Questions: Unquestionably Important

With one on my goals for the semester being to promote productive struggle, the types of questions I am asking students becomes a critical component in reaching this goal. So far, I am finding myself being successful in some situations but stuck in others, both in leading parts or all of a lesson and assisting students when they ask question. Some of these questions are leaving students like this.

Uh oh, that's not what I want at all. Rather, the questions I am asking should be leaving students thinking deeply and productively so that they can make sense of the mathematics at hand and have a reaction like Andy Dwyer after taking the time to think about the question.

"Oh, I understand it! It makes sense!"

Given that this reaction has not always been commonplace as of late, Steven Reinhart's article "Never Say Anything a Kid Can Say!" was definitely a helpful read! There were many takeaways from this article, and I would like to share a couple of them here: one involving leading a lesson and one about helping students.

"Be Patient. Wait Time is Very Important."(Reinhardt, p. 480)
As Reinhardt mentions earlier in the article, it is important for students to do the talking and explaining and the teacher to do this listening if students are to really learn mathematics. Thus, if students are taking more than a couple seconds to answer a question, I must become comfortable with the awkward silence, which may contain students looking this this.

Students may simply just need more time to process the question. After all, shouldn't we be asking some though-provoking questions, anyway? If I am not waiting and the same students are answering the questions because they process them quicker, I am doing a disservice to the students who take a few seconds more to process by taking away their opportunity to learn through making the connection the question is directing them to make. Better student responses and responses from more students will come from waiting. Thus, I will work to raise the wait time.

"Never carry a pencil." (Reinhardt, p. 483)
I have found that, when assisting students, I like to draw the pictures, write the expressions or equations, etc. I believe this practice stems from my 2+ years in the Math Center at GVSU, since we have lots of whiteboards and whiteboard tables at our disposal. Although this method is not inherently bad, since it allows me to make my responses not exclusively verbal, it is important that students be the one's creating the representations of their thinking as I assist them in making sense of what their struggling with. Carrying a pencil or using a whiteboard marker tempts us to do the thinking for the student or can unintentionally supply too much that we giveaway the opportunity for the student to make sense of it themselves. Thus, I will strive to ask thought-provoking questions that will allow students to develop a deep conceptual understanding of mathematical topics and to have the same reaction as Tony Stark does here.

These two takeaways, as well as the many others from the article, will definitely be taken into account as I answer and provide many questions for students as they learn, I hope to improve in asking thought-provoking questions that allow the students to do the thinking and sense-making themselves. Any feedback or methods that work for you are most definitely welcome! After all, asking better questions allows us to teach mathematics better.

"It [is] not enough to teach better mathematics; [we have] to teach mathematics better" (Reinhart, p 478)