Breathe

Regardless of the content or grade level, every teacher gets frustrated from time to time in the classroom. Research has shown that teachers make about 1,500 decisions in the course of a day. Add to that unexpected changes in the day, a student having a tough emotional day, the teacher feeling under the weather, or a dispute between students which needs to be addressed. It can all become the perfect storm for an overly stressed teacher. I know, because I’ve been there.

A few years ago I started reading more about yoga and meditation. My wife actually introduced me to both. Yoga and meditation had an enormous impact on my mood and physical wellbeing. Eventually, I started reading and listening Dr. Weil who practices integrated medicine.

One idea I heard from Dr. Weil, which has been incredibly useful, is the 4-7-8 breathing technique. It’s an exercise based off of yoga practice.

  • Exhale through your mouth;
  • Close your mouth;
  • Breathe in through your mouth to a count of 4;
  • Hold your breath for a count of 7;
  • Blow air out through your mouth to a count of 8.

This process is repeated for four breath cycles. The process takes only about 30 seconds and can be done sitting, standing, or lying down. (Not that I recommend lying down in the middle of your classroom.)

I tried the 4-7-8 breathing exercise about a year go for the first time. As Dr. Weil mentions in this video, it is a process that takes time to develop. Over time, it did become more natural and extremely relaxing.

The next time you are feeling stressed in the middle of a lesson, take 30 seconds and give the 4-7-8 breathing exercise a try. It take so little time that your students won’t even notice. It’s a win-win for everybody!

The Smartest Person in the Room

I absolutely love quotes. My favorite quote is “The two most important days in your life are the day you are born and the day you find out why.” Those fantastic words are from the author and humorist Mark Twain.

One of the my other favorite quotes is, “The smartest person in the room is the room.” There’s some debate who actually said these words, so we’ll just leave it at a pretty wise individual.

In 2020 that room, thanks to technology and the Internet, is as big as you want it to be. If you want to know something, you search for it on Google or ask Siri or Alexa for the answer.

Recently, I was looking for some new number sense routines for my fourth graders, and my Internet search took me to youcubed.org. It is a great site filled with videos, activities to do in the classroom, and other useful resources.

There are so many other wonderful resources for teachers of math, ELA, science, and every other content area. The Internet is a wealth of knowledge. It’s an amazing time to be able to connect to other teachers, share ideas, and learn from others. When the room is this big, it’s hard to be the smartest person in it. And that’s a wonderful thing!

The Curse of Knowledge

Every once in a while there’s a lesson that makes me take a step back and think about how hard it is to truly learn and understand something. For example, fractions are not an easy concept to grasp conceptually. It’s one thing to learn that 1/3 is greater than 1/4 because the smaller denominator is the bigger fraction. It’s another thing entirely to understand conceptually why 1/3 is greater – each fraction has one part but the parts of 1/3 are larger than the parts of 1/4.

Fractions are even a difficult concept for adults to conceptually understand. In the 1980s, the A&W company tried to compete with McDonald’s quarter pounder. They created a third pounder which was cheaper and bigger than the quarter pounder. It beat McDonald’s burger in taste tests and was accompanied by a marketing campaign. So a company produces a bigger, less expensive burger, and the public likes the taste. Seems like a slam dunk, right? No. The public didn’t go for it. Why? During focus groups it was determined that customers thought they were getting less burger for their money because they mistakingly thought 1/3 is smaller than 1/4. A&W’s problem wasn’t a quality of product problem. A&W had a math problem – literally.

This is another reminder of how difficult it is to really understand some concepts. I can manipulate the numbers in my head and explain why 1/3 is greater than 1/4. It’s easy for me to forget that it takes time, modeling, and repetition to truly understand how to compare fractions with like numerators.

This struggle with fractions reminded me of a concept I first heard in the book Make It Stick. The idea is called the curse of knowledge. “The curse of knowledge is our tendency to underestimate how long it will take another person to learn something new or perform a task that we have already mastered.”

It is hard to remember how difficult it is to first learn something. Take driving for instance. An experienced driver doesn’t think about all the decisions he makes behind the wheel of the car. He has built a knowledge base over years that allows the process of driving to become almost second nature. Now put a 16-year-old behind the wheel and you’re reminded of how much a person needs to learn to drive a car. You’re also reminded that this knowledge is not obtained overnight.

I try to go into lessons with the curse of knowledge on my mind. It is important to remember that the 9- and 10-year-olds sitting in my classroom haven’t had the years of math exposure I have. It’s why thinking through the lens of our students is so important.

In an attempt to combat this curse of knowledge, I try to anticipate prior to a lesson which concepts will give students difficulty and why. My goal is to overcome the curse of knowledge as a teacher. In the process, hopefully, my students will conceptually understand difficult concepts like fractions and know the mathematical difference between a third pounder and a quarter pounder.

Peaks and Valleys of the School Year

My first year teaching, somebody showed me a graphic similar to the Phases of First-Year Teaching. I’d also seen the research that 35% of teachers leave the profession during their first year and half of teachers leave the profession within the first five years. That visual of the Phases of First-Year Teaching stared at me, and I knew there was some truth to it.

Imagine a “U” extending for August to June. At the beginning of the year, new teachers are excited and filled with anticipation. As they move through September and October it becomes survival mode. November to January is a valley at the bottom of the “U.” This valley of disillusionment is brought on by nonstop stress, work, and the belief that things are not going as smoothly as they’d like. From February to the summer, teachers make the upturn through rejuvenation, reflection, and eventually back to anticipation for the next year.

Here’s a more light-hearted take on the phases of teaching.

Whether you’re a new teacher or a 20-year veteran, there are times throughout the school year which are more difficult than others. This time of year seems especially stressful for teachers. One of the messages shared with me as a new teacher: make sure you’re taking care of yourself and looking out for other teachers. It’s great advice for anybody in the profession, regardless of their years of service.

When Altogether Doesn’t Mean Add

I read an article a few years ago that really changed the way I talk to my students in math class. The article is called 13 Rules That Expire. It was published inNCTM’s August 2014 issue of Teaching Children Mathematics.

The gist of the article is that there are math “rules” used in classrooms. These are often presented as rules that always work, but in the case of these 13 rules, there is an expiration date. The article goes into greater detail about each of the rules, including the expiration date (or expiration grade). My goal is not to thoroughly discuss all 13 rules in this post, but wanted to at least list them.

  1. When you multiply a number by a ten, just add a zero to the end of the number.
  2. Use keywords to solve word problems.
  3. You cannot take a bigger number from a small number.
  4. Addition and multiplication make numbers bigger.
  5. Subtraction and division make numbers smaller.
  6. You always divide the larger number by the smaller number.
  7. Two negatives make a positive.
  8. Multiply everything inside the parentheses by the number outside the parentheses.
  9. Improper fractions should always be written as a mixed number.
  10. The number you say first in counting is always less than the number that comes next.
  11. The longer the number, the larger the number.
  12. Please Excuse My Dear Aunt Sally.
  13. The equal sign means Find the answer or Write the answer.

There is one rule I wanted to discuss a little further. Before reading this article, I was a big fan of teaching students to solve problems with the help of keywords. This often included making an anchor chart with the keyword on one side and the meaning on the other side (i.e. in all means add, how many more means subtract).

One common keyword strategy to teach students is that the word altogether means you should add. While that does work most of the time, it doesn’t always work. Take for instance the following problem:

Jimmy read 11 books in fourth grade, and Brian read 8 books. Jimmy, Brian, and Elyse, read 37 books altogether. How many books did Elyse read?

If students attack word problem by simply looking for keywords to help them solve problems, they will most likely see altogether and add 11 + 8 + 37. If students are thinking about the context of problem, and not just the keywords, they will see that they have to subtract 19 (11 + 8) from 37. This requires students to understand what is happening in the problem and not simply use the keyword as their only problem solving tool.

Teaching problem solving to our students is not an easy endeavor. It takes many tools in the mathematician’s toolbox. It takes constant repetition and exposure to many problem types. Teaching problem solving is not easy, but it is one of the most important skills we teach in any subject area.

Fun with Numbers

It’s always great to show students the wonder of math and numbers in the real world. Today, February 2, 2020 is one of those opportunities to have fun with numbers. Not only is today Super Bowl Sunday and Groundhog Day, but it is also an eight-digit palindrome. A palindrome is a word or phrase that reads the same forward and backward – Anna, nurses run, or my daughter’s favorite book Taco Cat.

Today is 02/02/2020 or 02022020. It is symmetry at its finest. How rare is a global eight-digit palindrome? The last time it happened was 909 years ago – November 11, 1111 or 11/11/1111. The good news is you won’t have to wait another 909 years. There will be another in a mere 101 years on December 12, 2121… 12/12/2121.

But wait, the math fun isn’t done yet. Today is the 33 day of the year and there are 333 days left in 2020. Thank you leap year for that. With all this math fun, it’s like Christmas in February!

Three for the Week

Saturdays are my time to reflect on what I read, heard, and discussed throughout the week. It is my “exit ticket” for the last seven days. So here are three ideas that made me think this week. (They are not in any particular order.)

1- If you’ve read more than a couple posts on my blog, you probably know that one of my greatest passions is math education. I am a total nerd when it comes to better understanding how to teach math, especially at the elementary level. I am also a huge podcast fan. So, when I heard Marilyn Burns on a podcast talking about math education, it was like Charlie finding Willy Wonka’s Golden Ticket. “I think that most teachers begin teaching the way we were taught,” Burns said on the podcast. As her teaching career progressed she started to change her thought process. “I got really curious about how do I get kids to be the stars in the classroom rather than me being the star in the classroom. So everything shifted for me from ‘How do I make myself as the most important person in the room?’ to making the students the most important people in the room.” Isn’t that what we should be striving for in every classroom?

2 – A teacher in Nebraska had his favorite pair of shoes stolen from his classroom. His students all chipped in to buy him a new pair. His reaction to the gift shows the impact a great teacher can have on his students. It’s impossible to not see how much he and his students care about each other. On a side note, when I watched this video, somebody must left some chopped onions near me.

3 – I generally save #3 for something light hearted. This story from CBS’s Steve Hartman fits that mold but also has an important message. The arts are so important to our children. We should do everything we can to protect music and art education in our communities. Seeing the look on this nine-year-old boy’s face when he sees the Michigan Marching Band proves that the arts are critically important.

Smartphones and Anxiety

A couple days ago my daughter was playing the piano for her grandparents. They love listening to her play songs she’s learning or old recital numbers. At least twice a week she’s playing for them after dinner. What makes this a really remarkable feat is that my in-laws live six hours away in New England. They’re able to watch and listen to my daughter play because of FaceTime.

Do I worry about the impact smartphones and other devices will have on my daughter as she gets older? Sure, I do. I’m a parent, so I pretty much worry about everything. It’s part of the job. But I also know that there are some amazing things this technology can do for my ten-year-old daughter – playing the piano for her grandparents, virtual field trips, research at the tip of her finger.

Just this week I was involved in a discussion about the rise in student anxiety across zip codes, socio-economic status, gender, and race. The common consensus among those involved in the conversation was that technology was to blame.

New research, however, is challenging that line of thinking. The researchers, lead by Candice Odgers, a professor at the University of California, Irvine, believe that devices are not the sole culprit but are just shining a light on an underlying mental health problem a child would have even without smartphones.

After reviewing other studies and data available, the researchers stated, “The review highlights that most research to date has been correlational, focused on adults versus adolescents, and has generated a mix of often conflicting small positive, negative and null associations.” Correlation does not equal causation. Just because the increase in smartphones and mental health problems in the United States happened at the same time, doesn’t necessarily mean one causes the other.

Some evidence to support such a claim can be found across the Atlantic. Larger parts of Europe have seen an equal increase in smartphone use without an equal increase in anxiety and other mental health disorders. If the smartphone was the problem then these parts of Europe would see an increase in anxiety comparable to the United States.

According to the study, the United States has been an outlier in suicide rates worldwide. Every adolescent age group in the U.S. has seen a rise in suicide deaths from 1999 to 2017. The greatest increase has been among girls 10-14. This group has seen rates triple during that same time. Worldwide, suicide rates have dropped during this same time period.

So what, other than smartphones, could be contributing to an increase in anxiety and mental health concerns? Jeff Hancock, founder of the Stanford Social Media Lab, offered some other possibilities for what might be making our kids anxious: climate change, income inequality, or rising student debt.

“The current dominant discourse around phones and well-being is a lot of hype and a lot of fear,” Hancock said, according to the New York Times. “But if you compare the effects of your phone to eating properly or sleeping or smoking, it’s not even close.”

Are there drawbacks to an increase in technology at our kids’ fingertips? Sure. We obviously don’t want children so involved on their devices that they don’t go outside and get exercise or have healthy conversations with people. This research, however, argues that the smartphone might not be the real reason children are more anxious.

We should still allow our children and students to have access to devices, but we need to have conversations about using them appropriately. Like any technological advancement, there are benefits and drawbacks. We just need to make sure we truly understand both.

Numberless Word Problems

A few years ago I was doing a lot of one-on-one work with a student who struggled in math. We often met before class to do some mental math and try to improve his number sense. After school, we would revisit the skill we discussed in class that day. He made a lot of progress and was starting to feel much more confident about math in general and problem solving in particular. Then we introduced fractions.

Shortly after we started our unit on fractions, he put his head down in frustration. I asked him what was wrong, and he replied, “I was just starting to get math and then… then fractions happened.” It was as if he had contracted a deadly virus named fractions. We talked about how good problem solving doesn’t change just because we moved from whole numbers to fractions. Over the next month or so, we continued to work and his confidence with fractions improved as well.

My approach with that student would be slightly different today. Instead of moving him right into word problems with fractions, I would use numberless word problems to help ease some of the anxiety. The numberless word problems would be a sort of scaffold to the problems with fractions. This would help him see that we’re still using the same problem solving strategies we used with whole numbers.

Numberless Word Problem in 4th Grade

Numberless word problems are just that – word problems without numbers. Let’s look at the following problem.

Brian eats 1/8 of the pizza and Julie eats 4/8 of the same pizza. How much of the pizza did Brian and Julie both eat?

This is a pretty basic word problem involving fractions. Some students might struggle with this problem simply because they are intimidated by the fractions. So, why not take the fractions out all together?

Brian eats some pizza and Julie eats some pizza. How much of the pizza did Brian and Julie both eat?

Now we can have a conversation about what is happening in the problem. We can talk about how one person has some amount of pizza and another person has another amount. We want to know how much they have together. That hopefully leads students to see that this is an addition problem. Once they understand the context of the problem and have determined the operations they need to use (addition), then they can start looking at specific numbers.

Depending on the students and the problem, I might put some whole numbers in the problem before moving to fractions. This will give the student another opportunity to see the context of the problem before the fractions are introduced. I did this today with my class.

I took a problem from our math book and covered up the fractions to create a numberless word problem. This is how I introduced the problem.
After we discussed the context of the problem, and determined the necessary operation, I put whole numbers into the problem.
Then, we looked at the original problem with fractions and talked about how the structure of the problem didn’t change because of the fractions.

This is a wonderful strategy because it helps students focus on the context of the problem. The focus on the narrative portion of the problem before worrying about the numbers. They can’t worry about the numbers, because they aren’t there yet.

Teaching Students with ADHD

One year I had a boy named Jimmy in my class, and he was one of the coolest kids I ever taught. (I always change names of students on this blog.) Jimmy asked me almost every day how my previous night was. This wasn’t just something he was taught to ask, Jimmy was genuinely interested in what I did and how I was feeling. He had the hardest time sitting still. Jimmy was such a kind kid who seemed to genuinely care for everybody around him and had a heart of gold. He had an extremely difficult time staying focused during a lesson. Jimmy would often display his artistic talents by drawing me pictures. If you’ve worked in a classroom, you probably know a kid just like Jimmy – kind, talented, sweet, but has trouble sitting still and staying focused.

It was clear to me early on that Jimmy had ADHD. I don’t think I heard the team ADHD (Attention Deficit Hyperactivity Disorder) when I was kid. The term ADD was initially used in an American Psychiatric Association manual in 1980. An upward trend of ADHD diagnoses followed a 1997 survey of parents nationwide. As many educators know, that upward trajectory has continued today.

Different students with ADHD benefit from different supports in the classroom. Some students see improved attention simply by sitting near the instruction. Other students need more supports like a timer to help keep them on task or a checklist to ensure they have the belongings they need at the end of the day. I was interested in creating a list of strategies to help students with ADHD, like Jimmy. I used a few websites to help me compile a list of non-medication strategies to use with students:

  • Give minimal number of directions;
  • Give directions in written form when possible for student to reference as they work;
  • Limit the amount of work on a page;
  • Cover up some work or text on a page to minimize distraction;
  • Use color coded folders to help student stay organized;
  • Periodically help students clean out backpacks, desks, folders, etc.;
  • Use checklist for assignments or homework materials;
  • Frequent redirection;
  • Peer tutoring;
  • Think/Pair/Share and other sharing strategies;
  • Give student movement breaks throughout the lesson and day;
  • Teach study skills explicitly;
  • Give student clear expectations;
  • Give students clear deadlines when assignments are due;
  • Use brain breaks;
  • Give students choice on assignments.

This is not an exhaustive list of strategies to support students with ADHD. It is, however, a place to get some ideas to get started. They are strategies I was so glad to discover when I had Jimmy in my class. Hopefully they can help the Jimmy you have in your classroom or school.