NOTE: Please do not use or cite these modules without permission from the Teach Math project.

Classroom Practice Module

Overview

Summary of module:

This module consists of three required activities, the third of which has a number of options. In these activities, PSTs analyze classroom practices from four perspectives, or lenses: teaching, learning, task, and power & participation.

Required activities:

  • Activity 1: Video CaseAnalysis

Pre-service teachers analyze video cases using a quadruple “lens” approach (e.g. task, learning, teaching, power & participation) to analyze each case. This activity takes place over time such that PSTs analyze multiple videos using the various lenses in a rotating pattern. This activity supports PSTs’ examination of mathematical funds of knowledge using video clips. Each case provides an opportunity for PSTs’ to examine the mathematical ideas (e.g. concepts, skills, problem-solving strategies); knowledge resources (e.g. mathematical, family, community, cultural, linguistic, personal); student participation, status issues, sense-making, and communication practices; and instructional strategies that facilitate mathematical thinking/reasoning and support students with varied cultural linguistic backgrounds, math experiences confidences.

  • Activity 2: Analysis of Curriculum Spaces

Pre-service teachers analyze and adapt one or more lessons from commonly used curriculum materials to create “spaces” for eliciting, building on, and integrating children’s mathematical thinking and children’s multiple mathematical knowledge bases. These adaptations are based on specific prompts from the lenses applicable for analysis of written documents[1].

  • Activity 3: Analysis of Mathematics Lesson Activity

PSTs evaluate their own math lesson’s potential to support mathematics learning using the lens prompts applicable for analysis of written documents. The analysis is designed to inform instructional planning and lesson development. Note: It is not expected that PSTs would or should address all aspects of each lens in a single lesson; rather, this is about looking at one’s teaching over time. If certain dimensions cannot be found in a particular lesson that is not a bad thing. But it is not in that lesson, so as teachers we then need to think about what we do over time.

AND/OR

  • Analysis of Field Lesson Activity

This activity engages PSTs in using one or more of the critical case lenses to analyze a mathematics lesson they observe in their practicum. The goal of this activity, in part, is to support students in looking in greater depth at the teaching in their practicum site and potentially notice things they may not have noticed before. Note: It is not expected that PSTs would see all aspects of a particular lens. Rather, it is expected that they will notice what is and is not happening in the practicum classroom and can reflect on mathematics teaching and learning within that context.

AND/OR

  • Analysis of Own Teaching Practices Activity

This activity engages PSTs in using one or more of the critical case lenses to examine their own practice. PSTs teach a mathematics lesson (video optional) and then use the critical case lenses to focus their reflection on the strengths and weaknesses of the lesson that they taught. Note: It is not expected that PSTs would or should try to address all aspects of each lens; rather, it is to notice what is and is not in a particular lesson such that PSTs can consider each of the lenses over time in their teaching.

Data Collection:

AUDIO or VIDEO RECORDINGS

  • Video record instructor’s introduction to each activity to capture the ways in which she might be framing PSTs’ noticing differently at different sites.
  • Audio record PSTs’ small group discussions around video cases, around analysis of curriculum spaces, and around analyses of own lesson plan, field observations or analysis of own teaching.
  • Video or audio record whole group discussions and/or presentations for video case analyses.
  • Video or audio record whole class discussion about adaptations to the curriculum.
  • Video or audio record whole class discussion(s)/debriefing session about analyses of own lesson plans, of field observations, or of own teaching practice.

WRITTEN WORK

  • For Activity 1, PSTs will be provided a blank lens sheet to take notes on as they watch each video. These notes should be collected as a work sample.
  • For Activity 1, if PSTs prepare posters to present to the class based on their lens, posters should be kept as a written work sample.
  • For Activity 1, if PSTs complete individual reflections as part of their ongoing video case analysis, these should be collected as written work.
  • For Activity 2, instructors should collect each PST’s curriculum analysis table as a PST work sample.
  • For the options with Activity 3 (analysis of lesson plan, analysis of field lesson, or analysis of own teaching), there are REQUIRED “essential prompts” that PSTs should respond to in writing. There are various options for how PSTs might respond to these prompts. Various options are listed below. This is not intended to be an exhaustive list.
  • Version 1: After Activity 3 (using lenses to examine lesson plan, field lesson, or video record of own teaching), PSTs do in class quick writes in which they respond to the “essential prompts” in writing. PST written work is collected as data.
  • Version 2: After Activity 3 (using lenses to examine lesson plan, field lesson, or video record of own teaching), PSTs complete an out of class written assignment in which they respond to the “essential prompts,” and if possible, additional optional prompts. PST written work is collected as data.

INSTRUCTOR REFLECTIONS Complete all portions of instructor reflections related to the activities in this module.

Classroom Practice Module

Detailed Instructor Guide

Goals for Pre-service teachers:

  • PSTs will identify and analyze aspects of mathematics teaching and learning that support teachers eliciting and building on children’s multiple mathematical knowledge bases.
  • PSTs will see mathematics classrooms in more detail, suspend everyday interpretation, and learn to look for patterns that otherwise go unnoticed at a conscious level.
  • PSTs will identify and analyze aspects of mathematics curriculum materials with respect to eliciting and building on children’s multiple mathematical knowledge bases.

General Description of the Module:

This module requires pre-service teachers to analyze mathematics teaching and learning video cases provided by their methods instructor using four lenses (teaching, learning, task, and power & participation), to use selected prompts from these lenses applicable to analysis of written documents to guide an analysis and adaptation of mathematics curriculum materials, and to use these lenses to analyze a lesson plan they’ve created AND/OR a field lesson they’ve observed AND/OR a video record of their own teaching practice.

Suggested Order: We suggest that PSTs engage with three video cases and their subsequent in-class small group and whole class discussions as part of Activity 1 before beginning Activity 2 or Activity 3. Activity 2 and Activity 3 could occur simultaneously.

Preparation Work (what comes before the module): noted for each activity in the module

Related Readings: noted for each activity in the module

Additional Documents Associated with this Module

  • Handout_Assignment and Write Up_Analysis of Own Teaching_CP_F2010
  • Handout_Assignment and Write Up_Field Observation_CP_F2010
  • Handout_Assignment and Write Up_Analysis of Lesson Plan_CP_F2010 (STILL NEEDED)
  • Handout_Activity_Introducing the Lenses_CP_F2010
  • Handout_Activity_Teaching Lens_CP_F2010
  • Handout_Activity_Learning Lens_CP_F2010
  • Handout_Activity_Task Lens_CP_F2010
  • Handout_Activity_Power and Participation Lens_CP_F2010
  • Handout_Activity_Video Case Discussion Guidelines_CP_F2010
  • Handout_Activity_Classroom Observation Guidelines_CP_F2010
  • Handout_Curriculum Spaces Table_CP_S2011
  • Instructor Information_Video Case Descriptions_CP_F2010

Activity 1: Video Case Analysis (four iterations)

GOALS for Video Case Analysis: For the PST to begin to see mathematics classrooms in more detail, suspend everyday interpretation, and learn to look for patterns that otherwise go unnoticed at a conscious level. More specifically, for PSTs to begin to identify and analyze aspects of mathematics teaching and learning reflective of eliciting and building on children’s multiple mathematical knowledge bases.

DESCRIPTION of individual activity:

Pre-service teachers analyze four video cases attending to specific foci – the teaching, student learning, the task, and power and participation patterns. The first video cases is required (Marshmallow video case), and should occur relatively early in the semester. The middle two video cases are selected by the methods instructors based on course needs. The final video, to be used in one of the last classes (as much toward the end as possible, and at least in the last third of the term) is also required (Questioning Data). It is also recommended that the fourth video case be an analysis of the Questioning Datavideo. Analyzing these video cases from different lenses allows PSTs to begin to see what it might mean to elicit and build on children’s multiple mathematical knowledge bases in instruction and supports PSTs in moving away from only looking at teaching to consider mathematics teaching and learning issues such as the role of the task, student learning, and power and participation patterns.

Possible Video Cases (more detail about each video is on a separate document, Video Case Descriptions)

  • Valentine Exchange (Annenberg)
  • People Patterns (Annenberg)
  • Lady Bugs (Annenberg)
  • Equality (Thinking Mathematically)
  • Almeta Hawkins (CGI)
  • Amazing Equations (Annenberg)
  • Questioning Data (Annenberg)
  • Sharing a Submarine Sandwich (Fosnot)
  • Buying and Cooking a Turkey (Fosnot)
  • Bean Sprouts (Annenberg)
  • What’s the Price? (Annenberg)
  • Fraction Tracks (Annenberg)
  • Pencil Box Staining (Annenberg)
  • Marshmallows (Annenberg)
  • Erin – clips from dissertation
  • Maura – girls math club digital story video

Related Readings for Instructors:

  • Sherin, M. G., & Han, S. Y. (2004). Teacher learning in the context of a video club. Teaching and Teacher Education, 20, 163-183.
  • VanZoest, L. & Stockero, S., (2008). Using a video-case curriculum to develop preservice teachers’ knowledge and skills. In M. Smith, S. Friel, & D. Thompson (Eds.) Cases in mathematics teacher education: Tools for developing knowledge needed for teaching (Association of Mathematics Teacher Educators Monograph No. 4., pp. 117-132). San Diego, CA : Association of Mathematics Teacher Educators.

INTRODUCTORY ACTIVITY: Video Analysis #1 (prep, during, after):

The “prep” for this activity consists of two components: (a) a brief overview by the instructor about the video case analysis that will be occurring over time in the course and (b) a quick examination of a central question from each of the four lenses.

Instructor Overview

PSTs are informed that they will be examining mathematics teaching and learning from four perspectives – teaching, learning, task and power & participation – over time in the course.

Introduction to Video Case Analysis

  • Ask PSTs in class to spend time reviewing each of the four questions on the Introducing the Lenses handout. Note: This introductory activity generally occurs early in the semester. As such, we suggest you direct PSTs’ attention to the four questions from each lens, rather than the center question, which you might note to PSTs you’ll return to later or you might omit completely for this introductory activity.
  • Provide PSTs a specific focus question from the Introducing the Lenses handout for the viewing of the first video case. Below are some suggestions for ways to distribute the focus questions across and within small groups:

Option A: Assign each small group a separate lens question.

Option B: Assign each small group all four lens questions, but have individual students in each group responsible for a separate lens question.

The during phase of Activity 1’s Introductory Activity consists of PSTs viewing of Annenberg’s Marshmallow video using their assigned focus question(s), followed by small and whole class discussion.

Analysis of Marshmallow Video

Watch the Marshmallow Video with students viewing from the perspective of their assigned lens(es). After viewing the video, give PSTs a moment to jot down notes on the front of their sheets based on their lens(es) (these will be collected as data). Have PSTs turn their papers over for additional notes such that when they begin to work in small groups, we can differentiate PSTs’ individual thinking from PSTs thinking after group discussion. Have PSTs engage in discussion in their small groups about their responses to their prompts, and support PSTs in grounding their claims using evidence from the video.

Whole Group Discussion

Next, engage in a whole group discussion. One goal of this discussion is to help PSTs begin to understand the nature of the four lenses and distinctions between them. Discussion questions might include (these are all OPTIONAL prompts):

  • What is the evidence in the video you have for that claim?
  • In what ways are our claims about teaching (teaching lens asks about ways teacher elicits and responds to student thinking) different from claims from the learning perspective (what math understandings or confusions are indicated in students’ work)? What might our evidence from the video consist of for each of these areas?
  • Foregrounding: Let’s look at the middle box (resources and knowledge bases students use). What do you think that means? Why do you think that is there?

RELATED IN-CLASS ACTIVITIES: Video Analysis #2, #3, #4 (prep, during, after)

The prep for this activity consists of PSTs taking time to review the four lenses – teaching, learning, task, and power & participation – in their entirety. This might be initially done outside of class with a follow-up review in class, or entirely in class.

Assigning Lenses: For Video #2, have your class focus on two of the lenses (e.g., learning and teaching). For Video #3, have your class focus on the other two lenses (e.g., task and power & participation). For Video #4, Questioning Data, consider repeating two lenses you most want to focus with in your class, or consider using all four lenses. In consideration of all four lenses, instructors could again choose to use the introductory activity handout that has just one prompt from each lens.

Option A: Each individual student has one prompt within a lens. Assign each table a lens. Next, assign each student at each table a particular prompt within the lens. Once lens prompts are assigned, ask students to think about their question, review the other questions and think about how their specific prompt is similar or different from the others, and to examine the second page of the lens description that includes more in-depth things to think about for each question. The last question on each lens goes to the “resources/knowledge bases” component and is the same for each lens. Instructors might consider assigning one student to this lens or assigning all students to this lens (in addition to their individual prompt).

Option B: Each small group focuses on one lens in its entirety. Assign each table a lens. Ask students to read through all of the questions for their lens and to examine the second page of the lens that includes more in-depth things to think about for each question.

The during phase of this lesson consists of PSTs watching the video from the perspective of their assigned lens/prompt and discussing their analyses. Recall that for Video #2 and Video #3 we recommend focusing on only two lenses at a time as a class. Another option to consider is having students watch a video multiple times on their own before class so that they are familiar with the context before being assigned a particular lens.

Small group discussion (audio record): After watching the video, have each student take a moment to jot down notes for their lens/prompt (to be collected as data). Then, have each table spend some time discussing their thoughts for their particular lens/prompt in their small group (have PSTs turn papers over and jot group notes on the other side of their sheet). Encourage students to focus on grounding their comments on evidence from the video.

Option A: Poster creation and presentation: Each small group will create a poster to summarize their findings. They should be careful to ground their claims using evidence from the video. They should include on their poster a short list of questions or unresolved issues their group faced. They should prepare to share their findings with the whole class. Note: Often the posters are bulleted lists identical to what PSTs have already written on their notes pages. Some suggested options that might help avoid this repetition are suggested below (this is not an exhaustive list):

  • Encourage PSTs to create a poster that consists of pictures rather than words.
  • Explicitly tell PSTs that you do NOT want the poster to be identical to the lists on their notes pages. Encourage them to choose one major point to highlight and explain why that was important. Encourage students to include with this major point a question they have or an unresolved issue their group faced.

Option B: Quick Write: Each individual student should do a quick write after their small group discussion of their lens, summarizing their findings and grounding their claims with evidence from the video.