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.

Angle Card Sets – Exploring Angle Relationships and Solving Equations with 3 Activities and 5 Variations

I wanted to create an activity that I could use to reteach and review angle relationships with some of my students who did not yet show mastery on these concepts.    I decided to create a card set that I can use multiple ways.    Each card has a picture of angles on a point.   They each include adjacent angles, vertical angles, complementary angles, and supplementary angles (with the exception of one card, which does not have complementary angles).   They also each include unknown angle measures.    This allows me to use the cards for five different purposes:  identifying adjacent angles, identifying vertical angles, identifying complementary angles, identifying supplementary angles, and using angle relationships to solve equations.

img_1758angle-relationship-cards  .

I can use the activity multiple ways for each concept.

Activity 1 – Give One, Get One 

Students form two lines.   Each student has a card.  I direct them to do a task (identify adjacent angles, identify vertical angles, identify complementary angles, identify supplementary angles, or solve for the unknown angle value)   Each student completes the task on his or her card and then steps forward.   When both partners have stepped forward, they discuss their respective cards/solutions.   When they are done, they step back into the line.    When all pairs have returned to their starting position, one of the two lines shifts (down or up) by one so that they have a new partner.   The cards are then shifted so that they also have a new problem.   This repeats until the allotted time for the activity is complete (usually about 5 minutes).

For this task, I have students use dry erase markers to identify the angles.

Variation 1 – Find complementary angles

Variation 2 – Find supplementary angles

Variation 3 – Find adjacent angles

Variation 4- Find vertical angles

Variation 5 – Find the missing angle measures

Activity 2 – Quiz, Quiz, Trade

Students solve their card.    They then find a partner.   They ask their partner to solve the card (find the angle pair or solve for the missing angle measure).   If the partner has difficulty, they may give a tip (hint).   If the partner still has difficulty, they may give another tip (hint).   If the partner still needs help, they show the partner how to do the problem.   (Tip-tip-tell).   The second member of the pair then quizzes the first partner with his or her card.   After the pair is done, they find new partners.

Variation 1 – Find complementary angles

Variation 2 – Find supplementary angles

Variation 3 – Find adjacent angles

Variation 4- Find vertical angles

Variation 5 – Find the missing angle measures

Activity 3 – War

Students each turn over a card.   They find the missing angle measure.   This requires them to use angle relationships to write an equation to find the missing angle measure.   They then solve the equation and use the value of the variable to find the missing angle measure.   The student who has the card with the greater angle measure wins the cards in that round.   The student with the most cards when I call time is the winner of the game.


For this card set, I used images from an EngageNY lesson to create the cards.


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.


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).


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.