A Series of Four CIVS Instructional Facilitators, Math Content Leads, Specialists and Administrators December 1, 2011 February 29, 2012 May 16, 2012 Questions Collect at your site Send as an e-mail [email protected] or [email protected] Deadline 12:30 pm AR Frameworks vs. CCSS Witten by Arkansas Teachers for Arkansas Teachers A National Working Group and a Three Person Writing Team http://www.youtube.com/user/TheHuntInstitute p/u/dnjbwjdcPjE Progressions Content Progression Learning Progression Learning Trajectories Construct Maps Content Progressions …narrative documents describing the progression of a topic across a number of grade levels, informed both by research on children's cognitive development and by the logical structure of mathematics. http://ime.math.arizona.edu/progressions/ Learning Progressions Four Interrelated Guiding Principles of Learning Progressions (LPs) 1. LPs are developed (and refined) using available research and evidence 2. LPs have clear binding threads that articulate the essential core concepts and processes of a discipline (sometimes called the ‘big ideas’ of the discipline) 3. LPs articulate movement toward increased understanding (meaning deeper, broader, more sophisticated understanding) 4. LPs go hand-in-hand with well-designed and aligned assessments http://www.nciea.org/publications/Math_LPF_KH11.pdf Learning Trajectories If it can be established that most students, at least within a particular society, within a wide range of ability, and with access to appropriate instruction, follow a similar sequence, or even a small finite range of sequences, of levels of learning of key concepts and skills, then it should be possible not only to devise instructional sequences to guide students in the desired directions, but it should also be possible to develop standards and expectations for students’ performance that are referenced to those sequences; so that the standards, and derived assessments, report in terms that have educational meaning and relevance. http://www.cpre.org/ccii/images/stories/ccii_pdfs/learning%20trajectori es%20in%20math_ccii%20report.pdf Construct Maps describe how children come to understand Richard Lehrer - Vanderbilt Standards and Curriculum Standard is the goal. Curriculum is a plan for achieving the goal. Relationship Standards drive curriculum. Curriculum leads to meeting standards. Example 1 2.MD.8 Solve word problems involving dollar bills, quarters, dimes, nickels and pennies, using $ and ¢ symbols appropriately. This does not give the learning progression (learning trajectory/construct map) necessary to achieve this goal. Example 2 No where in the CCSS is there a standard about divisibility rules but these rules might be a part of a learning trajectory leading to a standard like: 4.NF.1 Explain why a fraction a/b is equivalent to a fraction (n × a)/(n × b)…. 7.NS.2d Convert a rational number to a decimal using long division, know that a rational number terminates in 0s or eventually repeats. Learning Progressions Formative Assessment Formative assessments should be designed to help teachers identify where a student is in a learning progression, indicating the next steps for instruction with each student and or “group” of students. (RTI) We must attend to each students cognition (thinking) at each step in the instructional sequence.