Tuesday, December 21st, 2021
What I am reading now…
Civic Reasoning & Discourse from NAE
Learning for Justice
https://www.learningforjustice.org/magazine/spring2021/toolkitformathematicsincontextthepedagogyofliberation
Civic Reasoning & Discourse from NAE
Learning for Justice
https://www.learningforjustice.org/magazine/spring2021/toolkitformathematicsincontextthepedagogyofliberation
Social Justice in Mathematics
Reading to complement this blog https://sustainability.yale.edu/explainers/yaleexpertsexplainenvironmentaljustice ( This article really inspired me to think about how math modeling can be a powerful way to heighten awareness as well as take action in the locally to make a change.)
Through the Lens of Social Justice: Acknowledgment, Actions, and Accountability (TODOS/NCSM, 2015) write, affirming the value in presenting “mathematics as an analytical tool to understand, critique, and transform the world,” and proceeding to argue that “facilitating student mathematical proficiencies that transcend textbooks and promote quantitative literacy, civic engagement, as well as individual and collective agency, is a social justice act of mathematics education.” (National Council of Supervisors of Mathematics and TODOS: Mathematics for All, 2015).
The NCTM also appears to hold the view that mathematics for social justice should be incorporated into the mathematics classroom. Key Recommendations” in the 2018 publication Catalyzing Change in High School Mathematics: Initiating Critical Conversations, includes a call for providing students with opportunities to “determine whether or not claims made in scientific, economic, social, and political arenas are valid,” arguing that “Never have the broader aims of mathematics education been more important than they are today, when mathematics underlies much of the fabric of society” (National Council of Teachers of Mathematics, 2018).
The article linked above from sustainability.yale.edu state that “Environmental justice is the fair treatment and meaningful involvement of all people regardless of race, color, national origin, or income, with respect to the development, implementation, and enforcement of environmental laws, regulations, and policies.”
“Environmental justice is really concerned with documenting and understanding the disproportionate and unequal environmental burdens that certain communities face,” Dr. Dorceta Taylor, Professor of Environmental Justice at the Yale School of the Environment, says. “In the United States and around the world, lowincome, Black, Indigenous, Latinx, and Asian people tend to be living in spaces where environmental hazards, extreme natural and humanmade disasters, and environmental degradation occur more rampantly.”
Safe and affordable drinking water is a human right and it is especially critical that people have access to safe running water during the current COVID19 pandemic. But nearly 130 million people in the U.S. — disproportionately in communities of color and lowincome communities — receive their water from systems that often puts them at increased risk of cancer, infertility, developmental delays, and other health impacts.
Despite the Safe Drinking Water Act, pollution of drinking water sources, decades of poor oversight, underinvestment in drinking water infrastructure, and segregation and other forms of discrimination, have left people — especially communities of color — at greater risk. Water systems across the country are still using old lead service lines, and tens of millions of us are drinking toxic PFAS chemicals.
https://www.nrdc.org/issues/protecthealthlowincomecommunities
Thinking more deeply about …
These are some professional development resources that I will learn from:
https://www.teachingforchange.org/
https://www.mathalicious.com/lessons/seekingshelternew
https://www.mathalicious.com/lessons/youresofined
https://www.mathalicious.com/lessons/wagewar
https://docs.google.com/document/u/1/d/1PrAq4iBNb4nVIcTsLcNlW8zjaQXBLkWayL8EaPlh0bc/mobilebasic
Walk in my shoeshttps://youtu.be/oVmHO_ENnOE
Black Teachers on Teaching Caste: The Origins of Our Discontents Stamped: Racism, Antiracism, and You
Malcolm Gladwell’s podcast, Revisionist History: Miss Buchanan’s Period of Adjustment (A landmark Supreme Court case. A civil rights revolution. Why has everyone forgotten what happened next?)
Unequal Childhoods: Class, Race, and Family Life
https://padlet.com/lbenson3/antiracist
https://docs.google.com/document/u/1/d/1PrAq4iBNb4nVIcTsLcNlW8zjaQXBLkWayL8EaPlh0bc/mobilebasic
Culturally Sustaining Pedagogy builds upon the AssetBased Pedagogies that came before it but presents the need to not only affirm and connect to students’ cultural backgrounds, but also to sustain them through schooling.Django Paris and H. Samy Alim describe the key features across culturally sustaining educational settings in an Education Week Author Interview: ‘Culturally Sustaining Pedagogies’.
Valuing community languages, practices, and ways of being  Students’ languages, literacies, and cultural ways of being are centered meaningfully and consistently in classroom learning instead of being considered as “addons.” 
Schools are accountable to the community  Educators and schools are in conversation with communities about what they desire and want to sustain through schooling. 
Curriculum that connects to cultural and linguistic histories  Educators connect present learning to the histories of racial, ethnic, and linguistic communities both locally and nationally. 
Sustaining cultural and linguistic practices, while providing access to the dominant culture.  Educators value and sustain the cultural and linguistic practices of the community while providing access to the dominant culture (white, middle class, and standard English speaking). 
Reading more about learning trajectory research
http://cadrek12.org/sites/default/files/DRK12EarlySTEMLearningBriefReferences.pdf
Teaching through mathematical modeling within local community contexts in the elementary grades is at the very core of equitable teaching in mathematics. One way to see this connection is to draw upon the framework offered by Bartell et al. (2017) on the research linking equitable teaching with the Standards for Mathematical Practice. Below is the nine important equitable teaching practices (Bartell et al., 2017) and the tenets of math modeling situated in the local community context for early grades mathematics.
Equitable Mathematics Teaching Practices
MM as Equitable teaching.legal paper size
Equitable Mathematics Teaching Practices (Bartell et al., 2017)  Math Modeling (Suh, 2020)  
1. Draw on
students’ funds of knowledge 
*Build on community and cultural knowledge and practices(Civil, 2007)
• Recognize students’ cultural and linguistic resources (Gay, 2002; LadsonBillings, 1995) • Have robust knowledge of students, validate shared ideas and experiences, and connect instruction to students’ experiences and interests (Aguirre et al., 2013; Bartell, 2011; Hedges, Cullen, & Jordan, 2011; Wager, 2012) 
MM draws on students’ funds of knowledge by situating the problem posing in the local community, school and students’ lived experiences. Assumptions are drawn based on experiences and ideas draw from resources in their community.

2. Establish classroom
norms for participation 
•Recognize that student voice has implications for power and authority and builds agency (Cobb & Hodge, 2007; Turner, Dominguez, Maldonado, & Empson, 2013)
Set up and guide discussions so that students from nondominant backgrounds develop strong mathematical identities (Hodge, 2006) • Connect pedagogical practices to student participation (Boaler & Greeno, 2000; Wager, 2014) • Question whose participation norms are valorized (Planas & Gorgorió, 2004) 
MM utilitizes tools, structures and routines that promote equitable participation. Group think pads and carousel walks allows all students to have voice and agency in sharing mathematical thinking and build math identities.

3. Position students as
capable 
Construct social structures that enable students to “develop strategies that help maintain certain positions and reduce others” (Planas & Civil, 2010, p. 145)
• Challenge and counteract societal stereotypes and inequities to which students and communities are subjected (Bartell, 2011; Gay, 2002; LadsonBillings, 1995) • Attend to how the curriculum may influence perceptions ofstudents (Atweh, Bleicher, & Cooper, 1998) • Share power in the classroom by allowing students to provide meaningful input in making decisions about classroom practices, curriculum, and assessment (Cornelius & Herrenkohl, 2004; Sheets, 2005) 
In MM students have opportunities to share their thinking and how they made decision within their models.

4. Monitor how students position each other  Assign competence to support students’ repositioning of one another (Cohen, Lotan, Scarloss, & Arellano, 1999; Featherstone et al., 2011)
• Attend to reification of existing status structures so as to reposition some students with their peers (Forman & Ansell, 2002) • Position students to use one another as mathematical resources (Dunleavy, 2015) 
There is a reporting and refining stage that acknowledges that exchanging differing ideas is part of refining one’s model and advancing their thinking.

5. Attend explicitly to race and culture  • Make connections to students’ mathematical, racial, and cultural identities (Battey, 2013; Martin, 2007) • Recognize that certain groups have been positioned as antiintellectual (Martin, 2009; Steele, 2003)  MM allows the use of Cultural Sustaining Pedagogy where school becomes a place to sustain one’s cultural identity by sharing community and cultural math happenings . 
6. Recognize multiple forms of discourse and language as a resource  • Facilitate respect among students by cultivating culturally responsive relationships among students and validating possible differences in their language practices (Moschkovich, 2013) • Coconstruct resources with students in momenttomoment interactions around mathematics (Dominguez, 2014) • Consider linguistic choices and acknowledge home language as a valid language of mathematics (Meaney, 2005; Setati, 2005) • Bridge language practices through affirming students’ home languages, modeling code switching, and fostering interactional patterns familiar to students (Brenner, 1998; Howard, 2001; Lee, 1995) 
MM is a rich discursive process that includes students to use multiple representations such as visuals, numbers, words to express one’s mathematical thinking.

7. Press for academic success  Assess student learning, build on student strengths, explicitly communicate expectations for students, and communicate the teachers’ responsibility in student success (Morrison, Robbins, & Rose, 2008)
• Have high academic expectations while maintaining students’ cultural and psychological wellbeing rather than accept deficit views about students’ intellectual potential (Fine, 1986; Fordham, 1988) 
MM provides multiple points of assessment for teachers to look for and amplify the strength in student thinking. 
8. Attend to students’ mathematical thinking  Recognize, understand, and build from children’s understanding of mathematics (Carpenter, Fennema, Franke, Levi, & Empson, 1999) •
Respond to developmental needs so as not to expect a student to do mathematics they are not developmentally ready for (Jackson, 2009) 
MM has an asset based pedagogy in place to celebrate each students’ contribution and differentiate naturally in the MM process. 
9. Support development of a sociopolitical disposition  • Incorporate critical texts, discuss controversial topics, serve the community, and allow social issues to drive instruction (HicklingHudson & Ahlquist, 2003; Hyland, 2005; Tate, 1995) • Provide opportunities to explore sociopolitical topics using mathematics (Frankenstein, 2012; Gates & Jorgensen, 2009) • Engage students in conversation about realworld problems and how mathematics can be used to examine them (Gutstein, 2006; Skovsmose, 1994)  Having MM tasks situated within the real world, and the local community and the larger world makes the issues at hand connected to many social issues that can connects how math can be used to make important decisions and eradicate inequities. 
Of course, I also use Rico Gutstein’s work as well!
Here are some ready use tasks as well from Mathalicious
https://www.mathalicious.com/lessons/seekingshelternew
This is an excerpt from JMTE 2018’s article by Sarah Quebec Fuentes and Jingjing Ma entitled “Promoting teacher learning: a framework for evaluating the educative features of mathematics curriculum materials”.
Connecting to my research: Video studies deepen teachers’ knowledge about how students reason about mathematics. Russell (2007) promote that teachers must continue to augment their understanding of student conceptions throughout their career (Russell 2007). How can peer video coaching support this continuous growth? Can video peer coaching allow for teachers to customize their learning and create self initiated goals for enhancing their practice?
Fuentes & Ma, 2018, p. 360361
Teacher knowledge of student thinking in mathematics The curriculum materials support the development of teacher knowledge in anticipating and understanding student thinking.
Reasoning is a critical component in learning mathematics with understanding (NCTM 2000). In Adding It Up, a National Research Council (2001) report, literature is synthesized to describe the various, codependent components (conceptual understanding, procedural fluency, strategic competence, adaptive reasoning, and productive disposition) constituting learning mathematics with understanding, or mathematical proficiency. Student reasoning, or thinking, cuts across all components from understanding of (conceptual understanding) to representing (strategic competence) to explaining (adaptive reasoning) mathematical ideas. In order to foster student thinking, teachers must have knowledge about how students reason about mathematics. In particular, knowledge of content and students, a subdomain of PCK, represents an interaction between knowledge about students as learners of mathematics and knowledge of mathematics content (Ball et al. 2008). Teachers need to be aware of student reasoning and common misconceptions with respect to particular content as well as instructional approaches that support student thinking (National Research Council 2001). For instance, the use of representations, one of NCTM’s (2000) process standards, provides objects around which to reason mathematically and subsequently helps students develop an understanding of mathematical concepts (Leinwand et al. 2014). Further, different representations of a mathematical idea afford different conceptions about that idea (e.g., various interpretations of fractions such as part of a whole or quotient) (National Research Council 2001). Throughout their career, teachers must continue to augment their understanding of student conceptions (Russell 2007). Educative curriculum materials could support teacher learning in this realm by giving examples of how students typically respond to a task, including common difficulties, explaining how students’ responses relate to their understanding of a concept, and providing recommendations for ways in which to address students’ responses (Arias et al. 2015a; Ball and Cohen 1996; Beyer et al. 2009; Davis and Krajcik 2005; Dietz and Davis 2009; Duncan et al. 2011; Doerr and ChandlerOlcott 2009; Heaton 2000; Remillard 2000; Stein and Kim 2009). Collopy (2003) described a teacher’s approach to using curriculum materials, which provided examples of common student errors. She read the information about student misconceptions prior to teaching the lesson, observed student thinking during the lesson, and reread the information after the lesson to prepare for the next lesson. Teachers also have opportunities to learn content through examining student thinking presented in curriculum materials (Schneider and Krajcik 2002; Tyminski et al. 2013) and during the implementation of lessons (Remillard 2000), demonstrating a reciprocal relationship between subject matter knowledge and understanding student thinking.”
(p. 361)Teacher knowledge of disciplinary discourse in mathematics The curriculum materials support the development of teacher knowledge in fostering disciplinary discourse in mathematics.