A Thank You to my Students

Have you ever had a day like this?

While they are few and far between, I have.  They are the best!  I often joke with my students, "You will thank me later.  Even though your thank yous will just be in my head, I know that you mean them."  

When it popped into my head today, however, the thought was reversed.  Have I ever thanked a student who has had an impact on me?  Again, this is a conversation that I only have in my head. I thought I would write this post to thank some of my current students.  I will not be using any names, but I am certain they will be able to identify themselves.

Thank you to the students who always come with a smile.  It changes the energy of my classroom and puts me in a happy mood, even if my day didn't start that way.

Thank you to the students who are always curious and questioning.  I know you think you are just distracting me from the learning targets of the day, but we learn so much more and in an authentic way.  Those are some of my favorite days.

Thank you to the student who is truly trying to make sense of the math and asks questions that others are probably thinking.  I have never had such a clear view into someone's thinking before and it helps me reflect on how I can teach things better.

Thank you to the student who shares strategies that help me see the math in a different way.  I will continue to use your strategies and understanding with future students.

Thank you to the student who shared a personal story with me and helped me reflect on the pressure that comes with always trying to improve.  I hope to spend more time letting people know how awesome they are, just the way they are.  

Thank you to the student who did not share a personal story with me, even though I saw it there from the first time you looked at me.  It helped me realize that I do not need to know your story in order to help you. (But know that I am always here should you need someone to talk to.)

Each year all of my students have an impact on me.  These are the ones that are standing out for me today.  Are there people in your life you appreciate and never told? What are you waiting for?

What my students have taught me about leadership.

I was recently asked the following question:
What have you learned about leadership from your students?

My response is a bit of a blur in my head, but I think this is a great question and wanted to take some time to reflect on it.

Teaching middle school math definitely requires leadership skills because most of my students, if given a choice, would not choose to be in a middle school math class.  Here are some of the leadership skills I have figured out:

1.  People will put more time and effort into things that interest them.  
What that means for my math instruction is that I need to teach in a way that peaks their curiosity and pulls them into the math we are learning.  This is not always difficult for me because I find numbers and their relationships fascinating, and it comes across in my teaching.

• On a number line, the distance from 0 to 1 is finite, yet the number line is infinite between 0 and 1. 
• 1/2 is part of a whole, but it can also be a whole if I am trying to find 1/4 of 1/2.
• I can easily draw 1/3 as 1 out of 3 parts of a whole, but as a decimal it repeats forever.  Have you ever stopped to really think about that?  How can we so clearly draw it as a fraction, but in decimal form it never ends?

These are just some examples of the beauty and intrigue I see in math.  When I open my students' eyes to these wonders they come along happily to investigate with me.  They want to know more.

2.  People will respect you if you are genuine.
Everyone experiences struggles.  There are small daily struggles, like having to figure out what to make for dinner for the 12,876 night in a row.  There are large struggles, like my husband being diagnosed with cancer. My students' lives are exactly the same, though the struggles may be different.  All of this has an effect on our day together.  One slight change in their life or mine and the interactions we have could be very different.  I have found in my years of teaching that students open up to me.  They feel comfortable talking to me because I have shared my life with them.  I keep the door of communication open.  Aside from in person conversations, where I really learn a lot about my students, I have actually found that the activities where students can write to me is where they really open up.  Throughout the year I like to have students fill out get to know you sheets (the type that most teachers use at the beginning of the year).  By using these sheets throughout the year students become more comfortable with me and are willing to share more.  One of my favorites are having students pick a theme song to their life and then explaining why they chose that song.  Teachers genuinely care about their students, but from the student perspective that doesn't always come across.  By continually checking in with students in this way, I am constantly sending that message.

3.  It is good to be reflective but be careful not to push people too far.  
As teachers, we want our students to reach their fullest potential.  We work with them on identifying where they can improve and work with them on those things.  After 8 class periods of that they go to their sports and activities where it is pointed out where they can improve and they need to work on that.  Finally, off to home where they need to recap their day and analyze with their parents the things they need to work on and improve so they can begin to work on that.  One of the biggest lessons I have learned from a student this year is that we need to do a better job of helping students feel comfortable with who they are.  Take a look around this classroom through this filter.  What are you doing to help each student know how amazing they are?  How can we frame our feedback to help students grow in our subject areas without depleting their bucket of self-worth?

I would love to hear your responses to what you have learned about leadership from your students.  Please let me know in the comment section.

My experience with FiresidePD

This school year I took 2 different technology classes, both for 3 credits.  One was on my couch (an online/correspondence course taken through a school in California).  The other was on my coworker's couch (a personalized PD course through Josh Gauthier and Jason Bretzmann both of Bretzmann Group).

To be honest, the online class was selected because it would be cheap credits.  Having taken courses like this before, it was exactly what I expected.  I learned a few tips.  I now get an email every day telling me that there are no events on the calendar I created and don't use.  When I open a new tab, Google Earth takes me to a new random place on Earth.  The Great Wall of China really is quite impressive.  I spent my time creating fake assignments to get to know features of the technology.  Plus, I learned more about this thing called e-mail.  I hear it is really going to take the world by storm.  😉  The class was clearly outdated. This is the problem with technology courses, they become outdated so quickly.  They must constantly be revised, as anyone who teaches a technology course knows all to well.  As a former technology teacher at both the middle school and graduate levels, I have first hand experience with this.  The only constant is change.  (Thus my undying respect for anyone who is in this line of work.)  

As an educator, I want to learn more about technology resources and how teachers are using them in their classes.  I am connected on Twitter and attend EdCamps.  I learn far more from these experiences but do not earn the graduate credits I need by doing so.  Enter FiresidePD.  Needless to say I was so excited when this opportunity became available.  We met at someone's house once a month on Saturday mornings.  I brought my coffee and there were pastries.  (Food is just as important to me as learning.)  There was no et agenda for each meeting.  We talked about upcoming units and shared ideas, resources, links that would be useful.  We came with questions about technology resources we had heard about but didn't know what they were.  We shared things we have done that went well.  It was like a 3 hour lesson planning session where we could bounce ideas off each other.  I loved every minute of it.  

Some of the things I accomplished while in the class:

• I was able to successfully moderate the #msmathchat because I learned about how to schedule my tweets with TweetDeck and use Poster My Wall to create the questions. 
• I was able to make Notice/Wonder activities cross-curricular by finding pictures to go with what the students are learning in science and social studies through Google Arts and Culture Institute.
• Lead a professional development with the math teachers at my school, incorporating some Poll Everywhere to help facilitate discussions.  FYI: If you are presenting to math teachers the linear view is better than cluster (it's just the way our brains work).

Ideas I have played with but haven't fully accomplished yet:

• I am certain there is a 3-Act task involving rates and ratios, area and perimeter using Google Earth Engine and Screencastify as we watch the growth of our small town.  
• Create a quarterly house newsletter with Adobe Spark.  It's so simple and looks so impressive.  
• In 8th grade math our focus question has been, "What is a solution?" The definition of solution is always the same but it looks different in different problems, inequalities compared to equations, single variable, 2 variable, 2 equations with 2 variables, no solution, infinitely many solutions etc.  I would love to have students create Piktocharts showing the different types of solutions.  Then using the new File Upload feature in Google Forms, students can download their infographic as a PNG and submit the form with the file uploader. All of their infographics will come to one folder, and if I embed the folder in a Google site with a thumbnail display option we can all see everyone's work.  
• Spiral is another resource I need to explore more.  It seems to have the functionality of many of my resources all in one place, formatives (like GoFormative), polls (like Poll Everywhere), videos with embedded questions (like EdPuzzle), and collaboration features.  

This class was by far my favorite grad class and everyone felt that way.  No matter what level you were at, you took something away.  We had time to explore, collaborate, and create.  

My biggest question at this point is how do I create this type of experience for my students?

The Best Intro to Systems of Equations

This year I have been working with some talented educators from the University of Kansas.  They are creating a resource called Enhanced Learning Maps.  The gist of it is that it is a formative assessment tool aligned with the Common Core State Standards.  The maps unpack the standards and shows all the connected concepts, helping me identify what to work on with students at all levels of understanding.  Along with these maps are assessments to identify misconceptions, summaries of research, and lesson plans with activities.  Follow this link for more information on the Enhanced Learning Maps Project.

In the past, my systems of equations lessons followed linear equations and graphing so it seemed logical to start with graphs and having students create graphs from situations, which is standard 8.EE.8.a: Understand that solutions to a system of two linear equations in two variables correspond to points of intersection of their graphs, because points of intersection satisfy both equations simultaneously.

Today, I introduced systems of equations with a lesson from the Enhanced Learning Maps project.  It starts with a problem to get students thinking about these types of situations.

You are in charge of buying snacks for a class party. After going to the store, you determine that purchasing 20 bags of chips and 10 packages of fruit snacks would cost $23. Thinking this may not be enough, you also determine that 20 bags of chips and 20 packages of fruit snacks would cost $29. How much is each bag of chips and each package of fruit snacks?

I encouraged students to come up with more than one way to solve it.  We discussed different strategies.  We didn't linger too long on this problems.

Then we did a jigsaw.  My students work in teams of 4.  One person from each team went to a different corner of the room to work out a problem with their "new" group.  Each group was given the same situation, but given a different representation. (Full documents here).

Each group was asked to answer the following questions:

• Which option is the better choice based on cost?
• Is there a number of people for which the costs would be equal?
• Use any mathematics or representations that are useful to your decision making process.

After they answered the questions they returned to their original groups and shared their problem (they did not know they were the same) and their method for solving.  Afterwards we had a great class discussion.  Here are things we noticed/realized:

• The graph groups solved it the quickest by simply drawing lines and finding the point of intersection. 
• The group with the coupons took the longest.
• The group with the table felt theirs was relatively easy to solve once the table was filled in.
• The strategies were different depending on the representation they were given.  
• None of the groups without a graph created one to help them solve the problem.
• None of the groups without a table created one to help them solve the problem

After discussing the different strategies, students were given another problem.

You are shopping for a new cell phone and have pricing from two different stores, Cellular City and Mobile Mart. Cellular City sells a phone for $300 and charges $45.50 per month for service. Mobile Mart sells the same phone for $260 and charges $48 per month for service. Which store is the better choice based on cost? Is there a point in time at which the total costs would be equal for both stores? If so, when would this occur and what would the total cost be?

After the jigsaw activity, it was amazing to listen to their different strategies to solve. There was more variety than I have seen students come up with in the past because now they were focusing on all of their background knowledge of all the different representations.  It was clear they had a better understanding of the problem and the relationships within it.   Some groups realized that their two equations could be set equal to each other (equal values method/subsitution).  One group found the difference in the starting prices and the difference in the monthly charge (elimination).  I was blown away by the thinking, strategies, and discourse that occurred during this lesson.  It makes so much sense to pull from their knowledge of the 4 representations (graph, table, equation, situation) instead of focusing on just one at a time.  The math was more intuitive and less contrived compared to how it has felt in previous years.  

I encourage you to try this lesson.  Let me know how it goes in the comments.  

Thank you to the Enhanced Learning Maps Team.  Please note that this lesson and the linked document is Copyright © 2016 by The University of Kansas.