WIXLIB

MONTGOMERY COUNT Y PUBLIC SCHOOLSMATHEMATICSPROGR AMfor Grades K–12 KVILLE, MARYLAND

Board of EducationMr. Christopher S. BarclayPresidentMr. Philip KauffmanVice PresidentMs. Shirley BrandmanVISIONA high-quality education isthe fundamental right of everychild. All children will receivethe respect, encouragement,and opportunities they needto build the knowledge, skills,and attitudes to be successful,contributing members of aglobal society.Dr. Judith R. DoccaMr. Michael A. DursoMrs. Patricia B. O’NeillMrs. Rebecca SmondrowskiMr. John MannesStudent MemberSchool AdministrationDr. Joshua P. StarrSuperintendent of SchoolsMr. Larry A. BowersChief Operating OfficerDr. Beth Schiavino-NarvaezDeputy Superintendent ofSchool Support and ImprovementDr. Kimberly A. StathamDeputy Superintendent ofTeaching, Learning, and Programs850 Hungerford DriveRockville, Maryland 20850www.montgomeryschoolsmd.org

MARYLANDDear Parents,In the 21st century, a deep understanding of mathematics, and the ability to applythat understanding, is more important than it has ever been. In MontgomeryCounty Public Schools (MCPS), and across the country, mathematics instruction ischanging to make sure we provide our students with the skills and knowledgethey need for success in college and the workplace.This booklet will provide you with some important information about whythese changes are needed; how we are improving math instruction; what deepunderstanding means; and how we are working to meet the needs of all studentsto ensure their success.Please take the time to go through this booklet and visit the MCPS website to findmore helpful math resources and information. If you have further questions, pleasedo not hesitate to ask your child’s teacher or school principal.Sincerely,Joshua P. Starr, Ed. D.Superintendent of Schools

W H Y I S T H E M AT H C U R R IC U LUM C HA NG I NG ?The teachers and administratorsAs MCPS staff compared the CCSS with the 2001MCPS curriculum standards, several trends becameapparent. First, it was clear that many of the CCSSare more complex and challenging. In addition, manystandards in the CCSS are located in earlier gradesthan in the previous MCPS curriculum. Both theCCSS and the 2001 MCPS curriculum standardscontain a high level of rigor and coherence. But theCCSS, like standards in many successful nations,focus on students developing deep understandingin mathematics, defined as the appropriate balanceamong conceptual understanding, procedural skill,and problem solving with an emphasis on application.Math Work GroupFocusing mainly on procedural skill can reducethe development of students’ long-term conceptualunderstanding and blunt the growth of problemsolving skills. The Math Work Group teachers madesimilar observations. They noted that students oftencame well prepared to take formulaic tests but hadof Montgomery County Public Schools (MCPS)are committed to providing each student with achallenging mathematics program. To help reachthat goal, we review our curriculum, instruction, andassessments on an ongoing basis to ensure that a highlevel of rigor is available for every student. Periodically,there are wider reviews that result in systemwideimprovements in the mathematics program. Overthe last few years, there have been three majordevelopments that have significantly impacted themathematics program.In 2008–2009, a representative group of teachers,parents, principals, community members, and centraloffice staff gathered for 18 months to review the MCPSmathematics program. Their work resulted in a numberof recommendations regarding curriculum, acceleration,system achievement targets, and professional development. Several of the key recommendations includedadopting the then-in-development Common Core StateStandards (CCSS), reviewing the impact of the CCSSon the MCPS math program and system targets,expanding professional development in mathematics,and eliminating grade-level skipping of mathematicscontent, while continuing practices that challengestudents who consistently demonstrate proficiency.Internationally Driven Common CoreState StandardsOver the last decade, the United States has consistentlyranked below 20 other nations in K–12 mathematics.The CCSS in Mathematics were developed to improvestudents’ understanding of mathematics comparedwith their international peers.A consortium of 48 states was formed in 2008 to guidedevelopment of new standards, which outline whatstudents should know and be able to do. The authors ofthe CCSS reviewed best practices internationally andconsulted content experts to create a focused, coherent,and rigorous set of standards. Maryland adopted theCCSS in June of 2010.Words in blue italic are defined on the back of this booklet.The MCPS mathematics programhas been redesigned to reflect deeperunderstanding in mathematics.difficulty when presented with rich mathematicaltasks that required use of number sense and strategicthinking. The MCPS mathematics program hasbeen redesigned to help students gain a deeperunderstanding of math and apply that understandingin a variety of ways.The Changing Definition of Collegeand Career ReadinessBeginning with students who entered Grade 9 in 2011, thecolleges and universities within the University System ofMaryland are expecting students to complete Algebra 2 ora significant mathematics course with advanced contentduring their senior year. In addition, many schools andemployers are looking for the 21st century skills suchas persistence, collaboration, and critical and creativethinking that are the focus of Curriculum 2.0.

¾¾ What is Deep Understanding in Math?Students who demonstrate a deepunderstanding of mathematics see it as more thanjust procedures to memorize and replicate ona test. To reach a deep understanding, studentslearn to work collaboratively and to expresstheir understanding in multiple ways. The CCSSStandards for Mathematical Practice (SMP),represented below, are the definition of deepunderstanding in Curriculum 2.0 mathematics.Students who have a deep understanding ofmathematics content—¡¡ make sense of problems and persevere insolving them;¡¡ reason abstractly and quantitatively;¾¾ Curriculum 2.0 MathematicsProgram GoalsThe higher expectations of theCCSS, the recommendations of the Math WorkGroup, and new definitions of college and careerreadiness helped form the four goals of the K–12Curriculum 2.0 Mathematics program:¡¡ Develop students who valuemathematics and see it asuseful to solving problems andmaking sense of the world.¡¡ Engage all students inexperiences with mathematicscontent and processes that help them reachproficiency, defined as Understanding,Computing, Applying, Reasoning, andEngaging (UCARE) in mathematics.¡¡ Ensure that all students master theknowledge, skills, and understandingnecessary to be college and career readyby graduation.¡¡ Prepare students with the desire and skillsnecessary to have the opportunity to takeAdvanced Placement or other college-levelmath courses in high school.¡¡ construct viable arguments and critique thereasoning of others;¡¡ represent real-world situations withmathematical modeling;¡¡ use appropriate tools strategically(manipulatives, calculators, etc.);¡¡ use definitions, calculations, and estimationswith the appropriate level of precision;¡¡ look for and make use of patterns andstructure; and¡¡ look for and express generalities withinmathematics.

¾¾ How Do We Measure DeepUnderstanding of Math?Many of us recall math tests inschool when we memorized procedures andappeared to understand what we learned bycompleting the procedure on a test. Tests thatmeasure the CCSS will continue to measurestudent understanding of procedures andcomputation, but also will measure problemsolving and conceptual understanding. Moreimportant, teachers will be measuring studentunderstanding from a broad spectrum ofinteractions with students, conversations, tests,projects, and observations. Students who deeplyunderstand a mathematical concept are referred toas proficient in that concept. Proficiency is definedin the five intertwined strands of UCARE.¡¡ Understanding—comprehendingconcepts, operations, and relations¡¡ Computing—carrying out procedures¡¡ Applying—formulating and solvingmathematical problems¡¡ Reasoning—using logic to explain asolution or justify why the mathematicsworks¡¡ Engaging—seeing math as useful,sensible, and doableIn addition, integration of the SMP with themathematics content will aid in representing depthof mathematical understanding. Students will needto demonstrate their understanding in multipleways so the teacher can determine if they havereached proficiency.¾¾ How Will We Ensure that AllChildren are Challenged?The deeper understanding and higherexpectations of the grade-level CCSS, and theways of measuring that deep understanding, willchallenge students and help prepare them forcollege and careers. Many students will need morethan this. For these students, MCPS developedadditional enrichment and acceleration. When astudent demonstrates consistent understandingof a mathematical concept, there are enrichmentand acceleration opportunities designed within thecurriculum that extend students’ understanding.There also will be a few students who consistentlydemonstrate a deep understanding of all themathematical concepts of their grade level, andmay need to be advanced. Beginning in Grade 4,there will be access to a compacted curriculum forstudents who demonstrate this need.