Focus & Within Course Coherence in High School July 2018 1 We know from experience the hard work teachers face every day as they strive to help all of their students meet the challenges set by higher Standards. We are a diverse team of current and former classroom teachers, curriculum writers, school leaders, and education experts who have worked in the public, private, and nonprofit sectors. We are dedicated to empowering teachers by providing free, high-quality, Standards-aligned resources for the classroom, the opportunity for unbiased and immersive training through our Institutes, and the option of support through our website offerings.
2 FOCUS IN HIGH SCHOOL Introduction: Who I Am Insert photo Insert photo Name 1
Name 2 3 FOCUS IN HIGH SCHOOL Introduction: Who You Are Raise your hand if
You are a math teacher. You are a math teacher coach. You hold a different role. You teach in a district school. You teach in a charter school. You teach or work in a different type of school or organization. You teach monolingual students. You teach bilingual or multilingual students. 4
FOCUS IN HIGH SCHOOL Icebreaker Share with the people at your table: Where are you from? What do you do? What gets you up in the morning? No, seriously, why do you do this work? Look at the cluster headings on your table. As a group, decide which three clusters would you spend the most time teaching and why. 5 FOCUS IN HIGH SCHOOL The Shifts
1. Focus strongly where the Standards focus. 2. Coherence: Think across grades, and link to major topics within grades. 3. Rigor in major topics: Pursue conceptual understanding, procedural skill and fluency, and application with equal intensity. 6 FOCUS IN HIGH SCHOOL This Week Day Ideas Monday
Focus and Within Grade Coherence Tuesday Rigor and the Mathematical Practices Wednesday Across Grade Coherence and Instructional Practice Thursday Adaptation and Curriculum Study
Friday Adaptation and Practice Do the math Equity for all Connect to our practice 7
FOCUS IN HIGH SCHOOL We Will Go deeper on standards and shifts and see how they play out in curriculum and instruction. Examine standards-aligned resources. Do a lot of math problems.
Think about how we can ensure equitable math instruction for all students. Think about how what we are learning impacts what we will do in school. 8 FOCUS IN HIGH SCHOOL We Take Data Seriously Three-minute online Daily Survey.
Facilitators will address feedback the following day. Thursdaytenminute online Knowledge Survey Post-Test. Answer key will be available. 9 FOCUS IN HIGH SCHOOL Norms That Support Our Learning Take responsibility for yourself as a learner.
Honor timeframes (start, end, and activity). Be an active and hands-on learner. Use technology to enhance learning. Strive for equity of voice.
Contribute to a learning environment in which it is safe to not know. Identify and reframe deficit thinking and speaking. 10 FOCUS IN HIGH SCHOOL Today Morning: Focus in High School Afternoon: Focus and Within Course Coherence in High School
11 FOCUS IN HIGH SCHOOL Morning Objectives Participants will be able to describe the structure of the standards and how it translates to the learning and teaching of mathematics. Participants will be able to identify clusters of standards as major, supporting, or additional. Participants will be able to explain how specific content supports learning and teaching of major work. Participants will be able to explain how attending to the shift of focus is an equitable practice in Standards-aligned math instruction. 12
FOCUS IN HIGH SCHOOL Morning Agenda I. Framing the Challenge II. Understanding Focus III. Major, Supporting, and Additional Content
IV. Deeper Dive: Major Work 13 FOCUS IN HIGH SCHOOL I. Framing the Challenge 14 FOCUS IN HIGH SCHOOL Our Approach Our learning is grounded in the
intersection of the standards, content, aligned curriculum, and the equitable instructional practices that are essential for closing the opportunity gap caused by systemic bias and racism. 15 FOCUS IN HIGH SCHOOL Unpacking Equity Equity exists when the biases derived from dominant cultural norms and values no longer predict or influence how one fares in society. Equity systematically promotes fair and impartial access to rights and opportunities.
Equity may look like adding supports and scaffolds that result in fair access to opportunities or creating opportunities for all voices to be heard. Educational Equity ensures that all childrenregardless of circumstancesare receiving highquality, grade-level, and standards-aligned instruction with access to high-quality materials and resources. We become change agents for educational equity when we acknowledge that we are part of an educational system that holds policies and practices that are inherently racist and that we have participated in this system. We now commit to ensuring that all students, regardless of how we think they come to us, leave us having grown against grade-level standards and confident in their value and abilities. 16 FOCUS IN HIGH SCHOOL EquityEnvision It So You Can See It For educators, it is important to have a clear vision of what educationally
equitable environments look like. Gorski and Swalwell provide five principles to guide you. 4 min. Jot down concrete examples of what an equitable education environment would look like, sound like, and feel like to students, families, and staff. 6 min. Share in pairs at your tables, looking for commonalities and new ideas to expand your thinking. 5 min. Share with the whole group ideas you heard that will help all of us. Looks Like Sounds Like Feels Like 17 FOCUS IN HIGH SCHOOL
II. A Call for Focus A focused, coherent progression of mathematics learning, with an emphasis on proficiency with key topics, should become the norm in elementary and middle school mathematics curricula. Any approach that continually revisits topics year after year without closure is to be avoided. By the term focused, the Panel means that curriculum must include (and engage with adequate depth) the most important topics underlying success in school algebra. Improvements like those suggested in this report promise immediate positive results with minimal additional cost. National Mathematics Advisory Panel 18 FOCUS IN HIGH SCHOOL
Focus in the Standards The Common Core calls for greater focus in mathematics. Rather than racing to cover many topics in a mile-wide, inch-deep curriculum, the standards ask math teachers to significantly narrow and deepen the way time and energy are spent in the classroom. This means focusing deeply on the major work of each grade. 19 FOCUS IN HIGH SCHOOL Why Focus? This focus will help students gain strong foundations, including a solid understanding of concepts, a high degree of procedural skill and fluency, and the ability to apply the math they know to solve problems inside and outside the classroom.
20 FOCUS IN HIGH SCHOOL Review Conceptual Category Domain Cluster Standard F-IF.A.1 21
FOCUS IN HIGH SCHOOL Where to Focus? 22 FOCUS IN HIGH SCHOOL Where to Focus 23 FOCUS IN HIGH SCHOOL Focus by Course This shows where students and teachers should spend the large majority of
their time in order to meet the expectations of the Standards. Not all content in a given grade is emphasized equally in the Standards. Some clusters require greater emphasis than others, based on the depth of the ideas, the time that they take to master, and/or their importance to future mathematics or the demands of college and career readiness. More time in these areas is also necessary for students to meet the Standards for Mathematical Practice. To say that some things have greater emphasis is not to say that anything in the Standards can safely be neglected in instruction. Neglecting material will leave gaps in student skill and understanding and may leave students unprepared for the challenges of a later grade. 24 FOCUS IN HIGH SCHOOL
III. Focus by Course Major clusters are the highest priority. Supporting clusters are designed to support and strengthen areas of major emphasis. Additional clusters may not connect tightly or explicitly to the major work. 25 FOCUS IN HIGH SCHOOL Focus by Course ProtocolMajor Work 1. 2. 3. 4.
Read the framework document for your course(s). Identify the major work for your course(s). Identify the major work for the other high school subjects. Identify themes for major work across these subjects. 26 Deficit views of historically marginalized children, their families, and communities because of race, class, language, and culture persist in educational conversations and research (Valencia, 2010). Deficit thinking implies that students lack knowledge and experiences expected by the dominant group. National Council of Supervisors of Mathematics and TODOS: Mathematics for ALL, 2016 27
FOCUS IN HIGH SCHOOL IV. Digging Into Major Work Protocol: 1. Do the mathone task per course. 2. Identify the standard and why the task aligns. 3. Discuss the alignment with a partner at your table.
4. Explain how you could ensure equitable math instruction for all students with regard to the tasks you choose. 28 FOCUS IN HIGH SCHOOL Major WorkAlgebra I A-APR.A.1 29 FOCUS IN HIGH SCHOOL
Major WorkGeometry G-CO.B.8 30 FOCUS IN HIGH SCHOOL Major WorkAlgebra II A-APR.B.3 31 Lunch 12:00 1:00 32
FOCUS AND WITHIN COURSE COHERENCE IN HIGH SCHOOL Today Morning: Focus in High School Afternoon: Focus and Within Course Coherence in High School 33 FOCUS AND WITHIN COURSE COHERENCE IN HIGH SCHOOL Afternoon Objectives Participants will be able to identify connections between content within a grade level.
Participants will be able to evaluate a sample scope and sequence by determining whether or not it covers grade-level content; evaluating the amount of time spent on major, supporting, and additional work; and recognizing purposeful connections between content (i.e., between major and supporting and between major and major). 34 FOCUS AND WITHIN COURSE COHERENCE IN HIGH SCHOOL Afternoon Agenda I.
Deeper Dive: Supporting Work II. Connect to Practice: Impact of Focus III. Coherence Within the Course IV. Connect to Practice: Evaluate a Scope and Sequence 35
FOCUS AND WITHIN COURSE COHERENCE IN HIGH SCHOOL I. Digging Into Supporting Work Protocol 1. Identify the supporting work for your grade(s) using the focus documents. 2. Do the mathidentify the standard. 3.
Discuss how this standard supports major work. 36 FOCUS AND WITHIN COURSE COHERENCE IN HIGH SCHOOL Supporting in Algebra I F-LE.A.1 Distinguish between situations that can be modeled with linear functions and with exponential functions. City Bank pays a simple interest rate of 3% per year, meaning that each year the balance increases by 3% of the initial deposit. National Bank pays a compound interest rate of 2.6% per year, compounded monthly, meaning that each month the balance increases by one twelfth of 2.6% of the previous month's balance. a. Which bank will provide the largest balance if you plan to invest $10,000 for 10 years? For 15 years?
b. Write an expression for C(y), the City Bank balance, y years after a deposit is left in the account. Write an expression for N(m), the National Bank balance, m months after a deposit is left in the account. c. Create a table of values indicating the balances in the two bank accounts from year 1 to year 15. For which years is City Bank a better investment, and for which years is National Bank a better investment? 37 FOCUS AND WITHIN COURSE COHERENCE IN HIGH SCHOOL Supporting in Geometry G-CO.A.5 Given a geometric figure and a rotation, reflection, or
translation, draw the transformed figure using, e.g., graph paper, tracing paper, or geometry software. Specify a sequence of transformations that will carry a given figure onto another. 38 FOCUS AND WITHIN COURSE COHERENCE IN HIGH SCHOOL
Supporting in Algebra II A-REI.B Solve equations and inequalities in one variable. 39 FOCUS AND WITHIN COURSE COHERENCE IN HIGH SCHOOL II. Focus in High School Connection to practice: What are the common threads in the major work in high school?
How do supporting clusters connect to the major work? What impact do the focus documents have on your role? Why does a focused curriculum lead to greater student success for all students? 40
FOCUS AND WITHIN COURSE COHERENCE IN HIGH SCHOOL III. Coherence Within the Course 41 Within Grade Coherence: Coherence is built into the standards for each grade through the utilization of complementary topics to support and reinforce a major topic in a grade. This also
increases focus in the grade. FOCUS AND WITHIN COURSE COHERENCE IN HIGH SCHOOL Task Analysis Protocol: 1. Do the mathone task per course. 2. Identify the standards and why the task aligns. 3.
Stronger and Clearer Each Time: a. Write why this connection is important to discuss with students. b. Discuss why this connection is important to show to students with someone who is in a similar role. c. Revise your writing on why this connection is important based on your conversation. 43 FOCUS AND WITHIN COURSE COHERENCE IN HIGH SCHOOL Algebra I A-SSE.A.2 and F-IF.B.8a 44
FOCUS AND WITHIN COURSE COHERENCE IN HIGH SCHOOL Geometry G-GPE.B.4 and G-GPE.B.5 45 FOCUS AND WITHIN COURSE COHERENCE IN HIGH SCHOOL Algebra II F-BF.A.1a, F-BF.A.2, and A-SSE.B.3c Dani has $1,000 in an investment account that earns 3% per year, compounded monthly. a. Write a recursive sequence for the amount of money in her account after months.
b. Write an explicit formula for the amount of money in the account after months. c. Write an explicit formula for the amount of money in her account after years. years. d. Boris also has $1,000, but in an account that earns 3% per year, compounded yearly. Write an explicit formula for the amount of money in his account after years. years. e.
Boris claims that the equivalent monthly interest rate for his account would be the same as Danis. Use the expression you wrote in part (d) and the properties of exponents to show why Boris is incorrect. 46 FOCUS AND WITHIN COURSE COHERENCE IN HIGH SCHOOL Reflection How will the discussion on within course coherence impact what you do in school? Has your thinking about curriculum, instruction, or lesson planning changed, given the discussion on focus and within course coherence? How? What have you thought about doing to ensure equitable math instruction for all students in your class?
47 Break FOCUS AND WITHIN COURSE COHERENCE IN HIGH SCHOOL IV. Connect to Practice A focused, coherent progression of mathematics learning, with an emphasis on proficiency with key topics, should become the norm in elementary and middle school mathematics curricula. Any approach that continually revisits topics year after year without closure is to be avoided. By the term focused, the Panel means that curriculum must include (and engage with adequate depth) the most important topics underlying success in school algebra. Improvements like those suggested in this report promise immediate positive results with minimal additional cost.
National Mathematics Advisory Panel 49 FOCUS AND WITHIN COURSE COHERENCE IN HIGH SCHOOL Connect to Practice How do we know if our curriculum is focused and coherent? What are the focus criteria? What are the coherent criteria? 50 FOCUS AND WITHIN COURSE COHERENCE IN HIGH SCHOOL Connect to Practice
Focus Criteria Coherence Criteria Focus on grade-level standards. Complementary topics support and reinforce a major topic. Appropriate emphasis on major work. Supporting work integrated with major work.
51 FOCUS AND WITHIN COURSE COHERENCE IN HIGH SCHOOL Evaluate a Sample Scope and Sequence Look at the sample scope and sequence. Does the scope and sequence appropriately focus on course-level standards and focus on major content? What evidence do you have? Does the scope and sequence appropriately reflect the idea of within course coherence? What evidence do you have? Focus Criteria Focus on grade-level standards Appropriate emphasis on major work
Evidence of Focus Coherence Criteria Complementary topics support and reinforce a major topic Supporting work integrated with major work Evidence of Within Grade Coherence Ways to Improve/What I Want to Investigate Further 52
FOCUS AND WITHIN COURSE COHERENCE IN HIGH SCHOOL Evaluate Your Scope and Sequence Look at the scope and sequence or curriculum map that you brought with you today. Does the scope and sequence appropriately focus on course-level standards and focus on major content? What evidence do you have? Does the scope and sequence appropriately reflect the idea of within course coherence? What evidence do you have? Focus Criteria Focus on grade-level standards Appropriate emphasis on major work Evidence of Focus
Coherence Criteria Complementary topics support and reinforce a major topic Supporting work integrated with major work Evidence of Within Grade Coherence Ways to Improve/What I Want to Investigate Further 53 FOCUS AND WITHIN COURSE COHERENCE IN HIGH SCHOOL
Evaluate Your Scope and Sequence Further reflection: How will the focus shift impact your work with creating and/or coaching around scope and sequences? How will within grade coherence impact your work with creating and/or coaching around scope and sequences? How does attending to the shifts of focus and within grade coherence contribute to an equitable environment in your math class? 54 Feedback Please fill out the survey located here: www.standardsinstitutes.org. Click Summer 2018 on the top of the page. Click Details on the center of the page.
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