I've been interested in the
Principles to Actions publication by NCTM since it came out a year ago; however, I haven't found the time to read it. So, how do you accomplish something you want to do? You set a goal. My goal is to read the
Principles to Actions (PtA) book and I'm holding myself accountable by making a commitment to document my learning here through illustrations and reflections.
NCTM has a website specifically dedicated to PtA (check it out
here). I watched the
video of the presentation by Dr. DeAnn Huinker at last year's NCTM Annual Conference in New Orleans. She describes and illustrates the 8 Mathematical Teaching Practices.
At the beginning of the presentation, she asks "What is the best math lesson you ever taught?" The
Leaping Lizard! lesson came to mind and I thought it would be a worthwhile activity to reflect on that lesson within the framework of the 8 Mathematical Teaching Practices.
One of my favorite things about coaching is working with teachers to develop lessons and teach. The
Leaping Lizard! lesson
is a collaboration between myself and another teacher. I will use this lesson to think about the 8 Mathematical Teaching Practices. Let's look at #1.
1. Establish mathematics goals to focus learning. In full disclosure, we didn't start here. We actually chose the task first; but in thinking about what we wanted students to learn from doing the task, we needed to talk about the goal. So, we may not have started here, but we did get here quickly. The standards we were addressing were
G-CO.2 Represent
transformations in the plane using, e.g., transparencies and geometry software;
describe transformations as functions that take points in the plane as inputs
and give other points as outputs. Compare transformations that preserve
distance and angle to those that do not (e.g., translation versus horizontal
stretch).
G-CO.4 Develop definitions of rotations, reflections, and translations in terms of angles, circles, perpendicular lines, parallel lines, and line segments.
We wondered what students may already know about transformations. In 8th grade, students verify the properties of the transformations (8.G.1). They also describe a sequence that exhibits a transformation (8.G.2). We anticipated students would be able to recognize the transformations and use general descriptions such as flip, turn, or slide to define them. Our goal was for students to use lines, angles, and circles to verify a transformation. We also wanted students to represent a given transformation
(a skill we would continue to work on for the next few lessons).
How does this measure with the actions outlined on p. 16?
- The goals are clear and articulate the mathematics that students are learning. We knew we wanted students to take the transformations beyond just a simple movement. We wanted them to understand the relationship between the image and preimage points.
- The goals fit within the learning progression. This was the first lesson in the unit. We had to build upon the 8th grade standards.
- The goals were explicitly stated throughout the lesson to focus student work. During the lesson, we had to emphasize the goal multiple times. This helped to clarify with students how we expected their understanding of transformations to extend beyond the movement. Students were to explore the properties and develop definitions.
- The goals guided the planning and decisions made during instruction. This task could be used to accomplish a variety of goals. It was critical that we have a clear understanding of student learning.
There are a number of challenges with this practice. First and foremost is time. Teachers need time to research the vertical alignment of the standard and time to discuss and refine goal. In our district this means leveraging the PLC time to focus on goals of lessons. There is also a need for quality tasks. That is Practice #2 which I will address in the next entry in this series.
While selection of the
task is important so is its implementation. In an effort to help students that
are struggling, a teacher can inadvertently GPS the task by "taking over
the thinking" for students. This lowers the demand and effectiveness of
the task. I've witnessed this happening with the Leaping Lizards task. The
teacher told students upfront what they would discover and consequently
students were no longer invested in doing the task. A teacher has to mindful to
"support students without taking over their thinking" (p.24).
July was all about family. We took a road trip to Canada and spent a week by the lake. The Northern Pike are aggressive and a lot of fun to catch. I was super excited to catch a Lake Trout.
The end of the semester is upon us. Teachers and students are preparing for final exams. In North Carolina there is the End of Course exam for Math 1. This test is used to evaluate schools and teachers. It is one of the measures used by the state to determine the "grade" on the school report card. There are also NC Final Exams for Math 2, Math 3, Discrete, Advanced Functions and Modeling, and Pre-Calculus. These are used to measure teacher effectiveness.