August 30

Stop! Collaborate and Listen…

If you’re thinking this is a Vanilla Ice fan post, you’ll be disappointed.  However, “You’ve got a problem–Yo! I’ll solve it!” is the motto that my math team borrowed from the rap icon.  No, this is a post regarding some of the collaborative methods I use in the classroom.

The first method is MAN OVERBOARD.  In this activity I arrange students in groups of four and ask that they assign a “Captain.”  I leave this up to them–it’s always interesting to me whom they choose.  The Captain’s 1st job is to gather a marker board, marker and eraser for each member of his/ her group.  I present a problem and have each student work “secretly” on his/her board.  When the student has worked out a solution, he/she flips his/her board over.  When the Captain sees that everyone has finished, he/she will say “Man overboard!”  Then, the students flip their boards and discuss their responses until they can agree upon one.  The Captain also has the responsibility to make sure that everyone is comfortable with the agreed upon solution.  I’ve confirmed solutions for students in two ways:  either discussing it as a group when everyone has finished (this takes longer because I have to wait for everyone to finish) or I present the problems on cards that contain solutions on the opposite side.  Then, after the group has come to agreement, they have to reconcile their solution with mine as well.

The second activity is TAPS.  My friend across the hall found this on the internet somewhere and, like most things I do, it is either an exact replica or adaptation of something I’ve stolen from someone somewhere–most times I can’t even remember the source.  What I typically do is pose problems on individual slides in PowerPoint and print off the slides 6 to a page.  I write the solutions on the back of the cards by hand.  Then, I mass produce them so that each group has a set of problems.  I ask students to assemble in their groups of four and tell them that the person next to them in on their team and the people across from them are on the other team.  Students take one problem out of the envelope and all four of them work on the solution.  Teams are allowed to collaborate.  The first person to “TAP” the problem will have the opportunity to answer the question and check the solution.  If he/she is right, the team keeps that card and earns a point.  If not, the other team still has a chance.  One caveat is that students who are strong in the subject matter, and quick, can dominate this game leaving classmates in the dust and without adequate review.  I made it a requirement that the winner of each card present the solution to the rest of the group and answer any questions other group members might have.

Lastly I will present to you KNOTTY PROBLEMS.  I found this on a DePaul University website I’ve attached under “links.”  This activity requires a really difficult (AKA KNOTTY) problem.  Students are given several minutes to solve the problem and identify key frustrations or difficulties they are having with the problem.  Then, he/she presents the difficulty to an assembled group.  They listen without interruption.  After the student explains the difficulty, the rest of the group offers solutions.

I read recently that true collaboration really doesn’t happen unless the problem is too difficult/knotty to be solved by just one mind.  Just a thought.  

I’d love to hear what type of collaboration techniques that you’ve used, too–especially in a HS math classroom!

August 21

“You, You all, We”

I have to tell you–light bulbs are going off here!  My mantra for math instruction this year is “You, You all, We” and I’m amazed at the response from students.  It’s absolutely fabulous!  It’s amazing how many years of mathematical knowledge is inside those minds–yet, for many years, I approached my lessons as though they’ve never seen the concepts before (i.e. right triangles, Pythagorean Theorem, radicals, slopes).

For years I’ve followed the “Me, You all, You” mentality.  By that, I mean I would model for students the appropriate technique (Me), have them practice with a partner or a group (You all), and then expect them to perform the skill on an exit ticket (You).  While I’m still entirely a fan of exit tickets, I do think my philosophy of instruction may have yielded to a great paradigm shift.

It’s not that I haven’t take advantage of Professional Development–I have!  I’ve gotten a masters degree in Teaching and Leadership, went to many conferences, but it is all coming together for me after I read this recent article about “Why American’s Stink at Math” in the New York Times. That simple phrase “You, You all, We” connected some of the pedagogical dots between my training in problem based learning (PBL), STEM and courses on collaboration and engagement.

The past two days I’ve posed difficult problems, knowing (okay, hoping) that there was some foundation my students could draw from.  They amazed me!  I gave them 1-2 minutes to work on the problem individually (You).  I told them it was okay if they weren’t able to solve the problem, but to draw as many conclusions as they possibly could (for example, I asked them to write the equation for the perpendicular bisector given two endpoints–they could perhaps find the slope of the line, or find the midpoint, etc).  Then, they were to spend 2-3 minutes sharing with their partners what they concluded (You all).  I was thrilled at how quickly they engaged (even though it has only been days 1 and 2!).   When the conversation seemed to die down, I brought their attention to the board and asked students to share what they could about the problem (We).  In the end, I did very little more than facilitate.  It was fabulous!  The fact the some students were able to solve portions of the problem, but were stumped on others, highly motivated them to listen to the solution.

In year 10 of teaching–I think I’m finally connecting the dots–“You, You all, We.”  That’s all it took!

Hope you are all having a great start to your year!  So pumped to make this my #bestyearever!

August 11

B2S Reflections for #thebestyearever

It’s been…um a few years since I’ve posted on this blog.  However, it has been a personal goal of mine to blog regarding teaching, even if I am the only one who reads it.  That being said, summer is a great time for teachers to retool, rethink and reflect on the year past.  There are so many things I love about my job, but my favorite is a new year–new students, new methods, a fresh slate.  Who would like a fresh start at their job every year?  Well, maybe not everyone, but I do.  With that in mind, I wanted to share some thoughts and reflections on things I love and things I’d like to work on this year, in particular.  I’m sure I won’t hit them all, but if I make progress in just a few, that’s good too.  A journey of a thousand steps begins with just one.  Here are my reflections:

What’s Working

My classroom is a loud and noisy place and that’s the way I like it.  I didn’t always like it.  I used to be very uncomfortable with movement and talking–when it wasn’t mine.  I felt like I might not be able to wrangle my students back to attention.  Over the years I’ve picked up tricks that have given me confidence to unleash my student and know that I can corral them back in (3, 2, 1; music, online-timers; warning bells; etc).  With that in mind, this is what I think works in my classroom:

Full Group Engagement/Accountability If everyone is not working and actively engaged then I’m not happy with it.  I know teachers often play games (Jeopardy, etc.) where only one or two kids are battling it out for the win.  If everyone is not busy, then I’m not happy.  One thing I do to ensure student engagement is that I assign group roles or label each paper 1-4 and collect one for a grade at the end of the class based on the role of the dice.  If everyone is engaged and working cooperatively everyone benefits. If everyone is not engaged, then everyone suffers.

Collaborate and Listen Research shows that students are more positive about school, subject areas and teachers if they work in a collaborative classroom (Johnson and Johnson, 1984).  For that reason, I have several “go-to” activites when that involve active learning and cooperation, many of which I’ve shared in this class.

  1. Man Overboard
  2. Taps
  3. Knotty Problems
  4. Stations
  5. Speed Dating
  6. Think-Pair-Share
  7. Challenge Me with Role Assignment:  Scribe, Artist, Communicator, Quality Control
  8. “I say…, You say…”
  9. Collaborative Groups

Communicating Problem Solving Strategies  Since the Common Core Standards for Mathematical Practice require students to “Construct viable arguments and critique the reasoning of others” and “attend to precision,” I require students to present at least one problem per chapter to the rest of the class.  While this is difficult for some students, they increasingly grow in this skill and I have scaffolding in place for students who struggle to encourage them to speak.  For example, I offer students the opportunity for me to preview their work before they present.  This gives them them a little added confidence to present.

High Level of Differentiated Accountability  I place students in groups often and hold them accountable either by giving students roles or by assigning them a number 1-4 and then rolling dice at the end to collect work for activities.  Ina ddition, I have students work on “bellwork” and then collect each one, check it and separate correct from incorrect work.  If it is wrong, I like consult individually with each student or ask an “expert” student to work with them.  In addition, I ask students to perform the objective task with a “Ticket to Leave” so that I know exactly who understands and who doesn’t.  These tasks usually have students at 100% engagement.

Direct Instruction with Pizzazz I say “pizzazz” because I do not directly instruct in a typical, “I talk, you listen” fashion.  It truly is a discussion.  I pose problems that might have a connection but have a twist to former learning.  I ask students to walk me through the process, asking probing questions.  In that way, we are “discovering” together.

TI-84 Graphing Calculator  I use the TI-84 regularly for classroom instruction.  I feel like I have a good handle on its uses for Algebra II (and even some of the quirky technological issues that may arise) and how to use it for both group discovery and whole group discussion.  When we use the calculator as a whole group, I have found it really helpful to have a student model its use on the document camera.  I notice when I try to model it, I go too quickly and students find it difficult to keep up.

What Needs Improvement in my Classroom

For the most part, I like what I’m doing but I also know there is SO much that I can do to improve.  That is what I love most about our profession—there is ALWAYS room for growth!  The classes I’ve taken this summer have taught me that I have several weaknesses.  I will list them in order of priority of implementation.

PBL Problem Based Learning, rooted in Constructivist thought, forces students to go beyond gaining proficiency in algorithms and mastering foundational knowledge in mathematics, students in PBL environments must learn a variety of mathematical processes and skills related communication, representation, modeling, and reasoning (Roh, 2003).  This is, in part, due to a reluctance on the part of my district to wholeheartedly embrace the Common Core.  There is still a “drill and skill” mentality and curriculum to support it.  That being said, I’d still like to make room for at least one 3 Act type collaborative problem solving experience for my students per quarter.  This would allow students to draw conclusions for themselves making connections to former mathematical learning.

Scaffolding  I LOVE using groups, but I have been guilty of throwing groups together without the appropriate scaffolding and find that students are frustrated.  I need to assign roles and, even more so, teach the skills of active listening and speaking, supporting statements with viable arguments as stated in the CCSS MP Standard 3.  These can be taught to students and practiced.  Ideas for practicing these social skills can be found at http://www.edutopia.org/blog/deeper-learning-collaboration-key-rebecca-alber .

Variety is the Spice of Life   I would definitely like to expand my toolbox of Kagan Structures so that I could create a more collaborative environment where, according to Kagan, students develop a personal interdependence and desire to help each other learn.  Several structures I’d like to try in particular are Numbered Heads Together and Spin-N-Review so that students will have greater engagement and better performance.

Pit Stop In the middle of direct instruction I want to take a pause for students to “teach” one another or perform some other BRIEF collaboration like “mirror” or “think-pair-share.”  For example, if I teach a difficult example, I might pause for each person in a pair to take 30 seconds to explain it to their partner and then switch.  In doing so, students can reflect on their understanding.

Brain Based Learning   Brain breaks are a useful tool for students to use to help activate, energize and stimulate their brains by improving information storage and retrieval. Research indicates that brain breaks also improve students’ concentration and relieve stress.  I think it might be important for my regular Geometry students to have Brain Breaks and hand motions as well.  I plan to use the website gonoodle.com and place them in the middle of the lesson.

These are just MY thoughts–share yours–how will you make this your #bestyearever?