Monday, December 8, 2014

A Lesson In How Teachers Became 'Resented And Idealized' : NPR

In her new book, The Teacher Wars, Dana Goldstein writes about how teaching became "the most controversial profession in America," and how teachers have become both "resented and idealized."

Take 39 minutes to listen to this very interesting interview. It helped me understand why the teaching profession is both loved and hated.

A Lesson In How Teachers Became 'Resented And Idealized' : NPR:

'via Blog this'

The Common Core Curriculum Void

Yikes! Five months from now our students will be taking the SBAC math test. Ordinarily, this would be fine, but most school districts still do not have textbooks (now we call them instructional materials to allow for the possibility of online materials) to use for preparing our students.

Take a listen to this awesome 7-minute NPR segment.
If the podcast does show here for the direct link.

Why the Best Teachers Don't Give Tests

Frankly, I'm baffled by the number of educators who are adamantly opposed to standardized testing yet raise no objection to other practices that share important features with such testing.

Read more via Pocket

Friday, December 5, 2014

The Stereotypes That Distort How Americans Teach and Learn Math

Speed doesn't matter, and there's no such thing as a "math person." How the Common Core's approach to the discipline could correct these misperceptions. Mathematics education in the United States is broken.

Read more via Pocket

Monday, November 24, 2014

Teacher Advice from 1895: On Patience

When I was a mathematics teacher, being patient was easy. Really, all I needed to do was to make sure I was patient with my students. Rarely did I need to do much interacting with parents or colleagues such that my patience was put to the test. Worst case scenario: close my door and just teach my awesome students.

Now that I am an instructional coach, I often find myself in situations that require great restraint and patience. This is clearly an area in which I must grow!

As I was reading the Annual Report of the Public Schools of the City and County of San Francisco for the School and Fiscal Year Ending June 30, 1896 (yes...I'm a total edu-nerd!), I came across this list of advice on patience for teachers.

Still relevant after nearly 120 years...especially as we move to the Common Core Standards.

  1. Be patient with yourself. 
  2. Be patient with the other teachers. Their ideas cannot coincide with yours exactly. 
  3. It requires great patience for a teacher with high ideals to view with serenity her failure to meet her ideals. 
  4. Be patient with the school director who was once a teacher. He has to be patient with you for not teaching as he did. 
  5. Be patient with non-professional school directors. They cannot see things from your standpoint, but they may be of great service through their common sense loyalty to the school. 
  6. Be patient with your fad-admiring associate. She sees virtue only in the new things and thinks you very slow. If she can get along with you, you certainly ought to with her. 
  7. Be patient with the principal. He has to be patient with all of his teachers, and if he is equal to this trial with six, eight, ten, or twelve, you ought to be patient with him. 
  8. Be patient with the children. They are but children, untrained and untamed. It is neither easy nor natural for them to be even and reliable in their work, in their thought, or in their disposition. 
  9. Be patient with your conservative associate teachers. It frets them to see you so progressive, and you need good judgment in speaking to them or of them, as well as listening to what they say to you and in hearing about what they say of you. 

Monday, November 17, 2014

Teaching Math to People Who Think They Hate It

A popular Cornell professor tries to help language-arts types learn how to "make math" instead of just studying it. Math has never been my strong suit. I opted out of it at every turn, particularly in college, where I enrolled in linguistics to fulfill my quantitative reasoning requirement.

Read more via Pocket

How to Deal With Kids’ Math Anxiety

In children with math anxiety, seeing numbers on a page stimulates the same part of the brain that would respond if they spotted a slithering snake or a creeping spider—math is that scary.

Read more via Pocket

Projection: Poor Student Performance on SBAC in 2015

Here is one from the "No Duh" files: An article on Education Week, Cutoff Scores Set for Common-Core Tests, is "projecting that more than half of students will fall short" of proficient on the SBAC. In mathematics it appears as though this dire prediction is actually optimistic!

Check out the infographic below. Scroll down to the Projected Student Performance section for mathematics and click through each of the grade levels 3 through 8 and 11. Third grade is predicted to be the least "stinky" with 39% of our students projected to pass the test. Eighth grade is predicted to have the lowest percentage of students passing with 32%.

This is not a bad thing!

The whole purpose of Common Core is to improve the focus, rigor, and coherence of our math standards, and to make our students college and career ready. This necessarily involves ratcheting up the level of our testing, thereby resulting in low scores. I agree with a minor statement in the article that "the transitional stress of lower scores is justified by powerful payoffs".

What are the powerful payoffs? Students who are graduating high school college and career ready. Far fewer students will enter college needing to take a series of non-credit bearing remedial math courses before finally earning math credits.

The trick is how do we use the testing as a productive tool for measuring our progress toward the end-goal rather than as a tool for beating down students and teachers? (At least California is not even close to considering using the test scores as part of teacher evaluations...take that New York!)

Let us brace ourselves for the results that are likely to come in June, but also resolve ourselves to use the data to grow.

Monday, October 27, 2014

Do classroom decorations disrupt kindergartners’ learning?

Maps, number lines, shapes, artwork and other materials tend to cover elementary classroom walls. However, new research from Carnegie Mellon University shows that too much of a good thing may be bad because heavily decorated classrooms end up disrupting attention and learning in young children.

Watch the short, 4-minute video below.

Or read the article here.

The official study can be found here.

Thursday, October 23, 2014

What teachers need | American RadioWorks |

How often do we hear that "people are born to be teachers"? While there are aspects of this statement that may be true, it devalues teaching as a profession and turns it merely into an art form. If teachers want to be treated like professionals, then we need to act as if great teachers are MADE rather than great teachers are born.

Take 15 minutes to listen to this wonderful podcast interview with Elizabeth Green, author of Building a Better Teacher.

If the podcast does not show up below, click here.

For the full article with the podcast...
What teachers need | American RadioWorks |:

Praising intelligence versus praising effort

Take 5 minutes to watch this profoundly interesting video on the effects of praising student intelligence versus praising student effort. In a nutshell, when we praise a student for his intelligence we force him into a posture of a fixed mindset. In contrast, praising a student for his effort has the ultimate effect of teaching that student to have a growth mindset.

Praising effort = GOOD
Praising intelligence = NOT SO GOOD

Wednesday, October 8, 2014

Why the Growth Mindset is the Only Way to Learn

Do you know what these statements have in common? They’re all examples of the fixed mindset- the belief that intelligence, ability, and success are static qualities that can’t be changed.

Read more via Pocket

Monday, September 29, 2014

You say you want this, so then why are you doing that?

Unfortunately, myths are often more satisfying to us than the truth - in education we are satisfyingly distracted by a great many myths. Do we not recognize that there are a lot of children who hate school? For too long, school has acted for too many kids as the greatest extinguisher of curiosity.

Read more via Pocket

Friday, September 26, 2014

Common Core Endorsements

On August 29, the Association of Independent California Colleges and Universities (AICCU) wrote a letter of endorsement supporting the Common Core State Standards stating, "We believe California’s implementation of the Common Core standards and aligned assessments has the potential to dramatically improve college readiness and help close the preparation gap that exists for California students." 

Who the heck is AICCU? It is the organization representing the California State University system, the University of California system, and the California Community Colleges. So, clearly they know what they are talking about!

The letter of support goes on to say that they are updating the a-g requirements for CSU and US admission to "to align with the Common Core standards and the message is being transmitted to schools, parents and students". Well...I couldn't wait for them to get the message out, so I'm tooting my little horn and ringing my bell to make the announcement for them. Now parents and teachers can take great comfort in knowing that by shifting our teaching practices to meet the needs of the Common Core Standards, we are doing EXACTLY what the colleges and universities want us to do.

Not that it is a popularity contest, but check out this partial list of other organizations that endorse the Common Core State Standards.

Here is the link to the original page:

What about the mathematics community?
Every major mathematical organization has signed a letter of "strong support" for the Common Core math standards! If the math community has vetted the standards and are supporting them, then darn it, we should support the standards, too!

Whether we are parents, teachers, or students and we find ourselves struggling with the new ways math is being taught, let's remind ourselves that we are not alone! There are many, many organizations that are supporting us and are rooting for us to succeed!


Tuesday, September 23, 2014

The Common Core FAQ

The Common Core State Standards have vaulted into the national consciousness lately thanks to some high-profile dissenters, like Louis C.K. ("Kids teachers parents are vocally suffering.

Read more via Pocket

Elevator Speeches for Common Core Mathematics

A few days ago I finished my series @mr_stadel) sharing that he was planning to do a week's worth of elevator speeches. I am quite grateful for him putting out the challenge. This post is merely to put my list and his list on the same page, so that you can have twice as many elevator speeches at the ready.
of elevator speeches in support of the Common Core mathematics standards. This whole series was inspired by Andrew Stadel (

Duane's list
Day 1 ] [ Day 2 ] [ Day 3 ] [ Day 4 ] [ Day 5 ] [ Day 6 ] [ Day 7 ]

Andrew's list
Day 1
Day 2
Day 3
Day 4
Day 5
Day 6
Day 7

Currently, the Common Core Standards are a bit under attack. Often, the public (and many teachers) confuse the standards with curriculum or the two assessment consortia (SBAC and PARCC). It is my hope that we can move from ad hominem attacks on CCSS and work towards using the standards to meet the needs of all our students.

Please consider using these elevator speeches to better understand the Common Core math standards and why they are the right thing to do.

Better yet...write your own speeches and share them here!

Friday, September 19, 2014

What if Khan Academy was made in Japan?

Do yourself a favor. Spend 13 minutes watching this video. Ignore the "blended learning" or "flipping" if you want. Really, really focus on the difference between the American-style of teaching and the Japan-style of teaching.

Let's explore how to teach the way math instruction occurs in the countries that are doing better than us. Yeah...yeah...we'll have no clue what we are doing at first, but eventually we'll figure it out. I know we will.

More important than the guy's critique of Khan is the vision for what instruction should look like in the classroom.

Thursday, September 18, 2014

5 Habits of an Effective Teacher a mathematics instructional coach my job is to help teachers improve their craft. In general, I'm supposed to focus on the mathematics portion of their job, but invariably I find myself thinking about the entire job - not just math. Just the other day I Googled (how is that for verbification?) "habits of an effective teacher" and was a bit overwhelmed at the options. 

If you look closely at the screenshot, you'll notice that I only clicked on the short lists. Five habits? Sure I can handle that. 30 habits!?!?!? Goodness no. Clearly they need to learn the habits of succinctness, brevity, or self-censorship (if that is even a habit).

I clicked on each of the "5 habit" lists are here is what I got...
List 1
List 2
  1. clear and open communication
  2. clear classroom procedures
  3. create powerful relationships with your students and their parents
  4. have personal routines/hobbies to maintain your sanity
  5. plan in advance for how to participate in public activities
  1. Taking a wider view of student success.
  2. Recognizing instruction as a performance.
  3. Internalizing personal accountability.
  4. Understanding student motivation.
  5. Continuing focus on instructional improvement.

These are great lists, but somehow I couldn't shake the feeling that they don't capture the habits that are necessary as teachers move from the old, NCLB-influenced standards to the new CCSS. Then this list showed up in my Twitter feed. While it doesn't include classic buzzwords like procedures or accountability, any teacher who exhibits these habits would most likely be Educational Awesomeness in the classroom.

Let's try it! Can we enjoy teaching? Embrace the change brought upon by CCSS? Spread positivity while rolling with the turbulent transition to a new way of teaching? Find inspiration in people and things all around us? Make a difference for our students and colleagues?

If we can, then Educational Awesomeness awaits!

Do you have a SHORT list of habits that are devoid of educational mumbo jumbo? Post your list here...

Elevator Speech Challenge: Day 7

Unless someone sends me suggestions for hypothetical questions, this will the be final post in my Elevator Speech Challenge series. Not only has this been a challenging experience for me, there has been the added bonus of other teachers actually using my answers in their day-to-day conversations with parents and friends. Woo hoo!

HYPOTHETICAL QUESTION: “Duane…come on…what’s with the Eight Standards for Mathematical Practices? How can the same eight standards apply to students in kindergarten AND 12th grade?”

My Elevator Speech: Great question. To be honest, I’ve come across many teachers who have the exact same question. First, the eight standards are:

  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

A soccer game basically looks the same whether it is being played by a 6-year old or an 18-year old. In the same way, these eight standards are the behaviors we want our mathematicians to exhibit regardless of their age. Sure, a standard exhibited in kindergarten might look a little different than the same standard in twelfth grade, but the students are still working on the same standard. Just like soccer. 

For a list of the 8 Standards for Mathematical Practices written in parent-friendly language, please check out the site:

Day 1 ] [ Day 2 ] [ Day 3 ] [ Day 4 ] [ Day 5 ] [ Day 6 ] [ Day 7 ]

Wednesday, September 17, 2014

Elevator Speech Challenge: Day 6

I'm not going to lie...coming up with a new elevator speech challenge each day is starting to get difficult. Actually, the answers are pretty's the questions that are hard for me to come up with. So, if you have any suggestions for questions, please post them in the comments below!

Today's question isn't so hypothetical. It was inspired by a wonderful conversation I had with a concerned parent.

HYPOTHETICAL QUESTION: “Duane…come on…why does my child’s teacher teach multiple ways to solve everything. Isn’t that confusing? Shouldn’t we just expect our students to learn the ‘regular’ way and then move on?”

My Elevator Speech: Great question. It is important to understand that there is a clear distinction between “getting the problem right” and “understanding the mathematics”. With our old standards it was commonplace for the teacher to show the class how to solve a problem and then give 20 identical problems to practice. Solving 20 identical problems does not mean a student understands it. The Common Core math standards are organized to allow students time to go into each topic deeply. Students are encouraged to solve a problem in multiple ways and share those methods with each other. Students learn not only from the teacher, but also from each other. The idea of solving a math problem in multiple ways is the very essence of mathematics itself; for example, the Pythagorean Theorem has been proven (solved) in more than 300 different ways! By teaching students multiple solution methods, we are teaching students the very essence of mathematics.

Does this elevator speech need additional solutions? Feel free to suggest something in the comments section.

Day 1 ] [ Day 2 ] [ Day 3 ] [ Day 4 ] [ Day 5 ] [ Day 6 ] [ Day 7 ]

Tuesday, September 16, 2014

"I'm Not A Math Person" Is No Longer A Valid Excuse

Research published in Child Development found that hard work and good study habits were the most important factor in improving math ability over time. But bad attitudes about math are holding us back.

Read more via Pocket

Stereotypes About Math Hold Americans Back

Here’s the most shocking statistic I have read in recent years: 60 percent of the 13 million two-year college students in the U.S. are currently placed into remedial math courses; 75 percent of them fail or drop the courses and leave college with no degree.

Read more via Pocket

Elevator Speech Challenge: Day 5

Here is Day 5 of my Why-I-Support-Common-Core-Math rant. This one is prepared just in case I ever find myself standing next to Diane Ravitch in the elevator.

HYPOTHETICAL QUESTION: “Duane…come on…why should we treat our kids like guinea pigs by using Common Core Math Standards that are untried and never field-tested?"

My Elevator Speech: Great question. The Common Core math standards are not untried. They are the result of years of research in what works in other countries - countries that kick our butt in international comparisons. Ironically, many of the countries that are now doing significantly better than us are doing so after they adopted many of the recommendations proposed by our own National Council of Teachers of Mathematics. Moreover, the Common Core Math Standards are not the result of some whimsical effort by a select few billionaires; the Common Core Math Standards have been endorsed by every major math organization in the nation! By adopting the Common Core Math Standards, we will be more in line with the best practices of the highest performing countries in the world. Once our math standards are in line with the rest of the world, then we can begin improving our teaching strategies!

Day 1 ] [ Day 2 ] [ Day 3 ] [ Day 4 ] [ Day 5 ] [ Day 6 ] [ Day 7 ]

Monday, September 15, 2014

Elevator Speech Challenge: Day 4

Here is day four of my Common Core Math Standards Elevator Speech Challenge, in which I am trying to write a week's worth of elevator speeches designed to respond to a variety of ill-informed attacks on the Common Core Math Standards. This speech came in response to another one of those silly I-hate-common-core-because-I-can't-understand-my-daughter's-homework posts on Facebook.

HYPOTHETICAL QUESTION: "Duane…come on…why do the Common Core Standards force kids to learn fuzzy math?"

My Elevator Speech: Great question. If “fuzzy math” means students are using math techniques that are different from how we learned when we were kids, then guilty as charged. Rather than teaching rote memorization, the Common Core Standards are written such that students are given a chance to actually learn WHY math works the way it does. “Fuzzy math” is merely a label used by anti-Common Core activists as a scare tactic, but it does not reflect the reality of the Common Core Math Standards. Each grade level from K though 5 has at least one major concept for which students are expected to be fluent. Nothing fuzzy about expecting students to be fluent. Additionally, scattered throughout the standards are references to “algorithm” and “standard algorithm”. While the teaching may look a little different from the old days, the expectations are not terribly different: students will learn the standard algorithms. The difference is now they will actually understand it.

Is my response fuzzy? Maybe? What say you?

Day 1 ] [ Day 2 ] [ Day 3 ] [ Day 4 ] [ Day 5 ] [ Day 6 ] [ Day 7 ]

Saturday, September 13, 2014

Elevator Speech Challenge: Day 3

A couple of days ago, my 3rd grade son came home from school. Rather than just commenting that school was "fine" and asking for his customary after-school snack, he grabbed a piece of paper and - failing to find a suitable pencil - a crayon to show me what he learned in math. "A know at least four ways to show 2 x 3 = 6", he proudly announced upon completing the drawing. Thanks to the Common Core Standards and his teacher trying to use EngageNY curriculum, my son sees multiplication as something more than a list to be memorized, and he sees it as a useful concept connected to real-life...

...which brings me to today's Math Elevator Speech:

HYPOTHETICAL QUESTION: "Duane…come on…my kid’s homework looks nothing like when I was a student. Why do the Common Core Standards force my student to do math in stupid ways?"

My Elevator Speech: Great question. There is a big difference between the Common Core Standards and the curriculum schools are using to teach those standards. The “standards” are the carefully selected and arranged list of topics students are to learn each year, while the “curriculum” is the tool teachers use to make that happen. Since the standards are arranged such that students can spend more time on each topic, the curriculum now has a fighting chance to teach the concepts so that students actually LEARN. Instead of textbooks being filled with things to memorize, textbooks are now likely look different because they are trying to explain to students WHY math works the way it does. Some people are freaked out by this, but they should calm down and understand that the motivation for teaching differently comes from a good place. That being said, it will take a few iterations before textbooks finally figure to the best way to explain to students the WHY of mathematics. Give the educational community time to figure this out. In the meantime, our students will be fine…they will learn math better than in the past…and they will LOVE it.

To teach math better it will have to look different from the way way previously taught math.
What are your thoughts?

Day 1 ] [ Day 2 ] [ Day 3 ] [ Day 4 ] [ Day 5 ] [ Day 6 ] [ Day 7 ]

Friday, September 12, 2014

Blocking and Interleaving...Huh?


Does the title pique your interest? Or does it just make you want to move on to another blog? Give me just a moment to share a simple idea that may improve your students’ achievement dramatically!

Let’s begin with a golfing analogy: The typical golfer will practice by going to the range, grab a club, and then hit a bunch of balls with that club. Then after feeling good about that club, the golfer will grab a different club and hit another 20 or 30 balls with that club. This process will continue until the bucket of balls is depleted. This “...repetitive drilling on the same task is called ‘block practice.’ You do the same thing, over and over, in one block of activity. Schmidt argues that a better way to learn is to practice several new things in succession, a technique called ‘variable practice’ or ‘interleaving.’ So a golfer would interleave her exercises at the range by aiming at different targets each time, by mixing up the kinds of shots she takes or switching the clubs she uses.” (see here for the entire article)

It turns out that this concept can be applied to practicing mathematics. Traditionally, the teacher teaches a skill and then assigns 20 or 30 problems. This is blocking.

What might interleaving look like? One professor “... designed a simple experiment to interleave homework in [three teacher’s] classrooms. Half of the class’s homework assignments would stay the same. But for the other half, [the professor] would take all the homework questions the teachers had used last year and mix them up. So the interleaved assignments would have some questions about what the class was currently studying, and some questions about things they had studied earlier in the year.”

What were the results? “For the kinds of problems they learned with interleaved practice, the kids averaged 72 percent correct. With blocked practice, they averaged only 38 percent.” (Read the actual report here.) What is amazing is how little time, effort, or money was required to attain the more than 100% improvement! The curriculum stayed the same. The pedagogy stayed the same. The only thing that changed was the interleaving of the questions. This is a cheap, easy, and fast way to improve student achievement!

This news about interleaving versus blocking should not be particularly surprising. We have long known strategies that engage students in comparative thinking have the greatest effect on student achievement. More recently, Dr. Robert Marzano's research in The Art and Science of Teaching (2007) reconfirmed that asking students to identify similarities and differences through comparative analysis leads to eye-opening gains in student achievement.

Interleaving homework problems is just another way to create student opportunities to identify similarities and differences (and thereby the relationships) of the math topics being learned.

Please listen to the American Radioworks Podcast from which I learned all this.

For the segment on interleaving, scroll ahead to 28:42.

If you have an hour, please listen to the entire podcast. It is brilliant!

UPDATE (March 30, 2015):

The above is a quotation from a 4th grade textbook written in 1901. Clearly, mathematics teachers have long had the intuitive belief that interleaving is best for our students.

Elevator Speech Challenge: Day 2

Day 2 of my Elevator Speech Challenge. Each day for a week I will try to write a different elevator speech for why I am in favor of the Common Core Math Standards. Read on...

So the other day my wife asked me to switch the door knob on our front door with a brand new door knob. This wouldn't be such a bad idea if the door knob was broken, but it seemed like I was being asked to switch one perfectly fine door knob with another.

Which brings me to my Elevator Speech Challenge.

HYPOTHETICAL QUESTION: “Duane…come on…why are the new Common Core standards better than the old standards?”

My Elevator Speech: Great question. The old collection of math standards were largely a massively long list of discrete, unconnected math skills. At many grade levels, students were expected to learn about one new math topic each day! As a result, the curriculum was called “a mile wide, but an inch deep”. Students never learned anything in depth because they were always having to move on to the next topic. This meant students never learned anything well and had to spend large portions of each school year reviewing what was supposed to have been learned the previous year. In CCSS, there are fewer standards each year, allowing students to go into greater depth for each topic, resulting in AWESOME learning for all students.

There is no single elevator speech that addresses every facet of Common Core. This challenge, however, is forcing me to prepare myself for any conversation I may suddenly find myself in.


Day 1 ] [ Day 2 ] [ Day 3 ] [ Day 4 ] [ Day 5 ] [ Day 6 ] [ Day 7 ]

Thursday, September 11, 2014

Game on: The Elevator Speech Challenge (Day 1)

A few days ago I was reading through my Twitter feed (perhaps the BEST professional development technique ever) as I normally do most evenings. That is when I stumbled upon Andrew Stadel's (@mr_stadel) tweet that he is challenging himself (and others) to write a series of Elevator Speeches in support of the Common Core math standards. Recently, I have had a series of experiences with parents and teachers that really made it clear that I must develop my own series of Elevator Speeches.

No single elevator speech can address the many facets (some controversial) of the Common Core mathematics standards. So, I plan to write a variety of elevator speeches for a variety of potential conversations that I might suddenly find myself in.

Andrew…you don’t know me, but I seriously thank you for the challenge!

HYPOTHETICAL QUESTION: "Duane…come on…do you really think Common Core Math Standards are a good thing?"

My Elevator Speech: Great question. Prior to the Common Core standards, every state had their own math standards for each grade level. This meant that an 8th grader in Oregon is learning different stuff than an 8th grader in Michigan, Florida, or California. For many decades this might have been an okay thing, but now we live in an incredibly mobile world. It is commonplace for students to move from one state to another. However, with every state having their own list of standards, these students suffered greatly. With Common Core standards, states have gotten together to adopt the same list of standards (this is a state-by-state initiative, not a federal program) meaning students can now seamlessly move from one state to another virtually without missing a beat.

Please visit Andrew Stadel's blog to read his elevator speeches:

I encourage everyone to prepare themselves with their own elevator speeches. Try it for a week. See what happens to your own thinking. Game on? Game on!

[ Day 1 ] [ Day 2 ] [ Day 3 ] [ Day 4 ] [ Day 5 ] [ Day 6 ] [ Day 7 ]

Wednesday, August 27, 2014

Why there are no homework answer keys in EngageNY

Why there are no homework answer keys in EngageNY

Although homework is a great way to reinforce the mathematics that was learned in class, correcting it in class can be time consuming and can take away precious instructional minutes. Nevertheless, many teachers are desperately wondering why EngageNY does not come with an answer key for the homework. Without becoming an EngageNY apologetic, here are my thoughts on why having a homework answer key is unnecessary.

I maintain that reviewing homework - while it may have some benefits - is an extremely inefficient use of our precious classroom minutes. There are many other effective and efficient uses of our time: in-depth instruction, cooperative learning, project-based learning, formative assessment, etc. But before coming up with ideas for reviewing homework, we need to ask ourselves the prerequisite question: What is the purpose of reviewing homework?

To hold students accountable? If reviewing homework is primarily to hold students accountable, then the teacher can simply ask students to take out their work and place it on their desk. Without taking any class minutes, it is easy for the teacher to see who has or has not completed the homework. Once that is done, the teacher can get to the important task of teaching. Holding students accountable does not necessarily require an answer key.

To assess which students understand? While this is a great goal for the teacher to have, using class time for the teacher to drone answer after answer as the students put stars or checkmarks next to each problem is a horribly inefficient way to assess student understanding. Perhaps a better way to accomplish this is to have students compare their work with a partner. This fosters cooperative learning and places a bit of the responsibility on the shoulders of the students to explain their answers and to ask questions on their own. As this is going on, the teacher can collect formative assessment data by listening in on the conversations that the student pairs are having. No answer key necessary!

To briefly review yesterday’s topic before learning today’s topic? Merely rattling off the answer key does nothing to accomplish this. If this is the teacher’s goal, instead ask student volunteers to do selected problems on the whiteboard. Although not every problem from the homework will be posted on the board, enough problems will be on the board to allow students to ask clarifying questions. Essentially, students are creating the answer key for you. If you REALLY want an answer key, take a picture of the solved problems on the board. 

Here are three methods for dealing with homework WITHOUT requiring an answer key:
  1. Don't correct the homework, just ask students to take out the homework and leave it on their desk. During math time, the teacher can walk around and scan the work to identify which students understand and which do not.
  2. Ask students to compare their work with a partner. Then they can ask the teacher questions about any disagreements.
  3. At the start of math time ask several students to each do a problem (of their choosing or the teacher’s choosing) from last night’s homework on the whiteboard. Although not every problem from the homework will be solved on the board, it is enough to allow students to ask questions.

The method I use for any particular day depends on a variety of factors:
  • how difficult or easy the homework was;
  • how much math time I have available for the day;
  • the math topic I plan to teach today;

In a nutshell...Use class time wisely. Spending your time teaching in innovative and effective ways is paramount. Rattling off the answer key to a bunch of bored students? Not so much.

Anyone else with better suggestions?

Monday, July 28, 2014

Five steps for eliminating math anxiety

Five steps to eliminate math anxiety

When I meet someone new at a party and we exchange the customary small talk ("What about this weather?" or "How about those Giants?"), inevitably the question of what I do for a living comes up. Even before I share that I have been a middle school math teacher for 25 years, I can pretty much be certain that the response will be something along the lines of "Oh, math...I never understood algebra" or "I hated math in high teacher was the worst". What a buzz kill.

It doesn't take much of a detective to figure out that ours is a nation filled with mathphobics, or at least math-haters. There is plenty of evidence that babies do not come out of the womb hating math. So what happened between the time babies are born loving math and the time they become adults practically bragging that they can’t do math? SCHOOL.

School causes math anxiety. More accurately, the traditional instructional practices commonly used by math teachers - although it makes them highly regarded by their colleagues - are the very causes of the math anxiety experienced by our nation. I understand that there are other genuine causes of math anxiety that have nothing to do with schools, but for the purposes of this essay, I’ll only focus on math anxiety that is the direct result of our suck pedagogical practices in mathematics.

Five Steps
  1. Eliminate timed tests
  2. Provide students with a choice for assessing understanding
  3. Let students invent their initial understanding of the mathematics
  4. Teach multiple solution methods
  5. Encourage lots of student collaboration
It doesn’t have to be that way. Mathematics is an inherently interesting and beautiful and creative topic. So what can be done to keep our students thinking that is truly awesome? Here are my five steps for teaching math in a way that reduces the chance that students will develop math anxiety:

  1. Eliminate timed tests
  2. Provide students with a choice for assessing understanding
  3. Let students invent their initial understanding of the mathematics
  4. Teach multiple solution methods
  5. Encourage lots of student collaboration

Let’s take a brief look at each one.

1. Eliminate timed tests

It’s bad enough that math has the reputation for being a black-and-white, right-or-wrong subject, but the practically religious zeal with which teachers use timed tests is about the worst thing we can do in a math classroom. We know that when children are put under math stress they are less able to correctly solve problems. Timed tests also give students the idea that mathematical success is somehow connected to speed rather than critical thinking.

It is true that the Common Core State Standards of Mathematics uses the word fluency throughout the standards. Rather than using timed tests to teach (or measure) fluency, however, we should embed fluency building opportunities within number sense building activities. When students learn how to be flexible with numbers and quantities THIS is when fluency will naturally develop. Fluency, thus, can be developed in our students without causing fear and anxiety.

2. Provide students with a choice for assessing understanding

Since we know that students are less able to perform mathematical calculations when under stress, why do we continue to use stressful tests to measure student achievement? In a way, math tests are just longer versions of the timed tests that we already know are bad for students. Let’s seek methods of assessing our students without causing fear and anxiety.

Start by assessing students formatively and informally on a daily basis. As students are working in class, the teacher should wander around the room noting which students are confidently and competently solving the problems, and then record that with a clipboard and checklist. Why should the teacher bother with a stressful test if she has already personally observed students successfully solving the problems?

If an actual assessment activity is necessary, we should provide students with a choice in how they demonstrate their understanding. Students who like taking tests can take one. Students who would prefer an alternative can demonstrate their understanding by
  • making a video with screencasting software
  • performing a skit
  • standing at the whiteboard and solving problems
Giving students a voice in how they are assessed means students can choose the assessment method that they are the most comfortable with, thereby reducing math anxiety.

3. Let students invent their initial understanding of the mathematics

In a traditional classroom the teacher leads the discussion and shows students step-by-step how to solve the problem. Then students practice some problems in the classroom. Finally students go home to practice problems on their own. We in the ed biz call this the “gradual release” model.

This model of teaching leads students to believe that mathematics is not something discovered, but a fixed set of skills that is handed down from generation to generation. Since math is viewed as a fixed set of rules, a student who can’t immediately come up with the proper solution method is left only with the assumption that he is incompetent.

Instead, we need to foster an environment where students see mathematics as the creative endeavor that it is. Students should be empowered to create their own solution method or algorithm when necessary. We know that invention activities lead to deeper understanding in mathematics. Therefore, prior to teaching a particular content, students should be given the opportunity to use their natural number sense to invent their own solution method prior to being taught the “official” method.

4. Teach multiple solution methods

I have observed many of my Algebra students get stuck on a math problem that could easily be solved arithmetically or by guess-and-check. When I ask why they didn’t use one of the simple solution methods, students usually say that those are the “wrong” methods to use in an algebra class. Not only is math a bunch of rules, students also feel that there exists the added layer of complexity of using the “right” method.

As a direct result of #3, we need to teach students a variety of solution methods whenever possible. The very nature of mathematics is to find as many ways to solve a problem as possible. If this was not the case, the first time the Pythagorean Theorem was proven would have been enough for the mathematics community. Instead, the theorem has been proved over 300 different ways! We need to allow students to hunt for many different solution methods for a single problem, rather than forcing students to use one method to solve 30 problems. Students thrive when given the opportunity to re-create their own Pythagorean scenarios in class.

As students solve a single problem in multiple ways, they have the opportunity to compare and contrast the methods, see the connections between seeming unrelated methods, and develop a deeper understanding of the number sense that is inherent in that problem.

5. Encourage lots of student collaboration

Misery loves company? There’s safety in numbers? Two heads are better than one? Whatever meme you want to use, students thrive when given the opportunity to work with one another. We know that student discourse improves achievement. Let students talk, so they can learn! Math anxiety will not rear its ugly head when two students are talking to one another in their own kid-friendly language. While students are collaborating, the teacher should be grazing around the room collecting formative assessment data: who is using which technique, who invented something novel, who is struggling, etc?

Collaboration only makes sense! Imagine The Beatles trying to learn how to be a band together without being allowed to talk with one another. That is exactly what we do in class! Students are seated in rows, often with seating charts specifically designed to discourage talking.

While it’s no guarantee, my 25 years of experience says that implementing these five easy steps will go a long, long way towards preventing schools from causing math anxiety in our students! Reducing the math anxiety amongst our teachers...that's a story for another day.

Do you have anything you'd like to add to the list?

Tuesday, July 1, 2014

Is Math Anxiety Just Another Name for 'Bad at Math'?

This came through my inbox today. I wanted to share it with everyone.

Is Math Anxiety Just Another Name for ‘Bad At Math’?

            “To many people, ‘math’ is a scary four-letter word,” say Sian Beilock (University of Chicago) and Daniel Willingham (University of Virginia) in this article in American Educator. “They don’t like it, they don’t feel like they are very good at it, and they just want to stay away from it.” Math anxiety is associated with poor performance in schools and colleges – and with on-the-job errors by nurses, financial planners, and many others around the world. When does math anxiety get started, where does it come from, and what can be done about it?
            Beilock and Willingham report on research showing that math anxiety emerges early, affecting as many as 50 percent of first and second graders, is directly related to math performance (the more anxiety, the less well students do on math assessments), and is not correlated with performance on reading assessments. So is math anxiety just a manifestation of being bad at math? The authors think not. People with math anxiety would do better at math if they weren’t so anxious. That’s because anxious thoughts (fear of making a mistake, looking stupid in front of other students, displeasing the teacher) impair their working memory, or their mental “scratch pad,” and this means they’re less able to keep several things in mind at the same time – essential to manipulating numbers and solving problems. Brain scans have found this effect when highly math-anxious people even thought about doing math.
            What kicks off math anxiety? Beilock and Willingham say it is associated with children’s math abilities when they first enter school – for example, counting objects, deciding which of two numbers represents the larger quantity, and mentally rotating three-dimensional objects. Having difficulty with these basic skills starts a self-reinforcing cascade of anxiety and poor performance. Oddly, it’s students with the best working memory who are most impaired by anxiety, perhaps because they’ve come to rely on working memory in other areas and it’s shut down by anxiety.
A second source of math anxiety is the signals students get from home, the classroom, and society in general. Children can pick up signals from adults that math is, indeed, something to be worried about. Those students who enter school with math skill deficits are especially susceptible to a teacher’s or parent’s negative comments about the subject. Two studies have shown a direct correlation between female primary-grade teachers’ level of math anxiety and their students’ math performance at the end of the year: the more anxious the teachers were, the worse their students did, especially girls.
There’s a lot more research to be done, but given what we know so far, what can be done? Beilock and Willingham have these suggestions:   
• Ensure fundamental skills. Parents can build their children’s basic counting and spatial skills, and for students who enter school without them, teachers need to diagnose weaknesses and work quickly to improve them before anxiety sets in.
• Focus on teacher training. Building elementary teachers’ confidence and knowledge is essential to reducing their math-anxious vibes. Researchers have found that it’s more effective to teach teachers how to teach math concepts than focusing on the math concepts themselves.
• Don’t use timed math assessments. Racing the clock heightens anxiety; the simple remedy of untimed tests makes it possible for many students to do better work. [See Marshall Memo 538 for an article about timed tests.]
• Get students to write about their feelings. Studies have shown that having students write freely about their emotions about a specific situation (like a looming test) for about 10 minutes can help boost performance. The student thinks, “Oh, maybe this math test isn’t really that big of a deal” and working memory is freed up to focus on the math. Here is the actual prompt that was used in one such situation (students were assured that their writing was anonymous and would not be seen by their teacher): Take the next several minutes to write as openly as possible about your thoughts and feelings regarding the exam you are about to take. In your writing, really let yourself go and explore your emotions and thoughts as you are getting ready to start the exam. You might relate your current thoughts to the way you have felt during other similar situations at school or in other situations in your life. Please try to be as open as possible as you write about your thoughts at this time.
• Think carefully about what to say when students are having difficulty. If we say, “It’s okay, not everyone can be good at these types of problems,” students may interpret that to mean that the work is too hard for them and there’s no hope. “Consolation sends a subtle message that validates the student’s opinion that he’s not good at math, and can lower a student’s motivations and expectations for future performances,” say Beilock and Willingham. A better statement would be, “Yes, this work is challenging, but I know that with hard work you can do it!” Following up with specific study strategies and assistance adds to the power of that statement.

“Ask the Cognitive Scientist – Math Anxiety: Can Teachers Help Students Reduce It?” by Sian Beilock and Daniel Willingham in American Educator, Summer 2014 (Vol. 38, #2, p. 28-32, 43),