About 10 years into my teaching I started to really focus on kid's learning and really dissect how kids learn math.  I know this sounds like something you should do year 1, but honestly at the start of teaching you are just trying to survive.  My first school I was just hoping there wasn't a fight that day and I wouldn't get hit with a fist meant for another student.  I broke up fights, put out literal fires, watched a kid get pulled out my class with a weapon on him, and being physically assaulted by a student.  Analyzing how kids learn was an afterthought.

 

I then helped start a charter school and we had better behaved kids and I was able to put more thought into my teaching and how a kid learns.  This took about 5 years into the school, just due to how much work had to be done to start a school.  But around year 8 to 10 I really analyzed kids and their thought process and learning and I started to see some kids that just could not do math.  It just didn't make sense to them.  

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One student I had changed a bit of how I understood how kids learn and think.  I realized that this student did not understand the concept of 4 is bigger than 3.  A non-math teacher would just say, "look, just hold up 4 fingers on one hand and then 3 on the other and point out that 4 is bigger".  I had a co-worker tell me this and I just didn't have the energy to debate and just said, "oh yeah, I never thought of that.  Thanks."

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What is really hard for any human being understand is that some kids just don't understand the concept of math.  One may say, "well, this child must have an IQ lower than 70".  Nope.  He had average IQ and he was above average in English.  His vocab was advanced and his parents did everything they could for him to get him help.

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Before I go any further, I will give away the ending, I have no idea how this child thought and I did not really help him in the end.  This is not a feel good story with a solution to all other teachers.  Sorry.  I wish it was.  It is simply me putting my thoughts down so that maybe someone will see it, relate to it, and take some piece of what I say and combine it with their experiences and it somehow helps them.  Great solutions come with people talking, brainstorming, and sharing ideas.
 

I realized that Barry (name changed) just didn't have the concept of bigger or smaller or just what numbers are.  I pulled out a science balance and put some items on the right pan and told him to balance it.  He could not.  It was as if that part of his brain was just missing.  I was stunned.  I had not seen this before (thinking back I had but did not really have the time to recognize this).

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I decided that teaching Barry how to add and subtract fractions with unlike denominators was simply a waste of time.  He did not understand other concepts that way below the learning level of fractions.

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Sadly, I did not do anything that made me feel that Barry had improved much and was on the way to higher math learning.  I did see the dad when he was in HS and asked about him.  Dad was open about his math struggles but Dad was more at peace with it and conceded it was going to happen and to focus on what he was good at and how to help him become a productive adult.  In 6th grade, Mom and Dad were a bit hard to handle because of trying to help a kid that just couldn't get "math".

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Even though I didn't feel I helped Barry, it did start my journey of trying to educate kids differently that were just not getting it.  Here are things I have added to my classroom and things I have added to my mindset that I think have helped me and my kids.

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1) Worked on making kids smile in my class.  This meant I would show more videos (math related but many non-math related), tell more jokes, develop a calm classroom that wasn't so "rigid" but still disciplined, and have a more holistic classroom.

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2) For struggling kids, I would work on more basic stuff to fill in the gaps, which is where the website, www.myquickmath.com came from.

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3) I work on developing the kid's thinking ability through non-curriculum  problems.  I love doing IQ questions with them and letting them work in groups.  I enjoy just random logic problems.  Anyting that makes them think differently.  One of my favorites is just putting up a triangle broked up into many smaller triangles and saying, "How many triangles are there?".   Kids who struggle can do it.  Advanced kids can do it.  Any kid can do this type of problem.  It made them think differently and made them fill in some gaps with what numbers are.

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4) I have stopped stressing so much on note taking.  I have struggled with this and change each year.  But I give up some notetaking so I can work on teaching them how to think.

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5) For kids how really struggle, I only focus on basics.  I do not do any higher level problems (unless I see real improvement).  I just feel that filling in those gaps, learning how to think, and enjoying being in my class were the most important things.