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Learning Objectives

Teachers will …

Describe features of “current” math education (aspects of student learning - conceptual understanding)
Continue to identify and reflect on their values of, views of, and experiences with mathematics and mathematics education
(HS.AEE .A.2) Create and recognize an equivalent form of an expression to understand the quantity represented in an authentic context. (this lesson is lead into objectives of (a) factor a quadratic expression to reveal the zeros of the function it defines; (b) complete the square in a quadratic expression to reveal the maximum or minimum value of the function it defines; and (c) construct a viable argument to justify a method for solving equations or inequalities)

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Course Standards

Teachers will …

Deepen your understanding of how students learn mathematics and how a teacher can facilitate the mathematical growth and development of all students through creating an environment that supports individual and collaborative learning
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 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 Reed :)

Community Building Activities Sign-up

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Math Lesson

5:00 - 6:15pm

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Our First Math Lesson

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Our Second Math Lesson

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Our Second Math Lesson

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Our Third Math Lesson…

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Our Third Math Lesson…

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Math Lesson

Integrated 1

Integrated 1 Volume 1

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Math Lesson

Oregon Math Standards

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Math Lesson

Team 1: Gennie, Oliver, Pete, Riley

Team 2: Dom, Reed, Scott

Team 3: Duy, Noemi, Zion

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Math Lesson

Please do the following with your team:

Review your list of team norms

Have each person get familiar with their role (see this chart --->)

Work on the problems as follows follows for 20 minutes (original problem set):

Read the math problem you are working on aloud (all work on the same problem)
Each person independently works on task for 30-60 seconds
Each person shares their thinking about the problem

AND group members ask clarifying question, add on to,

or reason about the thinking shared

(Once each person has shared) Prepare to write a collective solution for 3-74

Red tiles = negative value

= negative tile

Resource Manager	Oliver	Reed	Noemi
Recorder/ Reporter	Riley	Scott	Duy
Facilitator	Gennie	Dom	Zion
Task Manager	Pete	Reed	Noemi

= positive tile

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Our group norms:

Listening to understand, not to respond

Mistakes are expected and accepted

Give space, share the mic of life

Accept feedback on different strategies

Learn from each other

Honor the wisdom of everyone

US—>

Team 1: Gennie, Oliver, Riley, Pete

Team Name: PROG Squog

PROG SQUOG

Oliver

Gennie

Pete

Riley

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Our group norms:

Constant communication
Fair distribution of work
Good faith in constructive criticism
Mutual accountability
Summary synthesis/debrief

Team 2: Reed, Scott, Dom, Kathleen

Team Name: In the works!!

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Our group norms:

Be respectful
Be open to giving and receiving constructive criticism
Be willing to collaborate and learn from each other
Invitation to speak up and hear each other out
Allow and expect a lack of closure.
Be aware of shortcomings and be understanding of special circumstances (We are all human)

Team 3: Zion, Duy, Noemi

Team Name: ZND (Zone of Notable Development)

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Math Lesson

Ask a clarifying question about the solution:“What do you mean by …?”, “Why do you think that?”, “Will you explain that again?”, “I have a question about …”, “I don’t quite understand. Can you explain it a little bit more?”, “How do you know your answer is right?”

Add on to the solution: “I would like to add …”

Reason about the solution: “I (dis)agree with your strategy because …”, “My strategy is like yours because …”, “My strategy is different from yours because …”

(Chapin, O'Connor & Anderson, 2009; Topcuoglu & Nelson (2018)

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Math Lesson

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Math Lesson

Whole Class Takeaways AND Big Math Ideas

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Math Lesson

Whole Class Takeaways AND Big Math Ideas

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Math Lesson Debrief

Let’s discuss …

How might this lesson help learners develop a conceptual understanding of factoring?

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Break Time!

6:15 - 6:45pm

Back at 6:45pm

Put your Mathgraphies in this Mathographies folder

so that Torrey can print it:)

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Reading Discussion

6:45 - 7:15pm

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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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Academic Achievement & Success

Aspects of Student Learning

(Standards for Math Content

and Practices,

Conceptual Understanding)

“Effective” Teaching Practices

Probe & Elicit Student Thinking

Promote Equitable Participation (drawing on student identity and assets)

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Reed’s notes

PROMPT 1: How do the articles/videos this week define/describe understanding and how a learner develops understanding?

Additional comments/points raised:

-what dimensions of the classroom can affect student understanding - tasks, norms (math norms such as how much work do you show), tools

-in equity class the professor suggested to establish norms immediately but some of us have found that it is better to build norms as students work in class across time

-generative knowledge - can map understanding onto novel situations, when there is no understanding they can not apply to new situations (isolated skills)

-it can be helpful to have students share what is happening and what they are doing (“read it to yourself”) - beyond figuring out what to do and how to do it

-students may be accustomed to not sharing their conceptual understanding so we need to establish new habits where they are critical thinkers who do not expect to be told what to do (so it depends on what their math teachers were like in previous grades/year)

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Aspects of Student Learning

Conceptual Understanding

Procedural Fluency

Math Reasoning

Problem-Solving Skills

Van de Walle, Karp & Bay-Williams Ch. 2 -->

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Aspects of Student Learning

Let’s identify examples of conceptual understanding:)

It might help to identify the “knows” a math content standard and think about what it means for a student to “know” the thing you identfied

Here are some examples of mathematical concepts that you might want to think about:

Area (what is an understanding of area?)
Proportional Relationships (what is an understanding of proportional relationships?)
Factoring (what is an understanding of factoring?)
Solution to a System of Equations (what is an understanding of a solution to a system of equations?)

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Equitable Participation Project Part 1

7:15 - 7:40pm

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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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Academic Achievement & Success

Aspects of Student Learning

(Standards for Math Content

and Practices,

Conceptual Understanding,

Procedural Fluency)

“Effective” Teaching Practices

Promote Equitable Participation (drawing on student identity and assets)

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Equitable Participation Project Part 1

Let’s check out our Mathographies

(look at at least 1 entry for each person in our class)

Then let’s chat about …

Themes that characterize our collective experiences
Similarities and differences we notice
Questions we have

Notes:

Our perceptions of math ability came from external place (often people) instead of internal place
Very early on we were told something and that either made us feel good or bad about math and that affected how we felt about things - problems during education
Shift to seeing math in more positive light
Fewer entries in the early stage so inflection points were in middle school or later
People have great art skills and showed emotion
Mentorship matters - wrote about older person doing something and all of us reacting one way or the other so mentor directly impact our path through math AND NOW we are going to be such mentors to people and will be memorable to our students a decade or more later and may impact students for the rest of their lives
How interact with kids can really influence students’ perceptions of themselves
Connection between math and real life - connections between what we learned and that we teach and the real world application
Want to know more about Raul’s illustration of a classroom setting (only latino in the classroom, other people thought he was a drop out, felt did not fit into classroom and friends were in another classroom, wonder if in the right place/class since could not find place and people in the class - identity of way felt in class affect how did in class; could not find someone to relate to in the class so drew faces to reflect this) and Scott’s graphs (equation s = 2p + 2m + t signifies scott = 2 parents + 2 math degrees + dad math teacher; the situation felt very quadratic; what do the axes represent; came up with events was easy but describing them is difficult and thinking in classroom about multiple representations so is showing the description as a graph; could tell ) - these sparked our curiosity

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Equitable Participation Project Part 1

Let’s check out our classroom survey summaries

Then let’s chat about …

What we learned about our students
How our assumptions about our students were affirmed or challenged
Connections to our Mathographies
Tensions and uncertainties we experienced giving the survey