Questioning+Strategy+(practica)

Type
QUESTIONING

Description
Asking Sincere Questions

**//Sincere Questions//** ask about the unknown. They are a kind of //**Open-ended Question**// and they are similar to //**Thick Questions**//. All of these types of questions aim to engage higher-order thinking skills, but whereas Thick Questions invite a more elaborate, reasoned, synthetic response that uses available—either newly built or currently being built—knowledge, Sincere Questions address the unknown. For example, a Thick Question in geometry might be: //What properties do polygons have in common?// A Sincere Question might be: //Can the same area be bound by polygons of any number of sides?// Sincere Questions invite a leap into the unknown. It is the preparation for making that kind of leap and the leaping itself that can guide a student with such a question towards an understanding of some very fundamental concepts.

That was my hope when I designed a Questioning strategy for my geometry unit on the classification of angles. I had found an idea while researching that was very similar to an idea presented in the Common Core math textbook that my school had been thinking of adopting. I made adaptations and wrote a lesson plan that framed questions around that activity. I saw this as an ideal way to guide students from their work with angles and their classification into the topic of triangles and polygons.

The concept that students would be inquiring into and which they would attempt to discover is known as the Triangle Inequality Theorem; it is an utterly fundamental idea. Now, seventh-grade students will not call this idea by that name and they will not be relying on it any time soon in order to write geometric proofs. However, the //act of finding// this important relationship through inquiry, experimentation, analysis, and inference is the rationale for this lesson. Critical thinking and close work with the side lengths (and later angle measures) of triangles will foster important habits of mind and help students build core knowledge, both of which are important for deep learning of the material that lies ahead.

I wrote different forms of questioning along the path through the activity. Some were prompts that tried to elicit questions from students, but most were //my// actual questions which intended to focus student thinking in specific directions and on specific objects (here, distance and relationships). The general theme of the questions was: rules—//Do you think there might be any rules about the lengths of a triangle's sides?// I gave students a graphic organizer in which to record the data that they collected (side length and triangle sustainability). In my presentation, I used the words //experiment, triangle lab, spaghetti lab,// and //data,// trying to encourage a scientific-inquiry frame of mind. The intended outcome of this strategy was for students to //see and find for themselves// the fact that any two sides of a triangle must be longer than the third, and, by the end of the lesson, students did come to this realization. The Sincere Questioning strategy made a compatible and highly supportive framework for this activity.

I have noticed that I have some natural dispositions for asking questions. NCTM has written examples for each of the five categories of questions that mathematics teachers should be asking their students. I recognize many of them as the kind I like to ask in my classroom. The NCTM categories represent collaboration, self-reliant truth-finding, mathematical reasoning, conjecture and inference, and connection-making. These all involve the application of higher-order thinking skills as well as communication, both important for deep, conceptual understanding in (math) classrooms. I like the Sincere Questions strategy because of the way it can guide my instructional planning in ways that I already highly value.

Nonetheless, I do have some reservations about my experience with this strategy. As I used it, I found that it was very difficult to encourage students to produce their own //I wonder...// kinds of questions. It was my questions that led the parade. Some students did see the fundamental idea here. They may have already had the idea in mind (prior knowledge), or they may have found it through data analysis and inference, or both, but too few students actually came up with the relationship themselves. The power of this strategy lies in its ability to lead students towards their own discovery by means of their own work with careful—but minimal, guidance from their teacher, but I feel that I //over-scaffolded// the process. Students found what I led them to find, and just in time, too! I was a more active participant than I think the teacher who is using this kind of strategy is intended to be.

I believe that each of these impediments can be explained in terms of culture and community. I believe we would have had a different, more successful experience if my students and I had been together since September, if I had succeeded in establishing a climate that thrived on curiosity, if I had succeeded in inspiring student accountability for the work they do, and if we had succeeded in creating an environment in which students feel safe and which invites them to speak their imagination. Still, putting their heads in the game and their hands in the //dirt//, coming up with however much as they did, this Questioning Strategy helped produce a fairly vivid learning experience. I know where to look to make improvements.

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