Better Questions

I know, I know.  Week 3 of the 2016 Blogging Initiative has long come and gone.  It's nearly the end of week 4!  I apologize for the tardiness.

I love the topic of "Better Questions" not only because the types of questions you ask can really dictate the type of classroom and style of teaching you have, but also because I need to continue to grow in the area of questioning.  Blogging about questioning will help me re-focus on the types of questions I'm asking my students.

This past fall, I presented a training module to HS / MS math teachers that focused on Effective Questioning.  The module brings to light the four levels of questions defined in NCTM's Principles to Actions (2014).

Question Type		Description
1	Gathering Information	Students recall facts, definitions, or procedures.
2	Probing Thinking	Students explain, elaborate, or clarify their thinking, including articulating the steps in solution methods or the completion of a task.
3	Making the Mathematics Visible	Students discuss mathematical structures and make connections among mathematical ideas and relationships.
4	Encouraging reflection and justification	Students reveal deeper understanding of their reasoning and actions, including making an argument for the validity of their work.

I've set the goal of asking more level 3 and 4 in my classroom, including on assessments.  These types of questions are sometimes tricky to create and grade.  Here is an example of a question that I asked my algebra 2 students.

I consider this a level 3 question due to asking students to make connections between the factors, solutions, and zeros on the graph.

Some example of student work:

Student 1: Excellent.

Student 2: This student did not understand the connection between the zeros of the graph and solutions of the equation.