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!

Volume is so much more fun with popcorn

So the school year is rapidly winding down, state testing is coming to an end and the students and myself are hitting that wall.  I am trying to find innovative ways to make these last few weeks run smoothly, and they in typical middle school fashion are shocked that we would actually have to "do work".  After all state testing is over, so basically there is the point of learning, right?

I have one final topic to cover in the last 14 days of school: volume.  While at NCTM and bouncing ideas off of my fellow colleagues Fawn Nguyen's blog (http://fawnnguyen.com/) was mentioned and in particular her volume lesson that was amazing.  So I went to her page, read the blog and immediately have started to follow it.

What I loved most after reading her blog, was how adaptable this lesson was, I could keep it very simple, or lead them towards maximizing volume (a calculus concept), plus there was food involved which is an instant win in middle school.
I paired the students up and handed each pair a piece of computer paper.  I explained that they needed to make a popcorn box as big as possible.  The only rule was that they had to do so by cutting the corners in order to create flaps that would fold up to form the sides.  Immediately one group raised their hand and asked: "Does big mean it can hold the most, or it has the biggest surface area?"  WIN!  In the past 3 weeks they had caught on to the idea to ask clarifying questions.  So I replied that they wanted it to hold the most popcorn.


Students began working, some immediately measuring and cutting, others discussing and drawing out possible plans.


Once they had all formed their boxes I displayed them for the class and we discussed which appeared the biggest?  How could we figure it out?  Find the volume they replied.  So while they calculated volume (I prompted them with the formula that we had discussed in an activity earlier that week) I filled their boxes with popcorn.


Then I sent them home with an extension for homework.  We talked about what we learned: the corners must be squares.  Then we talked about all the different boxes that could have been created.  Which one is the best?  How could we figure it out.  So we went through the first option (using only whole measurement), 1cm squares cut form each corner.  They recorded the volume in a chart that I provided, their homework is to come up with all the possible boxes and decide which is best.  So we will see what comes back on Monday!

My big take away is that my kids are talking, and excited to do math.  Since my return I have had numerous comments on how class is fun.  Is everyday perfect, certainly not.  Do I have those student who are off task, absolutely.  But I've decided they wont be my driving force, instead it will be the ones who are suddenly seeing a point to math and taking an interest.

My First Act

Setting the scene:  As soon as I got back I talked to my students about how I had learned so many great things that I was excited to try out in the classroom.  One of the first sessions I had attended was on 3 Act Math.  I had seen this topic presented in staff developments before, but the idea of making videos and coming up with lessons just seemed so daunting.  But at NCTM I discovered that teachers really want to share resources, and there were so many lesson already out there to get me started.

So after returning to my classroom, I made one simple change and took my 6 rows of desks and pushed them into pairs.  This was my way of forcing myself to develop and encourage discussion between my students.  I knew that if I didn't give them good guidance this would simply lead to a lot of “noise” in the classroom.  So I dove right in with a 3 Act Lesson that I found on Andrew Stradel’s site. https://docs.google.com/a/simivalleyusd.org/spreadsheets/d/19sms4MpuAOO71o4qFPJyVKK-OGLnNegMgSL6WAwIdb8/edit#gid=0

I was about to introduce surface area and decided to do the file cabinet activity with my students.  

The introduction is a video of someone covering a file cabinet with post it notes.  It shows the cabinet partially covered and poses the question:  How many post it will it take to cover the cabinet?

I then had my student talk about it and come up with a list of information they felt they would need to answer the question.  They were talking, and for the most part it was about math.  No one was sleeping, no one was begging to go to the bathroom, they were all discussing and making predictions.  Then I gave them the dimensions of the cabinet and told them to come up with their best “guess”.  

So after about 20 minutes I drew a chart on the board to track their guesses, well here I discovered that I needed to help guide them a little more.  The first group looked at me with wide eyes and asked: “we had to actually come up with a real answer?”  As I went around I discovered only about half of the groups had used any “math” to get their guess.  

Time to redirect, so I explained that this would be a competition and the groups with the right answer would win a prize, and sent them back to the drawing board for 10 more minutes.  They started sketching the cabinet, calculating how many post its would fit on each surface.  Some asked to replay the video, was the top being covered too?

After 10 minutes I recorded each group’s’ guess. The kids were reacting to each other's answer, asking the groups how they got it.  So I called up groups who wanted to explain their reasoning to come up and show how they got their answer.  Then we watched the solution, and the reactions were exciting.  Kids cheered as they discovered their answers were close.    They were ALL engaged and listening.  

At the end of my first week back during my 7am class I overhead a few students talking about their teachers and teaching styles.  (This class is an RTI class that they take as an elective).  One of my math students was explaining to the others that in Mrs. Van Keulen’s class they now had to do all the work.  That they got to talk, and explain and that it was fun.  She said that she was learning so much more now, and that she actually had to think.  

So there have been bumps, and I have been frustrated at times, but overall I am having more fun, and I think the kids are too.

Who is really DOING the math?

“The only way to learn math is to do math.”  Paul Halmos.  I think this quote resonates with all math teachers, and encompasses our daily struggle of getting kids to “do” math.  But what does it mean to “do” math??

I had the ability to attend the NCTM conference in San Francisco this week.  I hoped to get some new idea’s on lessons that would get my students to “do” math more effectively.  I have taught using a very traditional structure of direct instruction, guided practice, and independent practice.  I feel that I had been doing a good job of instructing them on the mathematics, but I was really struggling with getting them to “do” the math and retain it.  I figured I would come back with a few new “fun” lessons and suddenly they would be excited to “do” the math.

Well my take back from this conference was exponentially more than that.  My mind was blown! I feel inspired, motivated and eager to completely revamp my classroom and its climate.  My focus after the first day became focus not on what activities I could bring back, but what practices and strategies should I be using to engage and motivate my students.  

My curiosity was triggered with a 3 act math session, when you use media to capture attention and they promote student thinking and conversation.  The idea that students should be driving the conversation with each other was a constant theme throughout the conference.  This spiraling theme to do less, promote conversation, don't give or focus on answers, but let the kids talk, debate, and prove their perspective.  The simple idea that there are multiple perspectives, and even multiple “right” answers, YES, even in math!

The final push to make a drastic change came during a slam session where each presenter gave a call to action.  And I am running with these ideas.  I want to be a classroom that encourages students to love and crave talking about math, to be problem solvers and critical thinkers.  

Now that I've returned, I'm running with these themes, and for the rest of this year, I will strive to integrate these ideas and conversation into my classroom.  As I try something I'll blog and share the change, good, bad and ugly and hope to grow from it.