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Welcome to ITP 524:

Secondary Math Methods

Class 3: Wednesday October 16

Please get out out your nametag (or make a new one) :)

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Agenda

Welcome!
Community Building Activity (4:45 - 5:00pm)
Reading Discussion (5:00 - 6:15pm)
Break (6:15 - 6:45pm)
Check in about Assignments (6:45 - 7:05pm)
Intro to Math Standards (7:05- 7:40pm)

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Learning Objectives

Teachers will …

Identify and reflect on their values of, views of, and experiences with mathematics and mathematics education
Develop your understanding of student identity and assets
Describe features of “current” math education (the CCSS Math content standards)

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Course Standards

Teachers will …

Expand your mathematical understanding, your views regarding the nature of mathematics and mathematical activity
Plan instruction that supports each student’s progress toward learning goals by drawing upon knowledge of content, curriculum, and students and the community context
Recognize and appreciate the value of collaboration through your interactions in the course and begin to see yourself as part of a larger community of mathematics educators

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Community Building Activity

4:45 - 5:00pm

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Community Building Activity

Take it away Dom:)

Community Building Activities Sign-up

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Reading Discussion

5:00 - 6:15pm

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Student Identity & Assets

Student Personal Assets: “Specific background information that students bring to the learning environment. Students may bring interests, knowledge, dispositions, everyday experiences, family backgrounds, and so on, which a teacher can draw upon to support learning.”

Student Cultural Assets: “The cultural backgrounds and practices that students bring to the learning environment, such as traditions, languages and dialects, worldviews, literature, art, and so on, that a teacher can draw upon to support learning.”

Student Community Assets: “The common backgrounds and experiences that students bring from the community where they live, such as resources, local landmarks, community events and practices, and so on, that a teacher can draw upon to support learning .”

(edTPA handbooks)

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Culturally Relevant Pedagogy

Cultural Competence

(maintain students’ cultural integrity and use students’ culture as a vehicle for learning)

Critical/Socio-Political Consciousness

(develop students’ consciousness that allows them to critique cultural norms, values, mores, and institutions that produce and maintain social inequities)

Academic Achievement/Success

(develop students’ academic

skills and excellence)

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Cultural Competence

Personal Identity

(e.g., gender, race, class, culture, language proficiency)

Personal, Cultural, and Community Assets and Experiences (in your class, school, math ed)

Identity of Others

(e.g., gender, race, class, culture, language proficiency)

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PROMPT 1: The Aguirre, Mayfield-Ingram & Martin chapter comes from a book titled The Impact of Identity in K-8 Mathematics Teaching and Learning: Rethinking Equity-Based Practices. What do these authors say about the impact of identity in K-8 Math Teaching and Learning?

Gennie’s notes

Additional comments/points raised:

-A part of being a person and educator is knowing your identity and recognizing you cannot separate it from yourself and this transfers into being an educator and students cannot separate their identities from themselves and be aware of how be inclusive of all forms of identity

-Teachers need to help students not just learn math regardless of “identity elements” but because of them to avoid saying “you can learn math even though…” and change this to “you can do well in math because…” - getting away from deficit view and shift to what students can do and how this will help them in math

-it should not be about their math skills but about their identity - they are enduring different pain/trauma that have qualities they are overcoming which means they are resilient so how to channel resilience in academic setting

-constant interrogation of identity helps teachers consider positionality with students and how you are in a position of power

-”why is math important to us?” is a question that if we ask to students it brings our cultural experience and their personal reasoning about why math is important or they can say it is not important which is helpful information in a classroom - this gets students to think about when see and how use math in their life

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PROMPT 4: What does Featherstone mean by the term "math smarts" and how does this definition compare to other ideas in math ed about what it means to be "smart" in math?

Gennie’s notes

Additional comments/points raised:

-Math smart is something that has been perpetuated in math and other stem fields - people say they are book or street smart but not math smart

-calling kids “smart” is frowned upon but also told to feel bad for being called smart since other people are not called smart - smart isn’t a good compliment or it is a showcase of kids working hard

-we are their cheerleaders and we have to show them that they know more than they realize - they have all this knowledge and it is about putting it on display, students are coming from other classes AND they lie in that they say they do not know what they are doing but they do know - we can tell them they are doing the right things and are putting it together

-it is helpful to have the kids read the problem to you (the teacher) since this helps them have a sense to say

-Featherstone says kids wants to use the word smart and want to be smart so if we find situations where they get to be smart then this can be motivation for them - feeling smart can be intrinsic motivation for people/kids so it can be powerful - we can take advantage of having them use this term and have them use the teacher’s definition of smart in terms of the math practices (things that students do)

-Math smart is not the ability that someone is born with. It is something we cultivate over time by giving them problems and having them experiment with the problem. Let the student’s work on the problem themselves since these are the skills we want to cultivate

-in classrooms we hear kids described at “good at math” but we want all students to think/feel they are good at math and that they can work on problems (work on smaller problems to build up to a bigger problem)

-sometimes the people who are perceived as being smart are the ones who speak up

-if you are known as a student who is good at math then you are more likely to participate and have other people resort to you

- the students who are quicker calculators are seen as smart but other students may need more time to interpret the problem and are capable of solving it too - they will get to the same answer at different rates and/or use different methods (some of which take longer/more time)

-it is helpful to have students read problems out loud when students are sitting there and not getting to work on it - reading it out loud and having someone ask them what the problem is asking/about is helpful to students

-students speaking - it is hard to get a student to believe in what they are saying especially when they are stuck - it is scary to be wrong, are used to being marked down, have not had a chance to try ideas outloud, students are missing connective tissue - know what need to use/do but are unsure of the connection, there is a pressure to move on to the next lesson so students do not speak up since it will be seen as holding the class back, students need validation and encouragement when they are struggling (especially from the teacher)

-students who do not have a math identity need a mindset change - getting support and validation is part of this since they have to change a massive part of their self concept

-Jo Boaler’s fixed versus growth mindset - you can learn and there are not fixed intelligences, the fixed mindset is the idea that there are people who innately and not innately good at math and the problems is that it afflicts both high and low performers since high performers come to think they are not good at math when they had difficulty (so they are in fact failures)

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Student Identity & Assets

Take a look at this identity wheel. Think about how you identify within the given categories. Consider which identities are most (and least) salient for you, in what ways and in what situations.

Annotate the identity wheel handout to capture your reflections.

Image from Medical Group Management Association

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Student Identity & Assets

Please share the following with your table group:

Which of these identities are you most and least aware of in your experiences as a math teacher?

Which of these identities are you most and least aware of in your experiences as a math student?

Image from Medical Group Management Association

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Student Identity & Assets

Please do the following with a partner:

Have each person share 1 of their mathography entries

Talk about how your multiple identities are connected to the event

Image from Medical Group Management Association

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Student Identity & Assets

Leading by My Identity Definitions:

Ethnicity is “Often based on a group of membership organized by similar traits, such as a common language, common heritage , and cultural similarities within the group.”
Race is “Described as a social construct. Often is used to describe a category of people who share certain inherited physical characteristics, such as skin color, facial features and stature.”

Functional specialty = area of expertise

Here are some Identity Wheel Activities:

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Key Take-Away

Shift from this kind

of math class...

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Key Take-Away

… to this kind of math class

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Values vs. Experience Coordinate Grid

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Aligns with

My Values

Does Not Align with My Values

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Aligns with

My Values

Aligns with My Experiences

Does Not Align with My Experiences

Does Not Align with My Values

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Aligns with

My Values

Aligns with My Experiences

Does Not Align with My Experiences

Does Not Align with My Values

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Aligns with

My Values

Does Not Align with My Values

Aligns with My Experiences

Does Not Align with My Experiences

I am here because...

I

II

III

IV

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“This means redefining what we think of as ‘helping’ students – rather than showing students how to do something, your role in helping students is to ask probing questions that keep students engaged in the productive struggle until they reach a solution.” (Van de Walle, Karp, Bay-Williams, p. 23)

PLACE YOURSELF IN TERMS OF THE IDEA: Your role in helping students is to ask probing questions that keep students engaged in the productive struggle until they reach a solution rather than showing students how to do something.

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“I think another piece of it is this idea that somehow mathematics is separate from politics and from values and from ethics. Students often have told me that they feel like in math classroom all you really need is a brain and some kind of a stylus so whether that’s a brain and a computer, a brain and a paper pencil, a brain and a calculator, but it’s this idea that you shouldn’t bring, like you don’t need your body to do mathematics, the rest of your body, you just need a head to do mathematics and so I think that that’s pretty striking and it also makes me wonder if we think that mathematics is not political, not cultural, not any of these other things then how do we remind ourselves that it’s a human endeavor?” (Gutiérrez, 16:15-17:00)

PLACE YOURSELF IN TERMS OF THE IDEA: Mathematics is separate from politics and from values and from ethics

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“In the classroom, the ready availability of the answer book or the teacher’s providing the solution or verifying that an answer is correct sends a clear message to students about doing mathematics: ‘Your job is to find the answers that the teacher already has.’ In the real world of problem solving outside the classroom, there are no teachers with answers and no answer books. Doing mathematics includes using justification as a means of determining if an answer is correct.” (Van de Walle, Karp, Bay-Williams, p. 19)

PLACE YOURSELF IN TERMS OF THE IDEA: Doing mathematics includes using justification as a means of determining if an answer is correct as opposed to finding the answers that the teacher already has

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“If we think about the fact that mathematics is a compulsory subject, you must take it for this many years, … that we hold it up as the standard of intelligence in society so even if you don’t think of yourself as wanting to go into it as a career that there’s implications for whether you think of yourself as mathematical or not that continue on long into your adulthood, and we think about the ways in which mathematics often asks us to kind of leave parts of ourselves outside of the learning space … while we are doing it you can see that maybe there’s some parts of this that could feel like over 12 years of compulsory schooling ... there may be parts that could be felt like it’s dehumanizing.” (Gutiérrez, 7:09-7:54)

PLACE YOURSELF IN TERMS OF THE IDEA: There are parts of mathematics that are dehumanizing and has learners leave parts of themselves outside of the learning space

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Things We Notice and Wonder

Things we notice (in particular about group or whole-class trends)

Things we wondering

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Break Time!

6:15 - 6:45pm

Back at 6:45pm

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Check in about Assignments

6:45-7:05

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Check in about Assignments

Let’s check out the Student Thinking Project

AND Lesson Planning and Task Analysis Module

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Intro to Math Standards

7:05-7:40

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Intro to Math Standards

Let’s get familiar with the Oregon Math Standards

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Intro to Math Standards

Ideas and image from Richman () Unpacking ND Math Standards Intro - Math for Elementary Teachers II

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Intro to Math Standards

Ideas and image from Richman () Unpacking ND Math Standards Intro - Math for Elementary Teachers II

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Intro to Math Standards

Adapted from Brack (2022) Unpacking Math Standards When Lesson Planning

Steps to Unpack the Standards

Read and write the standard and any related standards
Identify the “knows” and “dos”
Determine if the standard is conceptual, procedural or application

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Intro to Math Standards

Ideas from Brack (2022) Unpacking Math Standards When Lesson Planning

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Intro to Math Standards

Ideas from Brack (2022) Unpacking Math Standards When Lesson Planning

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Intro to Math Standards

Ideas and image from Richman () Unpacking ND Math Standards Intro - Math for Elementary Teachers II

Underline = Know

Circle = Do

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Intro to Math Standards

Ideas from Brack (2022) Unpacking Math Standards When Lesson Planning

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Intro to Math Standards

Access the Oregon Math Standards
Pick one content standard and identify the “knows” and “dos”

Underline = knows
Color text = dos

Share your standards knows and dos with a partner
Select an example to share on the next slide

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HS.GM.D.13: Apply the Pythagorean Theorem in authentic contexts, and develop the standard form for the equation of a circle.

HS.AFN.C.7: Graph functions using technology to show key features.

RED = do UNDERLINE = know

STANDARD: HS.GM.A.1

Apply definitions of rotations, reflections, and translations to transform a figure and map between two congruent figures in authentic contexts.

8.GM.A.2:

Understand that a two-dimensional figure is congruent to another if the second can be obtained from the first by a sequence of rotations, reflections, and translations.