Loading in 2 Seconds...
Loading in 2 Seconds...
Introduction to the K-8 Publishers’ Criteria for the Common Core State Standards for Mathematics . October 22, 2012. Agenda. Brief overview of the shifts required by the CCSS-M Walkthrough/discussion of Publishers’ Criteria Opportunity for questions . The Three Shifts.
October 22, 2012
Brief overview of the shifts required by the CCSS-M
Walkthrough/discussion of Publishers’ Criteria
Opportunity for questions
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.
Move away from "mile wide, inch deep"curricula identifiedin TIMSS.
Learn from international comparisons.
Teach less, learn more.
“Less topic coverage can be associated withhigher scores on those topics covered becausestudents have more time to master thecontent that is taught.”
– Ginsburg et al., 2005
Mathematics topics intended at each grade by at least two-thirds of A+ countries
Mathematics topics intended at each grade by at least two-thirds of 21 U.S. states
1 Schmidt, Houang, & Cogan, “A Coherent Curriculum: The Case of Mathematics.” (2002).
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.
“The coherence and sequential nature of mathematics dictate the foundational skills that are necessary for the learning of algebra. The most important foundational skill not presently developed appears to be proficiency with fractions (including decimals, percents, and negative fractions). The teaching of fractions must be acknowledged as critically important and improved before an increase in student achievement in algebra can be expected.”
Final Report of the National Mathematics Advisory Panel (2008, p. 18)
4.NF.4. Apply and extend previous understandings of multiplication to 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.
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.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 Institutes for Research (2009, p. 13)
Example: Data Representation
Example: Geometric Measurement
3.MD, third cluster
Shift #3: Rigor: In Major Topics, Pursue Conceptual Understanding, Procedural Skill and Fluency, and Application
The CCSSM require a balance of:
Pursuit of all threes requires equal intensity in time, activities, and resources.
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)
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
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.
Available on www.corestandards.org/resources
“These standards are not intended to be new names for old ways of doing business. They are a call to take the next step.”
CCSSM, page 5
3/4 + 1/3 = ?
1/2 + 1/3 + 1/4 = ?
“All students must have the opportunity to learn and meet the same high standards if they are to access the knowledge and skills necessary in their post-school lives. The Standards should be read as allowing for the widest possible range of students to participate fully from the outset, along with appropriate accommodations to ensure maximum participation of students with special education needs.” (CCSSM, p. 4)
In any single grade, students and teachers using the materials as designed spend the large majority of their time, approximately three-quarters,* on the major work of each grade.
* Approx. 2/3 in grade 7
Materials do not assess any of the following topics before the grade level indicated.
Additionally, materials do not assess pattern problems in K-5 that do not support the focus on arithmetic, such as “find the next one” problems.
Supporting content does not detract from focus, but rather enhances focus and coherence simultaneously by engaging students in the major work of the grade.
Materials and tools reflect the balances in the Standards and help students meet the Standards’ rigorous expectations, by:
Materials are consistent with the progressions in the Standards, by (all of the following):
Materials foster coherence through connections at a single grade, where appropriate and where required by the Standards, by (all of the following):
Materials meaningfully connect content standards and practice standards.
“Designers of curricula, assessments, and professional development should all attend to the need to connect the mathematical practices to mathematical content in mathematics instruction.” (CCSSM, p. 8.)
What does it look like for materials to meaningfully connect content and practice standards? (1 of 2)
What does it look like for materials to meaningfully connect content and practice standards? (2 of 2)
Materials promote focus and coherence by connecting practice standards with content that is emphasized in the Standards.
Materials attend to the full meaning of each practice standard. A few examples (1 of 3)
Materials attend to the full meaning of each practice standard. A few examples (2 of 3)
Materials attend to the full meaning of each practice standard. A few examples (3 of 3)
Materials support the Standards’ emphasis on mathematical reasoning, by (all of the following):
What States, Districts and Teachers Can Do
Informing purchases and adoptions
Ensure that instructional resource purchasing criteria and decisions are aligned to the Publishers’ Criteria.
Working with previously purchased materials
Use the Publishers’ Criteria to review existing materials and adjust to improve alignment (remove or supplement).
Reviewing teacher-developed materials and guiding their development
Use the Publishers’ Criteria to support teachers in developing materials and ensure that teacher-developed resources are aligned.
As a tool for professional development
Share the Publishers’ Criteria with teachers and use it to support teacher understanding of the standards.
For additional resources for educators, go to achievethecore.org.