6 12 Mathematics Curriculum Study Report EXECUTIVE SUMMARY Purpose of Report: To provide the School Board with information regarding the 6-12 Mathematics curriculum review and to recommend the curriculum adoption for the 2013-2014 school year. The District s middle and high school students will be introduced to a new mathematics curriculum in the fall of 2013 that meets goals of the Common Core Standards a national initiative to re-align mathematical concepts so each state teaches the same concepts in every grade. The mathematics curriculum study began in the fall of 2011as the K-12 Steering Committee reviewed Common Core standards and identified similarities and differences between these and the current state standards. The committee met throughout the 2011-12 school year to study best practices in math instruction and discuss elements that would be expected in a quality math program. The new middle school standards provide a coherent and rich preparation for high school mathematics. The curriculum is divided into six basic domains and critical areas must be mastered before students can find success at the next level. The most significant change at the middle school level is the rigor of the standards. Middle school special education students will learn the same standards while being provided additional scaffolding, explicit instruction, additional practice and frequent progress monitoring. Since the high school standards call on students to practice applying mathematical ways of thinking to real world issues and challenges in preparation for college and career readiness, additional resources will be made available to teachers to provide challenging, hands-on learning opportunities for students at all ability levels. English Language Learners will have an opportunity to learn Algebra I content over a two-year timeframe. Additional materials and professional development are available for high school special education instruction to ensure all students can achieve the same success. Administrative Recommendation to School Board: Approve the 6-12 Mathematics curriculum adoption for the 2013-2014 school year. Report Prepared by: Curriculum Services and January 28, 2013
6-12 Mathematics Curriculum Study Report Purpose of Report: To provide the School Board with information regarding the 6-12 mathematics curriculum review and to recommend curriculum adoption for the 2013-2014 school year. District Priority Area: Student Achievement Goal: All students will improve math skills to achieve high standards. Strategy: SA2.1 Identify the middle and high school math curriculum delivery models and assessment options. Explanation: The South Dakota Department of Education adopted the Mathematics Common Core State Standards (CCSS) on November 29, 2010. Cognitively demanding tasks are at the heart of the implementation of the CCSS in mathematics. The content requires teachers to think both differently and deeply about the mathematics. The expectations require a deeper understanding of the mathematics on the students part. The mathematics curriculum study began in the fall of 2011 as the K-12 Steering Committee (teachers, administrators, parents, and community members) reviewed the CCSS and identified areas of similarities and differences between these standards and the current state standards. In October, it was determined that the differences between the two sets of standards was great enough to warrant a plan to identify the gaps and a procedure to close these gaps during the 2012-13 school year in the middle school grade levels and high school content areas. The K-12 Steering Committee met regularly throughout the 2011-12 school year to study best practices in math instruction and to discuss the elements that would be expected in a quality math program. The committee then used this information to create a philosophy statement, mission statement and goal statements. While the CCSS will guide teachers in what is taught, these three statements will guide teachers in how to teach. The CCSS are meant to be fewer, clearer, and more rigorous. For instruction that will mean spending more time making sure students master what they are learning at each grade level. By understanding concepts more deeply, students will be able to solve problems using multiple approaches instead of relying on rote memorization of formulas or equations. The middle school standards provide a coherent and rich preparation for high school mathematics. The high school standards call on students to practice applying mathematical ways of thinking to real world issues and challenges; they prepare students to think and reason mathematically. The high school standards set a rigorous definition of college and career readiness, by helping students develop a depth Report Prepared by: Curriculum Services and - 1 - January 28, 2013
of understanding and ability to apply mathematics to novel situations, as college students and employees regularly do. Middle School: The new middle school mathematics curriculum is based solely on the CCSS and divided into six basic domains: Ratios and Proportional Relationships, the Number System, Expressions and Equations, Functions, Geometry, and Statistics and Probability. While each level has several clusters of standards which define what a student should know and be able to do, there are fewer domains (large groups of related standards) to master. Each domain has critical areas which must be mastered in order for the student to find success at the next level. Table A shows the domains and clusters in each grade 6 8. Table A 6 7 8 Ratios and Proportional Relationships -Ratios -Unit rates -Analyzing proportional relationships -Percent The Number System -Operations -The system of rational numbers -The system of rational numbers -The system of real numbers -The system of real numbers Expressions and Equations -Expressions -Quantitative relationships and the algebraic approach to problems -Expressions -Quantitative relationships and the algebraic approach to solving problems -Slopes of lines in the coordinate plane -Linear equations and systems Functions -Function concepts -Functional relationships between quantities Geometry -Properties of area, surface area, and volume -Congruence and simlilarity -Angles -Congruence and similarity -The Pythagorean Theorem Plane and solid geometry Statistics and Probablility -Variability and measures of center -Summarizing and describing distributions -Situations involving randomness -Random sampling to draw inferences about a population -Comparative inferences about two populations -Patterns of association in bivariate data Report Prepared by: Curriculum Services and - 2 - January 28, 2013
The middle school math committee aligned the math curriculum to the CCSS and selected resources and materials. The most significant change for middle school is the rigor of the standards. The CCSS shifted Algebra I content to Grade 8 math, and what was previously taught in Grades 6, 7, and 8 has been shifted to lower grade levels. The instructional methods expected by the CCSS, with emphasis on inquiry, problem-solving strategies, and application, align with the current middle school math program, Connected Math 2 (CMP2). Through the launch, explore, and summarize instructional model of CMP2, students investigated problems that lead to the understanding and development of higher-order thinking. Students are asked to construct viable arguments, offer proofs, and use representations in math. Therefore, CMP3, the new version of Connected Math is being recommended for adoption by the middle school math committee. In addition to the alignment to the CCSS, the updates in the new CMP3 program include more rigorous performance tasks, online, interactive, digital student pages and online access to all student and teacher materials and resources. Also included is MathXL which provides online math support through individualized math skill practice. In addition to the regular math curriculum, middle school students who are not proficient in math will receive math instruction in Power Math, a class formerly known as Directed Math. The purpose of Power Math is to provide nonproficient math students with more instruction to fill gaps in math skills. A combination of direct instruction and software support will help students improve math skills. Math Navigator and Dream Box are being piloted for the Power Math classes. Math Navigator assesses and diagnoses student math misconceptions and gaps and then provides appropriate lessons and interventions to correct misconceptions and to fill gaps in math skills. For students who need very basic, foundational math instruction in addition, subtraction, place value, and number sense, Dream Box software will be used. FASTT Math software will continue to be used, for 8-10 minutes each day, to improve the memorization of math facts. Power Math teachers and ELL math teachers will receive Add+Vantage Math Recovery (AVMR) training. AVMR training helps teachers assess students accurately and custom-fit instruction to meet the needs of students. Table B delineates the projected costs for materials, capital outlay, software, and professional development for Grades 6-8 Report Prepared by: Curriculum Services and - 3 - January 28, 2013
Table B Middle School Costs Materials Cost Class Text/Materials Company Total Cost 6 th grade math Connected Math 3 (CMP3) + Online Pearson $157,500 7 th grade math Connected Math 3 (CMP3) + Online Pearson $156,600 8 th grade math Connected Math 3 (CMP3) + Online Pearson $153,000 Power Math Math Navigator Pearson $210,000 ($35,000/year; 7 years) Math $15,000 Manipulatives AVMR Kits 4 kits $2,000 Total for Textbooks and Resources: $694,100 Calculators-Computers Number Company TI-Nspires CX Calculators 13 Class Sets Scantex Business Systems Classroom Lap Tops 142 Lap Tops Hewlett Packard Key Pads for Computers 142 Key Pads Targus Numeric Total for Calculators-Computers: $180,550 Software Software Total Cost Dream Box Learning $3,000.00 FASTT Math Licenses (Scholastic) $23,000.00 SMART Notebook Math Tools $1500.00 Total for Software: $27,500 Professional Development Costs Math Curriculum Implementation PD and Technology PD $40,000 Math Navigator PD $6,000 AVMR PD $4,000 Total for Professional Development: $50,000 Middle School Special Education The middle school special education math committee reviewed instructional materials, research, software programs, and how best to meet the needs of students with disabilities in implementing the CCSS. The subcommittee participated in vendor presentations and piloted materials. The Individuals with Disabilities Education Improvement Act Part B (IDEIA) specifically states that individuals with a disability shall have specially designed instruction to meet the unique needs. IDEIA continues to state that to provide specialized instruction schools will adapt as appropriate to the child s needs, the content, methodology, or Report Prepared by: Curriculum Services and - 4 - January 28, 2013
delivery of instruction. The intent is for students with disabilities to be provided with services that allow them to achieve equal to their same age peers without disabilities. Specialized instruction does not mean working at a lower level, slowing down the curriculum or changing the standards. Specialized instruction includes additional scaffolding, explicit instruction, additional practice and frequent progress monitoring. Specialized instruction is focused, goal driven and targeted instruction that addresses the deficit as result of their disability in the students math skills. Using this information, the subcommittee recommended an additional option for students eligible to receive services. A general education math course would be offered with a paraprofessional to support a group of students with disabilities to access instruction in the general education classroom, and this group of students would also receive an additional 40 minutes of specialized math instruction with a special education teacher. Table C shows the middle school special education math costs for materials, technology, software, and professional development. Table C Middle School Special Education Costs Materials Cost Class Text/Materials Company Total Cost Specialized Math Do the Math Now Scholastic $32,625 Cluster Math Ablenet Equals Math Ablenet $17,820 Cluster Math Ablenet Equals Pre-Alg/Pre-Geom Ablenet $5,940 Total for Textbooks and Resources: $222,024 Computers Resource Math Mobile Computer Lab (3) $30,000 Total for Computers $30,000 Software Resource Math MATH 180 Scholastic $165,639 Total for Software: $165,369 Professional Development Costs MATH 180 PD & Teacher Hourly $68,466 Ablenet PD & Teacher Hourly $4,259 AVMR PD $5,000 Total for Professional Development: $72,725 Report Prepared by: Curriculum Services and - 5 - January 28, 2013
High School: After analyzing the gaps between the content of the standards currently taught and the CCSS, the high school math committee aligned the CCSS to the curriculum. Some changes to the content included a more defined path for English Language Learners, increased availability of online content and calculators, and increased teacher resources to provide challenging hand-on learning opportunities for students of all ability levels. Table D shows the domain progression for the 9 12 CCSS. Modeling is best interpreted not as a collection of isolated topics but rather in relation to other standards. Specific modeling standards appear throughout the high school standards within the domains. Table D M O D E L I N G Conceptual Category Number and Quantity Algebra Functions Statistics and Probability Geometry High School Domains Domains The Real Number System Quantities The Complex Number System Vector and Matrix Quantities Seeing Structure in Expressions Arithmetic with Polynomials and Rational Expressions Creating Equations Reasoning with Equations and Inequalities Interpreting Functions Building Functions Linear, Quadratic, and Exponential Models Trigonometric Functions Interpreting Categorical and Quantitative Data Making Inferences and Justifying Conclusions Conditional Probability and The Rules of Probability Using Probability to Make Decisions Congruence Similarity, Right Triangles, and Trigonometry Circles Expressing Geometric Properties With Equations Geometric Measurement and Dimension Modeling With Geometry English Language Learners will have an opportunity to learn the Algebra I content over a two-year timeframe. Throughout the mathematics lessons, vocabulary and English in context will be taught along with the math standards. The integration of literacy skills will help students gain English skills while learning mathematic concepts. Report Prepared by: Curriculum Services and - 6 - January 28, 2013
The publishers of the chosen resources have online access for both students and teachers. Students will be able to log-on to the publisher s website to read their textbooks, locate practice problems, and receive help with test preparation. This environment is a hybrid of online learning and direct instruction that further prepares students for college and careers beyond high school. Along with online resources for students, teachers will also have online access to assist with lesson preparation. A library of resources can be utilized to inform their teaching and differentiate content for all their learners. Table E delineates the projected costs for materials, calculators, software, and professional development for Grades 9 12. Table E High School Costs Materials Cost Class Text/Materials Company Total Cost Algebra I & II Textbooks and online access for Algebra I and Algebra II Pearson Glencoe $310,723 Geometry Textbooks and online access Glencoe $186,794 Pearson PreCalculus Textbooks and online access Holt McDougal $121,194 AP Calculus Textbooks and online access Cengage $56,357 AP Statistics Textbooks and online access Pearson $19,260 Data Analysis Textbooks and online access Pearson $17,453 Consumer Math Textbooks and online access Cengage $37,960 ELL Mathematics Textbooks and online access Pearson $21,259 Total for Textbooks and Resources: $771,000 Calculators Number Company TI-Nspires CX Calculators 26 classroom sets Scantex Business Systems TI-Nspires Navigators 6 classroom sets Valley Business Machines Total for Calculators: $120,300 Software Software Total Cost SMART Notebook Math Tools $3,713 Help Math (7 years) $45,000 Total for Software: $48,713 Professional Development Costs New Materials and Technology In-service $17,550 Common Formative Assessment/Essential Guides $11,700 Add+Vantage Math training $3,240 Total for Professional Development: $32,490 Report Prepared by: Curriculum Services and - 7 - January 28, 2013
High School Special Education The high school special education math committee reviewed instructional materials, research on instructional strategies, and software programs. The subcommittee participated in a vendor presentation and dialogued about addressing the needs of students with disabilities with implementing the CCSS. Courses I, II, and II were structured to provide instruction that could lead to the general education Algebra I curriculum. Table F shows the high school special education costs for materials and professional development. Table F High School Special Education Costs Materials Cost Class Text/Materials Company Total Cost Resource Math I, Textbooks, Supplemental Supports Glencoe $45,669 II, III, & Consumer Math & on-line access Life Skills Math Ablenet Equals Math & Ablenet Ablenet $15,120 Equals Pre-Alg/Pre-Geo Life Skills Math Miscellaneous (Manipulative, etc.) $7,572 Total for Textbooks and Resources: $68,361 Professional Development Costs Glencoe PD (Resource Math I, II, III & Consumer Math) free with purchase Teacher Hourly (Resource) $1,339 Ablenet PD & Teacher Hourly $4,679 Total for Professional Development: $6,018 Professional Development: Professional Development is an integral part of the mathematics adoption and has occurred throughout the 2012-13 school year. Last fall the District introduced the question-based, feedback-focused elements of Project SEED, an interactive method of instruction that engages students more deeply in their math understanding. Using a unique, highly effective, Socratic teaching methodology, Project SEED experts conducted an intense two-week modeling and training sessions with six mathematics teachers. A one-week onsite follow up visit with teachers will provide additional modeling and coaching with observation opportunities continuing. The next two additional years of Project SEED includes intensive training for another twelve lead teachers. All middle school math teachers will have the opportunity to attend Report Prepared by: Curriculum Services and - 8 - January 28, 2013
professional development sessions on interactive feedback and student engagement techniques. Also, as part of the Investing in Teachers money made available by the South Dakota Department of Education, each middle school and high school mathematics teacher, special education teacher, and ELL teacher will have received five days of specific training related to the CCSS and Eight Standards of Mathematical Practice. The Standards for Mathematical Practice describe areas 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. 1. Making sense of problems and persevering in solving them 2. Reasoning abstractly and quantitatively 3. Constructing viable arguments and critiquing the reasoning of others 4. Modeling with mathematics 5. Using appropriate tools strategically 6. Attending to precision 7. Looking for and making use of structure 8. Looking for and expressing regularity in repeated reasoning Committee Participation: The thirty-six member K 12 Mathematics Steering Committee was comprised of parents and community members, classroom teachers, special education teachers, English Language Learner teachers, and building and central office administrators. The committee began the review process in September, 2011 and met eight times through the 2011-12 school year. Committee participation rate ranged between 80 100%. The middle/high school regular education and special education instructional level subcommittees (with approximately 100 total members) met once a month starting in January 2012. Costs: All costs have been budgeted for and approved in the FY13 budget. Summary: The middle school and high school instructional level subcommittees, under guidance from the K-12 Mathematics Steering Committee, reviewed the newly adopted CCSS in preparation for this study. The 6 12 math curriculum, aligned to these standards, will support teachers in developing mathematically proficient students by focusing on reasoning and deep understanding. Professional development is an important part of this adoption and has occurred throughout the 2012-13 school year and will continue with curriculum writing and new materials in-service for 2013-14. Materials are available for review by teachers, parents, and community members at the Instructional Planning Center. Administrative Recommendation to School Board: Approve the 6-12 mathematics curriculum adoption for the 2013-14 school year. Report Prepared by: Curriculum Services and - 9 - January 28, 2013
ATTACHMENT Sioux Falls School District K-12 Mathematics Study Philosophy Statement The Sioux Falls School District will challenge each student to develop and extend mathematical proficiency and literacy through a focused and coherent curriculum, highest quality mathematics teaching, and meaningful assessments that together meet the learning needs of each student. Using the Common Core Standards as a foundation, the curriculum will provide an emphasis on depth of understanding with a focus on essential concepts and processes of mathematics. In meeting the demands of a changing world, the mathematics curriculum will prepare students to think critically, problem solve, innovate, communicate, and collaborate. K-12 Mathematics Mission Statement The Sioux Falls School District will develop mathematically proficient students through a focus on reasoning and a deep understanding to prepare each student to succeed in a changing world. Goal Statements Mathematically proficient students communicate verbally, numerically, symbolically, and graphically through: Making sense of problems and persevering in solving them Reasoning abstractly and quantitatively Constructing viable arguments and critiquing the reasoning of others Modeling with mathematics Using appropriate tools strategically Attending to precision Looking for and making use of structure Looking for and expressing regularity in repeated reasoning From: Standards for Mathematical Practice from Common Core Math Standards Report Prepared by: Curriculum Services and - 11 - January 28, 2013 A-1