Focus, Coherence, and Rigor May 2013 Common Core Training for Administrators Middle Grades...
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Transcript of Focus, Coherence, and Rigor May 2013 Common Core Training for Administrators Middle Grades...
Focus, Coherence, and Rigor
May 2013
Common Core Training for Administrators
Middle Grades Mathematics
Division of Academics, Accountability, and School Improvement
Mathematical Shifts of the Common Core State Standards:
Focus, Coherence and Rigor
AGENDA
Purpose and Vision of CCSSMImplementation TimelineSix Shifts in MathematicsDesign and OrganizationInstructional Implications: Classroom Look-forsExpectations of Student PerformanceCCSSM Resources: WebsitesReflections / Questions and Answers
Community Norms
We are all learners todayWe are respectful of each otherWe welcome questionsWe share discussion timeWe turn off all electronic devices__________________
Why Common Standards?
• Previously, every state had its own set of academic standards and different expectations of student performance.
Consistency
• Common standards can help create more equal access to an excellent education.Equity
• Students need the knowledge and skills that will prepare them for college and career in our global economy. Opportunity
• These new standards are clear and coherent in order to help students, parents, and teachers understand what is expected.
Clarity
College and Career Readiness: Anchor for the Common Core
• The Common Core State Standards were back-mapped from the anchor of college and career readiness because governors and state school chiefs realized there was a significant gap between high school expectations for students and what students are expected to do in college/career.
– Among high school graduates, about only half are academically prepared for postsecondary education.
Remediation rates and costs are staggering• As much as 40% of all students entering 4-year colleges need remediation in one or more courses• As much as 63% in 2-year colleges
Degree attainment rates are disappointing•Fewer than 42% of adults aged 25-34 hold college degrees
Source: The College Completion Agenda 2010 Progress Report, The College Board
College Remediation and Graduation Rates
Are We Mathematically Ready for College and Careers?
The Common Core State Standards provide a consistent, clear understanding of what students are expected to learn, so teachers and parents know what they need to do to help them. The standards are designed to be robust and relevant to the real world, reflecting the knowledge and skills that our young people need for success in college and careers. With American students fully prepared for the future, our communities will be best positioned to compete successfully in the global economy.
Common Core State Standards Mission
F – Full Implementation of CCSSML – Full implementation of content area literacy standards including: text complexity,
quality and range in all grades (K-12)B – Blended instruction of CCSS with NGSSS; last year of NGSSS assessed on FCAT 2.0
(Grades 3-8); 4th quarter will focus on NGSSS/CCSSM grade level content gaps
Florida’s Common Core State Standards Implementation TimelineM-DCPS
Year / Grade level K 1 2 3 – 8 9 – 12
2011-2012 F L L L L L
2012-2013 F L F L L L L
2013-2014 CCSS fully implemented
F L F L F L B L B L
2014-2015 CCSS fully implemented
and assessed
F L F L F L F L F L
F L
F L
2010-2011
FCAT 2.0
2011-2012
FCAT 2.0
2012-2013
FCAT 2.0
2013-2014FCAT 2.0
2014-2015
PARCC
2015-2016
PARCC
2016-2017
PARCC
2017-2018
PARCC
2018-2019
PARCC
K 1 2 3 4 5 6
K 1 2 3 4 5 6 7
K 1 2 3 (4th 9 weeks Common
Core Lockdown)
4 5 6 7 8
1 2 3 4 (4th 9 weeks Common
Core Lockdown)
5 6 7 8 9
2 3 4 5 (4th 9 weeks Common
Core Lockdown)
6 7 8 9 10
3 4 5 6 (4th 9 weeks Common
Core Lockdown)
7 8 9 10 11
4 5 6 7 (4th 9 weeks Common
Core Lockdown)
8 9 10 11 12
5 6 7 8 (4th 9 weeks Common
Core Lockdown)
9 10 11 12
NGSSS
NGSSS
NGSSS
NGSSS
NGSSS
CCSSM
CCSSM
CCSSM
CCSSM
CCSSM
CCSSM
CCSSM
CCSSM
CCSSM
NGSSS
FOCUS deeply on what is emphasized in the StandardsCOHERENCE: Think across grades, and link to major topics within grades
RIGOR: Require- Fluency
Dual Intensity
Deep Understanding
Model/Apply
Mathematical Shifts
Shift 1: Focus
Teachers use the power of the eraser and significantly narrow and deepen the scope of how time and energy is spent in the math classroom. They do so in order to focus deeply on only the concepts that are prioritized in the standards so that students reach strong foundational knowledge and deep conceptual understanding and are able to transfer mathematical skills and understanding across concepts and grades.
Students are able to transfer mathematical skills and understanding across concepts and grades.–
Spend more time on Fewer Concepts
Achievethecore.org
What the Student Does… What the Teacher Does…• Spend more time on fewer
concepts• Extract content from the
curriculum
• Focus instructional time on priority concepts
• Give students the gift of time
Mathematics Shift 1: Focus
Spend more time on Fewer Concepts
http://www.fldoe.org/schools/ccc.asp
- Ministry of Education, Singapore
K-8 Priorities in MathPriorities in Support of Rich Instruction and Expectations of Fluency and Conceptual Understanding
K–2 Addition and subtraction, measurement using whole number quantities
3–5 Multiplication and division of whole numbers and fractions
6 Ratios and proportional reasoning; early expressions and equations
7 Ratios and proportional reasoning; arithmetic of rational numbers
8 Linear algebra
Achievethecore.org
Shift 2: Coherence
Principals and teachers carefully connect the learning within and across grades so that students can build new understanding onto foundations built in previous years.
Teachers can begin to count on deep conceptual understanding of core content and build on it. Each standard is not a new event, but an extension of previous learning. A student’s understanding of learning progressions can help them recognize if they are on track.
Keep Building on learning year after year
Achievethecore.org
What the Student Does… What the Teacher Does…• Build on knowledge from year to
year, in a coherent learning progression
• Connect the threads of critical areas across grade levels
• Connect to the way content was taught the year before and will be taught the following years
• Focus on priority progressions
Mathematics Shift 2: Coherence
Keep Building on learning year after year
http://www.fldoe.org/schools/ccc.asp
Shift 3: Fluency
Teachers help students to study algorithms as “general procedures” so they can gain insights to the structure of mathematics (e.g. organization, patterns, predictability).
Students are able to apply a variety of appropriate procedures flexibly as they solve problems.
Students are expected to have speed and accuracy with simple calculations and procedures so that they are more able to understand and manipulate more complex concepts.
Spend time Practicing
Achievethecore.org (First Component of RigorRigor)
What the Student Does… What the Teacher Does…
• Spend time practicing, with intensity, skills (in high volume)
• Push students to know basic skills at a greater level of fluency
• Focus on the listed fluencies by grade level
• Uses high quality problem sets, in high volume
Mathematics Shift 3: Fluency
Spend time Practicing
http://www.fldoe.org/schools/ccc.asp
Grade Required FluencyK Add/subtract within 5
1 Add/subtract within 10
2Add/subtract within 20
Add/subtract within 100 (pencil and paper)
3Multiply/divide within 100
Add/subtract within 1000
4 Add/subtract within 1,000,000
5 Multi-digit multiplication
6Multi-digit division
Multi-digit decimal operations
7 Solve px + q = r, p(x + q) = r
8 Solve simple 22 systems by inspection
K-8 Key Fluencies
Achievethecore.org
Shift 4: Deep Conceptual Understanding
Students demonstrate deep conceptual understanding of core math concepts by applying them to new situations as well as writing and speaking about their understanding.
Understand Math, Do Math, and Prove it
Teachers teach more than “how to get the answer;” they support students’ ability to access concepts from a number of perspectives so that students are able to see math as more than a set of mnemonics or discrete procedures.
Achievethecore.org (Second Component of RigorRigor)
What the Student Does… What the Teacher Does…
• Show mastery of material at a meaningful level
• Articulate mathematical reasoning
• Demonstrate deep conceptual understanding of priority concepts
• Explain and justify their thinking
• Create opportunities for students to understand the “answer” from a variety of access points
• Ensure that students understand WHY they are doing what they’re doing-ASK PROBING QUESTIONS
• Guide student thinking instead of telling the next step
• Continuously self reflect and build knowledge of concepts being taught
Mathematics Shift 4: Deep Understanding
Understand Math, Do Math, and Prove ithttp://www.fldoe.org/schools/ccc.asp
Shift 5: Applications (Modeling)
Students are expected to use math and choose the appropriate concept for application even when they are not prompted to do so.
Apply math in Real World situations
Teachers provide opportunities to apply math concepts in “real world” situations. Teachers in content areas outside of math ensure that students are using math to make meaning of and access content.
(Third Component of RigorRigor)
What the Student Does… What the Teacher Does…
• Utilize math in other content areas and situations, as relevant
• Choose the right math concept to solve a problem when not necessarily prompted to do so
• Apply math including areas/ courses where it is not directly required (i.e. in science)
• Provide students with real world experiences and opportunities to apply what they have learned
Mathematics Shift 5: Application (Modeling)
Apply math in Real World situations
http://www.fldoe.org/schools/ccc.asp
Shift 6: Dual Intensity
There is a balance between practice and understanding; both are occurring with intensity. Teachers create opportunities for students to participate in “drills” and make use of those skills through extended application of math concepts.
Think fast and Solve problems
Achievethecore.org (Fourth Component of RigorRigor)
What the Student Does… What the Teacher Does…• Practice math skills with an
intensity that results in fluency
• Practice math concepts with an intensity that forces application in novel situations
• Find the balance between conceptual understanding and practice within different periods or different units
• Be ambitious in demands for fluency and practice, as well as the range of application
Mathematics Shift 6: Dual Intensity
Think fast and Solve problems
http://www.fldoe.org/schools/ccc.asp
Design Design and and
OrganizatioOrganizationn
Design and Organization
Standards for Mathematical Content K-8 standards presented by grade level Organized into domains that progress over several
grades Grade introductions give 2–4 focal points at each
grade level
Standards for Mathematical Practice Carry across all grade levels Describe habits of mind of a mathematically expert
student
Mathematical Practices
1. Make sense of problems and persevere in solving them
2. Reason abstractly and quantitatively
3. Construct viable arguments and critique the reasoning of others
4. Model with mathematics
5. Use appropriate tools strategically
6. Attend to precision
7. Look for and make use of structure
8. Look for and express regularity in repeated reasoning
Learning ExperiencesIt matters It matters howhow students learn students learn
• Learning mathematics is more than just learning concepts and skills. Equally important are the cognitive and metacognitive process skills. These processes are learned through carefully constructed learning experiences.
• For example, to encourage students to be inquisitive and have a deeper understanding of mathematics, the learning experiences must include carefully structured opportunities where students discover mathematical relationships and principles on their own.
Reasoning and
Explaining
Seeing Structure
and Generalizin
g
Overarching Habits of Mind of a Productive Mathematical Thinker
2. Reason abstractly and quantitatively
3. Construct viable arguments and critique the reasoning of others
Modeling and
Using Tools
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
1. Make sense of problems and persevere in solving them6. Attend to precision
Mathematically proficient students can…
explain the meaning of the problem and look for entry points to its solution
monitor and evaluate their progress and change course if necessary
use a variety of strategies to solve problems
Overarching Habits of Mind of a Productive Mathematical Thinker
MP 1: Make sense of problems and persevere in solving them.
Gather Information
Make a plan
Anticipate possible solutions
Continuously evaluate progress
Check results
Question sense of solutions
Mathematically proficient students can…
use mathematical vocabulary to communicate reasoning and formulate precise explanations
calculate accurately and efficiently and specify units of measure and labels within the context of the situation
MP 6: Attend to precision
Mathematically proficient students can…
have the ability to contextualize and decontextualize problems involving quantitative relationships:
decontextualize - to abstract a given situation and represent it symbolically and manipulate the representing symbols
contextualize - to pause as needed during the manipulation process in order to probe into the referents for the symbols involved.
Reasoning and Explaining
MP 2: Reason abstractly and quantitatively.
Mathematically proficient students can…
make a mathematical statement (conjecture) and justify it
listen, compare, and critique conjectures and statements
MP 3: Construct viable arguments and critique the reasoning of others
Mathematically proficient students can…
apply mathematics to solve problems that arise in everyday life
reflect and make revisions to improve their model as necessary
map mathematical relationships using tools such as diagrams, two-way tables, graphs, flowcharts and formulas.
Modeling and Using Tools
MP 4: Model with Mathematics.
Mathematically proficient students can…
consider the available tools when solving a problem (i.e. ruler, calculator, protractor, manipulatives, software)
use technological tools to explore and deepen their understanding of concepts
MP 5: Use appropriate tools strategically- In early grades, this might be as
simple as writing an addition equation to describe a situation.
- In middle grades, a student might apply proportional reasoning to plan a school event or analyze a problem in the community.
- In early grades, this might be as simple as writing an addition equation to describe a situation.
- In middle grades, a student might apply proportional reasoning to plan a school event or analyze a problem in the community.
Mathematically proficient students can…
look closely to determine possible patterns and structure (properties) within a problem
analyze a complex problem by breaking it down into smaller parts
Seeing Structure and Generalizing
MP 7: Look for and make use of structure
Mathematically proficient students can…
notice repeating calculations and look for efficient methods/ representations to solve a problem
generalize the process to create a shortcut which may lead to developing rules or creating a formula
MP 8: Look for and express regularity in repeated reasoning
GROUP ACTIVITY
Each group will receive:•An envelope containing 8 small cards and a handout of the listed mathematical practices.
Instructions:•Match each of the 8 small cards with its mathematical practice (using the handout of the listed mathematical practices).
Reasoning and
Explaining
Seeing Structure
and Generalizin
g
Overarching Habits of Mind of a Productive Mathematical Thinker
2. Reason abstractly and quantitatively
3. Construct viable arguments and critique the reasoning of others
Modeling and
Using Tools
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
1. Make sense of problems and persevere in solving them6. Attend to precision
Content Content Standards and Standards and ProgressionsProgressions
DomainsDomains are larger groups/categories of standards that progress across grades
ClustersClusters are groups of related standards Content standards Content standards define what students should
understand and be able to do
ClusterStandard
Domain
New Florida Coding for CCSSMNew Florida Coding for CCSSM
MACC.2.OA.1.1
MathCommon
Core
Grade Level
Domain
Cluster
MACC.7.EE.1.2
Standard
Note: In the state of Florida, Note: In the state of Florida, clustersclusters will be will be numberednumbered.
Florida Coding Scheme for Common Core State Standards
MACC.8.EE.3.7• Identify the cluster• Identify the grade level• Identify the standard• Identify the domain• Find the standard in your CCSSM binder
Common CoreProgressions
• The Standards are designed around coherent coherent progressionsprogressions from grade to grade.
• Teachers carefully connect the learning across gradesacross grades so that students can build new understanding onto foundations built in previous years.
• Each standard is not a new event, but an Each standard is not a new event, but an extension to previous learning.extension to previous learning.
Think across grades and link to major topics within gradesThink across grades and link to major topics within grades
6
3Understand that shapes in different categories may share attributes.
6Find the area of right triangles, other triangles, special quadrilaterals, and polygons.
Geometry
Progression- Activity
In your groups, use the geometry progression handout to identify the grade level corresponding to each bullet.
HS
6
3Understand that shapes in different categories may share attributes.
6Find the area of right triangles, other triangles, special quadrilaterals, and polygons.
KCorrectly name shapes regardless of their orientations and overall size.
1Distinguish between defining attributes versus non defining attributes .‐
2Recognize and draw shapes having special attributes.
4Classify two-dimensional figures based on the presence or absence of parallel and perpendicular lines.
5Understand that attributes belonging to a category of two dimensional figures also belong to all ‐subcategories of that category.
7Solve real world and mathematical problems involving area, volume and surface area.‐
8Know the formulas for the volumes of cones, cylinders, and spheres.
Geometry
Common CoreProgressions
Grades 3-5Grades 3-5
Elementary grades work with part to whole relationships in fraction form.
Grade 6Grade 6
In 6th grade, the concept of ratio is introduced, and students look at tables of equivalent ratios and their representations on a graph.
Grade 7Grade 7
In 7th grade, students focus more on the use of multiple representations to solve proportion problems, including ratio tables, graphs, and equations, with a special focus on the constant of proportionality or unit rate.
Grade 8Grade 8
Finally in 8th grade, students extend the proportional reasoning developed in 6th and 7th grade to examine linear relationships with multiple representations.
Ratio and Proportionality Grade Level Progression
PARCC Sample Items vs. FCAT 2.0 Sample Items
• Next generation assessment system
• Technology-based• Assesses at a conceptually DEEP level
The Standards & The Assessment
• Define what students should understand and be able to do in their study of mathematics
• These standards are “focused” and “coherent” (i.e., conceptually DEEP)
PARCC Assessments
WHAT
PROBLEMS WORTH DOINGMulti-step problems, conceptual questions, applications, and substantial procedures will be common, as in an excellent classroom.
BETTER STANDARDS DEMAND BETTER QUESTIONS
Instead of reusing existing items, PARCC will develop custom items to the Standards.
FOCUSPARCC assessments will focus strongly on where the Standards focus. Students will have more time to master concepts at a deeper level.
HOW
DRAG & DROP
FILL-IN RESPONSES
COMPARISONS
RADIO BUTTONS / MC
CHECK BOXES
WRITTEN RESPONSES
Transformative Formats
FOCUS
PARCC assessments will focus strongly on where the Standards focus. Students will have more time to master concepts at a deeper level.PROBLEMS WORTH DOING
Multi-step problems, conceptual questions, applications, and substantial procedures will be common, as in an excellent classroom.BETTER STANDARDS DEMAND BETTER
QUESTIONS
Instead of reusing existing items, PARCC will develop custom items to the Standards.
Overview of PARCC Mathematics Task Types
Task Type Description of Task Type
I. Tasks assessing concepts, skills and procedures
• Balance of conceptual understanding, fluency, and application• Can involve any or all mathematical practice standards• Machine scorable including innovative, computer-based formats• Will appear on the End of Year and Performance Based Assessment components
II. Tasks assessing expressing mathematical reasoning
• Each task calls for written arguments / justifications, critique of reasoning, or precision in mathematical statements (MP.3, 6).
• Can involve other mathematical practice standards• May include a mix of machine scored and hand scored responses• Included on the Performance Based Assessment component
III. Tasks assessing modeling / applications
• Each task calls for modeling/application in a real-world context or scenario (MP.4)
• Can involve other mathematical practice standards• May include a mix of machine scored and hand scored responses• Included on the Performance Based Assessment component
Design of PARCC Math Summative Assessments
• Performance Based Assessment (PBA)– Type I items (Machine-scorable)– Type II items (Mathematical Reasoning/Hand-Scored –
scoring rubrics are drafted)– Type III items (Mathematical Modeling/Hand-Scored and/or
Machine-scored - scoring rubrics are drafted)
• End-of-Year Assessment (EOY)– Type I items only (All Machine-scorable)
Grade 6 Example
Numbering / Ordering Numbers / Absolute Value
FCAT 2.0 – Grade 6
PARCC – Grade 6Part a
PARCC – Grade 6Part b
PARCC – Grade 6Part c
PARCC – Grade 6Part d
http://commoncore.dadeschools.net/
Office of Academics and Transformation
Division of Academics, Accountability, & School Improvement
Questions/Concerns:Department of Mathematics and Science
Middle Grades Mathematics1501 N.E. 2nd Avenue, Suite 326
Miami, FL 33132Office: 305-995-1939
Fax: 305-995-1991