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Focus & Within Course Coherence in High School. January 2018. 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.
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Focus & Within Course Coherence in High School January 2018
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 SCHOOLIntroduction: Who I Am • Name 1 • Name 2 Insert photo Insert photo
FOCUS IN HIGH SCHOOLIntroduction: 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
FOCUS IN HIGH SCHOOLIcebreaker 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.
FOCUS IN HIGH SCHOOLThe 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.
FOCUS IN HIGH SCHOOLThis Week “Do the math” Equity for all Connect to our practice 7
FOCUS IN HIGH SCHOOL We Will… • Go deeperon 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.
FOCUS IN HIGH SCHOOLWe Take Data Seriously • 3-minute online Daily Survey. Facilitators will address feedback the following day. • Thursday—10-minute online Knowledge Survey Post-Test. Answer key will be available.
FOCUS IN HIGH SCHOOLNorms 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.
FOCUS IN HIGH SCHOOLToday • Morning: Focus in High School • Afternoon: Focus and Within Course Coherence in High School
FOCUS IN HIGH SCHOOLMorning 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.
FOCUS IN HIGH SCHOOLMorning Agenda • Framing the Challenge • Understanding Focus • Major, Supporting, and Additional Content • Deeper Dive: Major Work
FOCUS IN HIGH SCHOOLEquity Equity is engaging in practices that meet students where they are and advance their learning by giving them what they need. It’s about fairness, not sameness. Equity ensures that all children—regardless of circumstances—are receiving high-quality and Standards-aligned instruction with access to high-quality materials and resources. We want to ensure that Standards-aligned instruction is a pathway to the equitable practices needed to close the gaps caused by systemic and systematic racism, bias, and poverty. All week, we will explore our learning through an equity lens, and we will capture those moments visibly here in our room. 15
FOCUS IN HIGH SCHOOLEquity—Envision It So You Can See It For leaders, it is important to have a clear vision of educationally equitable environments look like. Gorksi 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. 16
FOCUS IN HIGH SCHOOLII. 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
FOCUS IN HIGH SCHOOLFocus 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.
FOCUS IN HIGH SCHOOLWhy 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.
FOCUS IN HIGH SCHOOLQuick Review Conceptual Category Domain Cluster Standard “F-IF.A.1”
FOCUS IN HIGH SCHOOLFocus 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.
FOCUS IN HIGH SCHOOLIII. 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.
FOCUS IN HIGH SCHOOLFocus by Course Protocol—Major Work • 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.
“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
FOCUS IN HIGH SCHOOL IV. Digging Into Major Work Protocol: • Do the math—one task per course. • Identify the standard and why the task aligns. • Discuss the alignment with a partner at your table. • Explain how you could ensure equitable math instruction for all students with regard to the tasks you choose.
FOCUS AND WITHIN COURSE COHERENCE IN HIGH SCHOOLToday • Morning: Focus in High School • Afternoon: Focus and Within Course Coherence in High School
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).
FOCUS AND WITHIN COURSE COHERENCE IN HIGH SCHOOL Afternoon Agenda • Deeper Dive: Supporting Work • Connect to Practice: Impact of Focus • Coherence Within the Grade • Connect to Practice: Evaluate a Scope and Sequence
FOCUS AND WITHIN COURSE COHERENCE IN HIGH SCHOOLI. Digging Into Supporting Work Protocol • Identify the supporting work for your grade(s) using the focus documents. • Do the math—identify the standard. • Discuss how this standard supports major work.
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. Which bank will provide the largest balance if you plan to invest $10,000 for 10 years? For 15 years? 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. 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?
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.
FOCUS AND WITHIN COURSE COHERENCE IN HIGH SCHOOL Supporting in Algebra II A-REI.B Solve equations and inequalities in one variable.
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?
FOCUS AND WITHIN COURSE COHERENCE IN HIGH SCHOOL III. Coherence Within the Course
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: • Do the math—one task per course. • Identify the standards and why the task aligns. • Discuss why this connection is important to show to students.
FOCUS AND WITHIN COURSE COHERENCE IN HIGH SCHOOLAlgebra I A-SSE.A.2 and F-IF.B.8a
FOCUS AND WITHIN COURSE COHERENCE IN HIGH SCHOOL Geometry G-GPE.B.4 and G-GPE.B.5
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 𝑛 months. b. Write an explicit formula for the amount of money in the account after 𝑛 months. c. Write an explicit formula for the amount of money in her account after 𝑡 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 𝑡 years. e. Boris claims that the equivalent monthly interest rate for his account would be the same as Dani’s. Use the expression you wrote in part (d) and the properties of exponents to show why Boris is incorrect.
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?
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
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?
FOCUS AND WITHIN COURSE COHERENCE IN HIGH SCHOOL Connect to Practice Focus Criteria • Focus on grade-level standards. • Appropriate emphasis on major work. Coherence Criteria • Complementary topics support and reinforce a major topic. • Supporting work integrated with major work.
FOCUS AND WITHIN COURSE COHERENCE IN HIGH SCHOOL Evaluate a 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?
