Walter Lewis

 Welcome /Outcomes /Agenda  Overview-What is the direction of Math Education?  Math CCSS  Standards for Mathematical Practice  Content Standards  Assessment/Consideration/Reflection

Max bought 2 items in a sale. One item was 10% off. One item was 20% off. Max says he saved 15% altogether. Is he right? Explain.

Max bought 2 items in a sale. One item was 10% off. One item was 20% off. Max says he saved 15% altogether. Is he right? Explain.

Pam is thirteen today. She is holding a party at which she plans to play the game 'Wrap the mummy'. In this game, players try to completely cover themselves with toilet paper. A roll of toilet paper contains 100 feet of paper, 4 inches wide. Will one toilet roll be enough to wrap a person? Describe your reasoning as fully as possible. (You will need to estimate the average size of an adult person)

Pam is thirteen today. She is holding a party at which she plans to play the game 'Wrap the mummy'. In this game, players try to completely cover themselves with toilet paper. A roll of toilet paper contains 100 feet of paper, 4 inches wide. Will one toilet roll be enough to wrap a person? Describe your reasoning as fully as possible. (You will need to estimate the average size of an adult person)

The Perils and Promises of Discovery Learning

Quality instruction Checking for Understanding California Common Core State Standards TECHNOLOGyTECHNOLOGy 21 stCENTURYLEARNINGg

What I already know about the Common Core State Standards. What I would like to learn about the Common Core State Standards. What I learned today about the Common Core State Standards. Common Core State Standards

Ensure that our students are… meeting college and career expectations with text complexity increased K-12; provided a vision of what it means to be an academically literate person in the twenty-first century; prepared to succeed in our global economy and society; and provided with rigorous content and applications of higher knowledge through higher order thinking skills.

 Internationally benchmarked  Evidence and research-based  Expectations clear to students, parents, teachers, and the general public  Costs to the state reduced  Consistent expectations for all—not dependent on a zip code

Math Standards for Mathematical Practice ELA College and Career Readiness Standards

Standards for Mathematical Practice AND Content Standards

Professor JasonPhil William ZimbaDaro McCallumPh.D.

National Council of Teachers of Mathematics 5 Process Standards Problem Solving Reasoning and Proof Communication Connections Representations NCTM (2000). Principles and Standards for School Mathematics. Reston, VA: Author.

1. Make sense of problems and persevere in solving them …start by explaining the meaning of a problem and looking for entry points to its solution 2. Reason abstractly and quantitatively …make sense of quantities and their relationships to problem situations 3. Construct viable arguments and critique the reasoning of others …understand and use stated assumptions, definitions, and previously established results in constructing arguments 4. Model with mathematics …can apply the mathematics they know to solve problems arising in everyday life, society, and the workplace

5. Use appropriate tools strategically …consider the available tools when solving a mathematical problem 6. Attend to precision …communicate precisely using clear definitions and calculate accurately and efficiently 7. Look for and make use of structure …look closely to discern a pattern or structure 8. Look for and express regularity in repeated reasoning …notice if calculations are repeated, and look for both general methods and for shortcuts

2. Reason abstractly and quantitatively. 3. Construct viable arguments and critique the reasoning of others. 4. Model with mathematics. 5. Use appropriate tools strategically. 7. Look for and make use of structure. 8. Look for and express regularity in repeated reasoning. Common Core State Standards Mathematical Practices 1. Make sense of problems and persevere in solving them. 6. Attend to precision

Take a moment to examine the first three words of each of the 8 mathematical practices…what do you notice? Mathematically Proficient Students… Briars, Diane. “Getting Started with the Common Core State Standards.” Power Point Presentation. NCSM Winter Conference, 2011.

SMP1: Explain and make conjectures… SMP2: Make sense of… SMP3: Understand and use… SMP4: Apply and interpret… SMP5: Consider and detect… SMP6: Communicate precisely to others… SMP7: Discern and recognize… SMP8: Notice and pay attention to… Briars, Diane. “Getting Started with the Common Core State Standards.” Power Point Presentation. NCSM Winter Conference, 2011.

The 8 Standards for Mathematical Practice – place an emphasis on student demonstrations of learning…  that describe the thinking processes, habits of mind, and dispositions that students need to develop.  that describe mathematical content students need to learn. Adapted from Briars, Diane. “Getting Started with the Common Core State Standards.” Power Point Presentation. NCSM Winter Conference, 2011.

K HS Counting & Cardinality Number and Operations in Base Ten Ratios and Proportional Relationships Number & Quantity Number and Operations – Fractions The Number System Operations and Algebraic Thinking Expressions and EquationsAlgebra Functions Geometry Measurement and DataStatistics and Probability Statistics & Probability Findwell, Bradford & Foughty, Zachary. “”Preparing to Implement the Common Core State Standards for Mathematics. Indiana Department of Education and Ohio Department of Education. March 30, 2011

DomainK12345 Counting and Cardinality (CC)  Operations and Algebraic Thinking (OA)  Number and Operations in Base Ten (NBT)  Measurement and Data (MD)  Geometry (G)  Number and Operations – Fractions (NF)  Domain 678 Ratios and Proportional Relationships (RP)  The Number System (NS)  Expressions and Equations (EE)  Geometry (G)  Statistics and Probability (SP)  Functions (F) 

Concept 1997 Standards CCSS Dividing fractions by fractions Grade 5 Grade 6 Concepts of mean and median to summarize data sets Grade 5 Grade 6 Operations with numbers in scientific notation Grade 7 Grade 8 Pythagorean Theorem Grade 7 Grade 8

The Goal for 8 th grade students is Algebra 1. However, there are two sets of standards for grade 8  Standards for Algebra 1-Taken from 8 th grade Common Core, high school Algebra content cluster and CA Algebra standards  8 th grade Common Core-Finalize preparation for students in high school.

The CCSS high school standards are organized in 6 conceptual categories:  Number and Quantity  Algebra  Functions  Modeling (*)  Geometry  Statistics and Probability California additions:  Advanced Placement Probability and Statistics  Calculus Modeling standards are indicated by a (*) symbol. Standards necessary to prepare for advanced courses in mathematics are indicated by a (+) symbol.

Two Regular Sequences: Traditional Pathway 2 Algebra courses,1 Geometry course, with Probability and Statistics interwoven Integrated Pathway 3 courses that attend to Algebra, Geometry, and Probability and Statistics each year Courses in higher level mathematics: Precalculus, Calculus*, Advanced Statistics, Discrete Mathematics, Advanced Quantitative Reasoning, or courses designed for career technical programs of study. Algebra II Geometry High School Algebra I Mathematics III Mathematics I Mathematics II Traditional Pathway Typical in U.S. Integrated Pathway Typical outside of U.S. Two Mathematics Pathways

Accelerated Pathway Two additional pathways (one traditional and one integrated) that compact the curriculum and require a faster pace The traditional compacted pathway has students completing the content of 7 th grade, 8 th grade, and High School Algebra I in grades 7 (Compacted 7 th Grade) and 8 (8 th Grade Algebra I), enabling students to finish Algebra II by the end of the sophomore year. The integrated compacted pathway has students completing the content of 7 th grade, 8 th grade, and Mathematics I in grades 7 (Compacted 7 th Grade) and 8 (8 th Grade Mathematics I), enabling them to complete Math III by the end of the sophomore year. Both prepare students for Precalculus in their junior year and Calculus in their senior year

Briars, Diane. “Getting Started with the Common Core State Standards.” Power Point Presentation. NCSM Winter Conference, 2011

How to Read the Standards

Geometry Conceptual Category Example

Assessments will begin in 2014 California has recently signed on with SMARTER Balanced Assessment Consortium Assessments will include: Computer Adaptive Assessments (interim & summative) Performance Assessments (interim & summative) Selected Response Constructed Response Both Two-hour and Extended Performance Assessments

 3 Assessments Each Year  Reading  Writing, Listening and Speaking, Language  Math  Optional Interim Assessments in ELA and Math

 Computer-adaptive  2 ELA and 2 Math “performance events” for Grades 3-8  Up to six math and ELA “events” for Grade 11  Grades 9 & 10 Optional  Combination of computer and human scoring

 Computer-adaptive  To be implemented based on state and district policy  Teacher-administered “performance-events”  Combination of human and computer scoring within 2 weeks  Items will be non-secure for teacher and principal analysis

 Writing Prompts  Constructed Responses  Technology-Enhanced Items  Standardized Performance Events  Single Session; administered within 12 weeks of end of the school year

The K ‐ 5 standards provide students with a solid foundation in whole numbers, addition, subtraction, multiplication, division, fractions and decimals ‐‐ which help young students build the foundation to successfully apply more demanding math concepts and procedures, and move into applications.

 In kindergarten, the standards follow successful international models and recommendations from the National Research Council’s Early Math Panel report, by focusing kindergarten work on the number core: learning how numbers correspond to quantities, and learning how to put numbers together and take them apart (the beginnings of addition and subtraction).

 The standards stress not only procedural skill but also conceptual understanding, to make sure students are learning and absorbing the critical information they need to succeed at higher levels ‐ rather than the current practices by which many students learn enough to get by on the next test, but forget it shortly thereafter, only to review again the following year.

 Having built a strong foundation K ‐ 5, students can do hands on learning in geometry, algebra and probability and statistics. Students who have completed 7th grade and mastered the content and skills through the 7th grade will be well ‐ prepared for algebra in grade 8.

 The K ‐ 5 standards build on the best state standards to provide detailed guidance to teachers on how to navigate their way through knotty topics such as fractions, negative numbers, and geometry, and do so by maintaining a continuous progression from grade to grade.

 The middle school standards are robust and 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 of understanding and ability to apply mathematics to novel situations, as college students and employees regularly do.

 The high school standards emphasize mathematical modeling, the use of mathematics and statistics to analyze empirical situations, understand them better, and improve decisions. For example, the draft standards state: “Modeling links classroom mathematics and statistics to everyday life, work, and decision ‐ making. It is the process of choosing and using appropriate mathematics and statistics to analyze empirical situations, to understand them better, and to improve decisions. Quantities and their relationships in physical, economic, public policy, social and everyday situations can be modeled using mathematical and statistical methods. When making mathematical models, technology is valuable for varying assumptions, exploring consequences, and comparing predictions with data

COMMON CORE RESOURCES California Department of Education Resources Hunt Institute CCSS Video Library SMARTER BALANCED ASSESSMENT CONSORTIUM ICOE Math BoE Page