"Questions lead children through the discovery of their world..." (Keene and Zimmerman, 113)
Yet...as children progress through elementary school, something squashes this curiosity.
"Children enter school as question marks and come out as periods." (Postman, 116)
These opening thoughts in Chapter 4 definitely left me with something to think about. How can we continue to pique our students' curiosity and foster that endless stream of questioning that was second nature to them in earlier years? It's easier said than done, yet questions really are at the heart of teaching and learning (117).
I wonder why... What if... How can... are just a few of the questions we want our mathematicians to ask in order to develop deeper understandings. Another interesting point was that "it may be more important to find the right question than the right answer (118)." How can we flip our students' thinking to this mindset? A key takeaway was that students NEED to be the ones creating the questions, not the teachers. Students need to be explicitly taught to ask viable questions to enhance mathematical comprehension.
Laney Sammons then explains the types of questions and how they relate to math: Right There, Think and Search, and On My Own. Sound familiar in the reading world? Teaching students the difference between thin questions and thick questions can also improve the quality of their questioning (128).
Skill: multiplying a whole number by a fraction
Thin question: Is the product greater than or less than the original whole number?
Thick question: Why is the product less than the original number?
When teaching about thin and thick questions, Sammons recommends using sticky notes of different sizes for students to record their questions. 3" x 3" sticky note for thick questions; 1/2" x 2" sticky page markers for thin questions. Another recommendation was to have students write in a thick marker when recording a thick question or a thin marker when recording a thin question. The goal is to help students become more automatic and independent at creating questions that develop deeper thinking and understanding.
Questions that linger were also mentioned. How often do we ask questions that motivate students to continue to ponder and revisit those questions? These types of questions leave a trail of "math residue" that leads to invaluable learning (129).
Laney discusses strategy sessions and how they differ from a typical mathematics lesson (131). During these strategy sessions, the focus should be on helping students develop rich mathematical questions that enhance mathematical comprehension. To use as part of a bulletin board or as a bookmark for students, I created a few visuals called "Get to the point..." to help scaffold and build students' independence. If your students can benefit from these tools, click on the image and grab a copy.
Check out an earlier post on questioning in the math classroom for these color-coded question cards.
The next chapter is on visualizing mathematical ideas.
