The Sound of Silence – Not So Much

To the casual observer, my classroom bears very little resemblance to those of my childhood.   Table groups vs rows.   Guide on the side vs sage on the stage.   Sounds of kids vs sounds of silence.   Yet, there are elements of those rooms that I need, that some of my students need.

Amidst all of the mathematical discourse, we have done a really good job of de-privatizing mathematical thinking and thus moving everyone’s thinking forward.   We have also done a really good job of addressing the needs of students who process information better by talking about it.   Sometimes, though, I think we need to make sure that we have those small pockets of quiet.   Quiet to ponder, quiet to think.   Quiet.   I know that I need it when I am thinking deeply, trying to solve something.    I know that some of my students need it, especially in the face of challenging work.   .

So, how do we find those pockets of quiet without giving up the discourse?    It’s not something that will just happen.   We have to create those moments to just think.   Those moments when we pose a question but don’t allow anyone to answer, when we define a space to just think or to just write.   Then, we have a conversation.   We engage in discourse.   I really like to use structures to create these spaces of quiet followed by spaces of discourse.   It’s one of the reasons that I like Think-Pair-Share and Think-Write Share.   They create those moments to just think.   Then, they create a space where every single voice can be heard    Finally, they create a space where the whole class can engage in a conversation.   I like the Kagan Cooperative Learning Structures for the same reason.   Students work independently, then with a partner or small group, and only then discuss things with the whole class.

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Using these structures means that I have to teach kids to use the structures.   It also means I have to teach them to manage their volume.   I use a sign that is essentially a traffic light.   I show the color of the light that corresponds to the correct volume   Red is no talking.   Yellow is partner or table group voices.   (I tell them it is a 2 foot voice – loud enough to be heard 2 feet away but not much farther).  Green is whole class voices (loud enough for the whole class to hear so only one voice should be heard at a time).   I think the visual cue is really helpful for kids.   I also redirect by referring to the display when things get too loud (“I see yellow, but I am hearing green”.)

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Sometimes, I have table groups that have a little difficulty managing their volume.   I use a set of green, yellow, and red cups at each table group to help manage this.   If the outer cup is green, things are fine.    When the group is getting too loud or goes off topic, I go over and change their cup to yellow without saying a word.   If it gets to red, the group has lost the privilege of talking to each other temporarily.   Surprisingly, I’ve never actually had to go to red.

I want spaces for quiet and spaces for talking and spaces for laughing in my class.   For me, structure works (the laughter just happens).  It’s not what everyone needs.    Some people work fine with a lot less structure.   I just can’t.   Some of my students have told me that they can’t either.   So, the structure gives us a way to have those quiet moments without sacrificing the chance to have really rich discourse that I also want to be a central piece of my classroom.

 

It’s All Greek To Me – Managing Cooperative Learning

Group project.   Words that would make my sixteen year old self silently scream.  Yet again, I was going to have to do 95% of the work and three other people were going to just go along for the ride.   That was my best case scenario.   Worst case scenario, I was going to have to undo/redo their work so that I would get the A I wanted.   I was definitely not a fan.

Fast forward past college, graduate school, and years of working as an engineer (sometimes still not a fan of the whole group work thing but recognizing it was a reality with which I had to live) to my graduate licensure classes.  Naturally, the topic of cooperative learning was addressed.   The voice in my head was grumbling “Great.   New name, same old story.   No way am I doing this to my students.”    I firmly pushed the whole idea aside and focused on the important thing: math.

A funny thing happened, though.

As I focused on math, I discovered the importance of mathematical discourse.   If students were going to have discourse, they had to sit in groups, so I arranged my room accordingly.   It kind of worked, but it still seemed like the higher functioning students were doing a disproportionate amount of the thinking and talking and the lower functioning students were sort of “along for the ride.”     Not fair.    Not equal.   Not good.   I stuck with it, but was not completely happy.

About that time, a friend introduced me to Kagan Cooperative Learning Structures.   She had PD on them in another state and shared some of the structures.   I decided to try a couple of them out.   I started with Numbered Heads Together.   In it, each student works independently on a problem.   When he or she has solved it, he or she stands up.   When the whole group is standing, they discuss their thinking.    When everyone is in agreement, they sit down.   A student is called upon at random to speak for the group.   This resonated with me on a lot of levels.   Each student had to work through the problem.   The structure provided think time, no one rushing any one.  Discourse was embedded in the structure.   There was mutual accountability, no one knew who would speak for the group so everyone made sure everyone understood the problem.   This could work.

I am still not a fan of group work, but I use Cooperative Learning all the time.     It has been great.

These days, I still have the desks arranged in groups of four.

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I use colored index cards to put labels on each desk in the group.   Since I teach math, I use Greek letters that students see in mathematics (Delta, Sigma, Epsilon, and Pi) for the different tags.  (I make all of the Deltas one color, all of the Sigmas another color and so on).    When I call upon someone to speak for the group, I randomly select a seat position to speak  (think pulling a stick with Delta, Sigma, Epsilon, or Pi).

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When I arrange the desks, I put all of the Deltas in the same seat position within each group, all the Sigmas in the same seat position, and so on.   When I make my seating chart, I am intentional.   I place stronger students in the diagonals at the table group.   Then, I fill in the students who need more support between them.   That way, they have a strong partner to scaffold the discussion if needed.

I also use a task chart to assign responsibilities to each member of the group.

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Not a Moment To Spare

A few years ago, I read Steven Leinwand’s Accessible Mathematics – 10 Instructional Shifts That Raise Student Achievement.     The idea that small instructional shifts can have a big outcome really resonated with me.   My first reaction was that this is all so “do-able”. I found myself checking them off – I could do this and this and this to incorporate these shifts.

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I picked the book up again this weekend.   I wanted to revisit and check my progress.   Exactly how was I doing in bringing about these changes?   I thought I would take each of the ten shifts and look at what I have done or haven’t done to make that a part of my regular instruction.

The first shift is to incorporate ongoing cumulative review into every day’s lesson.

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I started tackling this shift by building specific time into my lesson for review every day.      I decided that I wanted to do a very quick review activity at the start of class to get students engaged as soon as they walked in the door.  I also wanted a slightly larger chunk of time to review ideas that take more than a minute or two.

I call my opening review the Math Minute because I wanted it to last only a minute or two.   I could use this time to do quick review on number operations skills (fraction, decimal, and rational number operations), order of operations practice, and estimation. These are usually problems that I post on the Promethean Board.

I call my larger review activity the Flashback.   I have it as the final 5 -10 minutes of the period.  (This is after I do the lesson summary.   Originally, I had it before the summary, but found that sometimes that meant the summary was too hurried.   I want to have a solid summary to make sure that everyone walks away with the main ideas of the day so I switched the order.   It’s easier to cut off the review early if I need to do so).I use the Flashback to review more time-consuming concepts.   When I first started this a few years ago, this was a whole class activity.   Over the last few years, though, I have begun to also use it as a chunk of time to differentiate the review to fill gaps in learning.

  • Sometimes, I use tiered instruction where students progress through a series of tasks or games as they demonstrate mastery.   An example of this would be the decimal division game that I use early in the year.   I have three versions of a Jenga game.   The simplest requires students to divide a decimal by a whole number.   The second version of the game requires students to divide a decimal by a decimal.   The final version of the game requires students to divide a decimal by a decimal but there are zeros in the quotient.
  • Sometimes, I use intentional pairing where I pair a student with mastery with a student without mastery to work on a problem together.  An example of this would be having students work on a more complicated word problem in which they need to make a double number line to solve a ratio problem.
  • Sometimes I use a series of games that address different concepts, with each student playing a game that corresponds to a gap or weakness he or she has demonstrated. An example of this would be when I have some students who are still struggling with decimal division play the Jenga game, some students who still struggling with decimal multiplication playing a Zap game, some students who are struggling with fraction addition working with a fortune teller, and some students who are still struggling with fraction division playing Fraction Flip It.

 

IMG_1281Since these two review chunks of time are a regular part of an instructional day, I have added specific spaces for them in the Interactive Notebooks that we use.   I use the first page for the day for the Math Minute, In, and Flashback.   The lesson starts on the second page for the day.

 

Laughter is the Best Medicine

Some people are just naturally funny.   I am not so fortunate.  I enjoy a good laugh as much as the next person, but I can’t tell a joke well if my life depends upon it.   Somehow I always manage to get to the punchline before finishing the story.

Given this decided lack of talent, Marzano’s recommendation that one use humor to increase student engagement (in The Highly Engaged Classroom) fell a little flat with me.  I tried out a lot of the other recommended strategies and really liked the impact they had.  Unfortunately, this made it hard for me to shunt aside the whole humor thing.   It just sat there, nagging at me kind of like my mom nagging me to do something that was good for me.

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Finally, I decided to take a baby step.   I started collecting cartoons from the comics that related to math or life in middle school and posting them in class.    I tried to put up different ones that somehow related to the work we were doing in class.   My students seemed to like them and they were a good conversation starter.    I’m not sure that I could say I was effectively using humor to increase  engagement in a lesson, but I was building relationships.

IMG_1263  This year, I decided to try to take the next step.   A friend had given me Math Jokes 4 Mathy Folks, which is full of math jokes and puns.    I decided to post a new joke or pun or riddle on the board each week.   If I could find one that related to our content, I used that.   If not, I just picked one that I thought the kids would like.    My students really seemed to like it.   They looked forward to the changing of the joke each week.   They even started asking if I would post one of their jokes.

Did this increase engagement?   I don’t know.   I do know that it helped to build relationships with students.    Laughing with them about silly things helped to make my classroom a happy, safe space for them.   I do know that is essential if I want my students to take academic risks.   I also know that it changes the way that I see my students, which makes me a better teacher.   So, for me, laughter really is the best medicine.

It’s Really Not All About the Rules – Creating a Collaborative Community

Growing up, my parents weren’t really grade-obsessed.   It was all about effort.  They always said a C would be fine if I had done my best but a B wouldn’t be if they thought I hadn’t.   I never really tested them on it, but I am fairly certain that they would have held true to that.   Behavior, on the other hand, was an entirely different matter.   I knew that if I got into trouble at school, I could count on getting twice as much trouble once I got home.  Maybe this is why I’ve always been a rule follower.   I guess it is an inherent part of my being.   I don’t know whether there is something genetic about it or if it is the way that I was raised.

Whatever the case may be, I started teaching with a mindset that there really was no excuse for bad behavior.   I created a set of rules that I was pretty sure covered everything I wanted without being too overwhelming for students to remember.   I posted them on the wall.   I intentionally taught them at the start of the year.    I enforced the rules when necessary.

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A funny thing happened, though.   As I worked to build a collaborative classroom environment where students engage in meaningful discourse about mathematics, I started thinking more about norms.    I spent a lot of time thinking about how I wanted kids to act and how I wanted them to interact.   After a lot of thought, I came up with a set of norms.

  • We are a community.   Everyone has to contribute.
  • Everyone has good ideas to share.
  • Treat others the way you want to be treated.
  •  Everyone makes mistakes.   That is how we learn.
  • Anything worthwhile is hard work.   It takes lots and lots of practice.

I had one of my student aides create a poster with the norms.   I posted the poster at the front of the room.   I intentionally taught the norms.

It’s been about five years since I started using these norms.   I still have the class rules posted, but the only time I ever talk about them or do anything with them is the first day of school.   Instead of enforcing rules, I find myself focusing a lot more on norms.  On those rare occasions when things go awry, I find myself reminding students of norms.   The funny thing is, this works so much better than rules ever did.   So, for this rule- follower, it’s all about the norms.

 

Building a Growth Mindset – Battling Perfectionism

There is something about math that seems to instill a deep-seated fear of making a mistake.   Maybe it is because there is a sense of objectivity to it.   Students tend to see answers as being either right or wrong, black or white with no shades of gray. My sense is that this tendency towards perfectionism is magnified with many students who are gifted. Research supports that perfectionism is a common trait in gifted students.  I think it is tied to the fixed mindset that so many of them have developed.  Things have come easily so they are “smart”.   They can’t be “smart” if things don’t come easily and they can’t be “smart” if they make mistakes.     Whatever the causal factor, I think perfectionism limits them.   The ability to take academic risks can propel their thinking forward in leaps rather than in small steps.    I want this for them.

To try to convince students that mistakes can actually be a good thing, I have been telling students the story of the First Penguin Award that Randy Pausch details in his book The Last Lecture.   Randy Pausch was a professor at Carnegie Mellon University.   In his virtual reality course, he always gave an award for the most colossal failure because we learn more from our mistakes than we do from our successes.   He called the award the First Penguin Award because the first penguin who jumps into the black water below is taking a risk in order to survive.

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After telling the story of the First Penguin Award, I implement something similar in my class.   My version of the First Penguin Award rewards a student who makes a mistake because allowing us to look at their work, to figure out the mistake, and to discuss how to fix the mistake moves everyone’s thinking forward.    The award is simply a piece of candy.   Students who find the mistake and help to fix the mistake also get a piece of candy.   Giving them a piece of candy for fixing the mistake helps them move beyond “I got a different answer” to actually analyzing someone else’s work.
It takes a little while, but the idea of getting a piece of candy has helped students to see that I really mean it when I say that mistakes are a good thing because that is how we learn.

 

 

 

 

Fighting a Fixed Mindset

The importance of establishing a growth mindset is clearly critical for students who think they aren’t good at math.   Helping those students to see that perseverance pays off can change their outlook and their outcomes.   How much does it matter, though, for those students who believe they are good at math?  This is a question that I have been pondering for the last year or so.

In considering this question, I have to acknowledge that I do think there are varying levels of ability when it comes to math.   That does not in any way mean that I think some people can’t “get math”.   Quite the opposite.   I think everyone can and should be “good” at math.  I think there are a lot of different ways to see and do math.   Often, when someone thinks they aren’t good at math it is because they haven’t had the chance to see and do it in a way that is meaningful to them.    Given the right opportunity and the right environment, I think everyone can be very successful at math.  I just think math comes more easily for some people than for others, just as is true of all things in life.    This seems to be counter to a lot of the conversation that I am hearing.     I’m not trying to debate anything here, just pondering ideas and trying to make meaning out of them in the context of my work, which currently is teaching math to students who have been identified as gifted.

This brings me back to my question of how much it matters to establish a growth mindset in kids who already think they are good at something.   Most of these kids come into my class with a very fixed mindset that they are “smart”.   Most of them also come having had an experience in which everything has always come pretty easily to them.   They just “get it” without really having had to work very hard.   I know that is not going to last forever, though.     I wonder how they will cope when they have to really work to figure something out for the first time.   I worry that they will just quit because they have not developed coping skills, they have not learned how to study, they have not learned how to persevere.   I worry that they will decide they are not “smart” because in their minds “smart” means things comes easily.

I talk to my students a lot about the importance of perseverance in the face of challenge and try to make sure that I stretch the content far enough that they all experience the need for perseverance.    I would rather that they face it for the first time now when the stakes are low rather than later when the stakes become much higher.

CgasMTXUMAAD_FZThis year, I tried using a self-assessment with my students to measure their perceived growth.   I wanted to give them something concrete to help them see the value of perseverance.   I made up a simple triple bar graph structure with categories for each of the broad topics we would address over the year.   I had students complete a bar graph showing their perceived level of mastery in each category in September.   They then added a second group of bars for each category in December and a final group of bars for each category at the end of April.   In September, I wanted them to see that no one was “good” at everything, that each one of them had strengths and weaknesses.   In December, I wanted them to see some growth in whatever area they found challenging.   In April, I wanted them to each see that they had gained mastery of all the material.

 

As I look back on how this played out, I think helping these “smart” kids shift to a growth mindset has been equally as important as if they were kids who struggle.    It was good for kids to see that no one was “perfect” during those early days.   It was good for kids who were used to getting an A and were suddenly getting a B to see the growth in their understanding in December.   They got to see that learning is so much more important than a grade.    It was good for kids to see that perseverance paid off in April.

I’m not done pondering these ideas, but I am feeling a little “growth”.