Conferring Instructional Activity Structure

Purpose

To develop students’ capacity to:

  • Make sense of problems and persevere in solving them (MP1)
  • Communicate their mathematical reasoning with precision (MP6)
  • Use specific mathematical practices (e.g. mp 2, 7, and 8)

To develop teacher’s capacity to:

  • Look at, make sense of, respond to students’ written work;
  • Listen to, make sense of, and respond to students’ mathematically substantive utterances;
  • Utilize talk moves, “re-voicing” and “wait time” as well as PTT. (BTR Instructional Goal #1)
  • Develop and pose purposeful questions that will clarify assumptions about student thinking, surface more of students’ reasoning, and support students’ continued thinking and reasoning (BTR Instructional Goal #2) and;
  • Assess students’ learning and use assessment to inform instructional decisions (BTR Instructional Goal #3).

Rationale

The National Council of Teachers of Mathematics (NCTM) Teaching Principal states that “Effective mathematics teaching requires understanding what students know and need to learn and then challenging and supporting them to learn it well”. TheConferring Instructional Activity Structure (IAS)responds to that principle by prompting teachers firstto gain a clear understanding of what students know, and then challenging and supporting students to deepen their understanding. Questioning is used as the vehicle to both surface and clarify student understanding as well as advance student thinking. The pre-work for this IAS is the clear articulation of math content and practice goal(s) and success criteria. A high cognitive demand task sits at the center of the Conferring IAS to ensure that all students are reasoning mathematically and that all students have something to talk and write about (BTR Instructional Goals 2 and 4). Thus, through the Conferring IAS, teachers are providing students the“opportunity for mathematical discourse using precise language to convey ideas, communicate solutions, and support arguments” (MA Mathematics Framework Guiding Principle #6Literacy Across the Curriculum).

Description

The Conferring Instructional Activity Structure (IAS) is situated in the “explore” portion of a lesson (i.e. after the lesson is launched and students are working together on a cognitively demanding mathematics task). The IAS begins with the teacher touring the room watching and listening as students work together to make sense of and solve the mathematical task at hand. The goal of this silent reconnoitering is to gain an initial understanding of student sense-making. The teacher then asks questions to check her understanding, clarify any confusion she may have about the students’ thought process, and/or seek more information to gain a more complete picture of student thinking. Once the teacher has an accurate understanding of students’ sense-making she can then pose questions to advance or orient their thinking. This questioning process helps the teacher know what the students know, helps the students both to clarify and extend their mathematical ideas, and provides an opportunity for academic language to be modeled and practiced with increased precision. In addition targeted questions can prompt the use of a particular mathematical practice.

Overview of the Conferring IAS

The ConferringInstructional Activity Structure (IAS) is made up of the following parts:

  • Observe students- make sense of what they are saying and doing.
  • Check your understanding- ask questions that allow students to explain their thinking.
  • Surface and/or Prompt Math Practices - askquestions that promote mathematical reasoning.

Preparation

As with all teaching, the Conferring IAS requires thoughtful preparation. Pre-work should include:

  • Defining the math content and practice goals for the activity
  • Articulating criteria for success
  • Solving the math task using at least two different approaches
  • Considering the approaches students might take

Lesson Launch
Explore / Part I (3-5 min)
Students are working on math independent of teacher. This gives students time to enter the problem.Students may be working individually, in pairs, or in small groups.
Part II (5-10 min)
While Students Work…
1. Observe students. Look at their written work and make sense of what they are writing on the page. Listen to student discussion and make sense of what they are saying. Take notes. Ask yourself the following questions:
  • What do I notice in the student work?
  • How do I think that students are approaching this problem?
  • Is there evidence of developmentand/or use of math practices? If so, what?
  • Is there evidence of understanding of the content standard? If so, what?
2. Check your understanding. Ask questions that allow students to explain their thinking.
  • Ask students to explain how they approached the problem.
  • Example: “How are you thinking about this problem?”
Listen to students: follow-up questions should be based on the student response!
  • Ask clarifying questions. Make sure you have an accurate understanding of student thinking!
  • Example: “When you say, ‘It goes up by more each time’what do you mean by ‘more’”?
  • Use re-voicing, a talk move that allowsthe teacher to, “ interact with students in a way that will continue to involve the student in clarifying his or her own reasoning”. Re-voicing also provides an opportunity for teachers to model academic language and precision (MP6).
  • Example: “So you’re saying that the output increases by consecutiveodd numbers?”
  • Use wait time to give students the think time they need to reason mathematically.
  • Example: Silence, after asking a question; Saying “So…” if student has given an incomplete explanation. This also gives the teacher time to make sense of what the student is saying.
3. Surface or Prompt Math Practices. Ask questions that promote mathematical reasoning, i.e.use and development of mathematical practices.Sample practice prompting questions:
  • What does this number represent in the problem context? And, does that number make sense given the problem context? (MP2)
  • What quantities should you pay attention to in this problem? (MP2)
  • How could you organize the data to see a relationship? (MP2)
  • Does this representation show you any relationships? (MP2)
  • Does this problem remind you of another that you have worked on? (MP7)
  • What would happen if you rewrote or complicated this expression? (MP7)
  • What repetition are you noticing in your calculations? (MP8)
  • Are you doing the same thing over and over again? If so, what? (MP8)
  • Have you included every step? How do you know? (MP8)
  • Where are you in your process? (MP8)
As students respond to your questions, use talk moves to gain clarity and understanding of student thinking.
Give suggestions to promote students continued thinking and reasoning without taking over the thinking and reasoning (i.e. keeping the demand high).
LESSON SummarY

Lewis/KelemanikBoston Teacher Residency 12/12/181