thank exh focuss
"One facet of my entire timespan on Earth has been a slow unfolding of understanding of all the different ways intelligence can be constituted"
Some bipoc may struggle academically if :
They are pushed to get the answer correct than to understand concepts and reasoning
Independent practice is valued over teamwork or collaboration.
Students are tracked (into courses/pathways and within the classroom).
Curriculum developers and teachers enculturated in the USA teach mathematics the way they learned it without critical reflection.
Preconceived expectations are steeped in the dominant culture.
Mistakes are addressed as failure rather than as opportunities to learn.
Control of classrooms is valued over student's agnecy over their learning.
Math is taught in a linear fashion and skills are taught sequentially, without consideration of prerequisite knowledge.
Superficial curriculum changes are offered in place of culturally relevant pedagogy and practice.
Only content standards guide learning in the classroom.
Procedural fluency is preferred over conceptual knowledge.
Rigor is expressed only in difficulty.
I do, we do, you do” is the primary format of the class.
Students are required to “show their work” in standardized, prescribed ways.
Grading practices that center what sutdents don't understand rather than what they do.
Language acquisition is equated with mathematical proficiency.
Either/Or Thinking
Perfectionism
Only One Right Way
Solutions:
Methods for deepening student conceptual understanding through orchestrated math discussions that build on and connect multiple strategies.
Equitable Math Discussions
through Student Discourse
Introduction
Have you ever taught a lesson and then encountered students solving the presented problems in a different way?
Do opposing student thoughts scare you or excite you?
Is your first reaction to differing thoughts “Tell me more!” or “Let me show you”?
Purpose
The purpose of this tool is to highlight the diversity of students’ thinking, misconceptions, alternative solutions, and connections so any student, regardless of level, can contribute and gain equitable access to grade-level content. Students gain agency, voice, and deep content knowledge through carefully planned discussions.
Teachers also build deep content knowledge, cultivate the flexibility to work with diverse students, and practice continuous improvement.
This tool is meant to be used with all grade levels and content. It is used for planning the lesson, data collection during the lesson, as well as reflection after the lesson and for future planning.
It is a cyclical, living practice of continuous improvement. For a detailed demonstration on how to use this tool, see the short video here.
STUDENT
Gains better access to meaningful and engaging grade-level content. Builds deep content knowledge.
Gains agency and uses their voice. Gains flexibility when confronted with diverse or unexpected thinking.
TEACHER
Builds deep content knowledge. Practices continuous improvement. Represent all levels of student thought: initial thoughts, misconceptions, alternative solutions, connections. Intentional anticipating and sequencing potential student thinking to reach learning goals.
Center content understanding around student questions, diverse thinking, misconceptions, and alternative strategies.
Explore diverse student thinking through class discussion and questioning. Facilitate active sharing, discussion, and connections between different students' thinking.
Reflect before, during, and after the lesson to grapple with your own development needed for the content.
5 Practices for Orchestrating Productive Mathematics Discussions, by Margaret Schwan Smith and Mary Kay Stein1
, is
the foundational reference for this tool. It involves five stages for highlighting and sequencing student thinking:
1. Anticipate likely student emerging ideas and alternative solutions to mathematical tasks.
2. Monitor students’ actual responses to the tasks.
3. Select student responses to feature during the discussion.
4. Sequence student responses in a purposeful order to build a coherent math story.
5. Connect different students' responses through math discussion.
Understanding this practice is the major step to begin implementation. If you are not familiar with the 5 Practices, it is recommended that professional development, coaching, and independent research be coupled with this resource. Level
1 and 2 readings are must reads, and level 3 is an optional deep dive.
LEVEL 1
INTRODUCTION
LEVEL 2
IMPLEMENTAT ION
OPTIONAL
LEVEL 3
DEEP DIVES
5 Practices for Orchestrating Productive
Mathematics Discussions (SFUSD)
Chapter 1:
Introducing the Five Practices
The 5 Practices in Practice: Successfully
Orchestrating Mathematical Discussion
PLANNING CHECKLIST
In order to use this tool, follow the Planning Checklist, which breaks down the
process into four distinct parts: Understand the Activity, Plan the Activity, Collect Thinking During the Lesson, and Reflect After the Lesson.
Understand the Activity by reading 5 Practices for Orchestrating Productive
Math discussions, how to choose cognitively demanding tasks, and how to facilitate equitable student discussions and honor student responses.
Then, Plan the Activity by identifying a specific learning goal, task, content, and math practice. Anticipate student strategies that may be used, practice sequencing student thinking, and consider virtual adaptations and necessary adjustments.
Then, During the Lesson collect student samples and data and guide student discussion. And finally, After the Lesson, examine what student data says about your students' current level of understanding, identify student responses you did not anticipate or understand, and identify potential areas of development for your own content understanding.
Understand the Activity
5 Practices for Orchestrating Productive Mathematics Discussions
a. Level 1: 5 Practices for Productive Math Discussions Overview (SFUSD)
b. Level 2: Using the 5 Practices in Mathematics Teaching (NCTM 2018)2
c. Level 3: 5 Practices for Orchestrating Productive Mathematics Discussions
(Smith & Stein Book)
2. Understand the Content Priority Standards by Grade Level a. Achieve the Core Priority Standards by Grade Level Website b. Achieve the Core Priority Standards by Grade Level 2020-2021 PDF
This tool was created to address the need for English learner (EL) supports in enhancing English proficiency, including language scaffolding, student talk, and clarifying their understanding of mathematical concepts.
This tool seeks to assist teachers with classroom actionables in the form of scaffolding and supports that model equitable instructional practices for ELs, and foster rigor to develop language and mathematical conceptual understanding. It specifically addresses considerations around educator biases and beliefs and the diversity that exist among ELs.
These issues are key to their success in both developing academic English proficiency and deepening their understanding of the mathematical concepts that were not addressed adequately in prior learning experiences.
Content Standards
Content Standards CCSS
Standards for Mathematical Practice CCSS
3. Understand the Sequence
Progression Documents by Topic
a. Achieve the Core Progressions by Topic
b. UnboundEd Content Guides
4. Cognitively Demanding Tasks
a. What are cognitively demanding tasks?
b. Math Assessment Project
c. Illustrative Mathematics
5. Facilitate Small Group Discussion
a. Complex Instruction
b. Facilitating Effective Discussions
c. More focused and relevant Discussion in a Multicultural Classroom
6. Virtual Adaptations
a. Select and sequence asynchronously.
Give students tasks asynchronously and submit to the teacher. The teacher selects, sequences, and prepares an asynchronous or synchronous lesson around students' responses.
b. Select and sequence using Google Slides deck. Provide a shared Google Slides deck for students to populate with their thinking by typing on their assigned slides or uploading a picture of their work. The teacher can then select and sequence the slides, and share with students synchronously or asynchronously.
c. Select and sequence with interactive whiteboards.
Use interactive whiteboards to select, sequence, and share solutions.
Cultural and Linguistic Assets
Students gaining proficiency in English, also known as English learners or ELs, have immeasurable assets stemming from their multicultural and multilingual experiences.
These assets include, but are not limited to, enhanced communication skills, better understanding of how language works, greater executive function, considerable cognitive flexibility, improved memory, more opportunity to develop multiple perspectives, better sense of self, and substantial empathy and tolerance for others. As students grow up they can also have increased career opportunities and less mental decline in old age (Pavlenko 2014).
These assets support the potential to attain high levels of achievement, in both English proficiency and academically.
This is most commonly evidenced by English learners who entered the school system with limited English proficiency, but were “Reclassified Fluent English Proficient” (RFEP). These former English learner students are among the best performing students in California (Hill 2014); in many instances, closely matching or outperforming their English-only (EO) peers.
In 2018-19, CAASPP reports that 56.45% of English-only students who took the Smarter Balanced Summative Assessments for English language arts/literacy scored in the “Met” or “Exceeded Standard” range. That group was outperformed by their RFEP peers, of which 60.07% scored in the same range. In mathematics, 44.37% of English-only students tested scored in the “Met” or “Exceeded Standard” range, compared to 43.10% of RFEP students.
However, for those students who remained in the English learner program, the data was far below both those of EO and RFEP students. In ELA/literacy, 12.81% of EL students tested scored in the Met or Exceeded Standard range, and 12.58% met the same range in mathematics.
Further examination of teaching practices reveals the lack of educators’ understanding of English learners’ linguistic needs—resulting in the underachievement of ELs in content areas, specifically in mathematics.
The widened achievement gaps are evidenced by how instructional practices focus on teaching vocabulary, but not in conjunction with many other higher order thinking skills that enable English learners to “actively use mathematical language to communicate about and negotiate meaning for mathematical situations” (Moschkovich 2010).
This tool will support teachers in providing instruction that addresses both language and mathematical development.
The patterns of underachievement historically seen among students gaining proficiency in English, many of which are also students who identify as Black, Indigenous, and people of color (BIPOC), are effects of a system that fails to seethe languages and cultures our students bring to their education as assets for their own learning.
Their language and culture are neither seen as an important contribution to their learning communities, nor to the rich diversity of America.
The systems that uphold this rigid and narrow apparatus are most clearly seen in policies that devalue students’ home languages and cultures, and instead force diversity and equity through English-only initiatives and the abundant shower of traditionally-only literature and learning materials.
This document was created to address the lack of language scaffolding used to nurture opportunities for students gaining proficiency in English, share their thinking, and clarify their understanding of mathematical concepts.
The tool in this document seeks to support teachers with classroom actionables that model anti antiblack instructional practices for ELs. This document specifically addresses considerations around educator biases and beliefs, as well as the variabilities that exist among English learners, as these issues are key to EL’s success in developing academic English proficiency, while gaining the mathematical concepts that were not gained by past practices.
Our tool will support teachers with examples of actionables that support rigor, as well as scaffolds and supports for simultaneous development of language and math content in order to support outside the box practices for ELs in mathematics to leave no one behind
The impact that teachers' beliefs have on no one left behind, more equal and anti anti black practices can not be understated. In her paper titled, Teacher’s Knowledge and Beliefs About English Learners and Their Impact on STEM Learning, Julie Bianchini explains that teachers’ “efforts to construct safe classroom communities and effectively implement reform-based strategies have been found to impact both ELs’ views of themselves as learners and their mathematics and science achievement.”
Herreview of research on the topic of teacher beliefs highlighted the mis/connections across teachers’ knowledge and beliefs, their instructional practices, and the implications for EL student learning.
One such mis/connection was the deficit-based views teachers had in regards to the EL students they service. One example of this view is seen when teachers do not implement practices that develop students' language acquisition, and teachers confuse emerging English language proficiency with the absence of STEM content understanding.
Teachers often assume ELs as lacking relevant prior knowledge, experiences, and/or language, when in fact in the early stages of second language acquisition, learners spend time in the “quiet phase” as they take in and process their understanding of their second language.
One deficit-based view shared by teachers was seeing ELs as being unable or unwilling to communicate with teachers and/or with their non-EL peers.
Teacher biases included stereotypes of ELs grounded in their first language, ethnicity, and/or country of origin. These stereotypes led some teachers to have low or unreasonably high expectations for their EL students.
Bianchini goes on to describe one scenario in which “researchers found that teachers valued ELs’ hard work and motivation over their mastery of content, which was often neither facilitated nor checked.
Teachers’ knowledge and beliefs resulted in ELs' placement in lower-track classes, limited support for ELs in classroom interactions, and low expectations for ELs’ learning of content. As such, ELs were denied access to academic supports and adequate college preparation, even though this denial was cloaked in teachers’ well-meaning concern.”
The tool created for this document seeks to challenge these beliefs as it contains actions that support students gaining proficiency in English through error analysis of common misconceptions. Students study a sample problem centered on a priority math standard.
Through analysis of an example and non-example solution, students will explain, conjecture, and justify their reasoning. Students are supported through rigorous activities and encouraged to build agency through productive struggle
One-Size-Fits-All Approach Does Not Work
English learner variability is the rule, not the exception. There is no such thing as a “typical” English learner student.
We use the term “English learner” as the briefest way to convey meaning and to describe a student who is adding
English to their existing linguistic assets, but it does not adequately capture the range of EL types in your classroom.
Each EL student is unique in their place on the language acquisition continuum and in their place in the world. Some are highly schooled in their primary language, others have experienced interrupted schooling, and many may be recent immigrants.
EL Students may also be dually identified as a student with disabilities or gifted and talented—in some cases, both. Gifted EL students are frequently overlooked in the classroom because of the limitations of verbal assessments and language access barriers.
In addition to the EL student types provided in the table below, EL students bring diverse life experiences.
Some of these may include internationally adopted EL students, unaccompanied EL students, EL Students from mixed-status families, EL students experiencing homelessness, EL students in foster care, and LGBTQ EL students. They are all accompanied by the gift of another language, experience, and culture, along with the potential to broaden the horizons of every class they attend.
Further, increased executive function and the ability to switch focus of attention, reason about other points of view, and reflect on the structure of language are all learning assets that EL students bring to the classroom (Promoting the Educational Success... 2017).
Metacognitive (learner awareness about learning) and metalinguistic (language learner awareness about language) skills can greatly enhance the learning experience and provide mathematics teachers with a head start in nurturing critical thinking skills needed for mathematical reasoning.
This tool is designed to assist mathematics teachers in designing lessons that support all EL students and their mathematical experiences. Below is a table of different types of EL students educators may have in their classroom, also known as EL Typologies.
This table is by no means exhaustive; but it can provide some insights, not just into astudent’s educational experience or needed level of linguistic support, but a way to consider more deeply their life experience and worldview.
When teachers invest time in expanding their own knowledge about the language and culture of a student, and observe how that same student’s language and culture have formed their unique identity, a much clearer instructional support path emerges. (Paris and Alim 2017).
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