I can’t be the person asking all the questions.

From the start of the semester until last Thursday, my students were working with systems in some form.

Graphing.

Substitution.

Elimination.

Word Problems.

A month and a half of teaching, practicing, assessing, reteaching, practicing, assessing, teaching, practicing, assessing, reteaching… you get the idea.

Linear systems was probably one of the most difficult concepts I’ve taught this year.  The ideas and methods involved literally pull together all of the algebra and rational number skills students learned in 6th and 7th grade.  There’s so many ways a minor mistake can derail a train of thought.  There’s also the concepts of variable, maintaining equality, substitution, and representing situations with algebra.  Even after so much time working with systems, I’m still not certain some students truly understand that substitution is just swapping out a variable for something of equal value or that we need to create an equivalent equation with one type of variable to be able to solve the system.

Without surprise, I found myself using a variety of questions throughout my lessons to help students make sense of a system.  As we got deeper and deeper into the content, I found practice activities devolved from productive group work to people attempting to do the same thing without regard for the problem or throwing up hands and declaring, “I need help.”

While recognizing that help is needed is a good starting point, later in the unit the process became exhausting.  A hand goes up from a student looking for help.  I ask the questions. Students answer correctly or incorrectly.  I tweak my approach if students were incorrect or move onto another question if the student was correct.  Rinse and repeat.  Later in the unit, my questions were pretty much the same and were able to guide students:

  • Can you read the system/problem aloud for me?
  • What are the variables in the situation?
  • How could we represent the word problem with equations? Why do we need two equations?
  • Does either equation have a variable that’s isolated?
  • Do you see any opposite coefficients between the equations?
  • Looking at the system, which method (substitution or elimination) would require less work/algebra?  How do you know?
  • Have we created an equation with only one type of variable?
  • We ended up with a nonsense equation? What does that mean?
  • We ended up with an equation that’s always true? What does that mean?
  • Do we have the whole solution to the system?
  • How can we find the value of x/y that we know the value of y/x?
  • Have we answered the question?

The interesting part about my questions is that most students were able to correctly answer them and got used to the routine. Nevertheless, students did not adopt these questions for themselves even with repeated reminders from me.

In some respects, I felt like I was getting trapped in a cycle I experienced during my first year of teaching.  I was somehow becoming the sole questioner in the class.  Naturally, I started to get down on myself about this development.  What was I doing or not doing that was causing students to avoid questioning themselves?  Was it the difficulty of the content that was driving students to only seek help from me?  Was it my explanation of concepts and examples?  Was it my progression of concepts?  Was it my pace?  Did the behaviors I was seeing reflecting a deeper problem that never got resolved earlier in the year?  Was I not explicit enough in directing students to self-question?  In a year that continues to make me doubt my abilities as a teacher, you can imagine that I was rapidly falling down the rabbit hole as I asked myself these questions about students not asking themselves questions.

After a week of what felt like nonstop questioning on my part and very little productive practice, I finally reached my breaking point.  I declared to my classes, “I can’t be the person asking all of the questions.  Time after time, people stare at a problem and call me over claiming they need help.  Every time I do help, I always ask the same handful of questions every single time. Every single time. Every single time.  Curiously, people are usually able to answer these questions every single time. Every single time. Every single time. At what point do people stop asking me for help and start asking themselves the questions they already know I’m going to ask?  Since day one, I’ve told you to ask yourself questions.  What’s been happening here is exactly why I’ve told you to engage in this process. You do know. You can make sense of the problem. Even if you’re uncertain, you know something you can always do to help you reason with a problem.”

At this point, the class was dead silent and I continued on for another couple minutes acknowledging that the content might not directly to the lives of my students, but the thinking they engage in as they work with systems builds the reasoning skills they will use later in life.  I ended my speech by reiterating the need for students to ask themselves questions.  In my later class, I wrote my questions on the board and stated I expected to hear and see students using these questions during the next practice activity.

Whether it was my delivery of my message or its content, students worked incredibly hard during the remainder of class.  When hands went up and I assisted students, the nature of the exchanges were different.  Everyone had something on their paper that they referred to as they spoke to me. In some cases, students just wanted to check if they were on the right track.  In other cases, students were uncertain, but they at least used phrases like, “I tried…  I noticed… Here’s the part that continues to confuse me…”  Students were purposeful in the help they were seeking.  I could tell people were questioning themselves and my help was to confirm their questioning.  Basically, it was the type of interactions I had been missing out on for a long time.

I’m sharing this post because I’m wondering how I can make students continue to self-question.  Does anyone have any activities, strategies, or routines besides constant verbal reminders that they use to promote self-questioning?  How do I teach and structure my classroom so that students are intentional with how they seek help?  How do I get students to move away from saying, “I need help. I don’t get this,” and start having specific questions planned when they seek help?  Once again, what can I do besides verbal reminders and modeling?

 

#MTBoSBlogsplosion: Positive Praise

This week’s #MTBoSBlogsplosion is about the soft skills of teaching.  When I look at the content of my blog, I feel like my posts swing back and forth between talking about content or questioning and the more personal side of teaching.  Part of me wonders if this oscillation is a product of being an early career teacher, but I think it’s more related to my experiences teaching at the middle school level.  It took me a while to realize that I do not teach mathematics; I teach students who are learning mathematics.  I teach human beings who are in the midst of significant mental, emotional, physical, and spiritual development.  This reality makes teaching a personal endeavor as much as it is academic.

A soft skill I’m working on this year is positive praise.

When I think about the words I use and how I interact with students on a daily basis, I’ve noticed that all too often I use reactive positive praise.  If a class goes well and students worked hard, I end class by saying how well it went.  If a student does an excellent job articulating his/her thoughts, I commend that student with brief praise during or after class (depending on the student).  If a student demonstrates leadership, I’ll say something to the student individually or call a parent to let them know.  In each of these situations, the positive praise is in reaction to behavior that was obvious to everyone in the room.  I’m trying to improve the frequency I use this type of praise.  Reflecting on this school year, I recognize that I could have praised students and classes more early in the year.  In some cases, I think being more liberal with my praise could have prevent some of the less productive days I experienced and encouraged more participation.

In conjunction with reactive positive praise, I’ve been working to include more proactive positive praise into my teaching.  For instance, I’ve dropped phrases like, “I’m looking forward to seeing how well you guys work today,” “I know you’ll be able to approach this topic with maturity,” or, “I know everyone in here is going to learn from each other and ask questions during this activity,” into my directions to premptively praise students.  On days when I’ve started classes in this way, I’ve noticed more productivity and a more relaxed environment.  One of my goals is start more classes with these statements.  I’ve also found myself proactiving praising students even when addressing misbehavior.  When I was talking with a student about her group’s off-task behavior earlier this week, I said, “I’ve seen you help other students and focus your group in the past.  I know I’ll see you do it in the future.”  The next day, I saw that student redirect a group member, help out a student who was absent the previous day, and offer to post work on the front board.  While I cannot be certain about the causes of this student’s positive choices, I think some of her motivation may have been the expectation I set with my proactive praise.  I was communicating confidence in that student’s ability to make good choice.  The student was validating my positive praise with her actions.  I want to include more proactive praise into my conversations with students this semester.

Overall, I think my ultimate goal is the have a cycle of compliments and praise in my teaching.  I want to start classes with proactive praise, drop more compliments and praise throughout a lesson, then end with reactive praise and a proactive comment to encourage future growth.  I’m getting better, but I’m far from perfect when it comes to implementing praise in my classroom.  Tweeting #onegoodthing has helped me be on the look out for positive elements of my day.  Reminding myself about what has been getting better has been helpful, too.  If you have any suggestions of ways to incorporate more praise into teaching, please let me know in the comments.  I know you have something to offer!

 

#MtbosBlogsplosion My Favorite: Meditation?

It’s a new year, which is a great time to start (or resume) blogging about teaching! If you’re uncertain about where to start, check out the handy-dandy post on Explore the MTBoS site!  Make sure to include hashtags!

The current schedule at my school has the 8th graders (my students) have PE and exploratory classes during the first two periods of the day.  As you can imagine, this arrangement makes the start of 3rd period seem a bit hectic.  I walk back to my room from teaching PE, set up my technology, and attempt to take attendance in a timely manner.  Simultaneously, students are rushing back from the other end of the building, asking to use the bathroom or get a drink of water, and generally seem a bit wound up after running around in the gym. Early in the year, I felt like the first 10 minutes of my 3rd period was a battle to get kids focused and ready to participate in the activities for the day.

Around mid-November, I got tired of how crazy the start of my 3rd period felt.  I decided to try something on a whim based on what I know works for me when I’m feeling stressed.  When the bell rang at the start of class, I calmly walked to the front of the room and waited for the class to end conversations.  It took a minute, then I directed everyone to close their eyes.  My students are used to blind surveys, so everyone complied thinking it would be another brief round of questions about the previous class.

Instead of questions, I began to slowly describe a map of the world.  I described the outline of the continents and their locations on a typical map.  I calmly told students to highlight the east coast of South America.  I waited a few seconds, then I asked students to highlight the west coast of Africa.  After letting silence fill the room, I directed students to visualize the continents slowly moving towards each other as I walked around the room taking attendance.  Slowly getting closer.  Slowly getting closer.  A minute or so later, I asked students to visualize South America tipping slightly to match up its eastern coast with the west coast of Africa.  I could sense the buzz and typical frenetic fidgeting of students melting away as I gave my description.  Expressions changed from annoyance or uncertainty to calm.  Shoulders were relaxing.  I directed students to visualize the continents slowly drifting away from each other.  Slowly drift.  Slowly drift.  Slowly drift.  A minute later, I asked students to take a deep breath, hold it, and slowly exhale.  When the exhales were finished, I told students to open their eyes.

Everyone looked much more relaxed.  I was more relaxed.  When I began describing the plan for the day for this science class (continental drift), everyone was making eye-contact with me and students typically more concerned with their snacks or their hair were following my movement around the room.  The rest of the period felt more laid back, too.  A partner reading activity seemed quieter, but more focused than the previous day.  When I described continental drift with the aid of an animation, I calmly connected the visualization we did at the start of class to the evidence Alfred Wegener collected for the theory.

It was amazing, so I had to see if this visualization exercise was a fluke or something of substance.  I decided to give it a try with my other science class.

At the start of 4th period, the results were the same.  In fact, one student mentioned it felt like she had meditated or listened to a yoga instructor.  Without getting religious, I think that’s exactly what happened in my classes.  Heartbeats slowed, minds cleared, breathing deepened, and bodies relaxed.  Everyone in the room (including myself) felt less tense.  The level of attention was stronger and sustained longer than in a normal class.

Naturally, two isolated incidents were not enough to convince me that I had found a new go-to strategy.  Throughout the month leading up to Winter Break, I tried out visualization exercises at least once a week with my science classes.  When we learned about the layers of the Earth, I had students visualize cutting an apple in half and seeing the layers.   One day, I had students visualize a dog attempting to squeeze between two people on a couch.  The visual connected to the rise of magma during seafloor spreading.  When we learned about plate boundaries, I had students visualize shoveling a driveway with a friend.  Each time, I spent about 5 minutes calmly describing the scenes and allowed silence to fill the room between my statements.  After each visualization, the classes seemed more relaxed and attentive than normal.

Call it meditation.  Call it visualization.  Call it a breathing exercise.  Whatever it is, it’s helping my students relax and focus.  For the benefits I’m seeing in my students, I’m calling it my new favorite and I hope to use this practice with all of my classes this semester.

 

Consistency for Flexibility?

The last unit in my Pre-Algebra classes involved many related topics, but a large portion of the errors and misconceptions arose as we learned slope.  Students who rocked out rate of change early in the unit kept flip-flipping things when we dropped context and looked at ordered pairs or a line on the coordinate plane.  Students who were easily able to catch their mistake when they wrote hours/dollar now were oblivious when they had run/rise instead of rise/run.

In some respects, I think some of the errors were related to my consistency.  I kept switching my wording for slope in hopes students would get flexible thinking about slope in multiple ways.  Rise/Run.  Change in y-values/Change in x-values.  Change in Dependent Variable/Change in Independent Variable.  Steepness of a line.  All of these definitions are helpful, but switching the wording of my questioning time after time is not helpful for students working with slope extensively for the first time.

As what tends to be the case in reflections, I noticed that my questioning was probably the largest contributing factor in all of confusion I witnessed in my students.  After rethinking how I would approach slope in the next couple days, I decided one of the best ways to address student concerns would be to use a set of questions consistently.

The next day, students walked in the room and I shared my observations.  We watched Slope Dude to revisit the more basic elements of slope (+, -, 0, Undefined), completed a couple examples, then I set students loose to practice.  Throughout the lesson (and the remainder of the unit), I kept using the same battery of questions when I encountered a student exhibiting misconceptions:

  • How are you reading this graph/table/set of points?
  • For the graph/pair of points/table, how would you describe the slope?
  • How are the y-values changing?
  • How are the x-values changing?
  • Did we write y-values over x-values?
  • Are we forgetting anything?

I chose these questions based on the success I saw students have with rate of change (change in y-values/change in x-values is the working definition we developed), but I also wanted to stress the importance of reading before calculating and self-questioning.  Thinking about the majority of mistakes students made with slope, most of the hiccups were due to students skipping the basic step of reading a graph/table/set of ordered pairs and deciding if the slope was positive, negative, etc.  After making a decision about the slope, it’s really just a matter of asking how the y-values are changing as the x-values are changing.  Not surprisingly, students began to make errors less frequently when I began using these questions consistently and encouraging students to adopt these questions to guide their thinking.

Deciding upon a uniform set of questions also made the remainder of the unit easier to plan.  When I began planning to teach linear functions and all of the elements associated with this concept (rate of change/slope, initial value/y-intercept, tables/graphs/equations/descriptions, increasing/positive slope, decreasing/negative slope, constant function/slope of zero, linear relation/undefined slope), I was overwhelmed by the various ways mathematicians talk about singular ideas.  Considering the way I kept switching the wording of my questions with slope, I recognized that I was probably causing the same amount of stress in my students.  Not good.  By streamlining my questions and sticking with the same wording, I was giving students the consistency they needed to get fluent with the topics we were exploring.  Beyond this comfort, I was providing students with more incentive to adopt and use questions I was offering to prevent mistakes and guide thinking.  Once students recognized that I was thinking about a problem in a similar fashion regardless if we were looking at a graph, set of points, table, or description,  students were able to see the meaning of my exhortation that, “It’s the same idea, just presented a different way.” Basically, students were able to build the flexibility that was my initial goal.

My experience with teaching slope and my use of questions leaves me with some unresolved thoughts.  People crave consistency, whether or not they are vocal about this desire.  As teachers, we also know that a hallmark of problem-solving is being flexible in one’s thinking.  Based on the struggles and success of my students with slope, is consistency is needed to build flexibility?  What elements of my teaching need to be consistent to encourage and build flexibility?  Is it a matter of consistent questions?  Is it a matter of routine experiences like asking students to develop questions to ask themselves or providing questions to adopt for personal use?  Do my students and I need a problem-solving framework?  Since I have more experience, I often don’t consider how I am solving a problem.  Am I consistent in the way I approach problems?  Do I need to be consistent?  Is my use of flexibility consistent?  How flexible is my thinking?  How does the connect to the way my students are thinking about problems?  Are my students consistent in their approach to problems?  Do my students ask themselves questions about problems?  What questions are the most consistent for my students?  Do my students recognize when they need to flex their thinking when they hit a cognitive obstacle?  How consistently are my students changing their approach to a problem?

Out of all of the questions I just wrote, the question that interests me most is whether or not consistency is needed to build flexibility.  I’m inclined to say yes, but I’m still uncertain about how that process looks in the classroom in relation to my teaching and student activity.  I’m guessing that there’s information out there about this idea and for all I know I might have just missed the session(s) at Twitter Math Camp that were focused around this idea.  If you have any suggestions, links, articles, or knowledge about using consistency to build flexibility, please leave this information in the comments!

 

Conversations with Individuals

I think everybody is prone to some looking back and looking forward this time of year, so I might as well add to the deluge of posts that are reflective in nature.

In the midst of a school year that can only be described as unprecedented, I have managed to try out some new strategies and methods of reflection.  One of the most helpful tools I’ve used in reflection is the Teacher Report Card from Matt Vaudrey.  At the end of first quarter and second quarter, I gave students in my math classes time to complete a slightly modified version of the form Matt created.  The results are interesting, so read through Matt’s posts to get a more detailed idea of what you can expect to gain from allowing adolescents to anonymously analyze a teacher.  Rather than describe all of the results of the Teacher Report Card I gave just a couple weeks ago (and proclaim myself president of the Matt Vaudrey fan club), I’m going to focus on one question I included in my version of the report card.

As I was setting up the Google form for the second quarter Teacher Report Card, I decided to add a couple questions based on the differences I observed between first and second quarter.  Among the largest differences I noted was how I chose to conduct conversations.  I was wondering if my gut feeling would match student thoughts on the survey, so I added the item, “I think that Mr. Hall talks to me individually (one-on-one).”  Here are the results (1 is not at all and 5 is definitely):

screen-shot-2016-12-31-at-8-23-51-am

The percentages were somewhat surprising, but the percentage of 3 or above was not that shocking.  During second quarter, I built more time into lessons for students to work with math.  Most of the time, these activities were in groups and I circulated to question students and check progress; however, I shifted to talking with individuals just as often as I talked with groups.  This difference might seem small, but I think it’s important for teachers to recognize the power of the individual conversation.

It’s easy to assume an entire group is comprehending a concept or skill, when in reality one or two people of a group are just following along and hoping to learn by repeatedly mimicking everyone else.  By questioning individuals as much as groups, I was able to better see which students actually knew what they were doing (and the depth of their knowledge).  I was able to offer help to students who just going through the motions with their group, then let them work with their group when they were feeling more confident.  I also liked the way I could praise students and encourage them to share when I called the entire class to attention to talk about problems.

Beyond talking with students during group work, I employed more individual conversations in the hallway or after class during second quarter.  The expectations students bring to these conversations is striking.  In most cases, a student had a look of dread of his/her face upon hearing my request for them to go in the hall or stay after class for a moment.  This expression slowly relaxed or a small smile appeared (a rare win when working with 8th graders) as the student heard what I had to say.  Most of the time, I was either celebratory (praising or encouraging hard work, thoughtfulness, leadership, etc.) or inquisitive (questions about group dynamics, level of understanding, comfort with the topics, etc.).  Even when I was celebratory, I included a question or two for the student to answer to make it a conversation.  I wasn’t talking to a student.  I was talking with a student.

I think most students associate hallway (or after class) conversations with negative behavior or poor grades.  When I flip the script students expect for these conversations, it creates moments where I get to know my students in detail.  I see which student responds better to praise for work, which student wants to be a leader, which student recognizes he/she needs to be more confident, and which student secretly cares more about his/her grade than he/she would ever admit in front of peers.  I get feedback about what’s working or not working for a student.  I chip away at the mental armor that so many students put on every time they walk into a classroom full of peers.  Basically, I like the way individual conversations allow students and myself to see the human element to the learning process.

I hope to continue my use of individual conversations during the second semester.  Hopefully, the number of 1s and 2s in the third quarter Teacher Report Card will be lower than the results for second quarter.  More importantly, I hope my students will recognize that I teach them as individuals just as much as I teach entire classes of students.  I also hope that I can change the stigma of the hallway conversation.  The fact that almost every student I talked with in the hallway this quarter was full of dread is an unfortunate product of how most teachers use these conversations.  Why does the deserted hallway during 3rd period (or any period) need to be a place for the uncomfortable conversations?  Can we make 2017 the year when teachers changed how they use the hallway for conversations with students?

 

Quick Post: ZipGrade

Another quick post about a tool that’s making my life a little easier this year.

At the start of this year, another math teacher in my grade decided to start making some of his quizzes multiple choice.  While neither me nor said teacher is the biggest fan of the level of rigor that’s possible with multiple choice, these quizzes have been a nice change of pace and a way to build some self-correction into the quiz taking process.  I’ve also been using some multiple choice activities are partner practice and using the tool I’ll describe to check student progress.  In addition, the quizzes have been a way to save time thanks to the app both of us have been using to grade.

ZipGrade is a free app for Apple and Android, but a annual subscription is needed if you end up scanning more than 100 papers.  On the full website, it’s easy to type or upload class rosters and print bubble sheets.  I’ve been using the ID numbers the website generates, but I’m guessing it wouldn’t be too much trouble to change the ID numbers to match school-issued numbers. Blank bubble sheets can be printed from the site, but I’ve been printing the bubble sheets from my classes so student names and generated IDs are prefilled.

On the app, the menu offers the ability to create quizzes and manage classes.  In the quiz menu, all you have to do is create a multiple choice key for a new quiz and choose the classes for the quiz.  When you’re ready to scan, hit scan papers.

After lining up a bubble sheet with the phone camera, the app takes a photo of the page and scores the paper using the key.  I tend to review the papers, which gives a snap shot with the correct and incorrect marked (see below).

What I’ve found helpful with this feature is the ability to immediately pinpoint which problems students missed.  When I’ve been using multiple choice activities for partner practice, I’ve used this feature to let students know what to revise or provide scaffolding with specific topics if a certain mistake is being repeated.

Another feature of the app I appreciate is the stats and item analysis that are generated from the scanned papers.

While I don’t like using multiple choice for everything, I’ve liked being able to use ZipGrade to provide students with quick feedback and encourage revision.  For instance, I scanned student bubble sheets during a recent partner activity and told students which problems to revise.  I made students turn in work with their bubble sheet, so I was pleased to see students talking about missed problems and revising work before asking me to scan their papers again.  I think the students also appreciated getting to see how their score was improving with each revision.

Check it out for yourself and let me know what you think in the comments.

 

 

Quick Post: Crowdsourcing Notes

It’s been a long time.  I’ve been really busy with my schedule and I haven’t been able to write as much because of fatigue or (I’ll admit it) feeling like I got nothing worthwhile to post.  This blog is more about my reflection than anything, but I feel like I haven’t done anything special that was worthy of a lengthy exposé.  Then again, I think I’ve been noticing more of the small things that make or break lessons as this year has progressed.  In that spirit, I’m going to begin posting about the little things in my classroom that have been saving my sanity and (hopefully) making my students think more and take more ownership of learning.

Today’s quick post: Crowdsourcing Notes.

I’ve used this strategy in the past, but I’ve barely mentioned on this blog.  It’s not the most creative practice in the world and it’s definitely not meant to be used with every concept.  When I use this activity, I like how it promotes clear communication from students and gets everyone involved in creating notes.  Beyond the benefit to students, I like how I can focus on asking questions as students work through problems as a class.

For my set up, I use SMART Notebook and an IPEVO interactive whiteboard pen system.  One could use a document camera and paper, but the technology makes it easy to print copies of notes for the class (which is the product of the activity).

Basically, I think up some examples of a topic that progress from what students currently know to what’s going to be new or require some reasoning.  For example, my 8th grade math classes were working on solving multistep equations last week.  After a few days reviewing  two step equations, I wanted to work ease students into multistep equations with variables on one side.  Students settled into class and I projected the following sequence of equations on the board:

multistep-equations-same-side_2

Only the first equation was visible, since I did not want students to blow through the problems without describing their thinking (or avoid contributing to the class).

I asked, “What can I do to simplify the left hand side of the equation?” for the first problem.  A student mentioned combining like terms, so I gave her the interactive whiteboard pen and had her write down what she was thinking.  Other students in the room gave nods of approval or looks of confusion, so I asked the student to explain why she combined 8x with 3x and 6 with -2.  After her explanation and general agreement from the class, I had her hand off the pen to another student to complete one additional step in solving the equation.

The activity continued in this fashion for about 25 minutes.  I questioned the class throughout and students even jumped into the questioning when they noticed errors.  When mistakes happened, we discussed the errors and identified how we could prevent them in the future.  For instance, we changed -x to + (-1x) in the third equation when multiple students added an x.  Overall, it was a good flow of students posting work and me questioning student reasoning.

By the end of the activity, we made the following notes:

multistep-equations-same-side_3

It’s definitely not not the most spectacular series of notes, but it’s awesome to point out to students how much of the math and the thinking they did as they crowdsourced the work for the problems.  Beyond this success, my 8th graders were pretty stoked about not having to write anything down and gluing a copy of the notes into spirals the following day.  Most importantly, I liked how the activity stresses verbal communication for everyone in the class.  I need to be specific in how I word questions so that students are able to make progress when they get stuck, but students also have to be specific when I question their reasoning or ask them to describe what they are doing for the rest of the class.

It’s not the greatest thing in the world, but crowdsourcing notes is one the small things that make some of my lessons better than average this year.