the Sound of Music

Writing from Brooklyn NY as we are visiting my brother, sister-in-law, and new niece!

Thinking about routines for the next school year.  I really loved the idea of musical cues from Matt Vaudrey at last years TMC.  I even bought a Bluetooth speaker for my classroom but just never got around to setting it up.  I'd like to use something for problem solving (when students enter the room). For those that do this at the beginning of class, do you start when the bell rings, or have it going when students come in.  I'm thinking I'd like it as a cue to record homework assignment, take out last nights assignment, and get started on "which one doesn't belong Wednesday" (for example). Or do you start when the other class leaves.  Maybe I could splice together 90 seconds of a have a great day song and 4 minutes of a lets get this party started type song.

I definitely want a cut/glue song as I am going back to some sort of interactive notebook this year.  I really missed it last year.  Trying to decide if I want to use a separate paper each week for warm ups.  I saw a few examples at a tmc warm up session, and I liked one that had a space for each day as well as a "how was your week?" prompt for the end of the week.  I think this will keep in line with my goal of connecting more with students in a non mathy way.  I'll post whatever I come up with (no computer on vacay- posting this from my iPhone.

I'm in the middle of reading "writing on the classroom wall" by Steve Wyborney.  I really like the section I've just finished that's about the importance of writing, and that writing is a thinking process and not just a way to summarize what you've already thought about.  So I think I'd like to have a song to strategically throw in to get students writing throughout math class as a way to think through what they have been learning.  More to come on that to as I figure out what that might look like along with my goal to have students do not discovery based learning of concepts.

For those that use music transitions, how do you set them up so they are easy to start...thinking from my iPhone or some sort of tablet?

Learning Names

I remember having teachers who just knew everyone's names.  On the first day.  Definitely a great trait to have if you are going to be a teacher.

But not me.  I am HORRIBLE at learning names.  I have to meet someone a bunch of times, have long conversations, connect, before I can remember their names.  I also don't know names/singers of songs, actors in TV shows/movies.  No one in their right mind would want me on their trivia team.  Unless its about Disney, lol.  Or school supplies.

One It's so hard for me to learn names in our 47 minute period with 20-36 students a period, 5 periods a day.  In the past, I have done assigned seats from day one, taken pictures of the group tables, and photoshopped their names over the top so that I could "study".  This year our gradebook has photos from last year, so I decided to try something new.  I made myself flashcards using an app on my iphone :)  I put in the photo and the student name, and in the next 2,5 weeks I'm going to try to learn as many names as I can!

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In the interest of getting to know students and letting them get to know me, I'm working on a couple of ideas of how I can do that while still teaching math.  First, I've been reading the book "Creating Cultures of Thinking" and I really liked one of the ideas shared about "What's Your Other Story?".  Students will obviously know me as their math teacher, but I'd like to be able to share some things from my "other story".  I love Disney, I went to "Twitter Math Camp", I'm a new aunt, I have two daughters, I struggle with learning names!, etc.  I'm also interested in hearing about their "other story".  Maybe a bulletin board? First homework assignment?

One of my favorite activities in the past was an assignment for parents/guardians called "A million words or less".  I asked them to write about things they would like to share about their child, both in an out of school (but please stick to a million words or less).  I loved the responses I got over the years, but I didn't hear back from everyone and I want to find a way to INCLUDE my students as well.

How do you get to know your students?

Always Learning

I was so fortunate to be able to attend TMC16 this year.  For me it was just so fantastic to be with a group of lifelong learners who love to talk about  learning and teaching math.  I came away with many ideas that I'd like to use this school year.

Probably the most important came in a conversation in the airport. Kathryn (@iisanumber) asked me what I love most about my classroom.  And I didn't have an answer.

This will be my 22nd year of teaching middle school math, most of it in 7th grade.  Each year I reflect on what I thought worked in my teaching, and look for ways to improve on what wasn't as successful.  I really do love my job.  I don't mind putting in long hours looking for new ideas, writing lessons, and giving students feedback on their learning.  I have lessons that I love to facilitate, especially those that allow students to discover conceptual understanding through exploration, or the learning that is motivated by an interesting/challenging task/problem/scenario.

Each year I get feedback from several students who had previously not met success in math classes but have really grown in our year together.  But I don't feel like I reach all my students, and wish I had opportunities to really get to know my students better, and for them to know me better,  and not just teach them content.  I think that has to go hand in hand with creating more opportunities to have fun with math and not be so focused on curriculum curriculum curriculum.  Which is so hard to do as I always feel like i'm under a time crunch.

I consider myself a risk taker as an educator.  Four years ago I started (independently but with approval from supportive admin) using standards based grading with my students. Two years ago I made another leap of faith and transferred to a school where the initiative was for the entire staff to do SBG.  What I love about SBG is that it improves my ability to use my gradebook to focus reteaching/relearning where it is needed and provide appropriate challenges.  I also love that students have multiple opportunities to learn at their own pace and their grades reflect their level of understanding without penalty for when they learned it.  But I still feel like students see relearning and reteaching as a punishment  rather than an opportunity.

At TMC I attended the Differentiate morning sessions with Michelle (@park_star).  I realized that I was mostly only using preassessment to identify students who already understood the content I was about to teach. When students showed learning gaps on pretests, I would look for ways to incorporate review into warm ups or early problems.  I think this is pretty common practice.  In Michelle's sessions she talked about strategic pre-teaching times before each unit so that all students entered in to the unit ready to learn the new content.  We also saw some flexible stations for student choice in practicing the areas where their learning has gaps.  I think this is the direction I'd like to go (although realistically developing this a bit each  year).

One of the biggest changes I made last year was in my warm ups- instead of traditional review of material from the day before we did things like "Which One Doesn't Belong Wednesday" (thanks wodb.ca !) and "Find a Pattern Friday" (thanks visualpatterns.org).  I loved the risk taking I saw students at all levels take with these warm ups. But I did miss the cycle of bringing back in yesterdays learning and need to find a way to combine those two to help student make better connections.

For this year my goals will be...
a) get to know my students- find ways to have more fun and spark interest in math outside of math class time.
b) continue refining SBG process and feedback through more strategic differentiation
c) design more lessons that help students discover concepts or have built in motivation because of the hook (include building on warm ups routines started last year
d) find ways to time manage as I work on these goals as I have a 5 and 13 year old at home!

Pythagorean Theorem

I love the wide variety of resources available for exploring the Pythagorean theorem!  I decided to go pretty low tech this year although I've seen some fun explorations using Geogebra and Sketchpad.  Yesterday I started with a set of squares and had students try to form a right triangle by using 3 squares as the sides of the triangle.  We recorded all of the trios of numbers they found, and then set that list aside.

Next, we explored a 3, 4, 5 right triangle, and built squares on the three sides and looked for patterns.  Students pretty quickly identified that the sum of the areas of the squares on the two shorter sides was equal to the area of the square on the longest side.  Using this information, we were able to generalize and "discover" the Pythagorean theorem.

Going back to our list of trios of numbers, students were able to check to see if their triangles were right triangles. We developed a list of Pythagorean Triples, and then just looked for other trios of numbers that would work.

Today I brought out Dan Meyer's Taco Cart Problem.  Students did a great job of asking questions and figuring out what they needed to know, and we brought back in a lot of the vocabulary we had used yesterday when exploring right triangles.  I supplied the information for Act Two and sent them on their way to work out the problem in groups of 3 or 4 on 2ft by 3ft whiteboards.  This was the first problem they had solved with the Pythagorean Theorem, and there were some great misconceptions for us to discuss!

When I started the discussion, I asked what was the first piece of information that we needed to agree on.  Students suggested the length of the hypotenuse, as all other calculations were based on that distance.  Some misconceptions: Students squared the legs and found the sum, but left that value for the hypotenuse instead of taking the square root.  Students added the legs and recorded that value as the hypotenuse.  Students squared the legs and found the sum, but then thought that dividing by two was equivalent to taking the square root.

The next part of our discussion was how to use the rates.  Also some misconceptions here, but I love that we were able to discuss if groups had a strategy that would have worked if their hypotenuse had been right.  Common misconceptions here:  multiplying the length by the rate of 2 or 5 ft per second instead of dividing.  Forgetting that one person had part of the walk on sand and another part on the sidewalk.

Monday we'll be looking at a few more problems, including a version of the television 3 act problem from Timon Piccini.  Also really liking revising the Wizard of Oz from Robert Kaplinsky.  Also looking forward to using Tilted Squares from NCTM as an enrichment activity- I think it's from an article that you have to be a member to see, but there is an illuminations activity that is pretty similar.

What are your favorite Pythagorean Theorem tasks or explorations?

Single Riders

I noticed this sign while visiting a local amusement park this week, and as we waited for the ride I noticed that there were often several open seats for each cycle of the ride.  Now I'm a bit of a Disney fan, and even though they sometimes have long lines, there are rarely empty seats on the big ticket rides.  They do this with single rider lines, and assigning people to specific rows so that they know how many single riders they need to fill the space.  Less wait=happier park visitors!

Then the questions start. How much would it cost to add single rider lines? How many open seats are there really in an hour?  Day?  Are people actually annoyed that there are empty seats- and how much time would adding a single rider line really take off of the average wait.  Certainly Disney went through this process when they decided to add the single rider lines, but how much more volume does Disney have per day over my local amusement park?

When I think about  SMP#3- Constructing Viable Arguments and Critiquing the Reasoning of Others- I want my students to really look at the world around them and use math as a tool to prove whether something does or doesn't make sense. To do this, students really need to observe and question what they see. They need to know how to collect data and organize it in a way that can be communicated with others.

How do we as teachers help to build this capacity in our students?  How can we use SMP #3 in our classrooms to help students model their understanding of a concept and identify misconceptions that are common with that concept?  How do we build a classroom culture where students are comfortable critiquing and having their understanding critiqued.

More to come....suggestions and thoughts are welcome!

Graphing Inequalties Exploration

This is an exploration lesson for students to discover the properties of linear inequalities in two variables. The link will download a copy of the files that I print out for students as well as a possible facilitation guide. The general idea behind the lesson is that students are taking a piece of a Cartesian plane and identifying whether points on the graph are or are not solutions to the inequality. If it is a solution, the point gets a "closed circle" sticker. If it's not, the point gets an "open circle" (a reinforcement sticker). Students work in small groups to fill up the plane with open and closed circles. I verify and ask questions as I walk around.

 When they are finished I pair up the groups and have them note things their graphs and inequalities have in common. There are 8 groups, but they are strategically paired. For example in the first rotation students are comparing inequalities that both have a boundary line with the same slope and y-intercept, but one is greater than or equal to, and one is less than or equal to. By the end of the discussion students should be able to identify solutions to inequalities in two variables, understand the concept of a boundary line, and connect what they know about slope and y intercept to the boundary line. 

The third part of the lesson is a set of cards for students to match up to inequalities. The purpose of this is to introduce the different boundary lines when the inequality is just less than instead of less than or equal to. For example, in the first pairing, all groups have inequalities with the same slope and y-intercept, but different inequality symbols.

Graphing Linear Inequalities Exploration Lesson

SBG

Some thoughts on SBG from my classroom this year...thoughts and comments always welcome- this is an ongoing process!