Thursday, August 30, 2012

The First Days

We just completed our second day of school today, which means I have now had each of my classes once (we're on an A/B day rotation).  I am happy to say that the Algebra I Questionnaire and Gatorade Problem were both successes and served the purposes I had hoped.  In both of my Algebra I classes, students were excited to share their answers on the Questionnaire and we definitely began to establish a strong classroom community as we laughed at responses and saw how different people interpreted the various questions. 

The two questions I found most productive to share were #1, What is the largest number you can write in the space below, and #7, In as many steps as possible explain how to make a bowl of cereal. Question one really allowed students to see how they could interpret questions differently from one another.  Students had numbers followed by lots of zeros, as many 9s as could fit in the box, physically large numbers that filled the space, and the infinity symbol.  Question seven allowed students to see the importance of detail when sharing their work with one another.  We also had great conversations about being respectful of classmates' work, organizing and writing work clearly, and the fact that we can learn from seeing others' and recognizing our own mistakes. 

Doing the Gatorade Problem with the aid of a document camera this year definitely beat not having one like last year.  After sharing their "safe" answers from the Questionnaire, many students wanted to volunteer their work for the Gatorade Problem.  It was great to share student work in this fashion; students shared correct answers, incorrect answers, answers in price per ounce, ounce per price, comparing the same number of ounces, and different numbers of big bottles and 6-packs.  I didn't get to finish part two in my second class, but I think by the end of class all students had a basic grasp (which is hopefully a review), of finding a rate.  In addition to the math, students recognized the importance of labeling units and organizing their work in a way that their classmates can follow.

Already, I feel as though I have established a better community of learners who are willing to share and discuss their work than I have in the past.  I look forward to many more discussions and analysis of student work by students in my classes this year. 

Tuesday, August 21, 2012

Welcome to Blogging

Two weeks ago, I was fortunate enough to be part of a great team that presented a workshop called "The First Six Weeks" through the VT Higher Education Collaboration.  The workshop focused on how teachers can use what we know about the brain, mind, and learning to re-design the first six weeks of their school year.  As the high school math teacher on the team, I presented a ninety-minute segment on how to incorporate brain-based strategies to establish a strong classroom community from day one.

After completing the workshop, the director of the TASS program (part of VTHEC) recommended  I keep a journal for the first six weeks of school to share with workshop participants.  Being an avid "lurker" on the Math Blogosphere, I decided to give blogging a shot myself.  First and foremost, this will be a space in which I can reflect on my teaching and my students learning.  Perhaps it can also be a resource for those who attended "The First Six Weeks", provide insight for next year's presentation, and who knows, maybe I'll get on the Math Blogosphere radar at some point and other math teachers can extend my quest for exploring changes in teaching and learning mathematics.

Here's my plan for day one in Algebra I, as outlined at the workshop: 

The very first thing I will do in my Algebra class on day one is an Algebra I Questionnaire based on CalcDave's Calculus Questionnaire.

After having the students complete the questionnaire on their own, I will have students display their answers using a document camera.  We will discuss similarities and differences between their responses and talk about how students interpreted the questions differently.  Through the survey and the sharing of work, we will all begin to get to know each other, I will begin to see some of students' previous math knowledge, and I will get a sense of their mindsets about themselves as mathematicians.

Next, we will dive in to a Dan Meyer problem on rates. Through this problem, students will get a review on how to work with rates in a way that is accessible to all.  As a class, we will generate a question about the image, students will make predictions about the outcome, and then show work to prove their predictions correct or incorrect.

My overall goal on the first day of school is to begin to establish a community of mathematicians.  I rarely lecture for more than twenty minutes, so why should I spend our first class together talking at them about rules and regulations?

I have two fifth mod Algebra I classes this year (that's ninth graders at the end of every day), which should be quite the challenge despite my previous eight years of practice.  Hopefully day one goes as well in reality as it's going in my head right now.  Stay tuned for reflections on the actual first day of Algebra I.