Why D You Ask That?

Why’d You Ask That?

Reflecting on Questions that Develop Mathematical Understanding

Assessment Session

March 3rd & 5th 2009

Math Teacher Leader Meeting

Lee Ann Pruske

Bernard Rahming
Janis Freckmann

DeAnn Huinker

Connie Laughlin

Session Goals

· To develop common understanding of a Framework for Question Types

· To develop understanding of Question Types used in a math lesson to support student learning.

· To continue our exploration of Lesson Planning with Formative Assessment Principles

Lesson Planning with Formative Assessment Principles

Date: ______Grade: ______Lesson: ______

Part 1: Selecting and Setting Up a Mathematical Task
This part contains four critical components that need to be considered when selecting and setting up a mathematical task. / Part 2: Supporting Student Exploration of the Task
In this sections, construct three questions that will develop the mathematics of the lesson. Be sure to consider the Depth of Knowledge to develop the questions. These questions could be used with students individually or in small groups. / Part 3: Summarizing the Mathematics
In this section, construct a question that focuses on orchestrating a whole group discussion of the task that uses different solution strategies produced by the students that highlight the mathematics of the lesson.
1. Important Mathematics to Develop:
2. Learning Target & Descriptors:
3. Lesson Objective in Student Friendly Language:
4. Success Criteria: / Q1. Access background knowledge:
Q2. Develop understanding of the mathematics by pushing student reasoning:
Q3. Summarize the important mathematics in the lesson. This should tie back to the success criteria. / Q. Summarize the important mathematics in the lesson as a whole class discussion. This should tie back to the success criteria.

Reviewing our assessment journey…

December-

· Lesson Planning with Formative Assessment Principles

· Focus introduction of multiplication concepts in 3rd grade using Houghton Mifflin Expressions textbook.

· Homework MTLs tried it in their schools

January-

· Lesson Planning with Formative Assessment Principles

· Focus introduction of multiplication concepts in 3rd grade using Scott Foresman textbook.

March-

· Focus is on column two- Questioning

· Delve deeper into the idea about questions to develop the mathematical ideas of a lesson.

Learning Intentions

We Are Learning To…

Identify questions that teachers ask to develop the mathematics of the lesson.

Success Criteria

We will know we are successful if…

At the end of the session

· I understand the six different types of questions discussed.

· I can think of at least one way to incorporate the session into my work with teachers at my school.

Reading

“An excerpt from Catherine Evan’s Class”

Turn & Talk

Focus question:

What do you notice about the types of questions Catherine Evans used to develop mathematic understanding?

Types of Questions

for Supporting Mathematics Learning Goals

The types of questions teachers ask during a class discussion creates or restricts the opportunities for students to deepen their mathematical understanding. The six types of questions listed below offers a lens for teachers to examine and reflect upon their questioning and the impact on student learning. Please note that this list does not delineate all types of questions a teacher might ask during a mathematics lesson but allows examination of questions asked during focused class discussions supporting the mathematical goals of the lesson.

Question Type / Description
1 / Gathering information or leading students / Seeks clarification of detail or checks for direct answer, facts, definitions, or procedures.
2 / Inserting terminology / Inserts correct mathematical language into the discussion once ideas are developed with the expectation that students then use the language to talk about the ideas.
3 / Exploring mathematical meanings / Brings out underlying conceptual ideas and establishes relationships among ideas or representations.
4 / Explaining one’s own thinking / Requests individual students to elaborate on his or her reasoning for one’s own benefit and for the class.
5 / Explaining another person’s thinking / Requests to explain or comment on another person or group’s thinking with the intent to generate discussion.
6 / Justifying thinking / Defends or proves some conclusion or claim by providing reasons for why a particular result has to be the case.

Developed by D. Huinker & J. Freckmann (February 2009).

References

Boaler, J., & Brodie, K. (2004). The importance, nature, and impact of teacher questions. Paper presented at the annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education, Toronto, Ontario, Canada.

Weaver, D., Dick, T., & Rigelman, N. (2005). Assessing the quality and quantity of student discourse in mathematics classrooms. (Oregon Mathematics Leadership Institute.) Portland, OR: RMC Research Corp.

02.13.09

Types of Questions for Supporting Mathematics Learning Goals

· Six categories of questions

· Questions grow in complexity and cognitive demand as you move from 1 to 6.

· Questions create or restrict opportunities for learning.

· A tool to help guide teachers into developing question types beyond the basic knowledge (Type 1) questions.

· Practitioners may want to focus on three or four question types in a lesson.

Type 1 Questions: Gathering Information or leading students.

Examples could be:

· What is the mode?

· What is 5 x 6?

· What is the coordinate of the intersection of the two lines?

Type 4 Questions: Explain one’s own thinking.

· Where did you start to find the perimeter of this figure?

· How did you know where to start?

· What made you think about that approach?

Group Movement

Students and Question Gallery

· Students will engage in the lesson with the teacher.

· Gallery will use the Question Type Recording Form to record the questions asked by the teacher during the lesson.

Lesson: Factor Game

Source: Connected Mathematics 2

Grade 6

Book Prime Time pages 15-24

Question Coding

1. As a table group, decide on which types of questions were asked during the lesson.

2. Write the corresponding question type on the line to the left of the question.

3. When you finish coding all of the questions, join another group and compare your findings.

4. What was similar or different in each group’s findings?

Charting Questions

1. As a table group, decide which question could be important in developing the mathematics in a real classroom.

· Label your chart paper: Developing the Mathematics Question

· Write your question and question type on your chart paper.

2. As a table group, decide which question pushes understanding of the math idea in a real classroom.

· Label your chart paper: Pushes Math Understanding

· Write your question and question type on your chart paper.

Poster Discussion: What do you notice?

· Which questions were chosen for the posters?

· What question type categories do these questions come from?

Success Criteria

We will know we are successful if…

At the end of the session

· I understand the six different types of questions discussed.

· I can think of at least one way to incorporate the session into my work with teachers at my school.

Questions to Ponder…

Pick one of the questions and talk to your neighbor.

· What did you learn about question types that support the development of the mathematics?

· What is your vision for using this in your school?

· What are your next steps?

School-based Work for March

1. Each MTL is to model a lesson in a classroom as the MTS did here. Ask the classroom teacher to list all questions asked for an approximate 10-minute whole group discussion component of the lesson.

2. After the lesson, the MTL can debrief with the teacher the question types; which questions seemed to be pivotal or important to move student thinking; and which questions were supportive to children’s learning in various ways.

3. At the April MTL meeting, we will share our classroom question modeling experiences!

The Milwaukee Mathematics Partnership (MMP), an initiative of the Milwaukee Partnership Academy (MPA), is supported with funding from the National Science Foundation under Grant No. EHR-0314898.

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