White Fragility, Teacher Fragility, or Both?

(I will attempt to remember everything that happened in class this day because I want it to be as genuine as I can remember it, so that I can come back to this blog often and read, reflect, learn and grow in this)

The other day I was watching Hidden Figures with my class, I told them I wanted them to watch it not only because it is a good movie, but in order to look at dynamics depicted in the movie and compare them to today.  One student, a student of color, remarked :Great, this is gonna get me upset.”  I didn’t acknowledge that remark, but started the movie (Which, as I now reflect on the situation, was my first mistake).

Towards the end of the hour, I stopped the movie and started talking about the dynamics students observed.  At first students were hesitant to bring up any issues, and I asked what they thought the main theme of the movie was, and they replied Racism.  We then started to talk about that a little bit, and I brought up the idea of white privilege.  As soon at those words left my mouth, the same student scoffed and turned away from me.  I kept moving forward and tried to talk about what that meant (there were 3 white students, 3 native American students and on African-american student in the class) and how this was a negative impact.  The student laughed and turned away when I talked about how this is something that I know I need to work hard on, and when I asked her why she reacted that way she replied that it was a habit when she is anxious. I continued the discussion (mistake two- at least as far as I am aware of at this time).

She interjected at one point, asking why we should talk about it in class when it wasn’t going to change a damn thing anyway.  I replied that in order for things to change, these conversations needed to happen- that if we didn’t talk about them that we were supporting the ideology of white privilege.  These were conversations we needed to continue to bring up in order to change what we observe happening today.  She said something to me in a very rude, snarky tone (and I can’t recall exactly what it was she said, it was the tone and sharpness that hit me- and it was shock in other SoC’s faces that I remember, not the words). I commented that we are trying to discuss a topic that causes a very emotional response from parties, and that she did not need to be disrespectful to me (Another mistake I now see- part of my white fragility).

She commented in an almost equal tone as before that she was sorry I took it as her being disrespectful, she didn’t mean and that these conversations set her off.  She turned away from me and I was taken slightly aback and didn’t know how to proceed.  I reiterated that these are conversations that need to happen and that will continue to happen in class, then class was over.  I was able to once again demonstrate what I now know as white fragility- I was able to remove myself from the situation.

I have a unique working environment, working at a juvenile center.  There are many issues that are amplified at my workplace, as well as many rules and procedures that directly oppose what I typically did at a public school.  I need to find ways to be able to address this topic in this place.

As I have reflected on this event, and continue to do- I realize one glaring thing: I was not prepared at the time to handle her reaction to the conversation.  Was I unwilling, as a teacher to deviate from what I wanted to address or was it because I was a white male in a position of power?  I wanted to ask about her reaction, but I also did not want her to be an unwilling representative of African-American students.  Until this point, we have had a good rapport in class, I didn’t want to compromise that and have her shut down on me.  There are a ton of other things/feelings/excuses I could write here but they would all be protecting my white fragility.  I realize that as a while male teacher, I am the totally wrong person to hold all the power in these conversations.

So I write this, in this public place, not as a post to inflame.  I write this to have a permanent place to have this so I may keep coming back and reminding myself that I need to do better, I have to do better, it is my responsibility to do better.  I need to research ways to have these conversations and be prepared for the strong emotions they illicit, I need to be able to be supportive, respectful and have the ability to listen to them.  This was not easy to decide to blog about, nor easy to tweet about.

I need help to do this work, this is not something I can do alone but something that I can not allow to be hidden as well.



OM in Scratch!

So a routine question I have when I tell people I work with OM is that Teachers want a better medium than an image to project on the screen.  There have been many other awesome colleagues who have blogged or tweeted about taking an OM problem and making manipulatives of the choices to allow students to physically interact with the problem.  Since I have also been kicking the coding side of the realm lately, I decided to start converting my OM problems into Scratch Interactive programs.  Here is my first program


Trig Ratios:



I encourage and appreciate input on this new venture in making awesome OM problems more accessible for Students and Teachers.




This IS a Test

This IS a test, it’s a test that has been a long time coming for me, but one I have prolonged as much as possible.  The title of the blog was supposed to catch your eye, make you think of a man I am truly honored to call a friend, José Vilson. I wanted the name to make you think of his book, and the many issues we have in classrooms all over America. I want you to also think about those same issues that lie outside the classroom, that permeate every second of every day. That issue is the one of race.

It is an issue I have struggled with, one that I have not engaged directly in- because I am a white man of privilege.  As such, I have never been sure of exactly where or when I should insert my voice on this subject. As someone of privilege, I am aware of how what I say (or what I do not say) can influence the conservation on race.  It wasn’t until one Sunday night, when I was trapped in MSP airport for 3 hours waiting to catch my flight home to Bemidji, that I decided to reach out for help. I want to be part of this conversation, but I truly do not know where to start.  That is where this blog, and those that respond to it, can help.

I before I type these next few paragraphs, I want you all to know this- that I am scared.  I am scared to continue, scared to hit publish, scared to share these thoughts publicly on social media because they represent an internal struggle within me and my life’s journey. They represent a struggle I continue to attempt to balance every day when dealing with my students and in my life. I am scared of the weight of judgement that will be rained down upon me as a man, a husband, a father, a teacher of our youth. Although I have this fear, I am continuing to type this, and hopefully when I reach the end I can finally find strength to hit send.

I was born in Virginia, and as such, I received a very strong message about people of color as I grew up.  Children are very observant of what is happening around them, and adults in the community did a good job in demonstrating the beliefs of those with privilege.  The issue was this- I never was comfortable with the message I was receiving. I kept silent, hearing those words but never pushing back on them. As a youth in a military home, questioning adults was not an option.  When I was 3, we moved to Minnesota and I grew up on a farm in a white community. I went to a school that was predominantly white, even though we were located between 3 reservations. I was not experienced in the issue of race, and my only really experience with people of color was still from the experiences of my early youth.

I continued to struggle with that view until college.  In college I lived in a diverse community, I had many friends- and those friends included many people of color.  I started to push back against those early images I retained from my youth. While living on campus, within the dorms, I was able to push past those prejudices and focus on the people I was interacting with. I did not have to worry about judgement from others about my friends there, although they still suffered from judgement every day.

As a teacher, I started teaching in a public school located on a reservation. Throughout my 15 years of teaching I have taught in a school that was primarily students of color.  I try to be aware of my message and my voice, but coming from my background I am sure I can’t help but fall into those times of “well intentioned” teaching. I need someone to push back on what I say or do in the classroom, sometimes it comes from my students. I have lost count of how many times I have been called racist by a new student, and each time it happens I reflect on what actually happened in the classroom before I respond.  Many times they are saying that as a knee jerk reaction. “Johnny, I need you to continue your work on your assignment” is immediately followed by “You’re racist.” It’s the other times that concern me. It’s like being slapped in the face, and I always try to reflect on the conversation, body language, body positions in the room, and who I addressed first in a situation in the classroom. If I ever have a doubt that what I said or done was wrong, I immediately apologize, although by that time it is too late- the damage has been done.

There are times throughout the year where the class will talk about race, and how that has affected their learning.  It is quite an eye-opening conversation with every group I have. Although many of the issues remain constant, there is always a new insight that I take from each talk.  All of the talks will have a racist versus prejudiced thread, and many of my students do not know the difference between the two. Many students do not know how to articulate themselves beyond using the word racist, so we talk about ways to talk with a teacher about how they are feeling and what factors within the classroom cause those feelings.  Many of my students come from very diverse and challenging situations, they have a need to be heard and respected for who they are. They typically are not allowed this, but it’s one thing I try to address and acknowledge. They need a place they can feel safe, respected and valued for being themselves.

Like my students, I need a place where I can feel safe and respected for this conversation of race. I want to learn more about what I am doing right or wrong, or even what I am implying by not saying anything at all. The biggest reason why I have been struggling with this for so long is that I feel ashamed.  I am ashamed because I have not pushed back against what I know is wrong for so long, but I also feel shame and fear of how my family and friends will react to my seeking knowledge and how I will interact with the topic of race. It’s the latter that has chained me into inaction, and although I keep struggling against those constraints- they keep me silent, firmly entrapped.

I want to have a conversation about race: within me, my classroom, my community, my country. I know that conversation won’t be neat or easy, but I also want to be able to know that while emotions may run hot- that I am having it with people in a constructive way.  This IS a test, we all are being graded on this every day, and for me- I need a lot of review and chances to retest so I can get it right.

So, about that Chat…

I enjoy my job, I really do. I get to talk to students about how they perceive mathematics and help them along their road to new applications. I keep finding that I learn more every day that I am in the profession, and I like that. If someone had asked me when I first started teaching what I would do if I didn’t know an answer, I am confident I would have had some cocky answer about never not knowing an answer. I now know that not only is it OK to not know, you are actually able to have great teaching moments when you don’t.


The same can be said about Twitter, and chats. Probably the most stress-inducing thing I have ever done is tell Justin Aion that I would take over moderating MSMathChat. It is a fairly well-established chat with wonderful people and ideas. My biggest error was that like teaching, I went into the job thinking I had to know all the answers. I started to get burnt out, as well as felt that I was letting members of the chat down because I couldn’t maintain a weekly schedule (due to family). Last year, numbers were really dwindling and I strongly considered letting the chat die, and talked a couple of great friends, Matt Coaty and Adrianne Burns into helping me moderate to keep it going. They were great and helped take a load off of me. Chat continued, more people started participating (which is the biggest reason I joined the chat and wanted to keep it going), and ideas flowed. It inspired me once again.

It inspired me so much, that it led me to take another risk. I “know” a lot of people on twitter, many I call friends even though we haven’t officially met, and I value their opinions and knowledge of teaching. I wanted to learn from them and I decided to start asking them to moderate a chat night. Guest moderators wasn’t something new, I had a google doc where people could sign up and moderate a chat, but it wasn’t often accessed or used. I took the less passive road and started directly asking specific people to chat. Something amazing happened-

They said YES.

I can’t thank my guest moderators enough these past 2 months, you have made MSMathChat great again. We have had many new people join chat, and the ideas have really re-ignited my passion for teaching. The topics have been stellar, and it seems to me like just when chat starts, the hour has passed. I spend another two hours sifting through the chat and following all the side-threads. I reflect on my views, my teaching and have found new ways to approach students, peers and math. It has been awesome and I have truly enjoyed chat.

Hopefully you will find time to check out #MSMathChat on Mondays, 8CST. We would like to have you there and hear your ideas. If you would be interested in moderating, let me know.

Share the spark of learning.

Remember the days…

I want to apologize for anyone who follows my blog, and I’m sure I have had a few people drop it off their feed this year, this year has been pretty scarce for insightful mathy posts.  As most of you know, I teach at a juvenile center- which can be a challenging endeavor.  I have always prided myself with the fact that while staying within the norms of what the center and school wants, I still treat these students as I would any public school student and provide them a “regular class, not juvie work.”

This is the first year I don’t feel I have done that, and that is the root of why I haven’t posted a lot this year.  This year has been all about social behavior and not academics for this group.  I have started to become the teacher I don’t want to be- I am giving students individual busy-work to keep peer interaction at a minimum.  It seems that every time I try to get back into my old swing with these students, they pop off again and remind me why I had to make this shift.  Part of my dilemma is also student interaction in the unit, things are in place because of the behavior that happens after school and those are enforced throughout the school day.  It is not something that I have orchestrated or encouraged, it is something that has come about because of the students.

This has been a hard year so far, and the struggle is really grinding on me.  As students are rotated and go to different placements things may go better and I can go back to the norms for my classroom.  I remember the days when I was able to do that, and I really really need to be able to get back to them.

My Biggest Fail…

First off, I would like to really say thank you to Annie (@Annieperkins) for being bold and posting her failure this week.  It was a great story, reminder, and way to cope with what we do on a daily basis.  Read her awesome post here.


This is why I really appreciate the MTBoS, there is no way I could have these discussions and reflections without it.  It is a conversation I could have with my close colleagues (CLOSE colleagues, you don’t want everyone in the building knowing this), and even then when you are the only math teacher in the building it makes it hard to really connect with any condolences you may receive (because you know, our profession is SO much different than anyone else’s).  It is comforting to know that others experience the same struggles that I do.

I can totally relate to Annie’s initial fears of “airing out” her failure.  When I started blogging, I wrote one post to begin with, and didn’t post another for 6 months.  Why was this?  Feeling of failure and insecurity.  I started blogging because I wanted a way to have reflections and records of what I did through the years, but I will be honest in the fact that “putting yourself out there” is very hard and immensely daunting.  I mean, anyone can access my blog and read what I post, how will I be viewed as a person, teacher or presenter when I write about all of my shortcomings?  Even now, I rarely tell anyone about my blog in district- I still have that fear.  I’m getting better, and presenting at NCTM San Antonio was a huge breakthrough for me in this.  I am far from where I feel I need to go, but I am a lot more accepting of what I do here on my blog and twitter.

MCTM Pic.png

(Like this Pic, I love that I’m presenting- but I’m like “My eyes are closed!  Thanks Nicole, I look like a dumb-___!”)

So, off to my biggest fail- and I really have to thank Annie for making me revisit this blast from the past.  It was a turning point in my teaching career, and it started me down this path to seeking people, research and resources to make myself into the teacher I wish I had (yea, here’s also to you Tracy!).

It was early in my teaching career, and I had gone through 4 administrators in the first 3 years of teaching.  This year was proving no different, this was my second administrator for the year (the first had gotten into a car accident and passed away, so our middle school administrator started servicing both buildings) I was in my final year of administrator observations.  Trying to lesson plan for that many different administrators and being a new teacher is a HUGE stress factor, I was used to test-taking for that many professors- having to focus on what they deemed important and be evaluated by their exams- but when it was the determining factor for my JOB it was a whole different level.  Every administrator has a different focus and what they deem is important to teaching in “their” building.  This administrator was a traditionalist, so I tried to “please” him for my observation.

The lesson was an exercise in boring.  We had “student note” workbooks, which meant I spent the hour in direct lecture, drawing beautiful diagrams and defining vocabulary for students to then copy in their workbooks.  This was one of the most difficult lessons I did (for me personally as a teacher, this wasn’t my style), it felt wrong- and there was a particular student who felt that way as well.  I noticed him right after defining the term polynomial- he had his head propped up on his hand and had is eyes closed.  This particular student was one who was “at-risk”: he rarely attended class, he had numerous discipline problems, a challenging home life, and he was behind on credits- but he was extremely smart.  It took me a while to catch a hook on this student, and typically we had a good working relationship for class.  He liked the way I typically approached class, and could not do “traditional.”  His current status for this lesson wasn’t a surprise, and I tried to gather his attention by allowing students near him to share with the class, I taught from his general area instead of by the board- but I knew that if I called him out directly in front of his peers and in front of the principal there would be a problem.  It was a tough choice to make since I was being observed, but since he was seated off to the side and towards the back of the room, I allowed him some space and continued with class.


The principal left during our “direct lesson note-taking” and when that was done, I followed through with the schema and assigned practice problems.  Once I had this done, I approached my student and quietly talked with him in class about what he was doing, what we had covered and what would happen next.  He told me he had a really tough night, there was a fight at his home and he stayed up most of the night protecting his siblings.  He stated that no one ever came to the back of the trailer to their room, but he was afraid to sleep.  He also told me he was sorry because he knew the principal was there, but he couldn’t stay awake.  I quickly reviewed what we had went over, and he found a partner to work with and catch up on his notes.  Not a major deal breaker in the least- as far as I was concerned.

The next day, I had a follow up with my administrator.  That is where I found out that for the first time since I had been teaching, I failed.  He did not have any sort of rapport with the student who was sleeping in class, and once he had come to the principal’s attention, everything I had done in class after that was forgotten.  I was supposed to confront the student, get them awake and attentive- or send him to the ISS room to “rethink” his actions.  This was a very hard observation meeting for me to attend, this was my last year of mandatory assessments, my last year of probationary teaching, and this man held the power to end my career at the school.  Instead of sticking up for myself and my student, I shouldered the burden of being a bad teacher and was referred to a “master teacher” with which to work and council.  I received an hour long “in-house PD” lesson on the fine arts of classroom management and student behavior from him.  I had an extra observation that year from him as well as three more that was required from my co-operating teacher.  At the end of the year, on the last day of school, I was called into his office (in the middle school building no less) to be told that I was no longer a high school teacher and I was moved to the middle school.  I was to have another year of probation where I could be overseen by him personally.  I won’t go into that next stress-filled year but all I could think about was that I was the worst teacher ever.  I even actively sought out new positions in my area because I felt so much shame that I wasn’t sure I could work in the district anymore.


I was a bad teacher, so bad I had to move to a different school, teach a different grade, have a mentor and be personally watched over by the principal

It was difficult for me that summer, my teaching self-esteem was shattered.  There wasn’t any local teaching jobs open in my area and although I applied for any other related type of field I didn’t get any calls for interviews.  This left me in a low that I had never really felt before- I even almost went back to bartending just so I didn’t have to work another year for a man I was sure was using me for another year before sending me on my way.

I can’t thank my wife and friends enough that summer, they kept me doing things and always were great ears for me.  They convinced me to keep moving forward, to prove who I was and to take this new challenge and make the best of it I could.  Standing outside my car, outside that building and taking that first step into the middle school, his place of power, was a very difficult step to take.  Although I never gave into his vision of what kind of teacher I should be, the whole experience did shape me into the teacher I now am.

Wow, I can’t believe I actually just typed all of this and am going to put it out there on the web- but I do realize that now that I have I can start being more accepting of the smaller failures I have along the path of teaching.

Teaching students is the biggest act of being human.  I hated that most instructors feel they have to come from a place of absolute power and certainty.  I knew this was never the truth because all through school I thought about Math differently than it was presented to me, I played the game however and on tests I would replicate the work they wanted me to do.  There were times I forgot and I had many long talks with the teacher explaining my work.  As teachers we can’t be afraid to show students that we too struggle with work, make mistakes and feel like failures.  Students need to know that it’s OK for that to happen, but it doesn’t have to shape who you are.  We also have to teach them how to get back up from failure and keep going, no matter how hard it seems.  This is what being a teacher truly is.


I failed myself that day, and I failed my students- not because of my lack of content knowledge but because I was afraid to show an outsider who I really was and how I used that to create a learning environment where all of my students have the opportunity to be successful.  If you see me in class, you will see one of these being used by me, in a way I feel comfortable with that allows my students to own their own mathematical ability- not mine.


What did I realize a few years later (well, actually 3 years later when that Administrator also left the district)?  I was a good teacher, I made the right call for all of my students at the time, and no one in that room (other than my administrator) thought I was not doing my job or supporting them to my fullest.

Sometimes, being a “failure” is actually the best thing that can happen to you.  Thanks Annie for inspiring me to share this story and many more in years to come.

My MCTMDuluth Presentation

It was a week before the Minnesota Council Teachers of Mathematics Spring Conference when Sara VanDerWerf @saravdwerf messages me because there have been canceled sessions.  She wants to know if I will do a pop-up session, and of course I will.  The only problem- the topic.

Last year at MCTMDuluth, and this NCTM, I spoke about using Open Middle Problems to Promote Classroom Discourse.  Around Minnesota, I’m the Open Middle guy (except that one random incident where I was the Desmos guy) and that is totally OK because I truly believe in the power of Open Middle Problems in the classroom.  Those problems have led me into thinking about two other changes to make in my classroom (and these are not new in any capacity for educators)- Problems you Pose to Students and How you Ask Questions.  This is actually what my proposal for NCTM DC is next year and it’s still a stream of consciousness for me, nothing really concrete.  This is the topic I chose to present, to get a feel for how it feels as a presentation as well as to get input from my awesome peers at the MN conference.

The Google Doc presentation is here.

Too often students don’t understand what is going on in math class.  Earlier on in education, this was deemed OK- these students were slow and needed to catch up to the others.  More often than not, I think that this clip is how students feel in a math class.


When this does happen, we lose these students, this is where the Math Identity of  these students is taken away.  This is when students need us the most.

Students who are behaving in certain ways in your middle or high school math classes are not acting that way because they WANT to, they act that way because they have LEARNED to act in that manner to hide their feelings about math.  I have yet to find a student who doesn’t want to be better in math class, but it takes a lot of trust building and showing that you care to get those kids to crack and admit it.

We are teaching in the 21st Century and still use 18th Century mediums.  Books are not new, like it or not they are slowly becoming a dying technology (much like typewriters).  Our students interact with electronics, and we need to provide instruction through mediums that they interact with.  When I was young, I was trapped on a farm outside of town with no way to get anywhere.  I did a ton of stuff outside and if I wanted to “get away” I had to read a book.  They took me on journeys and adventures that I could only imagine.  My son however can pick up his iPad instead of a book.  That is how he interacts.  Right now, I have tons of difficulty getting him to read- it is a constant struggle.  Too many of my Students are the same.  They don’t process information by seeing it in a book, written on a board, or even when they hear rationalization of the process (because once again, it is referencing text).  We need to provide students with other ways to see math.

Students have to have an experience with what you are trying to teach them.  An experience they can relate to.  An experience they can visualize, manipulate, interact with.  Notice that I’m not saying we have to use digital technology here, we need to give them experiences that they can interact with.  This can be provided in many different ways, some with technology and some not.  I do agree with Dan Meyer in his age old talk about Video Games- we need to provide students with experiences in a similar fashion as video games because that is how they have learned to learn.

Give students a video to watch, activity to participate in, a photo to view, a puzzle to solve.  Allow them to notice problems and wonder about how to solve them.  Have them verbalize patterns and make conjectures on how they are related.  Allow them to be mathematicians before you introduce “formal structure.”

I’m not saying you have to totally abandon whatever curriculum or groove you currently rock in the classroom, but I am asking you to take the time to introduce a front-end stimulus for students that will allow them to have some practical experience with the mathematics you teach before you start the “I do, we do, you do” process.

After you provide students with some experience with the math, AND allow them to notice and wonder about things, THEN you can start questioning.  Notice here that I have yet to talk about calculating answers or assigning homework problems.  There has to be a lot more that happens before that- even though we all feel the crunch of getting our curriculum in “by this time” and get kids to master skills “for the test.”  Trust me, if you can get students talking, wondering, and verbalizing their thinking through questioning you will have a TON less work in the form of student questions on “how do I do number 13?”

One of the biggest thing many teachers can do to help their students be successful in the classroom is to implement a universal lesson design.  This may seem like a special education method but it is truly best practices.  If you learn to design lessons taking all of these considerations into mind, you will have provided students the best possible learning experience and environment.  (And I’m willing to throw out there that you will enjoy your lessons more as well).

Like I said earlier, this is just a stream of thought, please drop some comments on your thoughts on this- I’m still learning and would appreciate any input on this.

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 robertkaplinsky.com):  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 mathmaddicts.net): 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.