Be Kind and Be Brave

At the start of each day, one of my friends tells her little boy, “Be kind and be brave” as he heads off to preschool.   I find it the perfect distillation of what I want for my children and what I want for my students.

Be kind.   What more is there to say here?  Just be kind.

Be brave.   Be brave enough to not be perfect so that you can learn and grow.   Be brave enough to try new things and new ways of doing things.   Be brave enough to persevere when things get tough.   Be brave enough to ask for help when you need it.   Be brave enough to offer help when someone else needs it.   Be brave enough to seek out an adult when someone needs more help than you can give.    Be brave enough to befriend someone who needs a friend.   Be brave enough to stand up for someone else when they need it.   Be brave enough to do the right thing instead of the easy thing.  Be brave enough to be different.   Be brave enough to be your very best self.   Be brave.

“Be kind and be brave.”   I think this is going to be my new way to send my students out into the rest of the world each day.

First Days of School

Is there anything scarier than the first day of middle school?   Probably not in the lives of most 11 year old kids.   Will I be able to remember where to go?   Will I get lost?    Will my teachers be nice?   Will I be able to manage 6 different classes with 6 different teachers who all want something different from me?   Will I have any friends in my classes?   Will I have anyone to eat lunch with?   Will I be able to do the work?   Will I fit in?   Will I be able to put on a brave face so that nobody knows I’m scared because I’m in middle school now and I don’t want anyone to know I’m scared?

These “not quite little kids anymore” and “not quite teenagers yet” arrive looking a little bit like deer in the headlights and leave utterly exhausted.   For most of them, it takes three or four weeks before they finally feel at home.   Given the high level of anxiety, I really want the first days to set a tone that is welcoming, accepting, and engaging.

Building a Growth Mindset  

  1. A Picture Book with A Dose of Girl Empowerment on the Side  Rosie Revere, Engineer tells the story of a second grade girl who secretly constructs great inventions out of rubbish.    She hides her inventions away because she is afraid of failure.   One day, she has a life-changing visit from her great-aunt Rose (nice reference to Rosie the Riveter included).   Her great-aunt shows Rosie that a first flop is something to celebrate because it is a first step toward success.   The idea that an initial “failure” (or mistake) is the beginning of the road to success is something that I want to impart to all of my students.   I like the idea of sharing this idea with a picture book because it’s a lot less like preaching and is a nice tie back to the normal events in an elementary classroom (maybe making this new place seem a little less foreign).  I also love that the protagonist is a female.  I want both my male and female students to see it as “normal” for women to be engineers and scientists.
  2. The First Penguin – Hooray For Mistakes  Randy Pausch, a former professor of Computer Science at Carnegie Mellon University, always gave an award to the group in his virtual reality course with the most collosal failure.   In his book The Last Lecture  , he explains that he wanted his students to realize that we learn more from our failures than we do from our successes.  He wanted his students to realize that being willing to take risks and make mistakes is an important part of the journey.    After sharing the story, I will introduce the class to our “First Penguin Award”.   When someone in class finds an error in someone’s work/thinking and can help them “fix” their thinking, both of the individuals will get a piece of candy because they both helped to move thinking forward (the “fixer” in finding/fixing the thinking and the “error in thought” in allowing everyone to examine his/her thought and think a little bit deeper).
  3. Lure of the Labyrinth – Powerful Problem Solving Hiding in a Video Game – Lure of the Labyrinth, a video game developed by MIT’s Education Arcade, engages students in rich problem-solving as they play a video game in which they go on a quest to save a pet.   The tasks are challenging and require a lot of perseverance.   My goal is to help students to grow a growth mindset by growing problem-solving skills.

Building Interdependence – Broken Squares with a Twist 

I want students to recognize their interdependence.     To accomplish this,  I give them a somewhat challenging task to accomplish as a group and then I give each group member a limitation that makes the task even more challenging.   The limitations ensure that the task can only be accomplished if they work together.

The Task

A group of four students are given a set of five envelopes.  Each student gets one envelope and the fifth envelop belongs to the “table”.   Working together, the group must build five equal-sized squares using the pieces found in the envelopes.  No group member may ask another group member for a piece.   (Members may give a piece to another member).


The task is taken from A Handbook of Structured Experiences for Human Relations Training.    You can download the files for the square pieces here 

The Broken Circles task in Designing Groupwork is very similar and is based on this Broken Squares task.

The Limitations (The Twist)

I want students to experience the need for interdependence and to recognize that each person has strengths and weaknesses.   Each member of the group is given a role that he or she must play as they complete the task.


The group member with the “See No Evil” card, must complete the task while blindfolded.   The group member with the “Speak No Evil” card must complete the task without speaking.  The group member with the “Look Ma, No Hands” card must complete the task without using his or her hands.   The group member with the “Mean Girls” card does not appear to have a limitation.   However, he or she must take on a “mean girls” persona, using only put downs in his or her communication.

The Ground Rules

Groups may begin working on the task when I say “go”.   Oh, one more thing.   The task is a race.   The group to complete the task first is the winner.

The Debrief

After a team has won, everyone looks to see how they did it.   Then we talk about what happened.   I usually begin by talking to the winning team about their process.   What did they do that helped?   Then I ask other groups what they found helpful.   It becomes really clear that they had to work together, to fill in the gaps for each other, in order to succeed.  From there, we talk about what didn’t work.   At this point, the impact of the negative talk always comes out.  We wrap up the activity by talking about the implications for our work as a community.    We document this in a circle map on “Good group work”.

Building Relationships

  1. Circle Maps – Getting To Know You and Learning a ToolAt my school, we teach students to use Thinking Maps across all content areas.   Each week, one of the content areas is assigned a different Thinking Map to introduce.   Math is assigned to teach the Circle Map (which defines something in context) during the first two weeks of school.   I teach this tool as a “getting to know you” activity.  A Circle Map consists of two concentric circles inside a rectangular frame.   The center circle is the topic being defined and the outer circle contains the things that define the concept.   The rectangular frame is a frame of reference.   For this activity, students will put their name/photo in the center circle and then define themselves in the outer circle.  The circle map will tell me a little bit about each student and will be a way for students to get know each other a little bit.  It will serve as the cover for the student’s portfolio.
  2. Math Survey – Each student completes a survey telling me how he or she feels about math and what makes a good math class.   Because affect is such a big piece of math success, I want to know how my students feel about it.
  3. One Thing –  I take a few  minutes to have everyone tell one thing about themselves.   I try to start with something a little silly like “my secret super power is that I can wiggle my ears and convince small children that I am an elf”.    The next day might be something like “‘Oh Lonely Peas’ is my theme song.   It is all about peas left on a little kids plate because she hates them.   That is exactly how I feel about slimy squishy peas.”    Asking an 11 year old for a super power or a theme song seems to open up windows that a language arts teacher might see in a student’s writing but that are a little less obvious in math.

Assessment – An Elephant Never Forgets

While this is not something I would choose to do with my first days, it is something that I am required to do.   To lighten this up a little bit, each student is going to pick a stuffed elephant to help them out, because “elephants never forget”.     I stole this idea from one of my friends.   The students would put the elephants on their heads (or their desks if they prefer – but most chose their head) to help them remember.   This will be my first year trying this, so we’ll see if I can carry this off.

Goals for 2017-2018

My grandfather was one of the most superstitious people I’ve ever known.   Every New Years’ Eve, he would go out into the street and hold his money in his hand as the new year arrived.    This was supposed to ensure that he would have plenty of money for the coming year.   I think it was a superstition or tradition that his mother brought from the “old country” and was definitely rooted in the very real need to make ends meet.   They always did manage to somehow make ends meet, so I guess it worked well enough from his perspective

In stark contrast to my grandfather, I think that the perfect place to be at midnight on New Year’s Eve is fast asleep in my bed.    While my grandfather did pass his two different colored eyes on to me, I can’t say the same is true for his superstitions.    I’m more inclined to adhere to Thomas Jefferson’s way of thinking .  “I’m a great believer in good luck and I find that the harder I work, the more of it I have”.    I’m convinced that my grandfather’s luck had a lot more to do with the hard work that he put in each and every day than it did with standing out in the cold with a pile of coins in his hand.

For me, the start of school feels much more like a “New Year” than January 1st ever has.   Each year, I get the chance to begin again, to do a little bit better, to be a little bit better.    As the new school year approaches, I’ve been thinking about the last year – the “I don’t want to make THAT mistake again” , the “that was the best thing I have ever done and it was a complete surprise”, and the “what is my end game for this year and how am I going to get there”.

For the record, my “never again” moment last year was having students slice butter to see the cross-sections of different 3D shapes.   I had my student aides form sticks of butter into cubes, rectangular prisms, triangular prisms, rectangular pyramids, and triangular pyramids.    There was one of each shape for each student.   Students tried to slice them in as many different ways as possible to find all of the possible cross-sections.   It was brilliant and a disaster simultaneously.   Everyone was engaged and got to see how to achieve each possible cross-section.   Unfortunately, it was also the worst mess that I have ever seen.    I did not think to have them where gloves and everyone ended up with butter smeared all the way up to their elbows and all over their desks (even though  we used paper plates).   We spent the last 20 minutes of class just cleaning up the mess and I’m pretty sure that the bathroom sinks were still covered in grease.

Strangely enough, my “best thing ever” moment was related to the same concept.   Shortly before the PARCC testing, I wanted to revisit the whole slicing solids thing and was talking to my class about how we should do it.   One of them asked if we could have a party.   They would each bring some kind of food to share that was one of the 3D shapes and then they would slice them to find cross-sections before eating up the goodies.   I was a little hesitant, but decided to dive in.   We listed all the solids we would need and kids signed up for the things they would bring:   triangular prisms (sandwiches), rectangular prisms (brownies), cylinders (cupcakes with the top sliced off), spheres (donut holes), cones (crepes) rectangular pyramids (jello cups cut into the right shape), triangular pyramids (rice krispy treats).   It was the best thing ever because it was their idea – they owned it and they loved it.

Which leaves me with the “what is my end game for this year” question.    This has been a little harder to narrow down this year because I just finished spending several days at one of Eric Jensen’s professional development sessions.   He challenged us to develop “gutsy goals”, to dream big in order to make big changes in students’ lives.   A tweaking of something I already do seems too small.  So, my goal is to open doors.  I want every single student I teach to be able to see the possibility of a career in STEM.   They may choose a different path, but I want them to see STEM as a path that they can choose.

  1. Every student will see learning as a journey and not a destination.   They will each know that some things come readily and some things come more slowly but that the more they work at them, the better they will get at them
  2. Every student will know how to problem-solve.
  3. Every student will know the math, all of it, whatever it takes.
  4. Every student will get the chance to see what real people who work in STEM fields do.
  5. Every student will get to do actual engineering – coding, building, creating.

Growth mindset.  Formative assessment.   Project-based learning.   Guest speakers.   These have all been part of my class in the past but will take on even bigger roles this year.   I think a grant application and a robotics club may be in my future as well.

A Sense of Belonging?

The sun baked down on the parking lot as I walked across the asphalt, my suitcase trailing behind.   I stepped through the door, into the blast of air conditioning, and basked in the crisp, cold air.   I breathed a breath of contentment.   I was “home”.   Women from various STEM fields were scattered around the room, each one deeply committed to engaging girls in STEM fields .   We would soon be joined by more middle school girls than the room could hold.   We would spend a week together, filling the girls days and nights with the best possible STEM experiences that we could devise.  As I stood there with the cold air blasting on my hot, sweaty face, I scanned the room for friends I had not seen since last summer’s camp and made note of the faces of new people who had joined  us.   I stood there soaking in the sense that “these are my people, this is exactly where I belong”.

What it means to have that sense of belonging has been trailing through my head all summer, like some sort of sticky spider web.   It started in May at the Harvard Law School graduation ceremonies.   Yes, ceremonies.   Harvard Law School has multiple days of speeches and ceremonies to mark the occasion of one’s graduation.   After so many years of hard work, I guess an extensive rite of passage is a fitting conclusion.

After hearing a quite interesting speech by Sally Yates, we were presented with what was for us the highlight of the festivities.   Mark Wu, the winner of the faculty award given by the students of Harvard Law School, spoke.      It was the most moving speech I have ever heard.   The thing that stuck with me the most, though, was his story.   He is the son of impoverished immigrants who came to make a better life for their children,   They worked low-paying jobs and pushed the importance of education upon their children.   The children worked hard in school and grew up fast in ways that are required of all immigrant children in such circumstances.   They were the interface between the American educational system and their parents – translating documents, explaining paperwork, navigating the college application process largely on their own.   It all paid off, though, when Mark Wu was admitted to Harvard as an undergraduate, or so they thought.   Once he got there, it was more complicated.   He didn’t feel like he belonged.    He wondered if he was smart enough (even though he was doing well).   He didn’t fit with the other students, he didn’t share their experiences and they did not share his.   He felt very much alone.   At the end of his first year, he went home and told his mother that he didn’t want to go back.   Think about what that must have been like for this 19 year old kid.    His parents had sacrificed everything to give him this opportunity.   He had worked so hard to get there.   Yet, he didn’t think he could go back.   After taking a year off, he did go back and went on to achieve great success.    What if he hadn’t gone back, though?

I keep pondering what this means for the students who walk down the halls of my school each day.   This question weighs upon me.   I teach at a school that most people would consider affluent   What they don’t realize is that 30% of the population at my school is on free or reduced lunch.   These kids walk down the halls with students who live in multi-million dollar homes.   Some of them sit in my gifted math class.   These kids are experiencing the same forces that Mark Wu experienced at Harvard but they are only 11 and 12 years old.   I find myself wondering how best to give them a sense of belonging.   They belong, but do they feel that they do?   I try to create a sense of community in my class, but does it carry out into the halls and the cafeteria?   Do they feel they belong in this space?    Can they be successful if they don’t?

I want for them to feel about school the way that I feel when I arrive at camp.   “These are my people.   This is exactly where I belong.”     Am I doing a good enough job?   Are we doing a good enough job?

In Search of A Puffin

images Riding over the waves on a chilly summer morning off the coast of Maine, my eyes scanned the horizon in search of a puffin.    A child of the desert, the wonders of the ocean filled me with awe.    The captain of the boat kept up a running commentary about the seabirds native to the area, those we encountered and those we might see.  I was in search of a puffin.    With every new species that we encountered, there was a moment of excitement and then a little sigh of disappointment.   It was interesting, but not quite what I was hoping to see.   We saw whales and rare seabirds that day, seabirds that are in fact more rare than puffins.   Alas, no puffins, though.

What did I take away from that day off the coast of Maine?  A wonderful experience discovering the wonder of the world in which I live, a nasty case of bronchitis, and the discovery that sometimes the things we aren’t looking for are the most important things that we see.

I was reminded of that discovery this week.   I had recently purchased Block By Block , thinking it might be an interesting addition to my math class.   Block by Block is a puzzle with 60 different building challenges.   I wasn’t quite sure how I was going to use it – maybe during our work with nets, surface area, and volume; maybe as a brain break activity; maybe as something else entirely.   I started out by giving it to my student aides to explore.     Seeing how they engage with something in play sometimes gives me insight into how it might work with my students (who are a couple of years younger).

img_2082-e1489367482156.jpgAs I glanced over while teaching my 2nd period   class, something caught my eye.   I looked closer to see if I was really seeing what I thought I saw.   I was pretty sure that I was seeing something I hadn’t expected.   Every time I looked over for the 50 minute period, my suspicion was confirmed.   So, I watched again during my 5th period class.   Two different student aides, but the same thing happened again.   Do you see it?

In both cases, I had two student aides – one male and one female.    In both cases, the student aides are highly developed mathematical thinkers.    In both cases, I gave them puzzle without any really direction, just a “try this out and see what you think”.   In both cases, the same thing happened.    In both cases, the male student aide reached out and started building.    In both cases, the female student aide was more passive, offering comments or suggestions, maybe taking a block and moving it around in her  hand, but letting the male student aide continue building.   This struck me for many reasons, not the least of which was that I have known these students for three years and these young women are not passive in an academic setting.     It also was an echo of what I had seen in many engineering labs during my college experience.   Young men jumping in and young women (not all, but many of them) letting them.

I tried an experiment.   The next day, the male student aide arrived first and jumped right into playing with the puzzle.   I sent him on an errand.   When the female student aide arrived, she saw the puzzle out on his desk.   She reached over  and pulled all the pieces onto her own desk and started building.    By the time he got back, she was deeply engrossed in the puzzle.   I watched to see what would happen next.   The previous day’s events were repeated, but this time the roles were reversed

As the week progressed, I found myself pondering what this little unplanned experiment implied for my instructional practice and for my female students.

  • When presented with an unstructured task, without clearly defined roles, why did the boys take such a dominant role and why did the girls let them?    Was it a matter of personality or was it a matter of social norms?    What role did experience play in the equation (the boys both play with puzzles frequently, the girls less so)?      Was intensity of interest a factor (the boys love puzzles)?   Why did the girl dive into the task more intently when the boy was not present?
  • What does it mean for my girls futures in STEM when they accept a more passive role?   The 10,000 hour rule for becoming expert at something implies that my girls are going to have a harder and harder time maintaining pace with their male counterparts on hands-on tasks if they are relegated to such a passive role (for whatever reason that it  happens).
  • What instructional decisions do I need to be making to ensure that my girls have equity?   While this experiment wasn’t intended as instructional, what does it tell me about the instructional decisions I should be making?   Do I need to formulate single gender groups all of the time?     Is it enough to just ensure that each member of each group has clearly defined tasks/roles and to ensure that those roles rotate?  While I use cooperative learning structures often, do I need to use them more often when engaging mixed gender groups in STEM activities?

I set out hoping to see how my students would engage with a puzzle.   Instead, I got to see how they interact with each other can have a profound impact on each student’s outcome. The decisions I make can do more or less to ensure that they each have full access to the best outcomes.   Just as was true when I was in search of a puffin, the things I saw were more significant than the things I started out hoping to see.

Seeing the Big Picture – Comparing and Contrasting Different Forms of Linear Equations

In order to review how to transform between different forms of linear equations on their upcoming quiz, I  revisited the concept using a foldable comparing and contrasting the different processes needed to move from one form to another.    In this foldable, I wanted my students to see the big picture.   As they worked down a column, they focused on the process for a single type of transition.    As they looked across a row, I wanted them to focus on the big ideas of each type of transition and how they are the same and how they are different.   I am hoping that this idea of seeing both the big picture and the details into the foldable will help them to make sense of the different processes.    Marzano’s research has shown this use of comparing and contrasting produces significant gains in student outcomes.   When I have used it with other concepts, my students have said that it really helps them.   This is true for all of my students, but is especially true for my students who are more conceptual in their thinking and who have difficulty with sequential thought processes.


You can download the file for the comparing-contrasting-changing-forms-of-equations foldable by clicking on the highlighted text.

Math for Small Children and Others – MTBosBlogsplosion Week 3

Math should be fun.    This is true for big kids, but is especially true for small ones.   One of my favorite blogs,  Design in Play, turns math for young children into a thing of beauty filled with play.    The author beautifully marries design into play.    She has posts on gumdrop engineering, spin art with  snap circuits, paper bridges, and architecture body building that all embed engineering into projects for young (and older children).   Her Snow Crystal Geometry post teaches children how to use a compass and a protractor as they create stunning paper snowflakes.    This blog is a must-read for anyone who has young children in their life.

Since I think math should be fun, I have to say that I love Sarah Carter’s blog.   This summer, I read her post on Function Auctions and thought that it sounded like so much fun that I spent the next two days making a Proportional Relationship Auction ,some proportional relationship anecdotal records and a proportional relationship card set that I can use7 different ways. Sarah’s blog makes you feel like you have this friendly, creative teacher down the hall.

In addition to being fun, math should be meaningful.   Students should be making sense and teachers should be thinking deeply to ensure that is happening.    The desire to think more deeply about my work and about my students’ work is part of why I have chosen to be part of MTBoS.   My students deserve the best that I can give them and Mark regularly poses questions that make me think.   His post  on exit cards was the first time I really considered whether my exit cards were addressing the spectrum of the things that I want to know about my students.   As I read his post, I realized I was doing a fairly good job of incorporating conceptual and procedural assessments, I really needed to incorporate more metacognition into my assessments.  I appreciate that his posts don’t allow me to be complacent.