Let's begin this
discussion with a question. What is a task? I once asked a teacher what task
students were going to do in class that day. The response was "No task.
They are just going to complete a worksheet and then start on an investigation."
Hmmmm..... aren't those tasks? My guess is that for some teachers a task is a
rich math problem that stretches your mind. Like the one below:

For me a task is any
activity given to students to do. That includes worksheets, quizzes, writings,
discussions, etc. Suffice it to say -- tasks come in all shapes and sizes. That may be a
little cliche but the emphasis is important. Teachers chose every day what
tasks to give students. This choice is extremely important and one that
bears deeper discussion.

*"Effective mathematics teaching uses tasks as one way to motivate student learning and help build new mathematical knowledge through problem solving."*(p.17)
What should a teacher
consider when choosing a task? The decision is about the opportunities afforded
students to make sense of problems and explore solution methods connected to
the established goal of the lesson. (see practice 1) So what do
I think about the task we used in the Leaping Lizard Lesson?

Using the taxonomy designed by
Stein and Smith, I think that the Leaping Lizard task
falls within the category of a higher-level demand. Students are encouraged
"to engage in active inquiry and exploration" (PtA p. 19) I lean more
towards

*procedures with connections*as suggestions are provided to students for ways to look at the transformations (i.e. connect image and pre-image points). However, students are required to expend some cognitive effort to develop a deeper understanding of the definitions of the transformations.
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).

Knowing not to GPS and
not doing it are two different things. It takes practice and intentional
planning to change and prevent oneself from falling into that habit. I
recommend the book

*5 Practices for Orchestrating Productive Mathematics Discussions*by Margaret Smith and Mary Kay Stein. A number of years ago I was introduced to this book during a lesson study. It has been my guide ever since in implementing tasks in the classroom. We will revisit this again in part 4 of this series when we talk about student discourse.
Next
time, the practice is use and connect mathematical representations and I will
share one of my favorite tools when studying functions.