Is more physical education at school linked to higher student math scores?

In January, we decided to post tips on my school’s facebook page for students to get organized as part of Get Organized Month.

I posted many many suggestions, and a few of them were selected, but one suggestion I gave was to organize time. I wrote:

Use a timer to help you organize your time and create a schedule for your courses. For example, set a timer for 50 minutes. Work as hard as you can until the timer goes off, and then take a 5 – 10 minute break from your studies. Your brain needs the rest before learning some more. During your break, do something active – exercise or do some stretches, have a snack or take a quick walk or jog, or play a quick game or read a book to activate your brain in a different way.

For me, it was important to include the part about exercise during a student’s break time. I’m a firm believer that a student needs to take care of their whole body to help them learn. Our parts are too connected between the brain and the rest of the body.

Imagine my delight when I found an article this week by the Washington Post called Is more physical education at school linked to higher student math scores?.

“This finding demonstrates that students’ academic performance improves when there’s a balance between time spent on physical education and time spent on learning,” said Stacey Snelling, dean of American University’s School of Education.

Granted, this study was just looking at a handful of elementary schools, but I don’t see why the results couldn’t be extrapolated to all people of all ages.

Recently my daughter and I started doing “pretend jump rope,” where we move our hands as if we were holding jump ropes, but our hands are empty. We also jump as if we were jump roping. (I started jumping rope after reading a different article by Drs. Oz and Roizen last August.

Can you think of any ways to introduce more activity for your students? Let me know in the comments.


Teach My Lesson 2

Check out my previous post for an introduction to my school and idea for where this came from. Student name was changed for privacy, and some spelling/punctuation errors were fixed (but I’m sure not all). Also, since we are writing in real time, there are several places where I posted something after the student did that would probably make more sense if it was posted before the student. I did not alter these situations, but if you have a question on anything, please ask.


Chad Lower:Hello Student. How may I help you?

Student:I have a math question.

Student:    The following set of coordinates most specifically represents which figure?(-4, 5), (-1, 7), (1, 4), (-2, 2) (5 points)                                 Parallelogram    Rectangle            Rhombus             Square

Student:I know that it is either a square or rhombus, but I don’t know which one

Chad Lower:Student, how do you know that part of it?

Student:I graphed it on graph paper and the figure had 2 pairs of parallel sides and all right angles

Chad Lower:how do you know they are right angles? They may look it, but may not be exactly right angles

Student:Oh I guess I don’t know if they are right angles

Chad Lower:okay, so that is one part we need to check.

Chad Lower:(and checking that will also verify if the opposite sides are parallel)

Chad Lower:the other part is the distance of the sides

Chad Lower:you can have 4 right angles, but then it could be a rectangle or a square


Student:so should i do the distance formula?

Chad Lower:exactly!

Chad Lower:for the length part anyway.

Chad Lower:you will need a different tool to show right angles

Student:they are all equal sides

Chad Lower:oh cool! so then we can narrow down to square or rhombus


Student:what should I use to find the right angles

Chad Lower:so think “perpendicular”

Chad Lower:how can I tell if two lines are perpendicular to each other?

Student:they make a right angle when they intersect

Chad Lower:okay–try this related question — how can you tell if two lines are parallel?

Student:can I use one of the proofs to prove perpendicular lines

Student:they never intersect each other

Chad Lower:so would you draw them forever and ever and see if they ever touched?

Chad Lower:I don’t think a proof will be helpful for this question.


Student:I guess you could

Chad Lower:that would take a long time

Student:but that wouldn’t work out

Chad Lower:and you would never finish — right

Student:hahah right

Chad Lower:so is there another way we could check if they were parallel?

Student:you can find their slopes?

Chad Lower:BINGO!!!!

Chad Lower:so now go back to the previous question. How can you tell if two lines are perpendicular?

Student:the slopes would be opposite reciprocals

Chad Lower:and that is what you need to prove or disprove to determine if it is a square or rhombus

Student:yes thank you!

Chad Lower:(and by finding slopes, you can also tell if opposite sides are parallel)

Chad Lower:but if the side lengths are the same, we get that as a bonus

Chad Lower:without needing to prove it separately

Student:so if they are all right angles, does that mean it is a square?

Chad Lower:correct

Chad Lower:since we know the side lengths are the same

Student:okay thank you!

Chad Lower:My pleasure, Student!

Chad Lower:Anything else today?


Chad Lower:Sweet! Be sure to tell your teacher you stopped by the Live room. Thank you for your effort


So when I reflect on this question in hindsight, there are some things I like about it. I never did any of the number crunching. In addition, the student came up with the ideas for what to do next; I merely verified if the idea was correct.

If I could do it again, I might not be as blunt about her ideas being correct–maybe ask her to justify why she thought that might help (like the idea of the distance formula). I also didn’t do the problem myself; I only relied on her answers and assumed them to be correct. If she made an error somewhere, then I verified that her incorrect answer was correct. This one doesn’t bother me as much as the first, but I know in the past I *have* caught student mistakes, so there could have been a mistake here as well.


Teach My Lesson

I feel like I always have to make the disclaimer that I teach for an online school. That in and of itself poses different challenges than a brick school.

However, not only is my school online, we are also asynchronous. That means we have students starting classes every day of the year that the office is open. Students can pace as quickly or slowly as they want, as long as they are finished with their course after 10 months.

Because of this dynamic, it is not uncommon for a teacher to have a student submitting their first assessment in a course on the exact same day a different student is submitting their final exam. It would be impossible to make presentations to all of our students on the topic they are at every day (or even every week). As a result, we use a static curriculum that the students can move through on their own.

Of course, sometimes students will need help on a topic they are learning. This fact is true for all subjects we offer, but is especially true for our math courses. To meet this student need, we have developed a Math Lab that we run weekdays, usually 4 times a day, for roughly 37 hours per week. Students can get math help outside of the Math Lab hours if a teacher is available, but these 37 hours, we promise a math teacher will be available.

So when I am talking about Teaching My Lesson, it is in the context of helping a student in one of these Math Lab sessions. The drawback to the Math Lab, since it is drop-in first-come-first-served, we never know what subjects or what questions will show up during Math Lab. I have helped a Pre-Algebra student and a AP Calculus BC student at the same time. All that to say, we cannot do much pre-planning of a lesson as they are all relatively spontaneous.

Wow! I’m glad you got through that. It seems like I need a separate blog post just to introduce this blog post!

So the other day, I was working with a student on subtracting polynomials (Algebra 1). She came in specifically to find out why, when subtracting polynomials, do you multiply the second polynomial by −1 (negative one).

Rather than directly answer, though, I thought it would be helpful to start with elementary school arithmetic and move to integer arithmetic and the distributive property in general before looking at the distributive property with algebraic terms.

We started with the simple 8−5. Anyone can do this problem from 1st or 2nd grade. Then we bumped up the difficulty by reminder her that “subtraction” was the same as “adding a negative.” 8+(−5).

Then back to 8−5, but instead of writing 5, I wrote the equivalent phrase (2+3). And then we explored that 8−(2+3) was the same as taking 8−2−3. (Take the 8, then subtract 2, then subtract 3.) All of these methods yielded 3 as a result.

From here, we went back to the 8−(2+3) line. I rewrote it, and then explained that we can multiply a 1 in front of the (2+3) since 1 times anything is just that anything. Multiplying by 1 doesn’t change the value. From here, I played the “subtracting” is the same as “adding a negative” game we looked at earlier to get 8+ −1(2+3).

From here, we used the distributive property to get 8+ −2+ −3. And then finally “adding a negative” is the same as “subtracting” to get 8−2−3. But we had already seen this line earlier in the lesson! I love it when things work full circle.


Now that we played with numbers (the concrete), I thought it was appropriate to bring in the abstract, really only now answering the question she came here for initially.


I will admit, I was disappointed when she asked that last question, “So what would your final answer be?” I loved the initial question she had. I appreciate students not wanting just “the rule,” but also wanting to know why the rule works. This question is especially fun because it isn’t covered in the course. The student doesn’t have to ask to meet the objectives of the course.

But at this point in Algebra 1, she has practiced combining like terms over the last several lessons. Initially just two terms. Then with adding polynomials the lesson before this. At this point in the course, she should be comfortable with combining like terms (especially before even attempting to subtract polynomials). In hindsight, I should have flipped a clean whiteboard out, and reviewed with her the few lessons leading up to this one.

I will say, this lesson wasn’t atypical, but also wasn’t typical. I get more questions akin to “how do I do this?” With those inquiries, I usually make the student do more writing than me. Math is not a spectator sport. In order to learn the math, you have to do the math.

If I get a student looking for a how, I will see if I can do more screenshots and post again (maybe this week, maybe next). Stay tuned…



For the 2016 Blogging initiative, Week 3 had the title of Questioning. In the article, it then proceeded to give suggestions for topics to write about. In previous weeks, the prompts were few in number, but I found one that seemed to be a good fit for me. This week, even though there were more prompts listed, I knew I needed to buck the system and write on a related topic that didn’t apply to any of the prompts.

As mentioned before, I teach in an online school. But I haven’t always. I started in a classroom and most of my experience is there as well. One thing I noticed while in the classroom is that students are observant.

If a student provided an answer to me, often they could tell by my body language or my facial expression if they were correct or not.

Slowly over the years, I was able to better mask my excitement or disappointment. If the answer they gave was to the question, “What is the next step?” often I would say, let’s try that and see what happens. Then we work through the problem as if they were correct.

If they were indeed correct, we have success. If, however, their thinking was flawed, I think it was helpful for them to see why it was flawed, or what would happen if we tried their method. Not only helpful for them, but helpful for the handful of other students who agreed with their initial response.

Other times, they wouldn’t be “wrong” per se. But their suggestion wasn’t helpful. For example, if we were looking at the problem x + 5 = 13, they might say to “add 5 to both sides” for the next step. Mathematically, this isn’t wrong. The Addition Property of Equality says you can add the same value to both sides of an equation and not change the answer to that equation (both sides are still equal).

When we use their suggestion, our next step would look like x + 10 = 18. Again, thier step wasn’t wrong; it just wasn’t helpful. I think students benefited for seeing this as well, especially because they have the right idea, just the wrong execution.

So what does that have to do with questioning?

More recently (and part of this is helpful in an online environment where students cannot always see my facial expressions as we work together), I hve started to question everything.

If they got the answer wrong, I would ask how they got their answer.

If they got the answer correct, I would ask how they got their answer.

They couldn’t tell anymore if they were right or wrong when I asked that question. Many students who were wrong were able to find their error and correct themselves as they explained why they did what they did. Even if the student could not find their own error, by asking the question, I (as the teacher) could better identify their thought patterns and discern what the true problem really was.

Although I can’t find the exact resource that lead me to start doing this, I believe it was in a blog post by Marilyn Burns, probably talking about the Math Reasoning Inventory (MRI). Alternately, it may have been from her article “Looking at How Students Reason” (bottom right paragraph on page 29).

Completely unrelated, but funny story. When I was in school training to become a teacher, I had the opportunity to pick up some free resources. Two of the items I chose were the books The I Hate Mathematics! Book and Math For Smarty Pants. I mostly picked them for their titles and fun graphic inside, along with the well written content. Just the other day, I was looking though them again, and I noticed they were written by Marilyn Burns! Who would have thought that she would have had an influence on me at the start of my career, and even now well over a decade later?!


My Favorite

So I’m reading the Week 2 challenge, and it reads, “Our week two blogging challenge is to simply blog about one of your favorite things.” I’m thinking, this is super easy; I will just write about my wife. She is my favorite (to the point that my kiddos get sick of me saying it).

But then it clarifies a bit more, “Called a ‘My Favorite,’ it can be something that makes teaching a specific math topic work really well.  It does not have to be a lesson, but can be anything in teaching that you love!” So I guess my wife doesn’t apply any more…

But… I do have lots of things in teaching that I love. Right now, I think my favorite is a MOOC published by Stanford University and created by Dr. Jo Boaler. It is called How to Learn Math.

I don’t remember how I first learned about this course, but when I learned about the basic premise, I immediately signed up for the How to Learn Math: For Teachers and Parents. The course was not free ($125 when I took it), but well worth the investment (and they offer a discounted rate for group sign-up). I didn’t get any Professional Development credits in my state for taking it either (although I heard some states do allow using it for credit), but given the opportunity, I would take it again. There are 8 lessons, each taking about 1-2 hours if you do the full lesson.

Shortly after I finished the course, I learned that they developed a second (shorter) version of the course called How to Learn Math: For Students. This version is free, only has 6 lessons, and each is 10-20 minutes long. The first three lessons talk about math and learning in general; the second three lessons talk about strategies for success.

As I teach in an online school, my students are already used to asynchronous learning, so this course isn’t too far from their comfort zone. I actually haven’t taken the student version, but if it has the same quality and information as the Teacher/Parent version, it has to be good.

When learning math, I think a big struggle we need to overcome for many students is negative self-talk. This course can help remove (or reduce) that negative self-talk. In some cases, I have just encouraged the student to take it on their own and at their own pace. With other students, I have encouraged them to talk with people at home about the course and what they have learned. Since the negative self-talk can sometimes be developed by parents unintentionally (“I was never good at math either.”), having them talk with parents can sometimes reverse this mentality at home.

I end with a quote from a parent:

I wanted to give you a quick update on [student] & a laugh…We went through Dr. Boaler’s course yesterday & did 3 lessons. [Student] was interested in the fact that other people said it’s ok to make mistakes, and when you try hard & even struggle your brain grows. Later that evening she played tennis & had the best night ever! On the way home she told me that when tennis was getting hard she just told herself that she could do & she was going to work hard. At that point I knew she had listened & thought about the video & its message.


One Good Thing

I’ve heard people express that life is like a rollercoaster. Sometimes you have the ups, and sometimes you have the downs. I have even felt this way before.

However, I once heard someone talk about rollercoaster tracks themselves, and not the hills and valleys. They said that life is like the two tracks of a rollercoaster. On one track are all the good things that are happening in your life; the other track is the not-so-good things. Both tracks are present all the time, but it is up to us which track we focus on.

I have tried to be intentional in focusing on that good track, even during some bad times in my life. I believe Chuck Swindoll was correct when he said, “I am convinced that life is 10% what happens to me and 90% of how I react to it.” By focusing on the good track, I can also react better, so a win-win all the way around.

I’ve even changed the way I talk. My wife and I used to joke that if it wasn’t for bad luck, we wouldn’t have any. Now I am more apt to say that today is going to be an awesome day, because I don’t know how to have bad days.

This past week was especially good for me as we had Spirit Week at our school. Granted, being an online school, we cannot see everyone in their spirit gear at the same location, but our marketing team housed a collection of pictures of our students (and staff) participating remotely all over the globe.

I didn’t participate everyday (one was dress up as your dream job — I do that everyday!), but the more fun ones I did participate in were Crazy Hair Day and Mismatch Day.

Yes, there are five “pony tails” in the crazy hair day photo. Yes, I think it is important that we as educators teach our students content, but it is just as important to develop relationships with them. Having fun together is one way to do that.

All that to say, it was another awesome week (and next week will be awesome, too). Getting to have fun with our students was just one good part of that awesomeness.


Kicking off the 2016 Blogging Initiative

I have been toying with the idea of blogging, not so much because I feel I have a lot to say, but because I enjoy reading the blogs of others. I do believe in the C.A.S.E. method of teaching (Copy And Steal Everything), because I know I am not as smart or as creative as others, but I also believe that if I take, I should also give.

The MTBoS (Math Twitter Blogosphere) is having a blogging initiative starting January 2016. I am also reading a book I received for Christmas called The Innovator’s Mindset. In chapter 3 (Characteristics of the Innovators Mindset), George Couros writes,

When students come to school, we continually tell them, “You need to share!” because we know the great benefits to their learning. Educators would all benefit if we decided to take our own advice. One way we can do that is through blogs. If you’re thinking, “I’m not a writer,” consider this: every opportunity to share with others on a global scale makes you think more deeply about what it is that you are sharing in the first place.

Those two ideas together gave me the desire to start this blog. We’ll see where it leads us! I’m looking forward to the journey.