Hank Kepner National Council of Teachers of Mathematics, Past-President

1. Implementing Math & Science Initiatives at the Federal & State Levels: What Needs to Happen to Move Forward Hank Kepner National Council of Teachers of Mathematics, Past-President University of Wisconsin-Milwaukee Milwaukee Public Schools kepner@uwm.edu

2. Common Core State Standards for Mathematics • Standards for Mathematical Practice • K–8 Grade level standards Domains across grade levels • High School standards – “conceptual categories”

3. Features of the Common Core • Focus attention on core concepts in number and numeration & their relationships to operations with a focus on the structure of the number system; • Aggressive timelines for teaching particular concepts in elementary and middle grades; • They introduce multiple measurement systems (metric, non-standard & English) simultaneously & tie the number line directly to scales to improve students’ visualization of number relationships; • They support the articulation of some key learning trajectories in numeration and geometry; and • They remain agnostic about sequencing and organization of high school math.

4. Standards for Mathematical Practice Mathematically proficient students: • Make sense of problems and persevere in solving them • Reason abstractly and quantitatively • Construct viable arguments and critique the reasoning of others • These are measures of Student behavior!

5. Standards for Mathematical Practice Mathematically proficient students: • 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 • These are measures of Student behavior!

6. The MSP programs can play a critical role in maximizing this opportunity • To strengthen the movement towards Common Core Standards implementation • To get your innovations to move to scale to the degree to which they can tie into a broader policy agenda

7. Window of Opportunityfrom now until 2014- 2015 when assessments are put into place. • The current circumstance is unstable and ambiguous at the state level. • The standards will make sense only when we have instructional and assessment exemplars to use and analyze—the operational definitions! • Most standards do not describe depth of cognitive demand to be assessed. Caution about trivial level • Monitor and influence the assessment developments to ensure sound assessment – beyond multiple choice: • Partnership for the Assessment of Readiness for College and Careers (PARCC includes Achieve) • SMARTER Balanced Assessment Consortium

8. Recent challenges to Mathematics for All students and constraints on STEMCurrent state sanctions and district policies have led administrators to emphasize only that mathematics content which is assessed and to de-emphasize or ignore what is not assessed.

9. The result in K-8 mathematics has been a narrowing of delivered curricula, a “test-driven curriculum,” in each state that: • Has clarity and specificity (expectations defined with sufficient detail to communicate intent and applicability); • Lacks coherence (expectations for mathematics content and processes are marked by logical disconnections and inappropriate trajectories); • Lacks focus (insufficient time available to learn concepts and skills critical for understanding the expected content, in part due to re-teaching of (un)learned content). Campbell

10. Simply teaching more mathematics/science content to teachers is not the answer! Teachers not only need to know the content they teach (including notation, language and definitions),

11. Teachers also need to know what mathematics/science to access and use it when they: • Pose math/science questions, • Evaluate & support students’ explanations, • Use or choose ways of representing the math/science, • Choose, sequence & design tasks & examples, • Determine whether and how to provide explanations, • Analyze/address student misconceptions, errors, and …

12. Address Students’ Lack of Engagement Lack of engagement in learning is the greatest problem in math classrooms • How can the CCSS help us with this? • The Mathematical Practices as a way to leverage discourse • Formative Assessment or Assessment for Learning • New technologies for networking

13. Goal for STEM education • Schooling is about: modeling our world (scientifically, technologically, mathematically, and statistically), • feeling engaged and empowered, • building opportunities for expressiveness • fostering collaboration, designing and testing solutions, • encouraging active citizenry, and • being well-prepared to earn a satisfying and sufficient living.

14. Implementation of the Standards for Mathematical PracticeStandard 3Construct viable arguments & critique the reasoning of others.

15. Construct viable Arguments &Critique the reasoning of others • understand & use stated assumptions, definitions, and previously established results in constructing arguments • make conjectures and build a logical progression of statements to explore the truth of their conjectures • justify their conclusions; communicate them to others • listen to or read the arguments of others, decide whether they make sense, and ask useful questions to clarify or improve the arguments.

16. Bridge of length 2 Bridge of length 3 LengthNumber of Beams 2 3 5 10 50 n

17. Number of Beams for length n? 3 + 4(n-1) n + 2n + (n-1) 3n + (n-1) 4(n-1) + 3 4n - 1 Next = Now + 4 Start: 3

18. Construct viable Arguments &Critique the reasoning of others • understand & use stated assumptions, definitions, and previously established results in constructing arguments • make conjectures and build a logical progression of statements to explore the truth of their conjectures • justify their conclusions; communicate them to others • listen to or read the arguments of others, decide whether they make sense, and ask useful questions to clarify or improve the arguments.

19. A Challenge of Phasing in Implementation A critical area that must be addressed in state implementation plans. -- Include the mathematical practices in all aspects of implementation.

20. Phasing the Implementation Simultaneously : • new curricular development including tasks addressing Standards for Mathematical Practice, • build professional development systems that expand instructional strategies, • comprehensive assessment systems, • build technological infrastructures

21. The need to couple curriculum, classroom instruction, & assessment via the CCSS

22. A learning trajectory/progression is: …a researcher-conjectured, empirically-supported description of the ordered network of constructs a student encounters through instruction (i.e. activities, tasks, tools, forms of interaction and methods of evaluation), in order to move from informal ideas, through successive refinements of representation, articulation, and reflection, towards increasingly complex concepts over time (Confrey et al., 2009)

23. Standards Progressions The Math Common Core presents and builds on conventional wisdom and experiences from best practices in presenting empirically-supported description of the ordered network of constructs a student encounters through instruction (activities, tasks, tools, forms of interaction and methods of evaluation), in order to move from informal ideas, through successive refinements of representation, articulation, and reflection, towards increasingly complex concepts over time Confrey et al., 2009

24. Common Core Fractions – Number & Operations - Gr 3 • 3.NF Develop an understanding of fractions as numbers. 1. 1/b as quantity when whole is partitioned into b equal parts. 2. represent a/b on number line 3. a/b mark off a lengths 1/b from 0. Endpoint is number a/b - cardinality! 4. Equivalences (same size, same point)

25. Common Core Fractions – Number & Operations – Gr 4 • 4.NF Extend understanding of fraction equivalence and ordering. • Build fractions from unit fractions, extend understanding of whole number operations. • Understand decimal notation for fractions, compare decimal fractions. • Gr 4 Limited domain-denominators: {2,4,5,6,8,10,12,100}

26. Common Core Fractions – Number & Operations – Gr 5 • 5.NF • 1. Use equivalent fractions as strategy to add/subtract fractions. • 2. Apply & extend understanding of mult/div to multiply & divide fractions.

27. Assessment The elephants in the room. • Accountability “high-stakes” testing of students and teachers. • Assessment for learning. • Formative assessment. • Diagnostic assessment:RtI, other

28. Assessment for Learning The UK Assessment Reform Group (1999) identifies FIVE PRINCIPLES OF ASSESSMENT for LEARNING • The provision of effective feedback to students. • The active involvement of students in their own learning. • Adjusting teaching to take account of the results of assessment. • Recognition of the profound influence assessment has on the motivation and self esteem of pupils, both of which are critical influences on learning. • The need for students to be able to assess themselves and understand how to improve. Assessment for Learning Defined: Stiggins et al. (2005) http://www.assessmentinst.com/wp-content/uploads/2009/05/afldefined.pdf

29. Formative Assessment …a process used by teachers and students during instruction that provides feedback to adjust ongoing teaching and learning to improve students’ achievement of intended instructional outcomes. • rely on learning progressions (Heritage 2008) • share explicit learning goals • provide students with descriptive feedback • promote a collaborative environment • include peer and self assessments (CCSSO, 2008)

30. Defining Diagnostic Assessment • Diagnostic Assessment requires an explicit theory of how a student’s thinking progresses over time. • Comes from a combination of dia, to split apart, and gnosi, to learn, or knowledge • Efficient, effective use of students’ responses, both to document growth in their learning & understanding (content and process) and to promote that growth, from initial states to more powerful, coherent and aligned conceptions

31. Issues in Diagnostic Assessment • Focus on big ideas in mathematics • Focus on how children’s mathematics understanding evolves over time, rather than replicating the ‘structure of mathematics’ • Rapid feedback to teachers on individual and group status of understanding • Provide recommendations and interventions for improving growth, remedying gaps in conceptual understanding • Professional Development: continuous instructional improvement

32. Defining and deploying a broader college-and-career STEM agenda of a state’s standards that builds on the CCSS.

33. Appendix AHigh School Course Pathways These are examples -- NOT mandated paths! • 4 possible approaches to organizing the content across several courses - by no means an exhaustive list. • States, curriculum developers, schools may use as guides in preparing instructional materials and assessments (End of course?)

34. High School Course Pathways Appendix A provides samples for: • Algebra-Geometry-Algebra 2 – a sequence used only in the US, and • Integrated possibilities – consider IB, international models, several US models. • Shaughnessy, J.M. (2011) An Opportune Time to Consider Integrated Mathematics. www.nctm.org/presmess0311.

35. Serious STEM Omissions • The math CCSS are conservative, and delayed on modeling, probability and statistics, and rate of change and early functions as an introduction to algebra. • Further, they only modestly focus on the use of new learning technologies: this could leave our students foundering in exciting arenas incorporating visualization, integration of topics, engineering, and design and the use of simulations. These topics constitute a critical agenda for our field, and we need a strategy to avoid their marginalization.

36. Mathematics for Non-STEM Often cited critical areas: • Confidence, communication, reasoning • Emphasis on ratio, proportional reasoning, and interpretations • Rate of change – Modeling • Discrete Probability, Data Analysis/Statistics • Collect, organize, analyze, interpret in context, inferences • Discrete Math topics • Strategic use of technology • Calculators, spreadsheets, dynamic geometry, CAS Why aren’t these for STEM students, too?

37. High School Course Pathways A question of my science colleagues: Will a high school science sequence and courses be aggressively studied in terms of STEM integration needs – or will it remain in disciplinary silos?

38. ELA standards: Reading in Science and Technical Subjects Key ideas and details Follow precisely a multistep procedure when carrying out experiments, taking measurements, or performing technical tasks. Reading Standards for Literacy in Science and Technical Subjects Craft and Structure: Determine the meaning of symbols, key terms, and other domain-specific words and phrases as they are used in a specific scientific or technical context relevant to grades 6–8 texts and topics. Integration of Knowledge and Ideas: Compare and contrast the information gained from experiments, simulations, video, or multimedia sources with that gained from reading a text on the same topic (grades 6-8) Range of Reading and Level of Text Complexity

39. Writing Standards for Science and Technical Subjects • Text Type and Purposes -- Write arguments focused on discipline-specific content • Production and Distribution of Writing • Develop and strengthen writing as needed by planning, revising, editing, rewriting, or trying a new approach, focusing on addressing what is most significant for a specific purpose and audience • Research to Build and Present Knowledge • Conduct short as well as more sustained research projects to answer a question (including a self-generated question) or solve a problem; narrow or broaden the inquiry when appropriate; synthesize multiple sources on the subject, demonstrating understanding of the subject under investigation

40. Developing advanced systems for professional development around points 1-3; • Professional development needs to be: • Content and curricular specific • Closely linked to classroom practices • Include intensive learning opportunities with year round follow up • Obligatory • Linked to building professional communities • States need professional development systems connecting district resources, departments of public instruction, universities, colleges, community colleges.

41. Developing advanced systems for professional development around points 1-3; • PD tied to standards -- including their interpretation and connections. • The Standards of Mathematical Practice are STANDARDS that the participating states have signed on to implement. • CAUTION: Too many implementation and assessment programs are already seeking to ignore or avoid the Standards for Mathematical Practice. • Placing attention and focus only on content standards is insufficient!

42. Using longitudinal data systems to decipher and study curricular effectiveness and provide empirical support for change.

43. Priority Six: Using longitudinal data systems to decipher and study curricular effectiveness and provide empirical support for change. On Evaluating Curricular Effectiveness (NRC 2004)

44. Recent Advances • Implementation fidelity(Huntley, 2010) • Opportunity to learn and related constructs (McNaught et al. 2010) • Fair Tests for comparison (Chavez et al. 2010) • Complexity of relationships among teacher and student variables and curricular effects Tarr et al. (http://cosmic.missouri.edu/aera10/) We need to continue to build on these to ensure that we can substantiate future effectiveness.

45. NEXT STEPSandThe Care and Feeding of the Standards

46. Next Steps for the Common Core Standards • The Mathematical Practice Standards are presented independent of content standards—risk of being isolated or ignored • Use of and competency with technology is not adequately or constructively addressed for students • There is limited attention to engaging students in mathematics through modeling with a robust and intriguing use of technology and skills required • Yet to be done: Math connections—across domains and interdisciplinary concepts & applications • The wording of many standards is obtuse—combining math propositions with combination of content and pedagogical advice, verbs hard to interpret for assessment

47. “Care and Feeding of the Standards” • Should include: • members of professional organizations • teachers • researchers, • assessment experts • Should have a three part timeline: immediate fixes, minor revisions and major reviews • Should be an NRC type process with documented responses to feedback

48. Sample Decisions that Should Be Re-examined over time: • The practices of mathematics are presented independently from the content standards: they could be isolated, under-emphasized, and without careful professional development; • There is limited detail to engaging students in mathematics through modeling with robust use of technology, and developing the skills and concepts of modeling; • The important need for mathematical connections • across mathematical domains and concepts • interdisciplinary fields, concepts and applications is mentioned, but there is a lack of guidance or specific examples;

49. Sample Decisions that Should Be Re-examined over time: • New standards for Probability and Statistics in early grades should supplant the current weak treatment of the topic in Measurement; • The CCSS construe Number narrowly tend to overemphasize additive structures—limiting early and foundational development of multiplicative/divisional structures related to ratio and rate, and many algebraic patterns of growth;

50. Major CCSS Focus • The success of the standards depends on the ability of teachers to assist students in learning the specified “fewer” standards at grade level. • Therefore, the success of the standards should be measured heavily, though not exclusively, on the narrowing of the performance gaps