1. “Common Core State Standards for Mathematics 9-12 Administrator’s Academy 1169”
Pippen Consulting
Randy and Sue Pippen

2. Warm-Up
You have three playing cards lying face up, side by side. A five is just to the right of a two, a five is just to the left of a two, a spade is just to the left of a club, and a spade is just to the right of a spade. What are two possibilities for the three cards? Be ready to discuss your thinking!

3. Introductions
Find a shoulder partner that is not in your school or district – move if you have to.
Introduce yourselves to each other:
Name, position, what you hope to learn today.
On a signal, tell the group what your partner told you.

4. What does the traditional math lesson look like?
Turn to partner and discuss
Does it look different at elementary, middle and high school?
Is this design effective? What is our evidence that it is? What is our evidence that it is not?
How long have we used this model?

5. Rate Your Knowledge
Signal your familiarity with the new Illinois State Standards for Mathematics (Common Core State Standards) by showing a signal of 1 to 5 with 1 being the lowest.

6. I D E A M O C

7. Participants will be able to:
- understand that the Common Core Math State Standards are the new Illinois State Math Standards and will be the basis for the Math State Assessments for grades 9-12;
-learn for evaluation purposes that the new Common Core Math State Standards involve content and practice standards - what mathematics is to be taught and assessed, and what instructional practices are expected to be used for grades 9-12;
-examine how grades 9-12 math instruction and assessment must change in order to teach and assess for understanding, making sense, and what to monitor through evaluation; and
-analyze the differences between the grades 9-12 scope and sequence of the old Illinois Learning Standards

8. Workshop Goals
Relate the New Common Core State Standards to the Illinois Standards and the upcoming change in State testing.
Relate the new Mathematics Practice Standards to the way instruction should look with the CCSSM.
Familiarize administrators with the instructional changes required for students to learn with depth, understanding and making sense of the mathematics.
Relate the differences in the old Illinois Math Standards and the new Illinois Math Standards (CCSSM).
Develop a plan to update staff on the key components of the Content and Practice Standards and how they will be assessed.

9. Major Ideas of the CCSSM
Fewer, higher, more focused
Benchmarked Internationally
Equal emphasis of understanding and skills
Much more specific than old Illinois Learning Standards
Emphasis on number early on, learning trajectories develop through the grades
Highly visual and connected with multiple representations of functions: graphs/verbal/symbolic/numeric

10. Major Content Differences
Emphasis on arithmetic and number patterns translating to algebra
Congruence and similarity based on transformations
Resurgence of constructions, but in a variety of ways
Algebra 1, Geometry, and Algebra 2 for all students
Modeling, modeling, modeling or “What’s it good for?”
Precalculus only for students who will take calculus
Not all students should take calculus – STEM standards (+)
A variety of fourth year courses
No longer push for more students in the 8th grade taking high school algebra

11. 8th Grade Algebra
Currently sending too many underprepared students to algebra at the 8th grade
Program may not be equivalent to high school due to time constraints of middle school, may not have a secondary-math- certified teacher
There cannot be any skipping in CCSSM
There are other ways to accelerate (p. 81 Appendix A)
Not all students need calculus, therefore do not need to accelerate at all.

12. Eighth Grade Expressions and Equations
Understand the connections between proportional relationships, lines, and linear equations.
5. Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways. For example, compare a distance-time graph to a distance-time equation to determine which of two moving objects has greater speed.
6. Use similar triangles to explain why the slope m is the same between any two distinct points on a non-vertical line in the coordinate plane; derive the equation y = mx for a line through the origin and the equation y = mx + b for a line intercepting the vertical axis at b.

13. Eighth Grade Expressions and Equations
Analyze and solve linear equations and pairs of simultaneous linear equations.
7. Solve linear equations in one variable.
a. Give examples of linear equations in one variable with one solution, infinitely many solutions, or no solutions. Show which of these possibilities is the case by successively transforming the given equation into simpler forms, until an equivalent equation of the form x = a, a = a, or a = b results (where a and b are different numbers).
b. Solve linear equations with rational number coefficients, including equations whose solutions require expanding expressions using the distributive property and collecting like terms.

14. New Assessment Design No ISAT or PSAE after 2013-2014.
May be pilot items in ISAT in
Some areas tested by current state tests will no longer be tested in new design.
NCLB has not been reauthorized nor made any adjustments for CCSS. Many states are refusing to continue with NCLB.
A waiver is to be available to states who meet the criteria.to be released in September

15. The PARCC System – Initial Design
English Language Arts and Mathematics, Grades
25%
Focused
ASSESSMENT 1
ELA
Math
50%
Focused
ASSESSMENT 2
ELA
Math
75%
Focused
ASSESSMENT 3
ELA
Math
90%
END OF YEAR
COMPREHENSIVE ASSESSMENT
PARTNERSHIP RESOURCE CENTER: Digital library of released items, formative assessments, model curriculum frameworks, curriculum resources, student and educator tutorials and practice tests, scoring training modules, and professional development materials
Focused
ASSESSMENT4
Speaking
Listening
Summative assessment for accountability
Required, but
not used tor accountability

16. Partnership for Assessment of Readiness for College and Careers (PARCC)
TALKING POINTS
PARCC is an alliance of 24 states, educating nearly 25 million students, that are working together to develop a common set of K-12 assessments in English and math anchored in what it takes to be ready for college and careers. PARCC is led by 15 governing board states (and D.C.) represented in Dark Blue.
CLICK: The chair of the governing board is Mitchell Chester, Education Commissioner of Massachusetts, and the state of Florida is serving as its fiscal agent.
CLICK: Achieve is the project manager for PARCC, essentially serving as the staff for the consortium and coordinating the work. Collectively the PARCC states educate nearly 25 million students.
Governing States will pilot and field test the assessment system components over the next three years and administer the new assessment system during the school year. Governing States will use the results from the PARCC assessments in their state accountability systems
The chief state school officers of the Governing States serve on the PARCC Governing Board and make decisions on behalf of the Partnership on major policies and operational procedures
Participating States (light blue) provide staff to serve on PARCC’s design committees, working groups, and other task forces established by the Governing Board to conduct the work necessary to design and develop PARCC’s proposed assessment system. By 2014–15, any state that remains in PARCC must commit to statewide implementation and administration of the Partnership’s assessment system Any PARCC Participating State prepared to make the commitments and take on the responsibilities of a Governing State can become one
NOTES
Leadership Team: Comprised of delegates of K-12 chiefs from Governing Board States (e.g., Assoc. Supt for Curriculum, Assessment and/or Instruction)
Technical Advisory Committee: Comprised of state/national assessment experts
Governing Board: Comprised of K-12 chiefs from Governing Board States
Operational Working Groups: Comprised of national, state, and local experts and leaders in their specific areas of expertise
ACCR: Comprised of national and state postsecondary leaders
Governing Board States Participating States

17. The PARCC Goals Create high-quality assessments
Build a pathway to college and career readiness for all students
Support educators in the classroom
Develop 21st century, technology-based assessments
Advance accountability at all levels
Create high-quality assessments that measure the full range of the CCSS AND the full range of student achievement, including the achievement of high and low performing students.

18. Priority Purposes of PARCC Assessments:
Determine whether students are college- and career-ready or on track
Assess the full range of the Common Core Standards, including standards that are difficult to measure
Measure the full range of student performance, including the performance high and low performing students
Provide data during the academic year to inform instruction, interventions and professional development
Provide data for accountability, including measures of growth
Incorporate innovative approaches throughout the system

19. Goal #1: Create High Quality Assessments
Summative Assessment Components:
Performance-Based Assessment (PBA) administered as close to the end of the school year as possible. The ELA/literacy PBA will focus on writing effectively when analyzing text. The mathematics PBA will focus on applying skills, concepts, and understandings to solve multi-step problems requiring abstract reasoning, precision, perseverance, and strategic use of tools.
End-of-Year Assessment (EOY) administered after approx. 90% of the school year. The ELA/literacy EOY will focus on reading comprehension The math EOY will be comprised of innovative, machine-scorable items
Formative Assessment Components:
Early Assessment designed to be an indicator of student knowledge and skills so that instruction, supports and professional development can be tailored to meet student needs
Mid-Year Assessment comprised of performance-based items and tasks, with an emphasis on hard-to-measure standards. After study, individual states may consider including as a summative component
Overview of two summative assessment components:
Performance-Based Assessment:
Administered as close to the end of the year as possible
Will include essays and other high-quality, complex items.
End-of-Year:
Computer-scored, but would be far from the traditional “multiple choice” tests.
There will be multistep problems and tasks that students must complete in order to find the correct answer.
Overview of formative components:
Early Assessments:
Designed to be administered close to the beginning of the year.
Will provide an early snapshot of achievement knowledge and skills so that educators can tailor instruction, supports for students, and professional development to meet students’ needs.
Mid-Year Assessment:
Designed to be administered near the middle of the school year.
Performance-based
Will focus on hard-to-measure standards in the CCSS
Teachers could score this assessment to get quick feedback on student learning relative to the CCSS.
These components are:
are formative assessments
are developed by PARCC with its grant funds
are available to all PARCC states and their local districts
are intended to be administered early and midway through the school year
however, allow for flexible administration-- they can be administered at locally determined times, including at the discretion of the classroom teacher
can be scored quickly -- some can be computer administered and scored, others can be scored by the classroom teacher -- so that teachers can have timely information that can inform instruction for their students

20. Goal #1: Create High Quality Assessments
The PARCC assessments will allow us to make important claims about students’ knowledge and skills.
In English Language Arts/Literacy, whether students:
Can Read and Comprehend Complex Literary and Informational Text
Can Write Effectively When Analyzing Text
Have attained overall proficiency in ELA/literacy
In Mathematics, whether students:
Have mastered knowledge and skills in highlighted domains (e.g. domain of highest importance for a particular grade level – number/ fractions in grade 4; proportional reasoning and ratios in grade 6)
Have attained overall proficiency in mathematics
Based on the priority purposes for the assessments, the PARCC states are designing the assessments so that they enable us to make the following claims about students:
ELA/literacy:
Students can read and comprehend complex literary and informational text
Can write effectively to sources
Have attained overall proficiency in ELA/literacy – e.g. whether they are “college- and career-ready” in ELA/literacy by the end of high school or are on-track in earlier grades.
Mathematics:
Students have mastered the knowledge & skills in highlighted domains in mathematics – these are the domains of highest importance for a particular grade level. For example, in grade 4, whether students have mastered numbers and fractions. The highlighted domain varies from grade-level to grade-level, depending on the area of focus emphasized in the CCSS.
Have attained overall proficiency in mathematics – e.g. whether they are “college- and career-ready” in mathematics by the end of high school or are on-track in earlier grades.

21. Goal #1: Create High-Quality Assessments – New Design
Flexible
Performance-Based
Assessment (PBA)
Extended tasks
Applications of concepts and skills
End-of-Year
Assessment
Innovative, computer-based items
Early Assessment
Early indicator of student knowledge and skills to inform instruction, supports, and PD
Mid-Year Assessment
Performance-based
Emphasis on hard to measure standards
Potentially summative
TALKING POINTS
Graphic depiction of the assessment system.
The PARCC assessment system will:
Better reflect the sophisticated knowledge and skills found in the English and math Common Core State Standards
Include a mix of item types (e.g., short answer, richer multiple choice, longer open response, performance-based)
Make significant use of technology
Include testing at key points throughout the year to give teachers, parents and students better information about whether students are on track or need additional support in particular areas
ELA/Literacy
Speaking
Listening
Summative assessment for accountability
Formative assessment

22. Goal #2: Build a Pathway to College and Career Readiness for All Students
K-2 formative assessment being developed, aligned to the PARCC system
Targeted interventions & supports:
12th-grade bridge courses
PD for educators
Timely student achievement data showing students, parents and educators whether ALL students are on-track to college and career readiness
College readiness score to identify who is ready for college-level coursework
K-2
3-8
High School
SUCCESS IN FIRST-YEAR, CREDIT-BEARING, POSTSECONDARY COURSEWORK
The PARCC assessment system will be aligned to the college- and career-ready, Common Core State Standards, and is being designed to challenge students, help identify when they’re not meeting the standards, and provide targeted instruction, supports and interventions to help them succeed
Students who score proficient on the assessments will know they are on track for the next steps in their education, creating a more meaningful target
In high school, results will send an early signal about whether students are ready for entry-level, non-remedial courses at higher education institutions in all 25 PARCC states
Students who are identified as not being on track, or who do not meet the college readiness score, will receive targeted supports and interventions
Higher education partners in PARCC—more than 200 institutions and systems covering nearly 1,000 campuses across the country—have committed to help develop the high school assessments and set the college-ready cut score that will be used to place incoming freshman in credit-bearing college courses
ONGOING STUDENT SUPPORTS/INTERVENTIONS

23. Goal #3: Support Educators in the Classroom
INSTRUCTIONAL TOOLS TO SUPPORT IMPLEMENTATION
PROFESSIONAL DEVELOPMENT MODULES
K-12 Educator
TALKING POINTS
The PARCC assessments will be built with the K-12 educator in mind around four different areas.
(CLICK) INSTRUCTIONAL TOOLS TO SUPPORT IMPLEMENTATION
Content frameworks
Sample assessment tasks
Model instructional units
PROFESSIONAL DEVELOPMENT MODULES
Common Assessment : PD focused on the implementation the new assessments
Common Assessment : PD focused on how to interpret and use the assessment results
TIMELY STUDENT ACHIEVEMENT DATA
Aligned performance-based assessments given throughout year
Data reports will be available, designed with teacher use in mind
EDUCATOR-LED TRAINING TO SUPPORT “PEER-TO-PEER” TRAINING
Training for cadres of K-12 educators around the instructional tools AND around training their peers to use the instructional tools
TIMELY STUDENT ACHIEVEMENT DATA
EDUCATOR-LED TRAINING TO SUPPORT “PEER-TO-PEER” TRAINING

24. Goal #4: Develop 21st Century, Technology-Based Assessments
PARCC’s assessment will be computer-based and leverage technology in a range of ways to:
Item Development
Develop innovative tasks that engage students in the assessment process
Administration
Reduce paperwork, increase security, reduce shipping/receiving & storage
Increase access to and provision of accommodations for SWDs and ELLs
Scoring
Make scoring more efficient by combining human and automated approaches
Reporting
Produce timely reports of students performance throughout the year to inform instructional, interventions, and professional development

25. Goal #4: Develop 21st Century, Technology-Based Assessments
PARCC assessments will be purposefully designed to generate valid, reliable and timely data, including measures of growth, for various accountability uses including:
School and district effectiveness
Educator effectiveness
Student placement into college-credit bearing courses
Comparisons with other state and international benchmarks
PARCC assessments will be designed for other accountability uses as states deem appropriate

26. PARCC Timeline Development phase begins
Sept. 2011
Development phase begins
Sept. 2012
First year field testing and related research and data collection begins
Sept. 2013
Second year field testing begins and related research and data collection continues
Sept. 2014
Full administration of PARCC assessments begins
Oct. 2010
Launch and design phase begins
Summer 2015
Set achievement levels, including college-ready performance levels

27. Key Challenges for PARCC
Technical Challenges
Developing an interoperable technology platform
Transitioning to a computer-based assessment system
Developing and implementing automated scoring systems and processes
Identifying effective, innovative item types
Implementation Challenges
Estimating costs over time, including long-term budgetary planning
Transitioning to the new assessments at the classroom level
Ensuring long-term sustainability
Policy Challenges
Student supports and interventions
Accountability
High school course requirements
College admissions/ placement
Perceptions about what these assessments can do
TALKING POINTS
Obviously this is a huge change for our consortium states and there certainly will be challenges. We really see these in three areas.
Technical Challenges: Addressing the technology gaps for the implementation, administration and scoring of these next generation assessments.
Implementation Challenges: We must make sure our states and districts are ready to transition to these new assessments by and that they can sustain. Obviously, the biggest concern of all states right now is the budget. That won’t change in the next few years.
Police Challenges: These assessments will require some, if not all of our states to review their policies and make adjustments. Through outreach and support we must make sure there are no “surprises.”
We will collaborate and innovate to overcome these challenges. While these are real challenge, they can be overcome.

28. Reason for New Assessment Design Change
Cost effectiveness in a difficult economy
The three summative through-course assessments could dictate the scope and sequence of the curriculum limiting local flexibility (not federal government right)
The potential that the required three through-course assessments would disrupt the instructional program on, and in preparation for, testing days

29. Intended to ensure results will be reported in categories consistent with the CCSS.
Separate scores in ELA for reading and writing as well as an overall score indicating on track to college and career readiness.
Separate score in a “highlighted domain” that reflects the CCSS’s emphasis at each grade level (e.g., fractions in grade 4, rations and proportional relationships at grade 6), as well as an overall math score indicating on track to college readiness.
Measures student growth over a full academic year or course
Provides data during the academic year to inform instruction, interventions and professional development activities.
Accessible to all students including disabled and ELL
Must be approved by the US Department of Education

30. Highlighted Domains - PARCC
Grade or
HS Category
Highlighted
Domains K CC 1 OA 2
NBT 3 4 NF 5 6
RP. EE 7
RP, NS 8
EE, G
HS-NQ RN
HS-A
SSE, REI
HS-F
IF, BF
HS-M
No separate score
HS-G
CO, GPE
HS-SP ID

31. Brain Break! Listen to directions See what it looks like
Stand up and try it

32. Comparison of Content Standards
Old Illinois Learning Standards
NCTM Standards
Common Core State Standards
Number
Number Sense
Number and Quantity
Modeling
Measurement
Algebra
Functions
Geometry
Probability and Statistics

33. Comparison of Process Standards
Old Illinois Learning Standards
NCTM Standards
Common Core State Standards
Solve Problems
Problem Solving
Model with Mathematics
Make sense of problems and persevere in solving them
Look for and express regularity in repeated reasoning
Look for and make use of structure
Working on Teams
Using Technology
Use appropriate tools strategically
Communicating
Communication
Construct viable arguments and critique the reasoning of others
Attend to precision (language)
Making Connections
Connections
Representation
Attend to precision
Reasoning and Proof
Reason abstractly and quantitatively

34. Progressions Kindergarten 1 2 3 4 5 6 7 8 HS Counting and Cardinality
Number and Quantity
Number and Operations in Base Ten
Ratios and Proportionality
Number and Operations - Fractions
The Number System
Operations and Algebraic Thinking
Expressions and Equations
Algebra
Functions
Geometry
Measurement and Data
Statistics and Probability

35. Number Goal – ILS (Old) Early Elementary Late Elementary
Middle/Junior High School
Early High School
Late High School
6.A.1a Identify whole numbers and compare them using the symbols <, >, or = and the words “less than”, “greater than”, or “equal to”, applying counting, grouping and place value concepts.
6.A.2 Compare and order whole numbers, fractions and decimals using concrete materi­als, drawings and mathematical symbols.
6.A.3 Represent fractions, decimals, per­centages, exponents and scientific notation in equivalent forms.
6.A.4 Identify and apply the associative, commutative, distributive and identity proper­ties of real numbers, including special numbers such as pi and square roots.
6.A.5 Perform addition, subtraction and multiplication of complex numbers and graph the results in the complex plane.
6.A.1b Identify and model fractions using concrete materials and pictorial representations.

36. Reason quantitatively and use units to solve problems.
N.Q.1 Use units as a way to understand problems and to guide the solution of multi- step problems; choose and interpret units consistently in formulas; choose and interpret the scale and the origin in graphs and data displays.
N.Q.2 Define appropriate quantities for the purpose of descriptive modeling.
N.Q.3 Choose a level of accuracy appropriate to limitations on measurement when reporting quantities.

37. Explain to your partner…
1a. How do you solve 3x + 1 = -14 ?
1b. Why did you do it the way you did?
Switch roles
2a. How do you graph y = ½ x -3?
2b. Why did you do it the way you did?

38. Algebra Goal - OLD ILS Early Elementary Late Elementary
Middle/Junior High School
Early High School
Late High School
8.D.1 Find the unknown numbers in whole-number addition, subtraction, multiplication and division situations.
8.D.2 Solve linear equations involving whole numbers.
8.D.3a Solve problems using numeric, graphic or symbolic representations of varia­bles, expressions, equations and inequalities.
8.D.4 Formulate and solve linear and quadratic equations and linear inequalities algebraically and investigate nonlinear inequalities using graphs, tables, calculators and computers.
8.D.5 Formulate and solve nonlinear equations and systems including problems involving inverse variation and exponential and logarithmic growth and decay.
8.D.3b Propose and solve problems using proportions, formulas and linear functions.
8.D.3c Apply properties of powers, perfect squares and square roots.

39. Understand solving equations as a process of reasoning and explain the reasoning. (CCSSM Algebra)
A.REI.1 Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method.

40. Geometry Goal – Old ILS Early Elementary Late Elementary
Middle/Junior High School
Early High School
Late High School
9.B.1a Identify and describe characteristics, similarities and differences of geometric shapes.
9.B.2 Compare geometric figures and determine their properties including parallel, perpendicular, similar, congruent and line symmetry.
9.B.3 Identify, describe, classify and compare two- and three- dimensional geometric figures and models according to their properties.
9.B.4 Recognize and apply relationships within and among geometric figures.
9.B.5 Construct and use two- and three-dimensional models of objects that have practical applications (e.g., blueprints, topo­graphical maps, scale models).
9.B.1b Sort, classify and compare familiar shapes.
9.B.1c Identify lines of symmetry in simple figures and construct symmetrical figures using various concrete materials.

41. Geometry - CCSSM
G.CO.1 Know precise definitions of angle, circle, perpendicular line, parallel line, and line segment, based on the undefined notions of point, line, distance along a line, and distance around a circular arc.
G.CO.2 Represent transformations in the plane using, e.g., transparencies and geometry software; describe transformations as functions that take points in the plane as inputs and give other points as outputs. Compare transformations that preserve distance and angle to those that do not (e.g., translation versus horizontal stretch).
G.CO.3 Given a rectangle, parallelogram, trapezoid, or regular polygon, describe the rotations and reflections that carry it onto itself.
G.CO.4 Develop definitions of rotations, reflections, and translations in terms of angles, circles, perpendicular lines, parallel lines, and line segments.
G.CO.5 Given a geometric figure and a rotation, reflection, or translation, draw the transformed figure using, e.g., graph paper, tracing paper, or geometry software. Specify a sequence of transformations that will carry a given figure onto another.

42. Why is Change Needed?
There is a train. It leaves a station an hour later than a plane flying overhead, flying in the opposite direction.
The number of the train is a 3-digit number whose tens digit is 3 more than its units digit.
The conductor of the train is half as old as the train was when the conductor was a third as old, just a third as old.
 The conductor’s niece and nephew are on the train. They head toward the club car at the back of the train to buy mixed nuts; some of the nuts are $1.79 a pound and some are $2.25 a pound.
 They have quarters, dimes and nickels in their pockets to pay for the nuts.
 The niece starts first and walks at 2 miles per hour and the nephew starts later and walks at 3 miles per hour.
 How long will it take them to get to the back of the train if they walk together?
Enuf said?

43. No Numbers Warm-up
If you know the width of a lawn mower in inches, how can you find how many square yards of lawn it cuts in running a certain number of feet?
Problems Without Figures
Gillan, 1909

44. High School – Appendix A
Traditional Path or Integrated Path
Same fifteen units – distributed by course
Illinois will have to choose one or the other to determine testing
Challenges: Materials for either path
Texts: May say they are aligned, probably not

45. Common Core State Standards
Algebra I
Mathematics I
Unit 1 – Relationships Between Quantities and Reasoning with Equations
Unit 2 – Linear and Exponential Relationships
Unit 3 – Descriptive Statistics
Unit 4 - Expressions and Equations
Unit 5 – Quadratic Functions and Modeling
Unit 1 – Relationships Between Quantities
Unit 2 – Linear and Exponential Relationships
Unit 3 – Reasoning with Equations
Unit 4 – Descriptive Statistics
Unit 5 – Congruence, Proof and Constructions
Unit 6 – Connecting Algebra and Geometry through Coordinates

46. Common Core State Standards
Geometry
Mathematics II
Unit 1 - Congruence, Proof, and Constructions
Unit 2 - Similarity, Proof and Trigonometry
Unit 3 - Extending to Three Dimensions
Unit 4 - Connecting Algebra and Geometry through Coordinates
Unit 5 - Circles with and Without Coordinates
Unit 6 - Applications of Probability
Unit 1 – Extending the Number System
Unit 2 - Quadratic Functions and Modeling
Unit 3 – Expressions and Equations
Unit 4 – Applications of Probability
Unit 5 – Similarity, Right Triangle Trigonometry and Proof
Unit 6 – Circles With and Without Coordinates

47. Common Core State Standards
Algebra II
Mathematics III
Unit 1 – Inferences and Conclusions from Data
Unit 2 – Polynomial, Rational and Radical Relationships
Unit 3 – Trigonometry of (+)General Triangles and Trigonometric Functions
Unit 4 – Mathematical Modeling
Unit 1 – Polynomial, Rational and Radical Relationships
Unit 2 – Trigonometric Functions
Unit 3 – Modeling with Functions
Unit 4 – Inferences and Conclusions from Data

48. Major Changes at the High School
More algebra at the eighth grade means a different algebra in high school, more technology for both
Geometry must be built upon grade school transformations – most books are not written that way
More Probability and Stats in all high school courses
Advanced Algebra has less content but more depth than previous courses, more technology

49. Discussion – Partner Talk
Turn to your shoulder partner and talk about what you see regarding the new and old ILS – specifically, talk about implications for instruction
Signal to start, signal to stop (about 2 minutes).
Whole Group Sharing

50. Brain Break! Listen to directions See what it looks like
Stand up and try it

51. Create the Vision of Quality Math Instruction
What is Mathematics Proficiency?
Two sources: Strands of Proficiency from Adding It Up and Mathematical Practice Standards (CCSSM)

52. Underlying Frameworks
Strands of Mathematical Proficiency
Strategic Competence
Adaptive Reasoning
Conceptual Understanding
Productive Disposition
Procedural Fluency
Some participants are likely to be unfamiliar with NRC Adding it Up. Mention that these build upon and expand NCTM Process Standards. Briefly mention inter-related nature of these proficiencies, then move to next slide that defines each of these proficiencies.
Adding It Up:Helping Children Learn Mathematics
National Research Council
NRC (2001). Adding It Up. Washington, D.C.: National Academies Press.

53. Strands of Mathematical Proficiency
Conceptual Understanding – comprehension of mathematical concepts, operations, and relations
Procedural Fluency – skill in carrying out procedures flexibly, accurately, efficiently, and appropriately
Strategic Competence – ability to formulate, represent, and solve mathematical problems
Adaptive Reasoning – capacity for logical thought, reflection, explanation, and justification
Productive Disposition – habitual inclination to see mathematics as sensible, useful, and worthwhile, coupled with a belief in diligence and one’s own efficacy.
Don’t read slide—participants can do that.
Consider doing turn and talk—how are these different from NCTM process standards.
e.g., strategic competence includes formulating problems Includes representation
Be sure to draw attention to productive disposition—since that is different than what is explicitly in NCTM Process standards and is very important for practices.

54. Standards for Mathematical Practice
In pairs, review the Standards for Mathematical Practice. Take the standards two at a time, one for each of you, then share what you read. Return to whole group to discuss. Then back to pairs, repeat.
When finished with all eight, discuss a new insight you had into the practices.
Overview Notes: Have participants divide the Standards for Mathematical Practice with a partner. Give participants time to read and think individually (no more than 5 min.) about their portion of the 8 Standards for Mathematical Practice. Remind participants they will need to summarize each of their four standards for their partner (step 2).
Once partners have had a chance to discuss the standards of practice and to consider the focus question “What implications might the standards of practice have on your classroom?” have them make notes regarding the implications they see for their classrooms, school, or mathematics program. If there is time, ask for a few thoughts to be shared with the whole group. This does not need to be a long discussion, just enough to encourage participants to begin to connect these practices to their work!
Let folks know that they will come back to this question near the end of the session.
Other session Notes:
Give participants time to review and think individually (no more than 5 min.) about the 8 Standards for Mathematical Practice. Let participants know that they will be asked to share their new insights with a partner (step 2).
Have participants select a partner and then discuss their new insights into the standards of practice. Next ask them to consider the focus question “What implications might the standards of practice have on your classroom?” have them make notes regarding the implications they see for their classrooms, school, or mathematics program. If there is time, ask for a few thoughts to be shared with the whole group. This does not need to be a long discussion, just enough to encourage participants to begin to connect these practices to their work!

55. Mathematics Practice Standards
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with Mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning

56. NCTM Vision
Are we there yet?
What will it take?

57. What Should a Math Classroom Look Like?
Brainstorming
Handout – What Should I look for in a Math Classroom?

58. Best practice instruction
LESS
MORE
Lecturing
Students passive
Value on student silence
Worksheet/seatwork
“Coverage”
Competition
Rote memorization
Tracking/pullouts
Reliance on outside tests
Experiential/hands-on
Active Learning
Student conversations
Higher order thinking
Deeper study of fewer topics
Choice for students
Student responsibility
Help within classroom
Heterogeneous grouping
Teacher’s evaluation of learning

59. On Motivation It is not something you do to others
Maximum motivation occurs when the person believes he has autonomy, mastery and purpose
Control leads to compliance, autonomy leads to engagement
Mastery is the desire to get better and better at something that matters
Choice plays into autonomy – turn homework into “homelearning”
“Now-that” rewards instead of “if-then” rewards, non- tangible are best

60. Seven Reasons Carrots and Sticks Don’t Often Work
5. They can encourage cheating, shortcuts and unethical behavior
6. They can become addictive
7. They can foster short-term thinking
From Drive, Daniel Pink
1. They can extinguish intrinsic motivation
2. They can diminish performance.
3. They can crush creativity
4. They can crowd out good behavior

61. Praise Praise effort and strategy, not intelligence
Make praise specific, not general
Praise in private, one-on-one
Offer praise only when there is a good reason for it

62. What is the Role of Curriculum?
“A curriculum is more than a collection of activities; it must be coherent, focused on important mathematics, and well articulated across the grades.” NCTM Principles and Standards for School Mathematics 2000
The curriculum is not the textbook!
NCTM Focal Points – a good elementary resource
Common Written Curriculum – Clear Objectives
Common Core State Standards

63. What is the Role of Assessment?
“Assessment should support the learning of important mathematics and furnish useful information to both teachers and students.” NCTM Principles and Standards, 2000.
Aligned to Objectives and Could be Arranged by Objectives
Common Major Assessments
Frequent Informal Assessments with Immediate Feedback
Feedback for Guiding Instruction and Goal Setting

64. Sample

65. Administrative Issues
Effective Professional development:
Develops teachers’ knowledge of math content, students and how they learn mathematics, effective instructional and assessment practices
Models examples of high-quality mathematics teaching and learning
Allows teachers to reflect on their practice and student learning in their classroom
Allows teachers to collaborate and share experience with colleagues
Connects to a comprehensive long-term plan that includes student achievement
Discussion

66. Effective Practices Video
Discussion: What is the teacher doing, what are the students doing?

67. Observing and Evaluating
Handout – During the Observation
Discussion

68. Activity to Demonstrate New Perspective on Learning
Seating people at tables
If each table can seat 8 people with three on a side and one at each end.
When tables are pushed together end to end, people can sit on each side and only at each end.
How many people can be seated at 2 tables end to end?
3 tables, end to end
5 tables, end to end
n tables, end to end

69. Focus on Meaning Emphasis on the mathematical meaning
Having students constructing their meaning
Making connections between mathematics and other subject matter areas
Building on student meanings and student understandings

70. Learning New Concepts and Skills While Solving Problems
Having students solve problems without prior or concurrent skill development.
Allowing students to explore and develop their own algorithms
Having students learn skill development through problem solving, conjecturing and verifying.
Drill on isolated skills can hinder making sense of them later.
“The joy of the task is its own reward.”

71. Teach Mathematics Right the First Time – Steve Leinwand
Students taught procedures tend to resist new ideas and appeared to apply procedures without understanding. (Kieran, 1984)
“Initial rote learning of a concept can create interference to later meaningful learning” (Pesek and Kirshner, 2000)
Based on an article in Educational Leadership,

72. Video Clip
Video Who is doing the work? What is the engagement level of the students?

73. Concrete Materials
Hands-on experiences enable students to construct their own meanings.
Teachers must be knowledgeable in the use of concrete materials.
Using the same material to teach different ideas help shorten the time it takes to see connections between mathematical ideas.
Do not limit to demonstrations.
Students must see the two-way relationship between the concrete materials and the notation used to represent it.

74. Try This One: 2x – 4 = 8
2x - 4 = 8
Add 4 to each side and remove zero pairs.
Arrange the tiles into two equal groups on both sides of the mat.
Answer?

75. Student Use of Calculators
Changes the content, methods, and skill requirements
Enables more high-level questions.
Actively involves students through asking questions, conjecturing and exploring – lots of exploring with discussion about what is happening and why
Positive effects on graphing ability, conceptual understanding of graphs, and relating graphs to other representations.
Students using graphing calculators are more flexible with strategies, have greater perseverance, and trying to understand concepts.

76. The Role of Tasks Teach through tasks instead of “telling”
Employ a variety of student thinking
Recognize and value different methods
May include manipulatives, but most of all relies on thinking and recording thinking

77. Nature of Classroom Tasks
Make mathematics problematic – you have not already taught them how
Connect with where students are – varied levels of entry
Leave behind something of mathematical value – mathematical learning

78. Role of the Teacher Select tasks with goals in mind
Share essential information
Establish classroom culture
Ideas and methods are valued
Students choose and share their methods
Mistakes are learning sites for everyone
Correctness resides in the mathematical argument

79. What Are Mathematical Tasks?
Mathematical tasks are a set of problems or a single complex problem the purpose of which is to focus students’ attention on a particular mathematical idea.

80. Why Focus on Mathematical Tasks?
Tasks form the basis for students’ opportunities to learn what mathematics is and how one does it;
Tasks influence learners by directing their attention to particular aspects of content and by specifying ways to process information;
The level and kind of thinking required by mathematical instructional tasks influences what students learn; and
Differences in the level and kind of thinking of tasks used by different teachers, schools, and districts, is a major source of inequity in students’ opportunities to learn mathematics.

81. Golden Crown Task - Sample
The King asks Archimedes if his crown is made from pure gold.
He knows that the crown is either pure gold or it may have some silver in it.
Archimedes figures out that the volume of the crown is 125 cm3 and that its mass is 1.8 kilograms.
He also knows that 1 kilogram of gold has a volume of about 50 cm3 and 1 kilogram of silver has a volume of about 100 cm3.
1. Is the crown pure gold? Explain how you know.
2. If the crown is not pure gold, then how much silver is in it?
Show all your work.

82. Five Practices Book A professional development resource
Released in April from NCTM
Aligns well with the CCSSM Mathematical Practices

83. Tasks in the Classroom Choose the task
Work it out and anticipate student methods
Conduct a classroom discussion to clarify the task, but not direct the students to a solution or method, close reading
Monitor the work and identify which groups are using which methods or new methods
Select and record which groups will present
Sequence the presentations for maximum discussion
Connect the ideas with a whole-class discussion
From the 5 Practices book

85. Where to Find Tasks
Adapt classroom problems – choose from the end of the unit before teaching the unit – make it an application problem.
Consult the Internet – see sources at the end of the PowerPoint
Focus on the math you want them to learn

86. Talk Formats
Talk to a partner
To get better participation in classroom conversations, move between three formats:
Whole-class discussion – before a task, after a task
Small-group discussion – time limit, specific directions on what they are to do/discuss/produce
Partner talk – short time limit to get more thinking when the whole-class discussion stalls out, specific directions on what they are to discuss (30 seconds)

87. Orchestrating Classroom Talk
Five productive talk moves
Revoicing (teacher)
Repeating (student)
Reasoning - Agree/disagree and why (student)
Adding on (student)
Wait time (teacher)

88. Examples Revoicing: “So you’re saying it’s an odd number?”
Repeating: “Can you repeat what he just said in your own words?”
Reasoning: “Miranda, do you agree or disagree with what Paul just said?”
Adding on: “Would someone like to add something more to this?”
Wait time: Wait beyond the time for a few students to raise their hands. Wait for the reluctant participants to think and offer an explanation. (10 seconds or more)

89. Implementing Classroom Talk
Five steps to implementing classroom talk
Set the classroom climate, respectful and supportive
Focus the talk on the mathematics
Provide for equitable participation
Explain your expectations for the new forms of talk and why talk in math is important
Try only one challenging new thing at a time

90. Video of Talk Moves
Identify talk moves in the video as the teacher launches a lesson on linear equations.
assroom-video-visits/public-lessons- comparing-linear-functions/269-comparing- linear-functions-problem-2-part- a?phpMyAdmin=NqJS1x3gaJqDM-1- 8LXtX3WJ4e8
Discussion
Second Video - from book: 6.2

91. Who’s Doing the Work? Is the teacher always the one talking?
Do students present solutions?
Do students work together?
Do students converse about mathematics with each other or with the teacher?
Are students building their own meaning or is the teacher dispensing it?

92. Changing Perspectives on Learning and Teaching
All learning, except for simple rote memorization, requires the learner to actively construct meaning
Students’ prior understanding of and thoughts about a topic or concept before instruction exert a tremendous influence on what they learn during instruction
The teacher’s primary goal is to generate a change in the learner’s cognitive structure or way of viewing and organizing the world
Because learning is a process of active construction by the learner, the teacher cannot do the work of learning
Learning in cooperation with others is an important source of motivation, support, modeling and coaching

93. Wrap-It-Up Carousel Number off by 7s
Go to the numbered poster with a marker.
Write implications for instructional leaders according to the topic at the top of the poster.
At signal, move to next poster and repeat.
Summary Discussion and Reflection

94. Write a Plan Required of the academy
Your plan should be how to disseminate the information you learned about today.
It must be submitted to Donna at the St. Clair ROE to be entered into the system for you.

95. Workshop Goals
Relate the New Common Core State Standards to the Illinois Standards and the upcoming change in State testing.
Relate the new Mathematics Practice Standards to the way instruction should look with the CCSSM.
Familiarize administrators with the instructional changes required for students to learn with depth, understanding and making sense of the mathematics.
Relate the differences in the old Illinois Math Standards and the new Illinois Math Standards (CCSSM).
Develop a plan to update staff on the key components of the Content and Practice Standards and how they will be assessed.

96. Final Thoughts What was most valuable to you today?
Contact info:
If you want a copy of this PowerPoint: %20AA.ppt

97. Task Resources www.nctm.org Illuminations www.insidemathematics.org
Navigations Books and Focus Books
Coming: illustrativemathematics.org
Coming: – Great Tasks and More (NCSM website)
- Common Core State Standards (CCSS) Mathematics Curriculum Materials Analysis Project
Challenge problems in texts
Enrichment activities – maybe
Word problems not taught yet

98. Other Resources
Five Practices for Orchestrating Productive Mathematics Discussions, Smith and Stein, NCTM,
Classroom Discussions, Using Math Talk to Help Students Learn, Chapin, Math Solutions, 2009.
Handbook of Research on Improving Student Achievement, Third Edition, Gordon Cawelti, Editor, Educational Research Service, 2004.
Common Core Standards, NGA, CCSSO, 2010
Annenberg Media Videos
Drive, The Surprising Truth about What Motivates Us, Daniel Pink, 2009.
Conferences
NCSM Annual Meeting, Philadelphia, April 2012
NCTM Annual Meeting, Philadelphia, April 2012