1. Robert Kaplinsky rkaplinsky@dusd.net Melissa Canham mcanham@dusd.net

2. Assessing Student Understanding Educators struggle to meaningfully assess students in a timely manner. Traditional options include: Multiple choice tests Written answer tests Asking questions like “Does everyone understand?” or “Does anyone have any questions?” One potential solution to this problem is as simple as teachers modifying their questions.

3. Teacher Questioning Research Teachers are aware that some questions require students to think more meaningfully. “About 60% of teachers' questions require students to recall facts; about 20% require students to think; and the remaining 20% are procedural.” (Gall 1970, p. 713)

4. Standards for Mathematical Practice Standard 1 Make sense of problems and persevere in solving them “[Students] can understand the approaches of others to solving complex problems and identify correspondences between different approaches.” Standard 3 Construct viable arguments and critique the reasoning of others “[Students] justify their conclusions, communicate them to others, and respond to the arguments of others.”

5. The activity begins with teachers in groups of three taking the roles of teacher, student, or observer. The individuals playing the role of teacher and student each receive a slip of paper describing their corresponding scenario. The individuals playing the role of teacher or student get time to read their card and learn their role. The observer waits to record all of the teacher’s questions to the student. Once the activity begins, the teacher will talk to the student in the context of the scenario they read about on the slips of paper. Questioning Scenarios

6. Questioning Scenarios Example

7. Questioning Scenarios’ Goals Teacher’s goal is to uncover the student’s misunderstandings by asking questions that will encourage the student to respond elaborately. The initial goal is not helping the student to solve the problem If the misunderstanding is uncovered quickly, the teacher can go in that direction.

8. Teacher Implementation Issues It is difficult to come up with questions that will challenge students to make connections without simply telling them what to do. Classroom minutes are limited and mathematical discussions will use some of them. We view the Questioning Scenarios activity as practice so that when you do ask questions, you make them count by asking ones that require meaningful responses. Finding the right balance is a process that will take many years to master.

9. Student Implementation Issues Students have been trained to believe that teachers only care about the answer to the problem, not how they thought about it. It takes time for students to adjust to explaining themselves and the idea of discussing the problem will seem foreign to them at first. Ideas for increasing student participation include: Think-Pair-Share Sentence stems to structure their responses Modeling the thought process using think-alouds.

10. Questioning Benefits Asking questions that encourage elaborate responses allows the teacher to uncover a misunderstanding that may have otherwise gone unnoticed. Having students explain their thinking is one of the simplest and most natural forms of assessment in the math classroom.

11. Teacher Feedback How helpful was the questioning scenarios activity in terms of developing questions that encourage elaborated responses? 1 = Not helpful at all 5 = Very helpful

12. What strategy or concept from this year's PD had the biggest impact in your teaching of mathematics? The questioning. I was always happy that the kids gave me the right answer, but I never asked the question "why"? That has really changed my way of teaching. I also got a lot of insight from the questioning work we did....How asking better questions can really help me understand what my students are REALLY thinking when they work out their math problems! I have been using the high level thinking questions across the curriculum. It encourages students to think deeper and in a more concise manner. The questioning strategy had the greatest impact on my teaching of mathematics. It made me realize how important it is to have my students actually answer with complete thoughts instead of one word answers. As a teacher I am able to gain so much more of what they understand and what they don't understand by having them explain their thinking!

13. Lessons We Learned When introducing Questioning Scenarios to a group for the first time, it is helpful to do an example. Pick a math topic that the teachers are certain to feel comfortable with even if it means picking a topic below the grade level they teach. Include as much information as possible about what the student knows or does not know so the individual playing the role of the student can portray it accurately. When including a picture, chart, or table, make sure to add it to both the teacher and student scenarios so they have the same thing to reference. Consider providing a list of questions for teachers to use when they struggle to find one to ask.

14. References Gall, Meredith D. "The Use of Questions in Teaching." Teacher Education Division Publication Series (1970): 713. K-12 California's Common Core Content Standards for Mathematics. Sacramento: California Department of Education, 2010. "Professional Standards for Teaching Mathematics." Introduction. Professional Standards for Teaching Mathematics. National Council of Teachers of Mathematics, 1989. Web..