PowerPoint Presentation

Mathematics in the Common Core

6 instructional shifts

cassandra sponsellerdirector of teaching and learning

Watch the video clip belowkey shifts in mathematics - common core

6 instructional shiftsShift 1

FocusShift 2CoherenceShift 3

Fluency

Shift 4

Deep Understanding

Shift 5

Applications

Shift 6

Dual Intensity

Watch the video clip belowa shift in focusMathematics Shift 1: FocusWhat the Student DoesWhat the Teacher DoesWhat Instructional Leaders DoSpend 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 focusPay 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 anotherBuild 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.5In 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.

5Priorities in Math

GradePriorities in Support of Rich Instruction and Expectations of Fluency and Conceptual UnderstandingK2Addition and subtraction, measurement using whole number quantities35Multiplication and division of whole numbers and fractions6Ratios and proportional reasoning; early expressions and equations7Ratios and proportional reasoning; arithmetic of rational numbers8Linear algebra6Focus on the math that matters mostFocusing 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.

6Stop here and complete the activity CC Math Instructional Shift 1 - activityMathematics Shift 2: CoherenceWhat the Student DoesWhat the Teacher DoesWhat Instructional Leaders DoBuild on knowledge from year to year, in a coherent learning progressionConnect the threads of math focus areas across grade levelsThink deeply about what youre focusing on and the ways in which those focus areas connect to the way it was taught the year before and the years afterEnsure that teachers of the same content across grade levels allow for discussion and planning to ensure for coherence/threads of main ideas

8We need to ask ourselves How does the work Im 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?8Watch the video clip below importance of coherence video clipMathematics Shift 3: FluencyWhat the Student DoesWhat the Teacher DoesWhat Instructional Leaders DoSpend time practicing, with intensity, skills (in high volume)Push students to know basic skills at a greater level of fluencyFocus on the listed fluencies by grade levelCreate high quality worksheets, problem sets, in high volumeTake on fluencies as a stand alone CC aligned activity and build school culture around them.

10Fluency 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; its not just getting to yes; its 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.10Watch the video clip below mathematics fluency: a balanced approach video clip

Key FluenciesGradeRequired FluencyKAdd/subtract within 51Add/subtract within 102Add/subtract within 20Add/subtract within 100 (pencil and paper)3Multiply/divide within 100Add/subtract within 10004Add/subtract within 1,000,0005Multi-digit multiplication6Multi-digit divisionMulti-digit decimal operations7Solve px+q=r, p(x+q)=r8Solve simple 22 systems by inspection12Make these a fun project; create contests around these fluencies12Mathematics Shift 4: Deep UnderstandingWhat the Student DoesWhat the Teacher DoesWhat Instructional Leaders DoShow, through numerous ways, mastery of material at a deep levelUse mathematical practices to demonstrate understanding of different material and conceptsAsk yourself what mastery/proficiency really looks like and meansPlan for progressions of levels of understanding Spend the time to gain the depth of the understandingBecome flexible and comfortable in own depth of content knowledgeAllow teachers to spend time developing their own content knowledgeProvide meaningful professional development on what student mastery and proficiency really should look like at every grade level by analyzing exemplar student work

13The 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 routesArticulate their mathematical reasoningBe 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 concepts13Watch the video clip below deep understandings video clip

Mathematics Shift 5: ApplicationWhat the Student DoesWhat the Teacher DoesWhat Instructional Leaders DoApply math in other content areas and situations, as relevantChoose the right math concept to solve a problem when not necessarily prompted to do soApply 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 learnedSupport science teachers about their role of math and literacy in the science classroomCreate a culture of math application across the school

15The 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.

15Watch the video clip below application video clip

Mathematics Shift 6: Dual IntensityWhat the Student DoesWhat the Teacher DoesWhat Instructional Leaders DoPractice math skills with an intensity that results in fluencyPractice math concepts with an intensity that forces application in novel situationsFind the dual intensity between understanding and practice within different periods or different unitsBe 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

17This 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.17Stop here and complete the activityCC Math Instructional Shifts 2-6 - teacher activity