage in mathematical thinking to support “science, technology, economic life…”? Then we must stop showing kids how to do mindless procedures and instead help them to develop the mathematical thinking that leads to procedural fluency. Procedural fluency does not just happen magically. It is developed…and can be developed in such a way as to also develop and support mathematical thinking.

Think about the last time you had to divide two fractions…like 7/8 divided by 3/4.

First…this probably last occurred on your 7th grade final exam! Just kidding…but think about it…would you just “invert and multiply”? Is it important to understand the mathematics entailed in this computation? I say yes….


Raising Arizona Kids

Posted: June 16, 2014 in Uncategorized

This article appeared in the online magazine in June 2013:

Math teachers prepare for Common Core standards

By Daniel Friedman | June 3, 2013

Your kids need to be smarter and better educated to get decent jobs when they graduate from college. Many states, including Arizona, have adopted Common Core State Standards to better prepare children for the job market.
Implementing new standards in education isn’t like flipping a switch. At the most basic level, teachers need to know if the textbooks and teaching materials they already have will work for the new standards. On a more complex level, they need to modify their the lessons, sequence and teaching approach to meet the new standards.

The Arizona Mathematics Partnership, led by Scottsdale Community College, was awarded an $8.7 million, five-year grant by the National Science Foundation to help 300 middle school math teachers understand and teach the new mathematics Common Core Standards.
Math gets more difficult during the middle school years. Algebra rears it’s ugly head and equations move beyond basic operations. Parents often bow out of helping their kids in middle school because it gets more complex and they haven’t factored polynomials recently.
I spoke to Scott Adamson, a math teacher at Chandler-Gilbert Community College. He is working with teachers this summer at a five-day Summer Institute at Scottsdale Community College, but that is just a small part of the program. He also visits teachers at their schools, observing lessons and giving feedback on how to implement the new math standards.
The new standards include the usual content standards. like this one for sixth grade:
6.RP.3. Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations.
This is a standard for third grade:
3.OA.7. Fluently multiply and divide within 100, using strategies such as the relationship between multiplication and division (e.g., knowing that 8 × 5 = 40, one knows 40 ÷ 5 = 8 ) or properties of operations. By the end of Grade 3, know from memory all products of two one-digit numbers.
Adamson says the current math textbooks don’t really line up with the new standards but having teachers create their own entirely new lessons to match the new standards isn’t practical. It takes hours to design a lesson, create the materials and the assessments to go with it.
He works with teachers to help them implement the new standards as efficiently as possible. If they try to create all new lessons “they’ll be burned out by October,” he says.
In addition to the content standards, the Common Core standards include Mathematical Practices:

1. Make sense of problems and persevere in solving them.
2. Reason abstractly and quantitatively.
3. Construct viable arguments and critique the reasoning of others.
4. Model with mathematics.
5. Use appropriate tools strategically.
6. Attend to precision.
7. Look for and make use of structure.
8. Look for and express regularity in repeated reasoning.

Adamson says getting the correct answer is not enough “The heart of it is, what do we want out of our students? It is not to mindlessly perform steps and arrive at answers without understanding why and how they got their answers,” he says. One example he gave is students should understand why multiplying a negative number times a negative number yields a positive number. (You remember that, right? -3 x -7 = 21)
Really, the new standards with the mathematical practices are building an intellectual framework within which the content standards are learned and understood, says Adamson. A calculator won’t help “construct viable arguments and critique the reasoning of others.”
The new standards will demand more of your children as well as their teachers.
Teachers in the Arizona Mathematics Partnership program will get 200 hours of professional development, and a $2,500 stipend for their efforts. In addition to SCC and Chandler-Gilbert, other partners in the project are Glendale Community College, Chandler Unified School District, Deer Valley Unified School District, Florence Unified School District, Fountain Hills Unified School District, J.O. Combs Unified School District, Salt River Pima-Maricopa Indian Community Schools and Scottsdale Unified School District.
Parents will need to support their kids and send them to school willing and able to work to meet the new standards in math and English language arts which will be assessed for the first time in the spring of 2015.
Read the Arizona Common Core Math standards.
Find out everything you can about the standards.
Tags: Arizona Mathematics Partnership, Arizona schools, Common Core Standards, math, Scottsdale Community College, teachers

Daniel Friedman
Daniel Friedman is a staff writer and photographer for RAISING ARIZONA KIDS magazine.