MathematicsAn Overview for School Level and District Level Leadership
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My purpose today is to provide you, our district and school leaders, with the tools you will need to discuss this very exciting time in Georgia mathematics with each of your stakeholder groups. We are very clear that communication is an integral factor in successful change. When stakeholders are made aware of the solid rationale upon which our decisions are founded, those same stakeholders will become ambassadors of change.
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We have a choice. We can simply defend what we have…or create
what we need.
Sixteen TrendsTheir Profound Impact on Our Future
by Gary Marx
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This quote very aptly speaks to the Georgia mathematics program in the last 26 years. We have been a part of a rapidly changing society where the workplace looks nothing like it did 25 years ago. A colleague of mine explained it so well – in the early 80’s, 20% of our students moved on to post-secondary institutions and the other 80% moved directly into the workplace. However, the workplace has undergone such drastic changes in the past 25 years, that now 83% of jobs require some form of post-secondary learning prior to employment. It has recently been determined that, in fact, the requirements to be career ready are identical to those requirements to be college ready. Certainly these changes have implications for a viable K-12 curriculum. Let’s take a quick look at mathematics in the past 25 years.
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Georgia’s Mathematics ProgramPast, Present, and Future
1986• Quality Core Curriculum (QCC) Objectives
2005• Georgia Performance Standards (GPS)
2012• Common Core Georgia Performance
Standards (CCGPS)
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In 1986, the QCCs offered objectives in which the teaching of mathematics was couched. At that time, computers were just being introduced into the educational process – often 4 or 5 apples 2Es for a mathematics faculty of 12 to 15, graphing calculators were still a dream for mathematics classrooms, and things like DNA profiling were unheard of. The QCCs, however, were clearly an improvement. Unfortunately, other than a cursory review in the early 90’s, the mathematics curriculum saw no changes for the next 20 years – all the while, technology was speeding along & changing our workplace dramatically. In 2005, the roll-out of GPS brought us into the 21st century in mathematics with an emphasis on evidence of student learning and not merely a checklist of objectives to guide teachers. Because not much had changed with regard to mathematics curriculum in 20 years, the transition was and continues to be, at times, rocky – but the transition to GPS closed the gap between career and college expectations and the mathematics that our students were learning in our K-12 program. And now we have an incredibly exciting opportunity to join at least 43 other states and the District of Columbia in our transition to Common Care Georgia Performance Standards. So what exactly is the CCSS Initiative and why is it right for Georgia students?
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Common Core State Standards
The Common Core State Standards Initiative (CCSSI) is a state-led effort coordinated by the National Governors Association (NGA) and the Council of Chief State School Officers (CCSSO).
www.corestandards.org
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It is important to note that CCSS is NOT a federal mandate – but rather a state-led effort in which Georgia has been a governing state all along the way. It is also important to understand why states even became interested in the initiative in the first place.
• Preparation: The standards are college- and career-ready. They will help prepare students with the knowledge and skills they need to succeed in education and training after high school.
• Competition: The standards are internationally benchmarked. Common standards will help ensure our students are globally competitive.
• Equity: Expectations are consistent for all – and not dependent on a student’s zip code.
• Clarity: The standards are focused, coherent, and clear. Clearer standards help students (and parents and teachers) understand what is expected of them.
• Collaboration: The standards create a foundation to work collaboratively across states and districts, pooling resources and expertise, to create curricular tools, professional development, common assessments and other materials.
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The governors and chief state school officers agreed that : 1.) existing disparate standards create confusing expectations across the states; 2.) the global competitive edge is lagging among students in the US; 3.) current workforce skills do not match 21st century workplace demands The goal of the CCSS initiative was to rectify those issues, so the priorities included: Preparation to ensure that students are both college and career ready Global competitiveness Equity for all Clarity of expectations for students, teachers, and parents Collaboration for the sharing of resources, curricular tools, and common assessments
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Common Core State Standards
Building on the strength of current state standards, the CCSS are designed to be:
• Anchored in college and career readiness
• Internationally benchmarked
• Focused, coherent, clear and rigorous
• Evidence and research based
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To summarize, the CCSS were designed to be: (read points) …but what exactly do the CCSS look like in K-12 mathematics?
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Common Core for Mathematics
Standards for Mathematical Content• K-8 grade-by-grade standards organized by domain• 9-12 high school standards organized by conceptual
categories
Standards for Mathematical Practice• Describe mathematical “habits of mind” • Offer standards for mathematical proficiency: reasoning,
problem solving, modeling, decision making, and engagement
• Connect with content standards in each grade
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The standards are categorized much as our GPS is: Content standards Process Standards The content standards are: (read points) The standards for mathematical practice: (read points) …but how do the content standards address domains in K-8?
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K- 8 Mathematics Standards
• The K-5 standards provide students with a solid foundation in whole numbers, addition, subtraction, multiplication, division, fractions and decimals.
• The 6-8 standards describe robust learning in geometry, algebra, and probability and statistics.
• Modeled after the focus of standards from high-performing nations, the standards for grades 7 and 8 include significant algebra and geometry content.
• Students who have completed 7th grade and mastered the content and skills will be prepared for algebra in 8th grade or after.
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Note: please emphasize the text presented in italics on the slide. The high school mathematics standards…
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High School Mathematics Standards
• Call on students to practice applying mathematical ways of thinking to real world issues and challenges
• Require students to develop a depth of understanding and ability to apply mathematics to novel situations, as college students and employees regularly are called to do
• Emphasize mathematical modeling, the use of mathematics and statistics to analyze empirical situations, understand them better, and improve decisions
• Identify the mathematics that all students should study in order to be college and career ready.
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Note: Again, please emphasize the text in italics. The high school standards are grouped by conceptual categories (number and quantity, functions, algebra, geometry, modeling, and statistics and probability) and are not designed to suggest an appropriate delivery system nor are they divided into specific courses. However, Achieve, who has worked in partnership with the CCSS writers, has provided us with two model delivery systems and has suggested flexibility at the course level in terms of standards addressed.
Model Course Pathways for Mathematics
Pathway ATraditional in U.S.
Geometry
Algebra I
Courses in higher level mathematics: Precalculus, Calculus (upon completion of Precalculus), Advanced Statistics, Discrete Mathematics, Advanced Quantitative Reasoning, or other
courses to be designed at a later date, such as additional career technical courses.
Pathway BIntegrated approach
Mathematics II
Mathematics I
Algebra II Mathematics III
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Please note that the first course in Pathway A is not consistent with our QCC Algebra I course. The standards suggest the same depth and rigor of our current GPS Mathematics I and GPS Algebra courses. While Achieve and the CCSS writers have not designed appropriate 4th mathematics course options, we have addressed appropriate options to include: Mathematics IV Pre-Calculus AP Calculus AB & BC AP Statistics Multivariable Calculus History of Mathematics Advanced Mathematical Decision Making Mathematics of Industry and Government Mathematics of Finance So why is this transition to CCSS right for Georgia?
• Previous work with the GPS has prepared Georgia for the implementation of the CCSS.
• Prior teacher and administrator GPS training ensures a smooth transition.
• Although some content may be in different grade levels in the CCSS, all of the standards are addressed in the GPS.
• CCSS expectations are consistent with a single/high-rigor diploma requirement for all students.
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Why are the Common Core State Standards for Mathematics right for Georgia?
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Although the points mentioned earlier would enhance Georgia’s mathematics program, how will this initiative blend with what we are already doing with GPS? (read points listed on slide) –and how does our GPS curriculum fare in terms of CCSS curriculum?
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Thomas Fordham InstituteGPS and CCSS in 2010
Georgia: Grade A-Clarity and Specificity 3/3Content and Rigor 6/7
Total GPS Score 9/10Georgia is one of eight states receiving at least 9/10
points.CCSS: Grade A-Clarity and Specificity 2/3Content and Rigor 7/7Total CCSS Score 9/10
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Note that Georgia is only 1 of eight states to earn 9 or more points out of a possible 10 points; that the GPS curriculum and CCSS curriculum both were awarded a grade of A-; and that while Georgia earned 1 more point than CCSS in clarity, CCSS earned an additional point in rigor. So exactly how much will change when we implement CCSS?
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What about the alignmentof CCSS with GPS?
90%
10%
What percentage of Georgia's mathematics standards appear in the Common Core?
Matched State Standards
Unmatched State Standards
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It is prudent to recall that while our GPS curriculum indicates a 90%+ alignment with CCSS, some standards will shift from one grade level to another and the match between GPS and CCSS is not always exact. So what exactly did our adoption mean to our stakeholders?
• Georgia adopted CCSS when our the standards authorizing body – the State Board of Education -took formal action in July, 2010, to adopt and implement the Common Core State Standards
• 100% of the Common Core K-12 mathematics standards must be implemented in Georgia within 3 years.
• We are allowed to add up to an additional 15% to the Common Core.
• We have flexibility as to how we communicate adoption relative to state standards - CCGPS.
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What does the adoption of CCSSmean to us in Georgia?
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Review points presented on slide.
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So, how exactly do we move from CCSS + GPS to arrive at CCGPS? Of course, we must first consider the non-negotiables associated with our adoption.
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What are the non-negotiables?
• 100% of the CCSS must be delivered in our curriculum.
• CCSS must be addressed at the grade level where they are assessed.
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We can address ‘pieces’ of the standards in grades and courses prior to the assessment year, but must ‘put those pieces together’ in the year in which they are assessed. For example, CCSS does not assess money standards until 2nd grade. However, our mathematics educators see the wisdom in beginning the conceptual development of money as early as kindergarten. Another example…while 6th graders are asked to determine the Least Common Denominator and Greatest Common Factor, prior discussions surrounding the connections between prime factorizations and equivalent fractions are certainly appropriate in 4th and 5th grade classrooms. Our adoption requires implementation in three years. So what exactly are we doing to prepare for our implementation?
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How are we preparing for CCGPS implementation?
• State Mathematics Team drafted initial alignment documents for each grade level; webinars and face-to-face sessions focused on the alignment; Educators across the state submitted feedback regarding the alignment
• Precision Review Teams were convened to review feedback and make recommendations regarding alignment issues
• The recommendations of the precision review teams were vetted by the RESA Mathematics Mentors and the K-12 Advisory Council for final approval
• District and School Level Leaders will be apprised of the decisions in spring/summer of 2011
• Professional learning for all Mathematics Educators will be the number one priority in school year 2011-2012.
• All K-12 Mathematics Classrooms will implement CCGPS in 2012-2013.
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The fact that the CCSS and GPS offered a close, but not exact, match suggested that we dedicate the 2010-2011 school year to mathematics educator awareness and to providing teachers with as many details as possible regarding the differences. We recognized the importance of offering our school and district level leadership an increasing awareness of the process prior to teacher professional learning sessions as you are the change agents in your schools and districts. You can view our progress in a timeline format…
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Mathematics CCGPS Timeline
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Please note that your professional learning pre-empts any professional learning for your teachers – that was quite purposeful. Notice that we have dedicated school year 2011-2012 to professional learning for teachers and to resource development. We will need your support to ensure that every teacher in Georgia takes advantage of the information and professional learning sessions next year. We are committed to speaking directly to every mathematics teacher at every grade level, but that will require your support and buy-in of the professional learning process. We need you to explain to your teachers that the professional learning opportunities are critical to the success of the transition and that their participation is required at each juncture. We will begin with an orientation session for every Georgia mathematics teacher. In subsequent grade level/course sessions teachers will dissect the CCGPS curriculum specific to their grade or course. In that second session, teachers will become astutely familiar with the exact matches of GPS and CCGPS standards and will scrutinize the specific contrasts between the standards as well. Let me show you an example of the document your teachers will examine at the grade level/course session.
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SAMPLE: CCSS + GPS = CCGPS
CC.6.RP.3d Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities. • Students will consider relationships between varying
quantities:
• Use proportional reasoning (a/b=c/d and y = kx) to solve problems
• Students will convert from one unit to another within one system of measurement (customary or metric) by using proportional relationships
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You are looking at a grade 6 common core standard in bold text. The code offers teachers both a cluster standard acronym, a standard number and element letter. (Read the CCSS text). Georgia teachers might not be comfortable with the language of the common core standard – which is why mathematics educators across our state have committed to many hours of effort to offer the descriptors you see below the common core standards. The descriptors connect the CCSS to our current GPS. The descriptors are frequently exact GPS standards or some part of the standard – they are all written in the recognizable language of GPS and will provide teachers with the explanation and definition they will need to fully understand the specifics of what they will need to teach. Note: In the transition year 2012-2013, standards that have shifted to a lower grade will be addressed in both grades. What about assessment in this transition period?
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How are we preparing for CCGPS assessment?
• Curriculum has been invited to the initial meetings of the design and development of the CCSS assessments through the PARCC Consortium – Georgia is a governing member of the 26 state collaborative.
• We have been assured by our assessment division that curriculum will continue to drive assessment.
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Review the first bullet. PARCC has begun its work with a focus on K-8 assessment systems. Their plans are to offer a series of summative assessments administered throughout the year, intended to focus instruction throughout the year on critical skills and concepts, and to allow for mid-year correction. The first and second quarter assessments will require that students complete one to three tasks; the third quarter assessment will require students to apply key mathematical concepts and processes to multistep problems; the end-of year comprehensive assessment will sample all of the grade level standards and will be composed of 40-65 questions. In consultation with higher education faculty, PARCC is looking into the best approach for the high school assessments. It is considering building the high school assessments into modules so that they can be assembled into end of course assessments for either a discrete or integrated format. The timeline indicates that the first Common Core Assessment will be administered in school year 2014-2015, but I know you are wondering what happens in the preceding years as we will begin our transition in 2012-2013. (Read bullet 2). So, what is happening next year – I know that you will want to keep your faculty abreast of the transition maybe even during pre-planning…
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CCGPS Precision ReviewStatus Report
• School year 2011-2012 will be focused on professional learning for K-12 mathematics educators.
• The mathematics team has coordinated with IT division representatives to develop the professional learning blueprint for both initial and ongoing professional learning opportunities.
• Race to the Top and Gates grants will target sustained and technology-enhanced professional learning and will provide the needed funding.
• Data analysis will direct decisions regarding the specific focus for professional learning.
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(Review the bullets on the slide) Educators will be provided with the curricular standards and maps at each grade level and/or course by summer 2011. Every mathematics educator will be able to participate in a fall 2011 orientation; plans are to follow up with grade level and course professional learning in the winter of 2012. We are working with IT to offer ongoing professional learning video snippets for teacher use as they progress through the course. My hope is that you will begin your conversations surrounding CCGPS in your pre-planning sessions and will devote all school and district level professional learning to this very exciting transition to CCGPS. I do want to speak directly to middle school and high school principals for a moment before we close today. We have just recently been given the go ahead, …
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Secondary CCGPS Roll Out PlanNinth Graders Tenth Graders Eleventh Graders Twelfth Graders
…to share this matrix with you. As you examine the matrix, you will realize that while we are fully implementing CCGPS in 2012-2013, we are always focused on what is right for our students. This matrix indicates that students who began their high school mathematics coursework in GPS will not be asked to shift to the CCGPS course pathway. In 2012-2013, only ninth graders entering high school in that year and eighth graders who are taking advantage of the accelerated pathway will participate in the CCGPS high school course pathway. Please note that students who take Accelerated Mathematics I or Mathematics I in 8th grade during the 2011-2012 school year will continue in the GPS pathway of courses.
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Leader ActionsCCGPS Mathematics Implementation Support
2011-2012 School Year
• Include a CCGPS Overview in your Pre-Planning Agenda
• Include a CCGPS Overview in your Parent, PTA, and community meetings
• Ensure that 100% of your mathematics teachers participate in the GaDOE and RESA facilitated professional learning sessions
• Make CCGPS the focus of your district level and school level professional learning
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As we close today, please take a moment to consider what you can do for your stakeholders to support readiness for the 2012-2013 implementation of CCGPS. Please remember that all stakeholders are impacted by the transition and implementation to CCGPS. (Read points listed on slide)
