Where Do Your Students Max Out?


Some of my tweets this week have gone insane.  Hedge (@approx_normal) and I have started Insanity Max 30  (Read: Twitter Math Camp is in LA this summer).  One of the major components is to write down the time in which you “max out” or take a break for the first time.  The obvious goal is to increase your time before maxing out with each consecutive workout.

This exercising format made me think about my own students and their ability to push further before maxing out.  The knee-jerk reaction for students is to seek clarification from the teacher rather than from their small group when they get stuck.  My personal take on this phenomenon is that students are fairly certain that the teacher will be able to provide the necessary clarification, whereas their classmates may not.  Regardless of their reasoning, I want to create an environment in my class where students try to push as far as they can before asking me for help.

Tomorrow being the last Friday before winter break, I’m going to take the opportunity to test them on their brain endurance.  Their task: the Catwalk Mystery problem I’ve shared before.  Unless, of course, the Problem Solving Fairy appears in my dreams and gives me something better.  You never know.  Dreams can be strange.

This problem seems suitable for a few reasons:

  • It provides an appropriate challenge for a class with a wide range of mathematical fluency.
  • It is well-suited for group work.
  • There are multiple ways in which to approach the problem.
  • There are specific places in the problem in which I know students will struggle, but I know it’s possible for them to unstick themselves.
  • Based on assumptions they make about the problem, they may arrive at different solutions.

My goal is for them to progress through the problem as long as possible without asking me for assistance.  When they feel like they are roadblocked, they can max out, ask a question and then get right back into the game.  But I want them to challenge themselves to take as few “breaks” as possible and arrive at a confident answer.  So send some good brain vibes up toward Minnesota because these kids are about to test their limits.

Times When I Suck

I’m pursuing a National Board Certification and am in the midst of preparing for the content knowledge portion.  An area in which I know I struggle:  Geometry.

I gave this problem to my students on Thursday, with the hopes that a student would be able to figure out (and show me) how to solve it.  When that plan failed, I knew I needed to start preparing more formally for my impending exam.


So I  spent my Saturday evening working on geometry.  (Math teachers lead such exciting lives, I know.)  I started with some problems from A+ Click Math.  Wrong answer after wrong answer lead me to seek out a more formal review.  I know there are other websites out there for geometry review (and if you can PLEASE point me to them, I’d appreciate it), but I sank to a new low and turned to Uncle Sal.  The 6 minute video was excruciating to watch as he repeated himself as he drew , but to be fair, I understood the triangle inequality theorem much better at the end of the seemingly endless 6 minutes.

Today, I tried Brilliant, which is geared toward problem solving.  I suppose I should be pleased with my progress and my willingness to try again in the face of defeat.

Some takeaways:

  • Failing sucks.  We need to remember that when we ask our students to be okay with failure and mistakes.
  • It’s hard to admit you aren’t good at something.  We need to acknowledge that when we expect students to approach us with questions about their learning.
  • To some, being wrong means admitting you’ve failed.  We can’t automatically expect students to transition into that mindset.
  • Tell your students that you struggle as well.  Give them specific examples of when you’ve failed and let them know that they can persevere.


Matchmaker, Matchmaker: The Algebra Way


I’m trying to make my blog less OMG-you’ve-got-to-try-this-amazing-activity-that-I-found-cuz-it’s-awesome and more analysis of my teaching and an examination of where improvements can be made. That being said, this post is going to be a little of both.

Today, my Algebra students did another Talking Points activity on linear functions.  I used the same format I did with Number and Operations where I gave them 5 minutes to look over the TP’s and make any notes they needed for the group activity.  Here’s the link if you are interested in seeing what they chatted about.  As I honed in on their exploratory talk, I noticed that many more of them were convinced by the reasoning of their tablemates and changed their “unsure” to “agree/disagree.”  I’m not sure if that was because the topic was a tad more difficult, or if they are getting better at listening to one another.  Of course, I am hoping it’s the latter.

At the end, after they wrote their self-assessments, we talked as a group about some of the points that they were still not convinced of agreement or disagreement (which included The opposite reciprocal of zero is zero).  I tried to do this using the Talking Points rules, even though the whole class was able to participate in the discussion.  I feel that this was a positive addition to the process.


Okay, onto the real star of today:  An Nrich Task. 

Each group of 4 receives a pack of 16 cards with algebraic expressions on them.

algebra match image (1)

They cannot take cards from other group members; they may only give cards to others.  Each person must have a minimum of two cards in front of them at all times, to alleviate the temptation of having one person sort the cards.  To complete the task, each group member must have four cards in front of them that have the same simplified expression.  Caveats:  no talking, no non-verbal communication, no writing, no taking others cards.

I used the Glenn Waddell #TMC14 Smartphone Camera Hack to position my camera in the back of the room and I took a time-lapse video with my old iPhone.  Although I can’t post that video online because it contains images of students, I did make a screenshot with blurred faces:


I mean, you can practically SEE the brain sweat pouring from their ears!

In our debriefing, we discussed what was hard, what was easy, and what strategies they developed.  Here are some highlights:

  • It was nice to be dealt a card that was already simplified.
  • Besides not being able to talk or non-verbally communicate, it was difficult to simplify some of the expressions mentally.
  • It was difficult to not take cards from others, knowing where they belonged.
  • A good strategy when starting was to see if there were any matches to begin with.
  • Another good strategy:  give unsorted cards to players who have completed sets so that they can help divvy those out.

I was so impressed with these kids today.  I know that they will learn more together by working with one another.  I’m so thrilled that THEY are beginning to see the truth to that.


Making a Point

Our school uses a 5-period, trimester schedule which means that every 13 weeks, I have a new group of angels in my classroom.  I decided to give Talking Points another try, with the goal of incorporating some exploratory talk related to the topics in our units of study.  Additionally, the practice of “no comment” has proven to be undeniably helpful in encouraging students to listen to one another.  [Note:  Elizabeth Statmore introduced these at Twitter Math Camp this summer.  See the “Talking Points” link for more information.]

My goal is the same:  Addressing status in my math classroom and allowing every kid to have a voice. I began with the math talking points and then transitioned into some talking points related to our current unit: Numbers and Operations.  (I’d love to have the students come up with their own talking points as well, although I haven’t tried that yet.)

In their self-assessment, I asked them how difficult it was to practice “no comment” and was quite pleased with some of their responses.  In particular, the student that explicitly stated that he failed in refraining from commenting.  It was an excellent opportunity to encourage them to be better the second time around.

Something awesome that I noticed today:  students respectfully called each other out on cross-talking violations.

Here are the talking points we used today:

Talking Points – Number and Operations

  • The sum of two fractions always results in another fraction.
  • There are an infinite number of fractions between any two fractions.
  • Using a fraction is always a more precise answer than using a decimal.
  • The commutative law of addition (a + b) + c = a + (b + c) only works for positive numbers.
  • For the fraction -x/y, it does not matter if x is negative or y is negative as long as one of them is.
  • The reciprocal of a number is usually smaller than the original number.
  • The square root of a number is always less than or equal to the original number.
  • Zero is neither even nor odd.
  • Taking a positive whole number to a power always results in a larger number.

When having them assess themselves the second time around, many commented that it was much more difficult not to comment immediately.  Although some of the points are intentionally ambiguous, a number of them have right and wrong answers.  Conversely, the topics yesterday were more general “math opinion” related bullets.  Fortunately, when listening to their conversations, I found that many who struggled yesterday improved on today’s task.

I’m encouraged by my take on this activity this trimester.  I think that centering the statements around our units will be helpful in examining mathematical statements that make students think critically and support their decisions.


Plan, Teach, Grade. Rinse, Repeat.

The serendipitous timing of a three hour layover in Newark must be maximized with a reflective blog on my weekend in Pennsylvania.  Specifically, about my day spent observing Justin Aion in his classroom.  If you follow Justin on twitter, read his 180-blog, or have the privilege of knowing him personally, you’re no doubt familiar with his harsh assessment of himself as a teacher and his no-nonsense way of sharing his opinions.  I knew heading into a day of observing his class that I was in for a treat, whatever that meant.

Justin let me blog about the experience as his daily entry, so if you’re interesting in reading about the amazing time I had, head on over there and get reading.  In the meantime, I want to discuss some implications this day-long observation had on me in my role at my school.

As a department head, I have the chance to view the classes of multiple math teachers, once, sometimes twice a year.  I find these opportunities incredibly valuable and I always have a take-away from each observation I do to benefit my own teaching practice.  Usually, I have a 20-30 minute conference with the observed teacher where we can reflect on what is working and how the students responded to the lesson.  These “after parties” are, hands-down, the most important part of the observation process because it is in those post-conferences that enlightenment results from the insights an outside observer can provide. Unfortunately, because all of these interactions have to happen outside of the school day, many of the important issues that arise in these post-conference meetings cannot be dissected and fully examined and therefore result in little or no long-term changes. For example, in the post-conference, a question addressed is “What changes or modifications would you make in the lesson?”  A few lines are filled in on a form and off they go to teach the next group of students. The discussion simply doesn’t happen because there’s not enough time to have it.   And because these observations are shared only with a small group of people (an administrator and an instructional specialist), there is no discussion of what issues arise over and over again in multiple classrooms.  As a result, few can benefit from the individual observation.  And there are hundreds of them done in the district each year.  And it seems as though the math department as a whole isn’t able to reap the maximum benefits of having a trained observer visit classrooms.

What was different about observing Mr. Aion’s class was that the observation happened from 6:30am until 2:50pm, but the post-lesson conference went on for the rest of the weekend.  I’m obviously not suggesting that we all spend a weekend math retreat discussing pedagogy over Thai food and club soda, but the conversations we have as teachers with teachers are important.

Important and not valued.

In fact, any time that isn’t spent actively teaching or planning and grading is consistently shoved outside of the 7-3 school day.  And it seems as though the teachers who want to engage in those discussions and realize their value must sacrifice personal time in order to do so.

Here’s another example:  Just today, at lunch, one of my colleagues brought up his frustration with a student that we share.  His grievances aren’t unique to this particular student and highlight an ongoing struggle that all teachers in our department share.  We were able to have a very meaningful discussion and came to a workable solution for this kid.  The problem:  this conversation, while incredibly productive, had to happen during our already rushed lunch period.

I think this bears repeating:  Teachers need time during the school day to talk with other teachers.  And I don’t mean to lesson-plan for common preps.  I mean to really dig deep into the outcomes of our teaching and have meaningful discussions on how to better serve all of our students.

Are Teacher’s Safe in Admitting Mistakes?

Image from http://en.wikipedia.org/wiki/National_Safe_Place
Image from http://en.wikipedia.org/wiki/National_Safe_Place

Sometimes on the way home, I tune my Iphone to the TED Radio Hour podcast.  I love the way Guy Raz re-captivates his audience by highlighting numerous, already captivating TED talks.  Today, I was listening to Making Mistakes and the first segment was an interview with Dr. Brian Goldman.  His words here are striking:

The redefined physician is human, knows she’s human, accepts it, isn’t proud of making mistakes, but strives to learn one thing from what happened that she can teach to somebody else. She shares her experience with others. She’s supportive when other people talk about their mistakes. And she points out other people’s mistakes, not in a gotcha way, but in a loving, supportive way so that everybody can benefit. And she works in a culture of medicine that acknowledges that human beings run the system,and when human beings run the system, they will make mistakes from time to time. So the system is evolving to create backups that make it easier to detect those mistakes that humans inevitably make and also fosters in a loving, supportive way places where everybody who is observing in the health care system can actually point out things that could be potential mistakes and is rewarded for doing so, and especially people like me, when we do make mistakes, we’re rewarded for coming clean.

If we replace doctors with teachers and medicine with student learning, would we proclaim that our profession fosters still safe space for teachers to talk about their mistakes?  Do we have the opportunity to be vulnerable in our classroom approach in order to improve our practice and learn from others who have made similar mistakes in the past?  In an age of education the covers of news magazines equate bad teachers to rotten apples, are we really able to grow directly from what is not working in our classrooms?  Or are we lead to believe that mistakes lead to labels like “ineffective teacher”?

We preach constantly about creating safe mistake-making environments for our students.  This strategy needs to be applied to teaching as well. We, too, need this loving, supportive environment that all may benefit from.   How do we, as teachers, create this space for ourselves so that ultimately, we can learn from those mistakes and make our profession stronger?

Female Feelings and Brash Boys??

It’s Friday, it’s Halloween, and our football team is playing tonight in the section finals for the first time in about 30 years.  To think that solidifying understanding of domain, range, increasing and decreasing functions was going to be a priority for my college algebra class was a farce and so I decided to make the class more productive.  We watched the Simpsons. And I ate my weight in Swedish Fish.

Image from Wikipedia

Image from Wikipedia

Girls Just Wanna Have Sums pokes fun at the stereotype that men do better in math and are inherently aggressive and women want to sit and talk about their feelings.  Consequently, Springfield Elementary is divided into a girls school and a boys school which embody those stereotypes.


(If you weren’t aware, every Simpson’s episode ever created is available on FX’s new website, Simpsons World.)

After the show, I asked the students to write about their feelings on this stereotype and how it plays out in the United States.  I then asked them to describe a satirical jab that they found particularly disturbing or upsetting.  As a math teacher, I sometimes lack the inclination to ask students how they feel on a particular controversial topic; but I’m always glad when I do ask.  Acknowledging differences that exist in the ways males and females approach math is important.  But this episode was more about educational access to high level mathematics.

The majority of what they found disturbing was that the girls weren’t given the same opportunities as the boys to experience challenging mathematics.  As I responded to their submissions, I took the opportunity to push their thinking further and ask “Are there instances, other than gender, where students are not given the same educational opportunities?”  I hope that my feedback will foster a dialog about the importance of all students having access to a high quality education, beyond inequalities based on gender.  Because these inequalities exist, maybe not based on gender, but definitely based on race and socioeconomic background.  I’d like to continue to help them think about what that means for those students.