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Learning Trajectory

Learning Trajectory. Everyday Mathematics Program Goals. The story behind Beginning, Developing, and Secure Goals. EM students are expected to master a variety of mathematical skills and concepts But not the first time they are encountered

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Learning Trajectory

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  1. Learning Trajectory Everyday Mathematics Program Goals

  2. The story behind Beginning, Developing, and Secure Goals • EM students are expected to master a variety of mathematical skills and concepts • But not the first time they are encountered • In 1980s when EM was first published, beginning, developing, and secure labels did not exist

  3. B, D, and S labels become Learning Goals • Teachers were uncomfortable “trusting the spiral” and didn’t know where a particular skill or concept fell in terms of curriculum • B, D, S labels were introduced in an update of 1st edition, to help teachers feel comfortable with spiral • In 2nd edition B, D, S labels are converted into learning goals

  4. Problem with Beginning, Developing, and Secure Goals • Main purpose of B, D, S labels was to provide information about the curriculum’s treatment of a topic • B- exposure to skill or concept • D- prior treatment and further exposure would occur • S- additional opportunities to practice and apply skills but no more lessons devoted to it • Secondary function was to indicate individual students’ levels of mastery of skills and concepts

  5. Questions from teachers forced authors to rethink B, D, and S • When do beginning or developing goals become secure? • Will a developing goal in Unit 1, still be considered developing at end of the year? • How do learning goals connect across grade levels? • Why do some grades have more secure goals? • If a child is not proficient on a secure goal in Unit 2, when will there be another opportunity to assess it? • What should the majority of third graders be able to do by the end of the year?

  6. Third Edition of EM introduces Program Goals • Aligned to Standards • Weave the curriculum together across grades • Organized by content strand • Carefully articulated across grade levels • Help teachers understand the structure of Everyday Mathematics • Help teachers understand what to assess • Express the mathematical content that all EM students are expected to master

  7. NCTM vs. Colorado Standards

  8. Everyday Math Program Goals Number and Numeration ♦ Understand the meanings, uses and representation of numbers ♦ Understand equivalent names for numbers ♦ Understand common numerical relations Operations and Computation ♦ Compute accurately ♦ Make reasonable estimates ♦ Understand meanings of operations

  9. Everyday Math Program Goals Data and Chance ♦ Select and create appropriate graphical representations of collected or given data ♦ Analyze and interpret data ♦ Understand and apply basic concepts of probability Measurement and Reference Frames ♦ Understand the systems and processes of measurement; use appropriate techniques, tools, units, and formulas in making measurements ♦ Use and understand reference frames

  10. Everyday Math Program Goals Geometry ♦ Investigate characteristics and properties of two- and three-dimensional geometric shapes ♦ Apply transformations and symmetry in geometric situations Patterns, Functions, and Algebra ♦ Understand patterns and functions ♦ Use algebraic notation to represent and analyze situations and structures

  11. Grade-Level Goals • Guideposts along trajectories that span multiple years • Clarify grade-level expectations for mastery • Big Ideas at each grade level • Do not capture all the content covered • Describe how EM builds mastery over time • Cumulative- thus it is essential that students experience the complete curriculum

  12. Assessment Opportunities • Linked to Grade-Level Goals • EM curriculum designed so that majority will reach Grade-Level Goals upon completion of that grade • As a result students are better prepared to succeed in higher levels of math • Recognizing Student Achievement provides benchmarks to judge student progress • Progress Checks have been reorganized to distinguish between formative and baseline assessments

  13. New and Improved Goals in Everyday Mathematics • B, D, and S labels and learning goals are not part of the 3rd edition of Everyday Mathematics • Essence and functions of B, D, and S remain in structure and features of 3rd edition: Program Goals, Grade-Level Goals • Losing these labels does not reflect a change in the Everyday Mathematics approach • 3rd edition makes that approach easier to understand and implement

  14. Reflections on Program Goals • 3 Learning points or understandings • 2 Components teachers will embrace • 1 Question you still have regarding the EM Program Goals

  15. Content Strand Development • Work with a partner • Select one envelope which contains a program goal for the content strand: Operations and Computation • Place each goal with its corresponding grade • Complete puzzle and discuss with your table group the progression of the goal

  16. How will this learning trajectory support students’ understanding of procedural skills and fluency in the Content Strand: Operations and Computation?

  17. How will this tool (content strand development) support teachers understanding of students’ mathematical learning?

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