My Favorites of NCTM- Global Math Department Presentation

I just finished talking at Global Math Dept and it was great!  After listening to my fellow presenters, I think I was the kid in the back of the room who doesn’t fully listen to directions and gave a half-finished assignment.  Whatever the outcome, it was what I have been thinking of since I left NCTM in San Antonio.

My presentation slides are here…



Overall, as my first experience at NCTM this was awesome, and has me hooked.  I would present there any time I was able (and I’m currently working on my proposal for next year!).

Drop my any questions you have…

My NCTM Presentation

In case you, like the rest of the mathematical community, was at Jo’s presentation Thrusday @12:30, here is my powerpoint for my presentation at NCTM.


Some big ideas from it:

Change the way you question to promote student thinking and conversations.  This is my new thinking kick, and now I am constantly looking at problems and trying to determine “how can I ask this better?”

Once we ask student for an answer, we ask them to stop thinking.  They become focused on one goal, and will no longer notice and wonder to make connections to mathematical meanings and possible solution paths.

Please try out an  Open Middle problem.  They can fit so seamlessly into your curriculum.  I use them in flexible ways: as warm ups, practice problems, exit slips and for formal assessments.  When you are assigning homework for students, examine your text’s problems and then check out our site- see if you can get them to practice in a more meaningful way that promotes understanding without burying them in paperwork.

It was a great experience presenting for the first time at the national conference, I really enjoyed NCTM and would like to thank everyone that made the conference possible.  I am definitely submitting a proposal for D.C.



Open Middle Introductions, Please.

Hello all, you may or may not know that although I do create a lot of Open Middle problems, I do work with a group of 4 other awesome educators who create the Open Middle team.  This blog is an introduction (re reminder) of what Open Middle is, the people behind Open Middle, and if you wish to accept the challenge- what kind of information we need to publish your great problem to the Open Middle site.

What is Open Middle?

Taken directly from the OM site (blatant plagiarism, thanks Robert K.):

Dan Meyer introduced us to the idea of “open middle” problems during his presentation on “Video Games & Making Math More Like Things Students Like” by explaining what makes them unique:

  • they have a “closed beginning” meaning that they all start with the same initial problem.
  • they have a “closed end” meaning that they all end with the same answer.
  • they have an “open middle” meaning that there are multiple ways to approach and ultimately solve the problem.

Open middle problems require a higher depth of knowledge than most problems that assess procedural and conceptual understanding.   They support the Common Core State Standards and  provide students with opportunities for discussing their thinking.

Some additional characteristics of open middle problems include:

  • They often have multiple ways of solving them as opposed to a problem where you are told to solve it using a specific method. Example
  • They may involve optimization such that it is easy to get an answer but more challenging to get the best or optimal answer. Example
  • They may appear to be simple and procedural in nature but turn out to be more challenging and complex when you start to solve it. Example
  • They are generally not as complex as a performance task which may require significant background context to complete. Example

In other words, we are asking kids to solve non-routine problems that may or may not have one single correct solution, but have multiple ways to arrive there.  This promotes rich classroom discussions about the mathematics behind the problem which develops deeper understanding.  Hopefully this is what you are all about in your classroom.

The people behind Open Middle

On to the people who drive Open Middle (well those who organize the website, because we appreciate everyone who uses our site!)  The project was founded with Robert and Nanette.  After flooding Robert with questions and problems for the site, I was invited to join the team.  Open Middle started to gain a following and problem submissions started pouring in, and we welcomed Dan and Zack to the team.  Here’s a rundown of each member (or what I can dig up through a web search).

Robert Kaplinsky (taken from his website  Hi, I’m Robert.  I train mathematics educators who want their students to be better problem solvers.  I help them build the tools needed to get students critically thinking and articulating their reasoning.  I do this while continuing to work full time for a K-12 school district in Southern California as a mathematics teacher specialist.  It helps me stay connected to current issues in education as a typical month involves me teaching students at multiple grade levels, mentoring teachers, and providing professional development.

Nanette Johnson (taken from her blog I am a wife to one amazing husband <3,  mommy of 3 awesome kids…a math teacher to more than 2000 students (over the years…and still counting).  I love teaching, and watching students break down their previous self-imposed beliefs that they “just weren’t good at math”.  I’m concerned about how teachers are expected to teach in ways in which we did not learn and in ways which were not appreciated.  I want to find ways to help teachers go from surviving to thriving.

Bryan Anderson:  Currently I am working at a public school that services a juvenile center in my area.  As such, I teach mixed classrooms where student age could fall anywhere between 10 to 18 years.  I also see a wide range of proficiency levels as most of my students typically have not attended school for at least one year.  A large majority of my current students qualify for special education services, and as a requirement to this I am picking up my special education certification for learning disabilities.

Dan Luevanos (taken from his blog Math Rockstars):  My name is Daniel Luevanos. I live with the intent to rock ‘n’ roll. I believe that we can change the world by challenging ourselves and others to do the unexpected.  I’ve been a secondary math teacher in San Marcos Unified School District since 2009, teaching at the high school and middle school level. Currently, I’m a Secondary Mathematics Teacher on Special Assignment in San Marcos Unified School District.

Zack Miller (taken from his blog A Math Education that Matters):  My name is Zack Miller and I work in math education in the San Francisco Bay Area. Teaching math was my first job out of college, and since then it has developed into my (sometimes fully-consuming) passion. Lately, I’ve been leading the charge re-envisioning the curriculum, assessment, and instruction for my charter network’s math program.  In the time since I started my career, I have earned a degree from the Stanford Teacher Education Program, been a founding teacher at two innovative charter schools, presented at numerous conferences, and became a Math for America Master Teacher Fellowship. I’m eager to share what I’ve learned, and to learn more from the community of folks focused on this important profession. That’s what this blog is all about.

What Information Do I Need to Submit a Problem to OM?

The first step is to click on the link for submitting problems on the Open Middle website, which can be found here.  It will take you to a page that looks like this:


This page gets slightly long, so let’s just cover the essentials

  1. Your name, address and blog (yes, please let us link your blog!)
  2. Any co-contributors
  3. Problem Title- please make this as descriptive to the problem as possible
  4. Directions- We are working on having a consistent wording for these.  Typical Open Middle format follows along these lines: Use the whole numbers 1 through 9, at most one time each, to find the largest ____________.
  5. Image link- please make sure this link is accessible as we have different members preview the problem, edit if needed and uploading.
  6. Hints- what can teachers say that could prompt student thinking about the problem?
  7. Answers- please, please provide at least one correct solution
  8. DOK- please indicate what Depth of Knowledge your problem requires.  If you are unsure, check out this DOK site.
  9. CCSS-M Standard.  Typical formatting for these are not the same as the CCSS site, we record the grade level, mathematical strand, and standard.  for example: CCSS.Math.Content.6.NS.B.3
    Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation.                                                                                                                            Would be labeled as 6.NS.3 for the Open Middle website.

Thanks for checking out the Open Middle website, we hope that these problems provide you with an alternate way of providing purposeful practice for students, and those practices will create rich discussions and empower students as learners.

MTBoS30- Day 26

Activating background knowledge…

My reading today really has me thinking about how casually I have thrown this statement around. Today I’m hoping this paragraph makes you think about your lesson more, like it did to me.


Echevarría, J., Vogt, M., & Short, D. (2013). Making content comprehensible for English learners: The SIOP model.  Pearson Education: Upper Saddle River, NJ.

#MTBoS30- Day 24

American students are lazy….


This is one statement I do not like, or even a teacher stating that “My kids are lazy.”  When we use the word lazy, we are making comparisons- and typically those comparisons are made against standards we hold (or held by the person making the statement).  Now I know what you’re thinking, “but I have expectations and rules for my class.”  I’m not talking about those, I’m talking about us having unjust conceptions of what is “normal” for our students.  The culture of the American student has drastically changed over the past years.  Trying to compare that culture to other countries’ teen culture is also unjust, and this is why (or, my takes on it at least).

American students are material, and its gradually getting worse.  This materialism is coupled with immediate satisfaction, which compounds the problem.  This is what I mean: Students want their “toys”, and will work extremely hard to attain them.  The modes of attainment are vast; some have jobs, some are extrinsic rewards, and some are attained by illegal means.


When students have jobs, they start them immediately after school.  When they are done with work, typically one of four things happen.  The first is that they go hang out with friends, fulfilling a social need.  The second is that they are too tired from work and go home and go to sleep (or they get home too late and have to go to bed).  The third is that they come home and attempt to do their homework in whatever time they have before turning in.  The last is that they purposefully do not do any homework (and I have yet to find a large percentage who truly fits into this last category).  In any of these cases, homework is not a priority and is hastily done without a lot of conscious effort (although there are a few exceptions- your top 5% students).  Does having and maintaining a job imply laziness?  I will go out on a limb and say no.


When students earn things extrinsically, they also are not being lazy.  In fact, most of these students are extremely clever.  They know how to work within the system of rules their parents constructed for them, and how to use those rules to produce results that are desirable to them.  They know what they  are doing, know how to push those limits- and how to act when an external award is proposed for them to attain.  Is this lazy?  Once again I would say it’s far from it, they are constantly working to maintain a reality that produces outcomes that are favorable to themselves.  (This is my least favorite subject, I truly dislike external rewards.)


When students have no other option, they attain their toys through illegal means.  These are the students I typically deal with on a daily basis.  They case the target, devise/review/revise a plan and execute that plan.  Once they attain the object they desire, they have to constantly be alert to not draw unwanted attention to the possession for fear of being caught.  Of the three possibilities, this is the one that actually requires the most mental load.  These students are on a 24/7 “fight or flight” status- causing them to be wired and hyper-alert.  These students are constantly balancing the status of their objects and what new objects are needed, they actually have no time to be lazy and let down their guard.

When we talk about being lazy students, we need to better define what that means.  Lazy to most teachers means not participating in class, completing assignments or showing any interest in the subject.  This is all comparisons that the TEACHER makes and reflects upon the student.  Teachers compare how these students act against the norm they have created, that norm typically follows what was expected of them as a student.  Times have changed, and those rules no longer apply- just as the rules for being a good educator no longer transcend both generations.

When foreign countries think of being lazy, once again they are viewing American students and holding them against their standard of achievement.  I am not sure how we can rationally do this when we all recognize that each student is a unique individual and has different needs.  The biggest issue here is the value that students across the world hold for education, and for American students that value is not immediate.  Instead of attacking our students, we should compare the ideals our countries and cultures hold for education, jobs, material possessions and social status.


Most of my students say they want to have a college degree, but most of them say that school has no impact on what they want to do once they get out.  They try to directly tie courses to jobs, a pitfall that many teachers have fallen into in the past decade.  As such, learning is not deemed important- while having cars, a job, cell phones, electronics, etc are important.  These things define a student’s social standing and status among their peers.

Teachers are well aware of student thoughts on the value of their education.  We plan and try to instill questioning, wonder and a need for learning.  There are many students we connect with, and many who just fill space in their chair.  The students we do push this year may or may not continue that growth dependent on their instructors next year.  We can’t do this alone.  We need help, and that help has to come from this country as a whole, our communities, families, parents.  We must make a statement that education is important, demand excellence (academic, personal and social) every day and hold ourselves accountable for those same standards.

Personally, when I see a student who I feel is being lazy in class I rarely blame them.  The reason they are being lazy in my class is that I haven’t created a need for knowledge- which is my job.  Identify why those actions are occurring, don’t lay blame solely upon the student.  Change your classroom environment, fix the “lazy” problem and get back to why you started this job in the first place- the passion for learning.