Growing Mathematical Minds

For whatever reason, today was a particularly difficult day.  And as I reflected on the day I tried to remind myself that the quarter, which just ended had been one of great growth and success for so many of my students.  I tried to focus on Spring break that had just started and the need for the break to refresh and rejuvenate myself.  As I was thinking of this, suddenly I remembered a letter I had just received from a student and I was almost in tears.

I have made it my goal over the past year to really try to reinvent the way I approached my classroom and instruction.  I had focused on changing so much about my routine, teaching style, classroom set up, and lesson delivery.  I have spent countless hours planning and search for activities that would engage my students and promote a growth mindset.  In fact, I had even focused on using growth language with my own children (age 5 1/2, 4 and 2 1/2) at home.  I want to be sure I was constantly encouraging effort, goal setting, critical thinking and problem solving.  I knew that to present this authentically to my students I had to embrace and encompass that mindset in all aspects of my life.

I have had so many wonderful moments, and days this semester where I left excited and loving math, and even where my students left telling me how much fun the lesson was that day.  But some how all those wonderful moments can so easily get over shadowed by negativity and disappointment, and for whatever reason I was having a really down day today.  Then I remembered this letter:

"Dear Mrs. Van Keulen,

How are you?  I have been enjoying math lately.  In fact, math is now one of my favorite subjects Because you made it easier to do math in your class.  I am writing this letter because you are one of my favorite teachers.  I wanted to let you know that you are appreciated.

You are one of my absolute favorite teachers.  Before your class I never really appreciated math and I didn't think of myself as being good at it either.  I thought it was frustrating. You made it more interesting.  I enjoy doing the critical thinking problems.  I also appreciate that you show us different ways to find the answer and you let us try to figure it out on our own before showing us how.  I also like how you let us do test review because then I don't feel as much pressure on the test, and therefore do better.  Thank you so much for all that you do.

Thank you,"

As I read this letter the first time, I literally wiped tears from my face, not because of all the nice comments that this particular student said, but because of the philosophies that she expressed in this letter were exactly what I had hoped to give to my students.  My goal has always been to show students that they could do math and that it really was fun.

Over the past year that philosophy transformed into the idea behind the growth mindset, and encouraging students to see the excitement and accomplishment in struggling through a task that they previously considered themselves to be "bad" at.  This letter gave me the reassurance and spark I needed to realize that I was reaching some of them, even if only this one, I was reaching them.

So while some days can be overshadowed with the negativity, in all if we keep our minds open, and persevere we all can have a mathematical mindset!

Embracing the Growth Mindset

My main goal this year has been to reflect on my teaching and make sure that my lessons and instruction was encouraging my students to think and problem solve.  About a week ago I began the proportions unit with my Accelerated class.  As I planned for this unit, I found a lot of great activities through the Math Assessment Project.  Looking through these lessons, and planning cause me to really think about what mindset I had been growing my my classroom.

The more I work on interactive lessons, problem solving and project based learning, the more I realize that for the past several years I had been teaching my students to be robots.  I was putting them in a box with 60 foot walls and only allowing them to think linearly. The had to show their work my specific way, the “right way”.  But as I approached this unit, I realized that as a student, even though I was always “good in math”  I was usually that student that approached the problem in a different way.  I was squashing that student in my own classroom.  

So with a little apprehension, and fear of the repercussions of their future success in other teachers classrooms, I have approached this unit from a completely growth mindset.  I wasn’t going to focus or even directly teach the correct proportional way to solve these problems, but we were going to discuss what proportionality meant, and look at many approaches to solving.  It was going to be about their thinking and approach to getting a clear understanding of what proportal relationships are.  

Today I just taught solving proportions using the math shell lesson, and the students came and presented their approaches to solving 3 separate problems.  Some did use the “correct proportional cross product” method I had been accustomed to teaching, but so many of them present beautiful explanations and approaches that showed they understood how a proportional relationship worked, but solved it in a different way.  The conversations were so excited.  They were eager to share their method, some even presented ways I would never have thought of.  

I have been coming off a bit of a low point in teaching this year, feeling like my methods were not getting through to my students.  But today I saw so much thought, enthusiasm and validation in my students.  And I realized this is what I got into teaching for, to engage and excite them to find a path to problem solve.  I feel like today i learned just as much, if not more, from them than they did from me, and it was wonderful.  

Riding the Waves

I’ve taken a break from the blog over the past several weeks, trying to come back from hitting a major low in the ups and downs of teaching.  I started the year off inspired from my summer school experience, working with the math leadership council, and all the great project based learning lessons I had been finding and planning.  I went into chapter 2 of the book, the dreaded fractions with positives and negative feel motivated and optimistic.  I worked on student centered lessons, discourse and visual models.  In class students were drawing, talking and representing operations with fractions. All seemed to be going great…. Then I assessed them.  To say it was horrendous would be putting it mildly.

I was so discouraged.  I, We, had all worked so hard on this chapter. I analyzed their work and kept seeing a common thread, negatives, they didn’t know what to do with the negatives.  So for the past several weeks, I have spiraled reviewed the material as we progressed through the next chapter.  But I had lost my drive and excitement that I started the year with.  I was feeling defeated, like all this planning and work wasn’t having a positive impact on the learning of my students.   I have really been struggling with this over the past quarter.  

I keep plugging away, looking for hands on lessons, encouraging error analysis but inside I have felt defeated.  I truly want to change the way they view math.  I want them to love the exploration and discovery in the process.  I want the lessons to be as exciting for them as I think they are.  But I have barely been treading water.  I have been lucky this year to be working with a grade level team, and talking through all of our struggles and successes has helped to get me through this low.  Yesterday I received a letter in my mailbox that has helped me to get some of my spark back.  It was from one of my summer school students, thanking me for working with him this summer and making math “fun”.  

I think what I have come to realize is that this h=journey is going to be full of highs and lows.  Some of my lessons will be amazing, and others might flop, but most importantly I need to fight that urge to slip back into the easy routine of lecture.  I need to challenge myself to be better and keep searching and trying new things, just like i am always challenging my students to persevere and work through the struggle.  So while currently I feel like I’m currently at the bottom of the wave, the next one is right behind me waiting for me to catch it.

Pattern Block Fractions

A new school year is underway and I am continuing my journey to make math hands on and fun while increasing student comprehension.  Over the summer I piloted a lot of different activities with an 8th grade bridge course, and I am now bringing some of the successful ones into my classroom.  My goal is to limit my "lecture" and to increase student discourse and participation.

   So as I started the dreaded chapter on fractions today, I really wanted to focus on helping them to comprehend the concepts and not just memorize algorithms.  I was luck to be able to be a part of the Ventura County Math Leadership Network, and attended a meeting last week.  From the summer lesson searching, and this meeting I introduced fractions in my classroom today using 2 techniques I had never done before.   Knowing that fractions give students, and all people, trouble I wanted the kids to play with the concept of fractions and discover equal parts before I taught any specific rules or concepts.

  So I passed out bags of pattern block (see picture below if you are unfamiliar)

and had the students compare them and give them fractional values.  Most were abel to do this very easily.  Then I created a new figure using the block, and discussed how the whole amount was no longer the yellow block.  Students talked about the new whole amount, and answered  a series of questions about what fraction each shape now represented in comparison to the whole.  Then we talked about how we had to divide the figure into equal size pieces to get these fractions.

Later this week I plan to introduce adding using the blocks again, and hoping they will see why we need to find "common denominators" in order to add the pieces together.  Overall the lesson was really fun, and the kids were talking and understanding how the whole size can change the value of a piece and the fraction associated with it.

Approaching the finish line.

This summer I volunteered to teach an RTI course to help prepare incoming 9th graders for Algebra 1.  I spent a lot of time planning what I wanted to teach and how I wanted to run my 2 hour class.  As the start of the course approached I was very nervous about how all my activities would be received by these students, after all, they were the kids who had no reservations about telling me how much they hated math.  The first few days most of them entered the room with very glum expressions.  It was very clear to me that they didn't want to be here.

Most of my lessons centered around problem solving.  I wanted them to integrate skills while solving "difficult" problems.  I used 3 act lessons, Scholastic articles, hands on manipulatives and everything I could think of to make math "fun".  After the first 2 days I was exhausted... this was going to be a long 4 weeks.  I practically was pulling words out of them with sheer force.

By about the 4th day something happened, they realized that I wasn't going to give up, and I wasn't going to let anyone hide in the corner (a strategy most of them had perfected by now).  The first week was fractions, EVERYONE"s favorite topic, HA!  Well we survived and 80% of my students passed a fraction test. (For those of you who dont teach math, in a typical class where fractions are taught I have a 50% pass rate with all students).  80% of students who HATE math passed a test on Fractions!  YES!

On Monday I was greeted by one of the most touching emails I have ever received.  It was from one of my students parents, her daughter had struggled last year in math and received an F after putting in a lot of effort.  The gist of the email was that she was so grateful that I had broken down the wall her daughter had in regards to math.  She even quoted her daughter to say: "The class is actually fun!... well as fun as a math class can be."  The mother even Cc'd the district office administrator who asked me to do the class.  I felt empowered!  Even though the first week had been "rough" for me, I had made a difference with at least ONE student!

As the weeks went on, my students started to come out of their shells.  Most of them were talking, participating and doing the Math.  Many of them were even excited to solve each task.  They would compete over who could solve a problem or get the "right" answer.  Just yesterday we were working on equations.  Every day there is about 20 minutes of skill practice, boring but necessary.  After 20 minutes I told them to take a break.  As I prepared to take one also, I saw several kids move across the room with their papers, and sit down with friends to compare work.  I was thrilled, on their own, Math Haters were voluntarily doing math together!  Success!

Today they took their test on the 3rd topic, and I conferenced with each students about their progress and effort.  Almost all of my 45 students are passing.  As I showed them their scores and discussed their growth I was greeted by smile after smile.  Many of them admitted they had never passed anything in math EVER!

My goal this session has been to focus on effort and growth.  We focus very little on grades, more on trying and meeting a goal.  Most students are surpassing each goal.  I've also made a big a point that after we get an answer we need to revisit it and look for mistakes.  I have given all tests with a first edit (I check them and show them problems to revisit).  They then go revise and turn back in for a final grade.  Most of these students are use to immediately throwing away every test they take, now they go back and usually fix most of their mistakes. They are taking pictures of their tests and texting them to their parents.

Overall this had been so much fun, and I think we all have learned a lot!

Why HATE Math?

As I prepare for the start of any school year, I have come to the very realistic knowledge that about 30% of my students enter my room on the first dreading my class.  Not because I have a “reputation” but because I teach that four letter word: MATH.  And not only do I teach math, but I teach MIddle School Math, 7th grade primarily.  I like to think of it as the perfect storm: the most awkward and scary time in adolescence, most students are starting at a new school, and math tends to be a highly disliked subject.  Lets face it, if you walk up to most adults and say you like MATH you get looks, but if you say you TEACH MATH you get even weirder looks, and if you say you TEACH MIDDLE SCHOOL MATH the look is usually followed by a: “oh bless your heart” or “yikes that must be rough” or “do you like that?”  (I’m pretty sure the reaction is similar anytime you tell adults you voluntarily chose to work with middle schoolers).  

But despite all of this I go to school on that first day excited to meet my students, and apprehensive for what the year ahead holds.  The discussion of why students struggle with math comes up in meetings often. My district is continually trying to implement programs and support systems to help kids be more successful in math.  So the idea of having a summer school bridge course was brought up, the focus would be students who struggled in middle school (MATH haters), to help them be better prepared for high school. Sounds great.  So naturally I volunteered.  As time when on, questions like: what should we teach? What materials will we have? How will we grade this?  Were answered with wide eyes.  

So I was excited, I would get to design and teach whatever I felt was most important.  This excitement was quickly met with anxiety: do I know what is most important?  So I talked to colleagues and got a direction on the topics I would focus on.  I sat down to plan.  I wanted to focus on hands on activities, application problems, explorations and growth mindset.  3 hours later I had successfully planned my first class.  Only 18 more to go… it was going to be a bit more time consuming than originally planned.  But I did it, and yesterday I had my first day.

This first day was a little different than the ones in my past.  This time I KNEW that 100% of those students who were entering my room were DREADING it.  A room full of 25 or so students who have never found success in Math and now got the privilege to give up a month of their summer to do MORE MATH.

Well I just finished day 2, the 2 hours periods have flown by, my students have been engaged, they got to “play” with pattern blocks, solve puzzles, play cards all while DOING MATH!  Now don’t get me wrong they aren’t all transformed into math enthusiasts, but they are ALL working, trying, and even smiling!  I told two of them today, that by the end of the month I wanted to hear them say that this really wasn't so bad after all.  And in all honesty I have had more fun teaching these past 2 days then I have had in awhile.  

Day 30

30 days ago I was boarding a plane on my way home from NCTM.  I was excited and ready to transform my classroom.  I had so many ideas that I couldn't wait to implement.  I had these grandiose visions that I'd come back and transform my students into math enthusiasts.  I couldn't wait to see them excited and eager to do math.

Over the past 4 weeks I've increased discourse, empowered students to discover and work towards learning before direct instruction was provided.  The main topic we’ve covered is surface area.  We have approached the topic by looking at nets, estimating how many post its would fit on a filing cabinet in a 3 Act Math lesson, creating popcorn boxes.  Woven into the hands on activities I've had them working in pairs to solve more traditional problems.  They have demonstrated their knowledge by teaching their peers.  I've seen average and struggling students become leaders as they helped a struggling partner and “taught” their partner how to work out problems.  

Most days I thought had gone great!  I was having fun, and so were the kids.  We had our momentum broken up a few times with state testing, but overall I was feeling great.  I went to work this morning excited for another week, and even more excited to begin lesson planning for a support class I'm teaching during summer school to help students prepare for high school math.  I couldn't wait to plan out all these great hands on, growth mindset lessons.

But as you many suspect, every high meets its equal low.  About halfway through my day, I seemed to dive into mine.  I had given a quiz on surface area, and as I'm looking through them, my scores were low…..VERY LOW.  Several zero percentage per class low.  At first I tried to justify this by looking at the students who did poorly and how much work they had done.  I saw a trend,  most of the zeros hadn't done ANY homework all chapter.  Sigh of relief, this exonerated me, for a minute.  After all now I could pass the blame.  They weren't working, so it's their fault.

The more I thought about it, the more bothered I became.  Wait a minute, at NCTM I had found the magic fix.  My class would be more engaged, so the kids would learn and everything would be wonderful!  But it wasn't.  I was lied to, no I was doing it wrong, see I should have just stuck to my tried and true routine.  I'm obviously not a good teachers.  Throw everything out the window…. Back to what I've always done.  These and many other thought went through my head.  I wanted to cry, then I wanted to scream, then I was just mad.  

Sometimes in the heat of the moment the best thing to do is nothing.  So I went home, played with my little girls and did some thinking.  Where would I go from here?  I had two apparent options:

• Give up, and return the the routine that I have been doing for the past 10 years
• Persevere and keep trying

My gut know that option 2 was the right one, but option 1 was so much easier.  Even as I'm typing this I have this little voice telling me stick it out, stick it out.  After all isn't that what ewe always tell our students.  How often have I told them that math would be hard, but if they stuck it out and kept trying it would get better.  Didn't I owe it to them to follow my own advice.  Don't I owe it to all those kids I'm getting this summer to try and teach them how to be thinkers?

So it was a rough day.  I'm exhausted, frustrated and discouraged, but tomorrow is another day and I'm going to try again.  And even if I only reach one of them, engage one of them, inspire one of me to enjoy math, the. That is one more than I had the day before.

Day 31 here I come.  Are you ready for me, because I'm not giving up!