Problems for Problems

The #slowmathchat discussion on Twitter got me thinking about what I assign for homework, why I assign it, how it has changed over my career and where do I think it is going?  I started as most teachers do at the beginning of their career.  After correcting the previous day's assignment, which consisted of me at the overhead (dating myself) demonstrating what was expected on each problem, I would then give a brief lesson on the day's new topic. After the lesson I would write the day's assignment on the board at the mid-point of the class period.  Whatever did not get finished in class, was to be completed as homework.

I relied on my sense of humor, engaging personality and excitement for learning to keep my students interested each day.  While I still use those aspects to my advantage, they are not the cornerstones to engagement in my class. Lessons have evolved to inquiry-based activities and investigations. Learning comes from student talk and not teacher talk, and thus I needed to change the homework assignments. They became hand-selected purposeful problems to practice previously learned concepts and not to finish the day's learning.

Usually on Monday and Tuesday we investigate new concept(s) in class and I assign specific practice from the concept(s) we investigated on Thursday and Friday.  Wednesday I start to assign problems we investigated on Monday and Tuesday.  The homework assignments typically are "naked math" and we work on "real life" in class.  Naked math are straight up math problems, no words.  This continues with each set of problems scaffolded in difficulty to the class's progress with a concept.  Once the skills have been mastered, I will assign "real life" problems for homework.

Depending on the concept(s), the typical assignment is 4-8 problems.  I find that 10-15 minutes of hand-selected purposeful practice improves skills, improves confidence, reduces frustration in students and provides access for all learners.

Stack It!

Whether students are turning in assignments for credit, turning in assignments for feedback, or turning in assignments to be checked for completion, the process used by a teacher needs to be fluid and be an effective use of the teacher's limited time.  Some teachers use baskets, folders or drawers. I have found the best use of my time and space is Stack It!

I am a firm believer that students learn more while working productively in groups, so my classroom systems and procedures are designed to maintain the group productivity and allow me to reach every student, hopefully on a daily basis.  After my students finish the correction process, which is no joke and will be laid out in a future post, I say, "Stack It."  These two words are a set of procedures for my students that should take 60 seconds to complete.

Step 1: Finish your last correction and make neat stack of assignments on the table group. Neat means all facing up and the same direction.

Step 2: Put your pen away, take out a pencil and a clean sheet of graph paper (all of my assignments are completed on graph paper). If we were working an investigation the previous day that had not been completed, students would take this out instead of a clean sheet.

Step 3: Put a heading on the paper, put the pencil down and wait for instructions for the next activity/investigation.

The transition time from corrections to work is a time-sucker for new and veteran teachers alike.  Practicing this process with students and maintaining the 60 second expectation saves a great deal of learning time.

Then as students are working on that day's activity/investigation, I am "forced" to stop by every group and "grade" the previous assignment. I put "grade" in quotes because my policies change from year to year, or class to class.  At times credit is helpful to motivate students, other times just feedback on their work is needed, or I just keep track of who did or did not compete the work.

No matter what I stop by every group, look at their work and use what I see to guide my instruction in the coming days.  If I am giving credit, it is usually given for effort toward learning. In other words, did they attempt every problem? Did they write sentences when asked? Did they make corrections and not just change answers? If the answer is yes to all three then credit is earned. If one or more is missing, partial or no credit is earned.

All in all, Stack It saves time, "forces" me to stop and talk to every group, everyday and informs my instruction.

Save Time, Increase Reflection with Go Position

In those last few moments before the bell rings, teachers want to sum up the day's learning, hint towards the next day's activities and have students reflect on their learning.  Maybe not all three in one day, and maybe you have other priorities in the last few minutes, but educators across grade levels, content areas and years of experience all want to squeeze this last chance for learning for all it's worth.

The "Go Position" is a method that has been in use in various forms for years and can save time and increase student reflection.  Here's how it works.  With three minutes left in the class period say, "Go position."  These two words are actually a set of procedures the students need to carry out in 60 seconds.  The time limit goal will not be met the first few times you use it, but after practicing and 5-7 times in use, the students will get the hang of it.  The set of procedures are critical for student success and continuity.

Step 1: Upon hearing "Go Position" students will finish their last thought on what they are currently working on and then add the day's assignment to their daily planner (hard copy or electronic).

Step 2: Students will secure handouts, assignments and other important documents by clicking them in the rings of their binder or placing them in the appropriate location in the student's folder.

Step 3: All pens, pencils, rulers and other supplies returned to their "home."

Step 4: Students "pack up" their belongs. This could be a backpack or merely stacking binders and books on their desk.

Step 5: Students will give full attention to the teacher.

The teacher should now have 2 minutes remaining in the period to review the day's learning, provide direction for the coming day's learning, or have students reflect on their own learning.  This can be done as a whole class, in A/B partners, in groups or as individuals.  The options are endless.  The important part here is that the Go Position has provided the time, without the distractions of students clicking binders, writing in planners, zipping pencil pouches or finishing their last problem.  By using the Go Position, teachers have an opportunity to have a greater impact in those last few moments of class.

How My Group Roles Keep The Learning Train Moving

Describing the group process in my class is easier when I use an example of the type of work that is group-worthy in my class.  Group-worthy is key here, as skill practice from a book or worksheet will not deliver the desired result.  Group-worthy tasks require students to share information, ask questions, press each other for reasoning and have multiple ways to think about the problem.

For example, I will show a video of four friends going to the movies. They buy tickets, popcorn, candy and in my state there is sales tax.  The video will show someone dipping into his or her wallet of cash for each purchase. By the end of it, students are asking how much did all that cost? (After they ask what movie they were going to?)  I feed them the information a little at a time, and they share that information with each other and progress as a group.  In my experience, the ideal number of people in a group is four.

Here is how the process works:

Reader:  This person reads the material from the text or the handout. The reader makes sure that everyone is working together.

No one likes to be reading out loud and have the people at their group talking.  So the Reader makes sure everyone is listening when they read directions, prompts or questions.  If they see someone starting to zone out, they gently bring them back to the group conversation using one of several sentences stems we have practiced in class. Once the information/question has been read then:

Coordinator: This person is the overseer of the conversation in the group. The coordinator is the only person who can ask the teacher a question if no one in the group knows how to find the solution to the problem. The coordinator also gets and returns necessary materials during the class period. The coordinator also makes sure the group area is clean before the class is dismissed.

The coordinator begins the conversation by asking everyone in the group what they think the group should do to start solving the problem.  This is a time to just collect everyone's ideas.  Once everyone's ideas are heard, the group decides on the best method to solve.  Their words at the beginning will sound like this, "What do you think? What do you think? What do you think? Here's what I think... Now what do WE think?"  Nothing should end up on paper until the group agrees.

For the example above the group's ideas could vary.  One person thinks they should find the cost of all the tickets, then the cost of all the popcorns, then all the sodas and then add it all together before finding tax.  Another person thinks they should find the cost of tickets with tax, then the cost of popcorn and sodas together with tax and add the two totals.  Another person says multiply the cost of one ticket by four, one popcorn by four, one soda by four, then add those totals and find tax.  Students will have to either defend their idea, or understand someone else's before moving on.  While the groups are working, the teacher will circulate to observe the students' work.  When the teacher sees a paper with a teachable moment, then:

Scribe: The scribe is the note taker of the group. Responsibilities include making sure everyone has the notes and handouts. This person also writes group responses (if necessary) and fills in the homework sheet and handouts for missing group members.  Scribe restates group’s responses as all members are writing them.

The teacher can use the Scribe's paper under the Doc Cam, or have the scribe write their work on the board for a whole class conversation.  

For the example above, the teacher may use the scribe's paper from two or three groups and ask the class which group's work appears to be the most efficient method, understandable method or best method. Students will need to justify their reasoning and build supporting arguments.  The scribe also restates the group's responses as they are being written is one more way to reinforce the math learning that just took place.  Some teachers claim that 30 problems are needed for repetition, but this process asks students to see it, say it, hear it and do it.  Four repetitions per problems means only 6-8 problems per day and deeper learning. 

But what if the group gets stuck and needs the teacher?

Spy:  The spy is the only person that is allowed to walk around during a group activity with the sole purpose of seeing what another group has done with the problem. The spy can seek help from another group. This person also makes sure that the group’s work is mathematically correct.

For the example above, let's say the group is moving along quite well, but after they found the cost of the tickets, popcorn and sodas combined, they forgot the sales tax percentage.  The coordinator can send the Spy to another group to ask that specific question.  The spy does not look at or ask for an answer to the problem, they just ask for one piece of information and then return to their group.  They can check with up to three groups and then they must return to their group. They cannot go around the room and talk to everyone. 

When the group is stuck, and the Spy did not find an answer, this is when the group decides, "Is this the one question we ask Mr. Adams?"  I tell them that each group only gets to ask me one question a day, so choose wisely.  This is fun to play up to the kids when a student will walk into class and say, "Hi Mr. Adams. How are you?"  And I respond, "I'm good. Your group's question is done for the day."  The momentary panic before they realize I am joking is priceless.  Back to the process.  If the group decides to ask a question, the coordinator raises their hand and I come ask them, "Are you the coordinator? Did you send your Spy to three groups?"  If either answer is no, I walk away.  If both answers are yes, then this is a formative assessment for me.  By this group needing to ask me a question, that means at least four of my groups will need assistance.  I should then momentarily stop class and redirect them on this topic to save them and myself valuable time.

This process keeps the conversation at the group.  They rely on each other and not just the teacher.  The first five weeks of the year is tough and it takes a lot of training.  Sentence stems are a must at the start, and don't be scared off when a one-day lesson takes two at the beginning of the year.  The students and you will get the hang of it and it will make the rest of the year run more smoothly.  A well-oiled learning train, moving forward.