Student Led Corrections

Thought inspiring administrators are imperative to successful teachers and schools.  Administrators that can pose a question about your teaching without judgement or evaluation, and get you to genuinely reflect on your teaching are the reasons why my pedagogy has improved over the years.

One instance dramatically changed my correction process on assignments.  Whether the class decided that they want to correct every problem on an assignment, or a select few, I used to be the one at the board showing the work and explaining the math.  I used formative assessments during this process to check for understanding, but it was usually me at the board.  Then my principal asked me during a post-observation meeting, "I know you can do math, but do the kids really know if they can do math when you are at the board?"  In pondering my response, I thought about my formative assessments.

I was able to figure out which students had understanding and which did not, but were the students getting the same feedback for themselves?  Do they need validation from me? Do they need validation from each other that they understand?  Were they learning that mistakes are good and help us learn, or were they merely fixing their work?  How could I get less of me, more of them, still be safe to make mistakes and maintain a learning focus?

Student led corrections are a staple of my classroom now.  At the beginning of the year, it takes a lot of training and practice, but after 5-6 weeks, the learning and engagement level during corrections is well worth the time and effort.  Here how it works:

1) Select the problems to be corrected.  This can be entire assignment if it's not too long, or can be a few intentionally chosen problems picked by you or the students.

2) Assign the problems to groups of students in the room.  I have eight small groups of four students in my room, so if I were assigning 8 math problems, each group would be assigned one.  They will send one student to the board for that problem. The next day the student that goes to the board must rotate around the group and one student cannot correct at the board for a second time, until everyone has taken their turn.

3) Give them one minute to discuss the work and explanation in their group before sending their representative to the board.  I have four largish whiteboards in the front of class.  The first four students can be writing their work on the board at the same time, then when #1 finishes the correction process, #5 comes up and starts their work while #2 is explaining their problem. This rotation of problems keep the class moving forward and we do not have to wait for work to get on the board.

4) When student #1 has their work on the board, they grab the microphone (our district has classroom speakers that has really improved listening) and explain the steps and mathematical reasoning of their problem.  Expectations for the explanation will vary from teacher to teacher.

5) Once the student at the board has finished, every single student should raise their hand to be called on by the student at the board.  If called on, they have only 3 possible things to say:

• "I agree."  By saying this, the student called on is claiming that the work on the board matches what is on their own paper, or that the work may be slightly different, but mathematically is equivalent. They agree with the work and explanation.
• "I disagree because on line __, I think ____"  The phrasing here is important.  The student is disagreeing with the work and says so by saying the line of work they see an issue. Disagreeing with work is safer than disagreeing with a person.  It feels less like an attack on the student. This also gets students to focus on the steps, math reasoning and accuracy more than just the answer.
• "I did not complete my assignment."  Students will take ownership of not doing their work and realize they still need to participate in the correction process in order to have a better understanding.  These students will not be writing anything down during this time, as the hope is that they do it on their own eventually.

Having three options of what to say makes this a safe process for the student at the board and safe for the student being called on as well.  Instead of just saying, "I got ___."  They can speak about the work.  All math teachers that I have spoken to do not like the "I got..." game that students like to say, and this definitely helps alleviate that issue. 

6) Once the student at the board has three "I agree" statements in a row, they can return to their seat as long as no one has a question for them.

The repetitive nature of this correction process also means I do not need to assign as many practice problems because students see and hear the math so many times.  At the end of the process, the students that were at the board feel good that other students agreed with their work.  They view mistakes on the board as an opportunity for the class to learn.  And at the end of the process, I know who can do the math and more importantly, the students know for themselves. 

Give Me Five!

No, not a High-Five.

How do you start a unit on Systems of Linear Equations, or Simultaneous Equations (depending on how your curriculum or school refers to this concept)?  Do you front-load the vocabulary?  Do you start with the visual solution, i.e. graph?  Or do you start with whatever example is in the book for that chapter?  I start with a Give Me Five!

Students have a good understanding of what it means to be tardy to class, and running laps in Phys. Ed.  I attach a problem to that understanding and ask a simple question.

Tardies have been a growing problem in P.E. lately, so the teachers have created their own system to try and quell the problem.  Mr. Crunch usually starts class with 2 laps around the gym as a warm-up, but now he will be adding an additional lap for every tardy student.  Mrs. Yogger usually starts with 5 laps as a warm-up, but now will add 1/2 lap for every tardy student.

Which class would you rather be in this semester?

It seems simple enough, but as students start to discuss in their groups, they come up with a lot of, "Well, it depends..."  Argumentation among students quickly ensues.   Once the groups are fully entrenched in their response to the question, I tell them they must back their response up with a Give Me Five.

Students must justify, prove or back up their answer using five representations of the problem and their answer.  Writing an equation for each teacher happens quickly.  Then the groups decide if they make two tables or one table and while making that decision they are debating the efficiency of the choices.  The graph spurs conversations on how far to go on the x and y axis, and then what scale to use to best represent the problem and solution.  The picture is a challenge for some students, but if they can draw a picture that makes sense, they definitely understand the math.  Then the written explanation makes connections among the representations and deepens the learning.

By the time the students finish the five representations, each student knows and understands that the point (6,8) is the most important point in their response.  They can clearly explain that in the table, the point (6,8) is where the number of tardy students and laps are the same, therefore the points before and after that depend on if you like running more or running less.  Students can clearly demonstrate understanding that finding the point (6,8) on the graph allows them to show where students would run more or run less.  There are so many teachable moments throughout this activity and you'll want to stop class use them all, but I suggest letting a lot of them go.  Allow for mistakes. Allow students to make tables that stop at five tardies. Allow students to make two graphs even though one is what you expect.  Respond to the mistakes later with respect and a learning focus. It pays off throughout the unit.

At this point students have an understanding of solving systems of linear equations using a table and graph. You may want to practice with different equations for a day or two.  Eventually students will ask, "Is their an easier way to solve for this point than building a table or graph every time?"

Yes! Now there is a desire to learn!

Red, Yellow, Green

While attending a PD session years ago I saw a video in which a math teacher had students using Red, Yellow and Green cards on their table tops to indicate how they felt about the day's learning target as a formative assessment.  Each day most students would start with a red card on the top right corner of their desk, and as the lesson progressed, students would take cards from their binder and switch them to yellow to indicate they were gaining understanding, but not quite ready to run alone with the content.  When a student felt like they understood it enough to help someone else, they would place their green card on their desk indicating they were good to go.

The simplicity of the colored cards was intriguing but I had so many questions.  Are the students being honest, or do they change their cards so they are not the only red in the room? Are middle school students organized enough to keep these cards with them for the year? What do I gain from seeing a lot of yellows?  How does this impact the students' math self-esteem?  A student's math self-esteem can be one of the biggest barriers to success in my experience.  I try to create a WE learning community in my class. Our goal is not that YOU do well, it's that WE do well.  This takes a little pressure off of individuals and helps to create a safe place when asking for help.

Attempting to use the simplicity of Red, Yellow, Green but also address my questions, I first tried using the idea with colored pencils and a unit review.  My 7th grade class was approaching the end of a unit on Linear Relationships and we were gearing up for the final assessment.  Two days before the assessment I passed out the unit review and asked the students to have red, yellow and green colored pencils on their desks. I also asked that they not speak to each other and not to begin working on any of the problems.  I told them that before we begin working, we are going to have some private think time about each problem. I asked them to follow along as I read each problem aloud.

After reading the first problem I asked them to color over the problem number with the red, yellow or green colored pencil with these thoughts in mind.  If you color the number ________ that means if you see a problem like this, or similar to this on the assessment:

Green: You are going to dominate this problem. If your grade were based on this one problem, you'd have an A. You are saying, "I can demonstrate understanding of this problem with math work and a written explanation. I am good to go!"

Yellow: You have a pretty good idea of how to attempt this problem. Sometimes you do well on these problems, but sometimes you don't do well.  You will need to slow down and really think to make sure you are not missing something. You are saying, "I see this problem as a challenge but I am willing to take on that challenge."

Red: You are not yet ready to take this challenge on and would like to have more conversation, practice, instruction or think-time.  You are saying, "I will be able to take this problem on, but I need some help before I can rise to this challenge."

I repeated these descriptions for each of the first five problems that I read aloud.  Once they got the idea, I let them finish coloring each problem number.  Then I asked anyone that has at least one red or yellow to raise their hands.  This gets just about every hand in the air, and students see that even the "A-Kids" have red and yellow.  It's important for the students with a lot of red and yellow to see that everyone struggles from time to time.

Next I asked students who colored #1 green to raise his or her hands and keep them up. Then I asked students who colored #1 as red or yellow to find a green person and have a conversation.  Students began teaching students while I floated around the room collecting data which problems had a significant amount of reds and yellows. I also began jumping in to help the "greens."  We continued this process through all of the review problems.  Students were using the colored pencils to change their colors after each conversation.  Reds became yellow, yellow to green and some greens found out they were really yellow.  After the dust cleared, students knew exactly what they understood and could demonstrate, and they made a plan for the next two days to get themselves where they needed.  I used the red and yellow data to plan for the next day, and the learning was more purposeful and targeted than just passing out the review and saying we got two days to be ready.

Since that first time, I have adjusted the process slightly from year to year, and class to class.  I have used my group roles (see early post on group roles) to guide groups through red, yellow, green conversations, and I have had students make posters of what they feel is demonstrating red, yellow, green level of understanding.  The students will ask me for a red, yellow, green activities when they feel like the levels of learning in the room are out of balance because they understand that until everyone is green, we have not met our goal that WE will do well. Each time I try something new, the basic idea stays the same, but it's the subtle differences that keep the students digging my red, yellow, green chili.

Hope Can Raise More Than Grades

Many years ago in my first 9th grade Algebra 1 class I had several students that entered the school year having always struggled in math, had low math confidence and were lacking the skills required to be successful in Algebra.  I started math help sessions in my classroom after school for anyone that wanted to attend.  Some students were "forced" to attend by their parents, but eventually they saw the benefit.  During this school year it started as Tutor Tuesdays, then Want Help Wednesdays and finally Math Mondays.  The expansion to three days a week was to supply enough help for the demand coming from my students.

We used this time to supplement Algebra with the concepts they were lacking from previous math classes.  Numeracy, fractions, decimals, percents, integers and basic math properties.  The road was rough at first, but as we drew pictures and developed a better understanding of how numbers worked in relation to each other, tremendous gains were made. Students who once failed an assessment on two-step linear equations, were solving systems of equations with ease.  I was curious as to how well these students would do on assessments from earlier in the year, but first semester grades were "final" and we were approaching the end of third quarter.

I asked my school registrar about the possibility of changing someone's first semester grade because I no longer felt it was representative of their knowledge.  I was told it was not possible from her point of view, but that the Principal can override the rules.  So I was off to plead my case. Luckily I work for a  Principal that is all about whatever is best for student learning, and keeps kids on track to graduate. I began reassessing these students and everyone one of them increased their semester grade by at least two letter grades.

Since then I have used a Recovery Contract in which students can recover their first semester grade if they are willing to relearn concepts and reassess.  The offer is made to anyone that earned a D or F first semester. Of course I do not inform my students of this contract until late in first semester because I do not want students thinking they can slack off and then just recover their grade later.  And I have been amazed that students from year to year do not talk about the contract and thus incoming students do not have a clue until the time comes.  No one has ever declined the offer either.

Using the contract the past two years have been particularly inspiring for me and my students.  One particular student this year has made all of the extra hours of tutoring, designing new review materials, new assessments and grading worth it!  She transferred to my school because of the progress her cousin made in my class (on contract) last year.  Her childhood has been rougher than most students.  She now lives with her cousin's family and English is not her first language.

When she transferred to my 9th grade Algebra class in October, we spent three weeks learning integers.  She did not understand the concept of that positives and negatives cancel each other out.  We drew pictures, number lines, used mini poker chips and when I finally put some cash money on the table, she finally started to get it.  From there we worked on combining like terms, distributive property, equivalent expressions and two-step solves.  While the rest of class was working on systems of linear inequalities, she and I worked on ratios/proportions.  She finished first semester with 26% on Alg 1 assessments.  Today is the end of third quarter and she has now earned an 86% B for first semester, and is up to a B+ for second semester.

The hope of recovery has led to a completely to new student. A student that needed help with her math on a daily basis is now helping other students.  Her complete lack of math confidence is now climbing and is having a positive impact in her science and tech classes.  A student who saw a gloomy future, is looking towards an open and bright future.  Hope.

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.