Mathematics in the Common Core 6 instructional shifts cassandra sponseller director of teaching and learning

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6 instructional shifts Shift 1 Focus Shift 2 Coherence Shift 3 Fluency   Shift 3 Fluency Shift 4 Deep Understanding Shift 5 Applications Shift 6 Dual Intensity

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Mathematics Shift 1: Focus What the Student Does… What the Teacher Does… What Instructional Leaders Do… Spend more time thinking and working on fewer concepts. Being able to understand concepts as well as processes (algorithms). Make conscious decisions about what to excise from the curriculum and what to focus Pay more attention to high leverage content and invest the appropriate time for all students to learn before moving onto the next topic. Think about how the concepts connects to one another Build knowledge, fluency and understanding of why and how we do certain math concepts. Work with groups of math teachers to determine what content to prioritize most deeply and what content can be removed (or decrease attention). Determine the areas of intensive focus (fluency), determine where to re-think and link (apply to core understandings), sampling (expose students, but not at the same depth). Determine not only the what, but at what intensity. Give teachers enough time, with a focused body of material, to build their own depth of knowledge. In reference to the TIMMS study, there is power of the eraser and a gift of time. The Core is asking us to prioritize student and teacher time, to excise out much of what is currently being taught so that we can put an end to the mile wide, inch deep phenomenon that is American Math education and create opportunities for students to dive deeply into the central and critical math concepts. We are asking teachers to focus their time and energy so that the students are able to do the same.

Priorities in Math Grade Priorities in Support of Rich Instruction and Expectations of Fluency and Conceptual Understanding K–2 Addition and subtraction, measurement using whole number quantities 3–5 Multiplication and division of whole numbers and fractions 6 Ratios and proportional reasoning; early expressions and equations 7 Ratios and proportional reasoning; arithmetic of rational numbers 8 Linear algebra Focus on the math that matters most Focusing on far fewer topics and treat them with much better care and detail. As shown by the TIMMS study, in the high performing countries there is a relentless focus on specific areas of mathematics ie. addition and subtraction and the quantities they measure at the K-2 level. For the first time, we will model these countries by having fewer topics learned more deeply. These core masteries will lead much fuller level of understanding. In middle and high school, students with this mastery can move on to do work in data and statistics and applying their knowledge to fields such as Algebra, Trigonometry and Calculus. It will also enable them to engage in rich work in modeling multiple representation to other fields such as economics. 6

Stop here and complete the activity CC Math Instructional Shift 1 - activity

Mathematics Shift 2: Coherence What the Student Does… What the Teacher Does… What Instructional Leaders Do… Build on knowledge from year to year, in a coherent learning progression Connect the threads of math focus areas across grade levels Think deeply about what you’re focusing on and the ways in which those focus areas connect to the way it was taught the year before and the years after Ensure that teachers of the same content across grade levels allow for discussion and planning to ensure for coherence/threads of main ideas We need to ask ourselves – How does the work I’m doing affect work at the next grade level? Coherence is about the scope and sequence of those priority standards across grade bands. How does multiplication get addressed across grades 3-5? How do linear equations get handled between 8 and 9? What must students know when they arrive, what will they know when they leave a certain grade level?

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Mathematics Shift 3: Fluency What the Student Does… What the Teacher Does… What Instructional Leaders Do… Spend time practicing, with intensity, skills (in high volume) Push students to know basic skills at a greater level of fluency Focus on the listed fluencies by grade level Create high quality worksheets, problem sets, in high volume Take on fluencies as a stand alone CC aligned activity and build school culture around them. Fluency is the quick mathematical content; what you should quickly know. It should be recalled very quickly. It allows students to get to application much faster and get to deeper understanding. We need to create contests in our schools around these fluencies. This can be a fun project. Deeper understanding is a result of fluency. Students are able to articulate their mathematical reasoning, they are able to access their answers through a couple of different vantage points; it’s not just getting to yes; it’s not just getting the answer but knowing why. Students and teachers need to have a very deep understanding of the priority math concepts in order to manipulate them, articulate them, and come at them from different directions.

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Key Fluencies K Add/subtract within 5 1 Add/subtract within 10 2 Grade Required Fluency K Add/subtract within 5 1 Add/subtract within 10 2 Add/subtract within 20 Add/subtract within 100 (pencil and paper) 3 Multiply/divide within 100 Add/subtract within 1000 4 Add/subtract within 1,000,000 5 Multi-digit multiplication 6 Multi-digit division Multi-digit decimal operations 7 Solve px + q = r, p(x + q) = r 8 Solve simple 22 systems by inspection Make these a fun project; create contests around these fluencies 12

Mathematics Shift 4: Deep Understanding What the Student Does… What the Teacher Does… What Instructional Leaders Do… Show, through numerous ways, mastery of material at a deep level Use mathematical practices to demonstrate understanding of different material and concepts Ask yourself what mastery/proficiency really looks like and means Plan for progressions of levels of understanding Spend the time to gain the depth of the understanding Become flexible and comfortable in own depth of content knowledge Allow teachers to spend time developing their own content knowledge Provide meaningful professional development on what student mastery and proficiency really should look like at every grade level by analyzing exemplar student work The Common Core is built on the assumption that only through deep conceptual understanding can students build their math skills over time and arrive at college and career readiness by the time they leave high school. The assumption here is that students who have deep conceptual understanding can: Find “answers” through a number of different routes Articulate their mathematical reasoning Be fluent in the necessary baseline functions in math, so that they are able to spend their thinking and processing time unpacking mathematical facts and make meaning out of them. Rely on their teachers’ deep conceptual understanding and intimacy with the math concepts

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Mathematics Shift 5: Application What the Student Does… What the Teacher Does… What Instructional Leaders Do… Apply math in other content areas and situations, as relevant Choose the right math concept to solve a problem when not necessarily prompted to do so Apply math including areas where its not directly required (i.e. in science) Provide students with real world experiences and opportunities to apply what they have learned Support science teachers about their role of math and literacy in the science classroom Create a culture of math application across the school The Common Core demands that all students engage in real world application of math concepts. Through applications, teachers teach and measure students’ ability to determine which math is appropriate and how their reasoning should be used to solve complex problems. In college and career, students will need to solve math problems on a regular basis without being prompted to do so.

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Mathematics Shift 6: Dual Intensity What the Student Does… What the Teacher Does… What Instructional Leaders Do… Practice math skills with an intensity that results in fluency Practice math concepts with an intensity that forces application in novel situations Find the dual intensity between understanding and practice within different periods or different units Be ambitious in demands for fluency and practice, as well as the range of application Provide enough math class time for teachers to focus and spend time on both fluency and application of concepts/ideas This is an end to the false dichotomy of the “math wars.” It is really about dual intensity; the need to be able to practice and do the application. Both things are critical.

Stop here and complete the activity CC Math Instructional Shifts 2-6 - teacher activity