Module 2a: Connecting Modeling to Culturally Responsive Mathematics Teaching
NSF Award 2010269, 2008997, 2010202, 2010178 �Contact eqstemm@gmail.com
Professional Learning Cycle �Adapted from Lampert et al., 2013; McDonald et al., 2013
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2
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4
Participants will explore the Culturally Responsive Math Teaching Framework.
Participants will plan a task and use the CRMT teacher move to support their teaching practice later in the series.
Participants will enact a modeling task using the CRMT practices in their classrooms.
Participants will reflect how the CRMT Questions Stems opened up space to honor student knowledge and identities, support rigor and distribute power and participation.
What is Mathematical Modeling?
“Mathematizing the World” Routine
Introduce
Participants will explore the Culturally Responsive Math Teaching Framework
Facilitator Notes
Participant Pre-Work
Participants will take an inventory of their own teaching practice with this prompt-
Facilitator Pre-Work
This Culturally Responsive Math Teaching Framework will be the pedagogical focal point with modeling.
What does culturally responsive math teaching mean to you?
CRMT2 Framework (Zavala & Aguirre, 2021)
Cultural and Community Funds of Knowledge
(Re) Humanizing
Student Thinking and Ideas
Cognitive Demand
Distributing Intellectual Authority
Scaffolding
Up
Affirming Multilingualism
Disrupting Status and Power
Analyzing and Taking Action
Knowledges & Identities
Rigor & Support
Power & Participation
CRMT2 Area 1: Knowledges & Identities
Cultural and Community Funds of Knowledge
(Re) Humanizing
Student Thinking and Ideas
How does my lesson help students connect mathematics with relevant/authentic issues or situations in their lives?
How does my lesson support creativity, broaden what counts as mathematical knowledge, and affirm positive math identities for all students?
How does my lesson create opportunities to elicit, express, and build on student mathematical thinking in multiple ways? (e.g., through gesture, pictures, words, symbols)
(Zavala & Aguirre, 2021)
Assets
Assets
Cognitive Demand
Scaffolding
Up
Affirming Multilingualism
CRMT2 Area 2: Rigor & Support
How does my lesson enable all my students to closely explore and analyze math concepts(s), procedure(s), and problem-solving/reasoning strategies?
How does my lesson maintain high rigor with high support for all students?
How does my lesson make space for multilingual learners (MLL) to be central participants in mathematics activities?
(Zavala & Aguirre, 2021)
Distributing Intellectual Authority
Disrupting Status and Power
Analyzing and Taking Action
CRMT2 Area 3: Power & Participation
How does my lesson distribute mathematics authority and make space for multiple forms of knowledge and communication?
How does my lesson disrupt status differences, entrenched stereotypes and inequitable power relationships present in all mathematics classrooms?
How does my lesson support student use of mathematics to analyze, critique, and address power relationships and injustice in their lives?
(Zavala & Aguirre, 2021)
What area/dimensions resonate with you?
What area/dimensions will stretch your practice?
Watch a video focused on CRMT using the CRMT noticing guide
https://eqstemm.org/tools/crmt/
But before we watch the video…. Let’s brainstorm possible approaches and solutions to a similar task.
Sharing Task: We have two boxes of rice crispy snacks. How many days will it last for our class? | |
Important Quantities: | Image of snack |
Assumptions: | |
Anticipate Student Strategies and Solutions (pictures, equations, words) | |
Prepare
Participants will prepare a lesson using the Culturally Responsive Math Teaching Framework
Facilitator Notes
Participant Pre-Work
Participants will revisit their teaching inventory and work on a teacher move that will strengthen their culturally responsive teaching practice.
Facilitator Pre-Work
This Culturally Responsive Math Teaching Framework will be the pedagogical focal point with modeling.
Connecting Modeling to
Culturally Responsive Mathematics Teaching
“Look Fors” and Teacher Moves
Formative Assessment “Look Fors”:
Students Make Sense of Real-World Situations and Pose Mathematical Questions (Math Modeling Competency)
Formative Assessment “Look Fors”:
Students Make Sense of Real-World Situations and Pose Mathematical Questions (Math Modeling Competencies)
During Problem Posing: Elicit student connections to the situation including understandings, cultural and community experiences, and diverse math ideas; Encourage curiosity, and support students to pose meaningful problems. | |||
Elicit and honor students’ diverse ideas, experiences, and questions related to the situation What this sounds like: • What do you notice? • What do you wonder? • What do you know about this situation? • Who has an experience to share? • What math questions can you ask? • Why are these questions important? • Who might care about the answers to these questions? | Build on students’ curiosities and questions to define a modeling problem to investigate. What this sounds like: • Several people wondered about ________ and _____. We are going to investigate these questions as we work on our problem. • This is our problem for today: [state problem]. How does this problem connect to your questions and wonders? •We need to figure out _______. Which of the questions that you posed can help us? | Provide varied opportunities and modalities for students to contribute ideas. What this sounds like: • Before we share wonders with the class, talk to a partner about your ideas. •You can share your questions in English or [another language]. •Everyone write down one thing you notice in your notebook. Then we’ll share. •Who has a story to share about this situation? •You can share drawings of your ideas. | Ensure that multiple students have opportunities to pose problems, and to refine / add to problems posed by the teacher. What this sounds like: •We are going to work together to pose a problem. I need everyone’s help to make our problem better. What can we add? • ______ just shared a really interesting wonder. Let’s see if we can build on their idea to decide on our problem. • [student], you helped us understand why this situation is important. What questions should we ask? |
Pivotal Teacher Moves to Support these Math Modeling Competencies
Module 1 Formative Assessment “Look Fors”:
Students Make Sense of Real-World Situations and Pose Mathematical Questions (Math Modeling Competencies)
During Problem Posing: Elicit student connections to the situation including understandings, cultural and community experiences, and diverse math ideas; Encourage curiosity, and support students to pose meaningful problems. | |||
Elicit and honor students’ diverse ideas, experiences, and questions related to the situation What this sounds like: • What do you notice? • What do you wonder? • What do you know about this situation? • Who has an experience to share? • What math questions can you ask? • Why are these questions important? • Who might care about the answers to these questions? | Build on students’ curiosities and questions to define a modeling problem to investigate. What this sounds like: • Several people wondered about ________ and _____. We are going to investigate these questions as we work on our problem. • This is our problem for today: [state problem]. How does this problem connect to your questions and wonders? •We need to figure out _______. Which of the questions that you posed can help us? | Provide varied opportunities and modalities for students to contribute ideas. What this sounds like: • Before we share wonders with the class, talk to a partner about your ideas. •You can share your questions in English or [another language]. •Everyone write down one thing you notice in your notebook. Then we’ll share. •Who has a story to share about this situation? •You can share drawings of your ideas. | Ensure that multiple students have opportunities to pose problems, and to refine / add to problems posed by the teacher. What this sounds like: •We are going to work together to pose a problem. I need everyone’s help to make our problem better. What can we add? • ______ just shared a really interesting wonder. Let’s see if we can build on their idea to decide on our problem. • [student], you helped us understand why this situation is important. What questions should we ask? |
Pivotal Teacher Moves to Support these Math Modeling Competencies
Which of these teacher moves have you used?
Which moves do you think might work well with your students?
What did you notice in the video?
Students…
The Teacher….
During Problem Posing: Elicit student connections to the situation including understandings, cultural and community experiences, and diverse math ideas; Encourage curiosity, and support students to pose meaningful problems. | |||
Elicit and honor students’ diverse ideas, experiences, and questions related to the situation What this sounds like: • What do you notice? • What do you wonder? • What do you know about this situation? • Who has an experience to share? • What math questions can you ask? • Why are these questions important? • Who might care about the answers to these questions? | Build on students’ curiosities and questions to define a modeling problem to investigate. What this sounds like: • Several people wondered about ________ and _____. We are going to investigate these questions as we work on our problem. • This is our problem for today: [state problem]. How does this problem connect to your questions and wonders? •We need to figure out _______. Which of the questions that you posed can help us? | Provide varied opportunities and modalities for students to contribute ideas. What this sounds like: • Before we share wonders with the class, talk to a partner about your ideas. •You can share your questions in English or [another language]. •Everyone write down one thing you notice in your notebook. Then we’ll share. •Who has a story to share about this situation? •You can share drawings of your ideas. | Ensure that multiple students have opportunities to pose problems, and to refine / add to problems posed by the teacher. What this sounds like: •We are going to work together to pose a problem. I need everyone’s help to make our problem better. What can we add? • ______ just shared a really interesting wonder. Let’s see if we can build on their idea to decide on our problem. • [student], you helped us understand why this situation is important. What questions should we ask? |
Module 1 Formative Assessment “Look Fors”: Identify Important Quantities (Math Modeling Competencies)
Module 1 Formative Assessment “Look Fors”: Identify Important Quantities
During Important Quantities Discussion: Elicit students’ ideas about important quantities and assumptions, while supporting students to explain how each quantity/assumption relates to the problem posed | |||
Invite students to identify important quantities and explain how they relate to the problem posed What this sounds like: •What do you know that will help us with this question? •What do we need to know, or find out? •_____ said that we know how many students are in our class. How can that help us with our problem? •____ said we need to find know _____. How can that help us? | Provide just in time information in response to key quantities that students identify What this sounds like: •You mentioned that you need to know _____. Here is a table with some information that might help. •_____ said that we need more information about ______. I did some research and this is what I found out. •_____ said we need to know how many students are in ___’s class. Let’s find out. | Use targeted prompts and graphic organizers to help distinguish key components of the situation. What this sounds like: •You said ______is important . Is that something we already know, or something to find out? • _____ said we need to know _____. Is this something we can find out, or do we need to make an assumption / best guess? •Let’s use a chart to organize our ideas. This column is what we already know, and this one for decisions we need to make. | Ensure that students have opportunities to make (and revise) assumptions and decisions What this sounds like: •You get to make an assumption here. What seems reasonable? • ____ has an assumption will help us answer our question. Let’s listen. •You get to make decisions with your group. It is ok to make different decisions. •_____ had an idea about a decision we need to make. •It’s ok to revise your assumptions/ choices. What do you want to change? |
Pivotal Teacher Moves to Support these Math Modeling Competencies
Module 1 Formative Assessment “Look Fors”: Identify Important Quantities
During Important Quantities Discussion: Elicit students’ ideas about important quantities and assumptions, while supporting students to explain how each quantity/assumption relates to the problem posed | |||
Invite students to identify important quantities and explain how they relate to the problem posed What this sounds like: •What do you know that will help us with this question? •What do we need to know, or find out? •_____ said that we know how many students are in our class. How can that help us with our problem? •____ said we need to find know _____. How can that help us? | Provide just in time information in response to key quantities that students identify What this sounds like: •You mentioned that you need to know _____. Here is a table with some information that might help. •_____ said that we need more information about ______. I did some research and this is what I found out. •_____ said we need to know how many students are in ___’s class. Let’s find out. | Use targeted prompts and graphic organizers to help distinguish key components of the situation. What this sounds like: •You said ______is important . Is that something we already know, or something to find out? • _____ said we need to know _____. Is this something we can find out, or do we need to make an assumption / best guess? •Let’s use a chart to organize our ideas. This column is what we already know, and this one for decisions we need to make. | Ensure that students have opportunities to make (and revise) assumptions and decisions What this sounds like: •You get to make an assumption here. What seems reasonable? • ____ has an assumption will help us answer our question. Let’s listen. •You get to make decisions with your group. It is ok to make different decisions. •_____ had an idea about a decision we need to make. •It’s ok to revise your assumptions/ choices. What do you want to change? |
Pivotal Teacher Moves to Support these Math Modeling Competencies
Which of these teacher moves have you used?
Which moves do you think might work well with your students?
Sharing Marshmallows at Camp Cooper to make Smores
https://drive.google.com/file/d/1YTMXGgqCYvvjCgE4wLBF3k-I7obrKdI4/view?usp=sharing
What did you notice in the video?
Students…
The Teacher….
During Important Quantities Discussion: Elicit students’ ideas about important quantities and assumptions, while supporting students to explain how each quantity/assumption relates to the problem posed | |||
Invite students to identify important quantities and explain how they relate to the problem posed What this sounds like: •What do you know that will help us with this question? •What do we need to know, or find out? •_____ said that we know how many students are in our class. How can that help us with our problem? •____ said we need to find know _____. How can that help us? | Provide just in time information in response to key quantities that students identify What this sounds like: •You mentioned that you need to know _____. Here is a table with some information that might help. •_____ said that we need more information about ______. I did some research and this is what I found out. •_____ said we need to know how many students are in ___’s class. Let’s find out. | Use targeted prompts and graphic organizers to help distinguish key components of the situation. What this sounds like: •You said ______is important . Is that something we already know, or something to find out? • _____ said we need to know _____. Is this something we can find out, or do we need to make an assumption / best guess? •Let’s use a chart to organize our ideas. This column is what we already know, and this one for decisions we need to make. | Ensure that students have opportunities to make (and revise) assumptions and decisions What this sounds like: •You get to make an assumption here. What seems reasonable? • ____ has an assumption will help us answer our question. Let’s listen. •You get to make decisions with your group. It is ok to make different decisions. •_____ had an idea about a decision we need to make. •It’s ok to revise your assumptions/ choices. What do you want to change? |
Enact
Participants will teach a Mathematizing the World routine or a lesson using the CRMT Question Stems for opening up space to honor student knowledge and identities, support rigor and distribute power and participation
Math Modeling
Lesson Analysis Tool
Student “Look Fors”
Lesson Reflections
“In a learning community where Culturally Responsive Pedagogy is vibrant, teachers and students can engage in formative assessment with recognition of the diversity and variation of ways (e.g., style, pace, connections) that students think about and learn mathematics. Hence, the evidence of student learning will mirror this diversity and variation.”
Lott & Bonner (2018)
NCTM book: A Fresh Look at Formative Assessment in
Mathematics Teaching
Next Steps
Reflect
Participants will reflect how the CRMT Questions Stems opened up space to honor student knowledge and identities, support rigor and distribute power and participation.