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.




Gunner gives me a Lesson

Finally, May 2nd and we have 67* weather.  I get home, throw on my old shoes and take Gunner for a walk.  I don’t have any specific plan in mind other than I love going for walks with him.  For those who don’t know, this is Gunner:


As you can probably tell, Gunner is a character and I’m not totally convinced that he knows he’s dog instead of a human. Anyway, back to the walk.

I’m on the walk, and it’s on a off-road so the pups can run around and enjoy themselves while I get to enjoy nature as well. (When I say pups, we also have 2 other dogs in the “family” Autumn and Harley).  I love being outdoors- I hunt, fish, run, play sports, but all of a sudden I noticed something.


The ground gets sandy and deep, uneven, tough to walk and I notice that my view suddenly becomes that of the top of my feet.  While this gets me through the tough part of the walk, I can’t see the pups or where they are.  Walking this way has slowed me down, and I realize I don’t hear their collars jingle nearby.  I panic like any other parent and find them.  I make an effort to not watch my feet but keep my focus on the road, the end goal.  My view becomes this:


As you can see, I’m way behind Gunner and Harley, but I know where they are, where I am and where I’m going.  Walking was faster, I found I could still make sure of my footing most of the time, as long as I visualized what was coming up and remembered that when it came near.  I walked this way a while until I noticed Gunner and the pups running back and forth, zig-zagging their way around the area.  It reminded me why I was here, not to quickly walk through the woods for some end goal, but to relax, have fun, take in the sights, perhaps see some other wildlife.  I quit focusing so much on the road and a great thing happened, I saw the outdoors.


This stretch of our walk took us along the pipeline, opening things up a bit an allowing me to see farther.  I even stopped, circled around and took in the view.  That turned out to be a good thing, since I saw this guy:


I love watching animals in the wild, and I have always loved watching birds in flight.  I can’t tell you how many times I have imagined I was there alongside them, riding the air currents, enjoying the ride and appreciating the view from above. I never would have noticed Mr. Bald Eagle if I hadn’t slowed down, looked around and took my time.  After watching him for a while, the puppies were worried about me and the next thing I knew we were all together again:


I gave them some love, and we started off again.  A little slower for me, and looking around appreciating the beauty of nature.  Once again I was left behind by Gunner, but Harley and Autumn were sometimes with me, sometimes behind, but we were all enjoying the great afternoon.

We were in the walk a ways, and got down into a swampy area in the path.  I had to take things slow and I also had to worry about an obstacle in the trail- a mud-hole.  The funny thing about mud-holes however, they are an obstacle for you but a refreshing distraction for the pups.  By the time I got close, this is what I saw:


I was taking time to plan how I was going to cross, what would be the best path- yet Gunner and Autumn charged straight through the puddle, and even took refreshment from the water within (No, I didn’t drink from a mud-hole.  I may be outdoorsy, but not that much!) It was during this time that things started connecting to me about this walk, my recent trip to NCTM at DC, and teaching.  But that will all come later, back to the walk as things kept filling my brain.

As I was walking, I started noticing things about the walk, how I moved, how the puppies moved, how we moved together.  There were times I was leading, and times that the puppies went off on their own, and others where they went together to investigate a particularly good-smelling track.


By the end of our walk, we were all tired- it had been a great afternoon!  We piled in the truck and enjoyed a much needed ride back to the house:


The odd thing I noticed, is that even after that long walk there were different attitudes and energy levels in the pups. Autumn just wanted to lay down and sleep.  Harley was tired, but she was still interested in what was going on and was looking at where we were going.  Gunner didn’t seem phased by the walk and wanted me to roll the window down the whole way- I almost thought he’d jump out and start running around some more!

This adventure got me thinking about my teaching, my paths, my student’s paths, and our adventure together.  I don’t want to spoil all the fun right away but I want you to read and reflect on how this story could connect to you.  Perhaps you can even anticipate what I will tell you in the next blog in a few days, when I talk about how I reflected and made connections.

Thank you Gunner, for showing me the path.

Park in a Different Spot…

Funny how seemly random things come together. Take for instance this quote by my good friend Casey:


As usual, I replied with a smart comment about riding a bike instead of driving. After some good-natured banter about riding bike versus driving, I didn’t think anything of it until yesterday morning when I drove in to this:


This doesn’t look bad, does it?  Well actually it is. We have a small parking lot, and space is cramped.  I have been working here for four years, and I have always, always parked in the same spot (yes, for 4 years!).  Recently we had a long-term substitute come into the school and now this newcomer has the audacity of just parking where she pleases?! What the heck?!

Needless to say, I was pretty mad and fuming all the way into school (mind you that this isn’t the first time the long-term sub has done this, it just came to a head yesterday).  All I could think about was how I wouldn’t have the nerve to do that, and if I did goof up and noticed someone else’s vehicle in the spot I was parking in that I would find a different area to park.  These rampant thoughts of the maliciousness of co-workers and the thoughtless self-absorbed culture of today festered in my mind all morning.

Then came Julie (OK, her name is not really Julie, but that anonymity thing), she had a question- of which I had the perfect answer!

OR… not…


This is how it went down (with comments I could see going through my student’s head as we were working on this problem- and were confirmed by me talking with her today):

Julie: Mr. A, I don’t understand how to do this problem.

Me: No problem, what problem is it? Do you know what it is asking you to do? (After I said that, I was like THANKS Captain Obvious! Of course she doesn’t know, that’s why she is asking for help!)

Julie: I don’t know, I don’t get it, that’s why I asked you for help.

Me: Did you read the problem? What did it say? Can you reread it for me? (Oh yea, I’m on top of my game today, why the HECK did she park in my spot!)

Julie reads the problem quietly aloud: See, this confuses me.

Me: What do you think it is trying to ask you?

Julie: I think it’s asking me this…

Me: Right!

Julie: But I don’t know how to solve that. (Mr. A, you really have no clue how to help me)

At this point I start into some great student-led conversation where I ask her questions that are supposed to lead her to an answer… (I wonder if I should just go talk to her about parking in my spot- even though it doesn’t have my name on it) Julie does some work and we get to an answer.

Me: Nice job! Way to work through that. (Maybe I could just talk to her and she would understand that’s my spot)

Julie: Mr. A, I don’t understand what we just did.

Me: But you did all the work, I just asked you a few questions…

Julie: Yes, but I don’t understand how all that relates to the problem. (GOD MR. A, you are so stupid!)

Me: Oh, So this problem is… At this point I start some hardcore direct instruction on the problem type, how to solve it and how curriculum presents these type of problems to students.

Julie (with a glazed over look): Yea, I still have no clue.

Me (getting frustrated- WHY did she park in my spot and ruin my whole day today?): OK, how about this? I try to explain it in a slightly different way which connects to what we have done.

Julie: I’m just going to ask Jared

“Jared” is another student who does well in math and he promptly explains the problem to Julie in a way I haven’t considered or seen, but it makes total sense!

Julie: I get it! Thanks Jared (why couldn’t Mr. A just say that in the first place!)

Me: Awesome, thanks Jared! (Why didn’t I think of that? That made total sense, why wasn’t I taught that?)


During prep I thought about what happened with Julie, and wondered why it was such a train wreck for me- until I thought about what actually happened.  I was so caught up in where I didn’t get to park that morning that I had closed off my thinking, I had boxed myself in like Casey’s car.  As I think on it, there are too many times that I approach student questions that way.  I know what is going on, where students are expected to get, and how to get there.  I work through the problem with them and if they can’t understand after a couple of approaches then something is wrong with them!  I always think I have an open mind about student learning and what is going on, but that isn’t always the case.  I wonder how often this actually happens in the classroom- we get too used and comfortable with our routine and how thing are supposed to be that we forget about the awesome thing of learning- actually LEARNING!

Students frequently ask me to do work that is familiar and easy to them, they lack the confidence to push themselves and they want to fall back on what is comfortable.  I always ask them if they think they are truly learning if they keep doing the same thing over and over, something they already know.  The tell me that it’s not, and yet here I am getting caught up in the same thing.

Just like Casey, I came into the building 4 years ago with this grand idea of what I wanted for my classroom, a fresh start.  Here I am four years later finding myself straddling the trench of comfort and conformity- not fulling falling in that trench but slowly slipping down the slope.  I have noticed a slow change in what I do as I get feedback from peers, admin, and center staff.  I should thank my co-worker for parking in “my spot” and forcing me to realize that in order to be the teacher these students deserve I need to continue to push myself as hard as I push my students, I need to find new parking spots- new ways to get to the same destination.


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.

The Moment…

One of my good friends once said that “we need to let go of the things we can’t control and focus on those we can” she also said that “until we want to, we truly can’t change anything” (OK, so maybe I paraphrased a bit @veganmathbeagle).  It wasn’t until NCTM in San Antonio that I had that moment, the moment where I wanted to change how I approach conferences.


I flew into San Antonio on Wednesday and picked up my program.  I first double-checked when my speaking session was , the time and where, then I started looking through the program to find sessions.  While I was looking I had my moment.  The moment I am talking about is when you realize that you are stuck in a rut, that you are doing the same things over and over even though you are wanting to change.  It’s no one’s fault that this happens, it seems to be a condition of being human- finding safety and security in doing the same things, finding a pattern to your life.  The bad thing is when you do these in a profession such as ours (that is, unless you are a super-teacher whose students are exceeding in their learning).

My moment was realizing that when I come to these conferences, even though I want to find new things to implement in my classroom I also want to talk with and hang around my friends on the #MTBoS that I never see.  As such, I revert to the high school student who takes all their friends’ classes- and while that is not necessarily bad it also doesn’t fully address MY needs, I am attending sessions that satisfy their needs (and as we know sometimes those overlap in areas).


Looking at my program, I was highlighting people I interact with through the #MTBoS (and by interacting, I also mean stalking because there are times I don’t feel like I can approach them).  I do this at my local conference a lot- I go to my friend’s sessions.  That hasn’t been bad so far because I still need those connections, my friends do push me to become a better teacher.  The problem is that, for the most part, I am already aware of their passions and know about their session.  This is not NEW material to push myself as a teacher.  So when I caught myself highlighting my “peeps”; Dan Meyer, Robert Kaplinsky, Andrew Stadel, etc, I realized that perhaps I need to find a different direction for this conference.  This feeling was further enforced as I stood on the second floor balcony and observed how many math people were present at the conference.  I thought I had a large network of math people because of my involvement in #MTBoS, but here was concrete evidence that my potential mathematical network could be much, much larger.

So I took a different approach, I sat down and really read through the program and found sessions that really touched on areas for myself as a teacher.  I didn’t hang out with all my twitter people as I usually do (and I will say I am sorry for that, I was being purposeful this conference but I always tried to say Hi when I saw you guys around).  I went to sessions of people I didn’t know (or perhaps I did but I’m getting old and didn’t remember).  I looked for sessions that would directly impact my needs as a teacher working at a juvenile center where 90% of my students have special needs.  A funny thing happened, there were a couple of sessions where I did go to my “twitter friends”, and there were sessions that friends also attended.  The big thing is that I met new friends, heard new voices, got fresh ideas.

I am hoping that I will be able to attend NCTM again next year in DC, if I do I will plan a balance of “being with my friends” and “finding something new”.  I also hope that ShadowCon will consider @delta_dc’s comment on “the Next Generation”, allowing newcomers to present and add their voice to our great community.

If we truly want to change, we can’t continue to travel in the same circles we always do.  I find it funny that we, as a community, lament the fact that teaching always seems to revert to those strategies and curriculum that we strongly feel is wrong- but that we are unable to see those same qualities within ourselves.  Perhaps this blog will inspire the moment within you where you realize that you also need to step outside of your current zone- that every one of us needs to in order to challenge our ideas, our absolute belief that we are teaching the only way possible to teach our students.  Because in reality, there is so much more we can learn from those on the sidelines of our #MTBoS community that can enrich our own learning and that of our students.


PEMDAS? Is order of operations the only way?

This year I have had quite a few students who are pushing themselves mathematically and doing a lot of great thinking.  This also equates to making me think as well, and I really need that.  Now a student has me thinking about PEMDAS, how it is taught, and how it is a coveted norm of mathematics.

One thing I have always struggled with when talking with students about PEMDAS is how to make it meaningful for students without pulling out the “This is the way it is” card.  I don’t want it to become a memorization practice only, I really want students to understand why we do operations in a particular order.

One thing I have used and students understand (not surprising because I adopted this because of a student) is that multiplication implies “groups of.”  I’m sure many pure mathematicians might frown upon this, or the fact that it also leads to repeated addition, but students really grasp the concept and start visualizing order of operations.


3 groups of 4 plus 2



When students think of it this way, they don’t want to add 4 and 2 and then multiply that by 3.  This is also true when they see 2+3×4, the “groups of” thinking prevents them from adding 2 and 3.  Is this just replacing a trick with a trick?  It took me a few years to even accept this type of thinking for my students- I don’t want to provide a new crutch for students.

This all leads me to the other day, when a student was solving the equation 3X + 2 = 8.  He was unsure of what to do, so I asked him what step he would try.  He repled: “I would divide by 3 since I want to solve for X.”  I immediately balked, that answer went against all of my mathematical fiber, but I tried to not show it visibly.  I told him to go ahead and try his idea.  This is what was produced:

student solution 1.PNG

Wait now!  Hold on, that is the answer I expected, but not attained in the way I assumed it would be.  I can’t tell you how many times I have used the last in- first out type of thinking with students to solve equations, and I expected seeing something like this:

Expected Solution 1.PNG

But all of these provide the same solution!  Is that a fluke?  Some weird oddity that can’t be reproduced?  It had me thinking of possible counter-examples and what else it could imply.  Does order of operation last in-first out thinking absolute in solving equations?  Or is it something like the standard addition algorithm that we accept as the best method and ignore others?  My student gave me another example to consider later that hour.

This problem involved the area of a trapezoid.  They wanted him to algebraically solve it for b2.  I was very curious what he was going to do, and instead of starting with the parenthesis, so subtracting b1 (which is what I assumed he would do because of his previous reply), he told me he needed to distribute before solving.  His work was this:

Student solution 2.PNG

Which again produced the correct solution after he cleaned up the compound fraction.  Once again his work produced the right answer without doing the expected procedure:

expected solution 2.PNG

So currently I am rethinking approaches to solving equations.  How will not using the standard approach effect him later on?  I can see how trying some sort of variation on this with powers will be messy.  I’m totally open to suggestions and comments on this, as it has my brain working on overload ATM.

Where our youth go…

I haven’t been on the blog horn or even Twitter that much other than #MSMathChat, and that is because right now I am struggling a bit to keep my head above water this year.  There is a lot going on (and taking Grad classes on top of everything wasn’t a good call).

This post is gonna be short, but it just hit me yesterday and I wanted to get it on my blog so I have it and remember.

This week has been fairly slow, I have had 6 new students come in and 6 leave.  I’m getting used to that, it really makes trying to keep a cohesive classroom hard- but I have been managing.  That’s not the factor that hit me, it’s this one:

70% of my current students are return students.

Normally high school teachers don’t bat an eye at that statistic, in fact they expect a lot higher one, but not when you are teaching in a Juvenile Center.  That number means that even though these students get a grip on their lives while they exist within these walls, they can’t maintain that when they go back home.

As a parent of a 5 and 8 year olds, I am getting more and more sensitive to factors that influence their lives, their behaviors, their choices.  When I talk to my “returning” students, they have ALL told me that they go back home fully intending to keep out of trouble, yet they fall into the same group negatives or they can’t cope with the bad family environment at home.  As a teacher and parent, this makes me immensely sad.


(this is a random picture taken from the WWW, it is not any student that is enrolled  in my school or staff that works at my school)

Our youth make their own choices, but many are too unsure of themselves to be confident to walk their own path individually.  They need their friends and family, and if those happen to be a negative influence on them- returning them to that environment is setting them up for failure.  I don’t know what the correct answers are for this issue, they go beyond my scope of expertise or experience, but I am beginning to believe that in order to truly change things for these students then those outside factors also need to go through the “treatment” processes these children face.

We can’t keep placing them in the same situation and expecting different results.

All children deserve to be loved, and have a safe positive environment to learn and grow in.