Blog #7

Encourage collaborative learning by assigning group projects and fostering peer-to-peer interactions.  I feel it is imperative that we give students opportunities to collaborate with other students in our classrooms, now more than ever.  In this day and age when social media consumes a too-large portion of our students’ attention, these face-to-face interactions help students to develop appropriate communication and behavior skills that are not nurtured online.  Depending on the age of your students, you may need to actually teach students how to interact in respectful, productive ways.  You may need to teach your students how to consider all input from their teammates before proceeding, or how to disagree politely, or how to resolve conflict when there is an impasse.  Even if your students are older and you think they already know what the norms for collaborative work should be, you need to be vigilant that they are, in fact, following those norms.  Many of them do not practice this skill regularly and need frequent, gentle reminders for how to work well together.  Intentionally providing opportunities to collaborate with a variety of other students will help your students develop “people skills”.

I also feel collaborative work is essential because of what students can learn from each other.  Sometimes, it takes another teenager to explain something in a way that a teenager will understand.  The interaction is beneficial to both the explainer and the receiver, as it reinforces the understanding of the explainer and grows the understanding of the receiver.  Other times, takes a divergent thinker who has an approach that no one else has thought of (maybe even the teacher) to open our eyes to new possibilities for solving problems.  Personally, I really love creating and setting up collaborative tasks for my students because I love hearing the “math talk”.  One of my favorite things is listening to two students with different ideas “defend” (respectfully) why their approach is better.  Those conversations don’t happen if I, as the teacher, am doing all of the talking.

When I think of collaborative tasks, I consider them on two levels, which I will call “formal” and “informal”.  Formal collaboration is when a teacher presents a project, task or activity that is designed to be completed in a group.  Informal collaboration are the in-the-moment, more spontaneous chances for students to interact with another student about the math at hand.  Here are a couple of examples of each to show you what I mean.

Formal Collaboration

Projects/Activities  At least once a chapter/unit, I try to give students the opportunity to work on a larger task together.  Usually, it is either an exploration to introduce a topic, or an application to see if they can use the math we have been learning in a real-life setting.  These are the times when I feel that discussions about ideas, observations and/or approaches to the problem are the most helpful.  These are a couple of my favorites.

• Skittles Activity (available at my TPT store) – I use this activity as an opening activity to exponential functions in precalculus.  Students have already learned about exponential functions in Algebra 2, so this is a way to “brush the dust off the brain cells” and get them to recall their previous knowledge.  It could also be an application activity at the end of the Exponential Functions unit in Algebra 2.  The Skittles represent fish in a pond.  There are two scenarios, one for a growing population and one for a decaying population.  This activity is an open-ended mathematical modeling activity (see blog #1) because groups will collect different data sets. Students get the chance to practice creating scatterplots and finding regressions on their graphing calculators to find a reasonable equation to match their data. 

• Projectile Motion Activity (available at my TPT store) – This is a great activity for introducing the idea of parametric equations.  Students use a Geogebra applet to predict the settings for shooting a nylon ball from a Pasco launcher to come as close as possible to a target on the floor.  In the process, they realize that the horizontal and vertical displacement of the ball both rely on a third variable, time.  This leads to discussions about why parametric functions are helpful in situations where a third variable may be “secretly” involved, even though an equation in x and y could represent the graph.

Review Games  This is a fun way for students to prepare for an assessment while having the support of their teammates for concepts that aren’t quite solidified yet.

• Relay Races – These are fairly easy to set up.  Write/choose problems that you want students to practice before the assessment.  Cut the problems apart so that there is one problem on each slip of paper.  You can leave room on the paper for students to work, or they can work on separate paper or a mini whiteboard.  Since I usually create groups of four, I want the number of problems to be a multiple of 4 for (8, 12, 16, depending on the complexity of the problems) so that each member of the group is responsible for the same number of problems.  In each group, students decide the order in which they will go.  I usually set up desks in the front of the room by me, and then groups of desks for the teams.  Each team sends their first member to the front desks.  When the teacher says “GO!” those students take the first slip and work out the problem.  When a student has an answer, they show it to the teacher.  If they are correct, the team earns a point, the student returns to the group and the next member comes to the front to work on the next problem.  If the answer is incorrect, the student may take the problem back to the group for help.  The original team member must still do all of the writing, but the team can help them figure it out.  When they bring a correct answer back to the teacher, then the next team member may proceed to the next problem.  There are two ways to determine the winning group:  1)  First group to correctly complete all of the problems wins; or 2)  The group that completes the most problems correctly in a set amount of time wins.  I prefer the first method because the problems are more even distributed among the members of the group, but the second method could be used if you have limited time.  I also like to have little prizes for winning teams, like candy or stickers.  Even high school students still like to win a “prize”, no matter how cheesy.

• Jeopardy (PowerPoint slides available through this link.  Make a copy to edit.) – This is my version of a Jeopardy-like game for review.  The “dollar” amounts are hyperlinked to a problem, when you advance from the problem the answer will show, and there are links to get you back to the main board.  I use mini whiteboards for this activity, one for each group of 3 – 4 students.  Students must take turns doing the writing, even though the whole group can work on the problem.  As you can see from the directions on slide #2, the group that chooses gets the first chance to answer (I don’t have them “ring in”), but if they are wrong, the next group gets a chance to “steal” the points.  I designed it this way so that all groups would be engaged with each question, not just sitting around waiting for their turn.  I usually only give one group the points for a problem, but have sometimes played where every group with a correct answer gets the points (all groups show answers simultaneously instead of one at a time).  The second way does keep the scores a little more competitive throughout the game.  With about 10 minutes left, we will move on to final jeopardy.  Each group makes their wager, and then the problem is revealed.  For this problem, all groups show their answer when time is called.  This is the only problem when an incorrect answer can deduct points from their totals.  The PowerPoint that is linked is for a Trigonometry Review, but you can use this template to create reviews for other topics as well.

Informal Collaboration

• Think-Pair-Share – I mentioned this in my first blog as a great way to help students feel more comfortable with contributing in the classroom.  It is also a great way to encourage students to interact with one another.  This can be something that you do on the fly or you can plan to use it with certain problems  in the lesson.  To do a Think-Pair-Share, you present the class with a problem or a question.  For Think, they are expected to work quietly on their own, writing out the solution or their thoughts on the question.  When the teacher says, “Pair” the students talk to someone nearby.  You can let students choose their partner or you can assign partners ahead of time, just be sure everyone has someone to discuss with.  During Pair time, the 2 (or 3 if necessary) students compare their solutions/thoughts and arrive at the best possible answer that they can.  For the Share step, the teacher can call on a few students to share their answer with the whole class, or can gather students into bigger groups of 4 – 6 to share with one another. 

• Stay Home/Cross Country – this is something I started doing a few years ago to also incorporate a little movement during class time.  I would present a problem for students to solve.  As with the Think step above, students are expected to work quietly on their own first.  After an appropriate amount of time, I would call out “Stay Home” or “Cross Country”.  If I said “Stay Home”, they had a few minutes to compare their work and answer with a student nearby or their table group.  If I said “Cross Country”, students were expected to stand up and go talk to someone who DID NOT sit near them to compare answers.  It was fun, easy, and got students up and moving in the middle of long block periods.

Accountability  One of the biggest concerns with collaboration, for teachers and students, is making sure that everyone in a group is contributing and doing their part.  We all know (and have probably lived) the stories of the responsible student who cares about their grade doing everything because they will not turn in an incomplete task.  OR, the smart, possibly pushy student who just takes over everything with the mistaken belief that they know best so they will just do it all to ensure their grade.  If we go back to the reasons I gave at the beginning of this blog for encouraging collaboration, neither of these is appropriate.  As teachers, we need to do our best to build accountability into the process so that everyone in the group has the chance and the expectation to contribute.  Here are a few quick ideas that may help:

• Roles – It may be beneficial to assign roles to the different members of a group.  Roles like Gatekeeper (ensuring everyone has a chance to speak), Timekeeper (updating the group about the amount of time left to complete the task), Taskmaster (redirecting focus if the group gets off track), Scribe (recording all of the data or writing the final version that gets handed in) or Materials Manager (getting and returning the materials that are needed for the activity) can help all students feel that they have a part to play in the success of the group, regardless of the strength of their math skills.

• Task Design – You can see from a couple of the tasks mentioned above (Relay Races and Jeopardy), you can design the task in a way that expects everyone to hand in some part of the task in their own handwriting.  Since math solutions are rarely typed out, this is a fairly easy expectation to follow up on.  You can also see in activities like review games whether everyone is taking their turn participating.  With other tasks, teachers should design an activity that is relevant to your students and offers multiple entry points so that all students can find a place to start and have something to contribute. 

• Reflection – If the students work on a bigger project that requires time outside of the classroom or work over multiple periods, I give the students a reflection survey at the end.  The very first question asks them to rate themselves in different areas like considering all ideas, resolving disagreements respectfully, doing their share of the work, etc.  The second question asks them to explain/provide evidence for why they rated themselves the way they did.  I think it is important that students examine their own contributions and whether they were a productive member of the group before considering someone else’s role.  Then, I ask the student to give ratings and provide evidence for each of their teammates.  I collect the reflection on a Google form and encourage students to answer honestly, assuring them that only I will see their answers.  I think this works best with groups of 3 or more so you have multiple reflection ratings for each student.  This helps cross check if one student decides to be unfairly critical of a teammate.  If the reflection uncovers a serious issue, then I can have discussions as needed to restore the current situation and help students improve their collaboration skills for the future.

One last thought about collaboration…just like Trix, collaboration is not just for kids (where are my veteran teachers who understand this reference???)  We as teachers need to collaborate with our colleagues, too.  We work with amazing people who have a wealth of knowledge and experience from which we can learn.  Practice your collaboration skills, benefit from the wisdom of others, and model appropriate interactions with your colleagues for your students to see.  It’s a win-win!!  As always, email me if you have questions or comments.  Have a great week!!