The Common Core Math Standards for Parents Parent Math Night Denise Rawding April 28, 2014
The Background of the Common Core • Result in College and Career Readiness • Based on solid research and practice evidence • Internationally benchmarked to ensure our students are globally competitive. • Fewer, higher and clearer • Allow for collaboration 2
College Math Professors Feel HS students Today are Not Prepared for College Math • 3
What The Disconnect Means for Students • Nationwide, many students in two-year and four- year colleges need remediation in math. • Remedial classes lower the odds of finishing the degree or program. • Need to set the agenda in high school math to prepare more students for postsecondary education and training. 4
If you don’t know where you are going, you’ll end up someplace • Yogi Berra else.
Shift #1: Focus Strongly where the Standards Focus • Significantly narrow the scope of content and deepen how time and energy is spent in the math classroom. • Focus deeply on what is emphasized in the standards, so that students gain strong foundations. 6
Focus • Move away from "mile wide, inch deep" curricula identified in TIMSS. • Learn from international comparisons. • Teach less, learn more. • “Less topic coverage can be associated with higher scores on those topics covered because students have more time to master the content that is taught.” – Ginsburg et al., 2005 7
Traditional U.S. Approach K 12 Number and Operations Measurement and Geometry Algebra and Functions Statistics and Probability 8
Focusing Attention Within Number and Operations Expressions Operations and Algebraic → and → Thinking Equations Number and Operations — Algebra → Base Ten → The Number System Number and Operations — → Fractions K 1 2 3 4 5 6 7 8 High School 9
Key Areas of Focus in Mathematics Focus Areas in Support of Rich Instruction and Grade Expectations of Fluency and Conceptual Understanding Addition and subtraction - concepts, skills, and problem K – 2 solving and place value Multiplication and division of whole numbers and fractions 3 – 5 – concepts, skills, and problem solving Ratios and proportional reasoning; early expressions and 6 equations Ratios and proportional reasoning; arithmetic of rational 7 numbers Linear algebra 8 10
What Better Focus Means for You and Your Child • More time spent teaching each topic • More time to learn each topic well • More time on really important ideas that keep reappearing in mathematics 11
Shift #2: Coherence: Think Across Grades, and Link to Major Topics Within Grades • Carefully connect the learning within and across grades so that students can build new understanding on foundations built in previous years. • Begin to count on solid conceptual understanding of core content and build on it. Each standard is not a new event, but an extension of previous learning. 12
CCSS 4.NF.4. Apply and extend previous understandings of multiplication to Grade 4 multiply a fraction by a whole number. 5.NF.4. Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction. Grade 5 5.NF.7. Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions. 6.NS. Apply and extend previous understandings of multiplication and division to divide fractions by fractions. Grade 6 6.NS.1. Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions, e.g., by using visual fraction models and equations to represent the problem. Informing Grades 1-6 Mathematics Standards Development: What Can Be Learned from High-Performing Hong Kong, Singapore, and Korea? American 13 Institutes for Research (2009, p. 13)
What attention to coherence brings to the classroom • A logical order of instruction • Emphasis on helping children connect new ideas or numbers to what they already know • Key ideas to help students organize what they are learning and provide a foundation for later learning. 14
Shift #3: Rigor • The CCSSM require a balance of: Solid conceptual understanding Procedural skill and fluency Application of skills in problem solving situations • Pursuit of all threes requires equal intensity in time, activities, and resources. 15
Solid Conceptual Understanding • Teach more than “how to get the answer” and instead support students’ ability to access concepts from a number of perspectives • Students are able to see math as more than a set of mnemonics or discrete procedures • Conceptual understanding supports the other aspects of rigor (fluency and application) 16
17
Fluency • The standards require speed and accuracy in calculation. • Teachers structure class time and/or homework time for students to practice core functions such as single-digit multiplication so that they are more able to understand and manipulate more complex concepts 18
Required Fluencies in K-6 Grade Standard Required Fluency K K.OA.5 Add/subtract within 5 1 1.OA.6 Add/subtract within 10 Add/subtract within 20 (know single-digit sums from 2.OA.2 2 memory) 2.NBT.5 Add/subtract within 100 Multiply/divide within 100 (know single-digit products 3.OA.7 3 from memory) 3.NBT.2 Add/subtract within 1000 4 4.NBT.4 Add/subtract within 1,000,000 5 5.NBT.5 Multi-digit multiplication Multi-digit division 6 6.NS.2,3 Multi-digit decimal operations 19
Application • Students can use appropriate concepts and procedures for application even when not prompted to do so. • Teachers provide opportunities at all grade levels for students to apply math concepts in “real world” situations, recognizing this means different things in K-5, 6-8, and HS. • Teachers in content areas outside of math, particularly science, ensure that students are using grade-level-appropriate math to make meaning of and access science content. 20
Rigor is not harder problems; It is deeper understanding • The Past • a) 106 = 1 hundred + ___tens + ___ones • b) ___ = 3 hundreds + 4 tens + 8 ones • The Future • a) 106 = ___tens + ___ones • b) True or false? 2 hundreds + 3 ones > 5 tens + 9 ones • c) Write two fractions that each equal 4. • d) Write a fraction that is greater than and less than. Hint: find equivalent 21
A Few Changes • No carrying or borrowing • Decomposing – new to many • Not rushing children to do fraction computation before they are ready • Taking time to lay a foundation for writing expressions and equations before formal algebra but giving the youngest time to really know how to work well with whole numbers 22
Standards for Mathematical Practice The Standards for Mathematical Practice describe varieties of expertise that mathematics educators at all levels should seek to develop in their students. These practices rest on important ‘ processes and proficiencies ’ with longstanding importance in mathematics education. - Common Core State Standards for Mathematics, page 6 23
Standards for Mathematical Practice • Make sense of problems and persevere in solving them. Understand the problem, find a way to attack it, and work until it is done • Reason abstractly and quantitatively. Break a problem apart and show it symbolically, with pictures, or in any way other than the standard algorithm • Construct viable arguments and critique the reasoning of others. Be able to talk about math, using mathematical language, to support or oppose the work of others • Model with mathematics. Use math to solve real-world problems, organize data, and understand the world around you. 24
Standards for Mathematical Practice • Use appropriate tools strategically. Select the appropriate math tool to use and use it correctly to solve problems • Attend to precision. Speak and solve mathematics with exactness and meticulousness. • Look for and make use of structure. Find patterns and repeated reasoning that can help solve more complex problems • Look for and express regularity in repeated reasoning. Keep an eye on the big picture while working out the details of the problem
Resources • National Council of Teachers of Mathematics – Homework Help http://www.nctm.org/resources/content.aspx?id=2147483782 • Math Education Today (NCTM) http://www.nctm.org/mathedtoday/ • A Math Teacher’s Perspective on the CCSS (video) http://vimeo.com/58268918 • Teaching and Learning Elementary Mathematics (blog) http://utahelementarymath.wordpress.com/ • Parent’s Guide to Student Success (National PTA) http://pta.org/files/Common%20Core%20State%20Standards%20Reso urces/2013%20Guide%20Bundle_082213.pdf
Recommend
More recommend
