Post on 24-Dec-2015
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 In 1980s when EM was first published,
beginning, developing, and secure labels did not exist
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
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
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?
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
NCTM vs. Colorado Standards
Everyday Math Content Strands
Colorado Math Content Standards
Number and Numeration
Number Sense
Patterns, Functions, and Algebra
Algebraic Thinking
Data and Chance Data & Probability
Geometry Geometry
Measurement and Reference Frames
Measurement
Operations and Computation
Computation
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
Everyday Math Program GoalsData 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
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
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
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
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
Reflections on Program Goals
3 Learning points or understandings
2 Components teachers will embrace
1 Question you still have regarding the EM Program Goals
Content Strand Development
1. Work with a partner
2. Select one envelope which contains a program goal for the content strand: Operations and Computation
3. Place each goal with its corresponding grade
4. Complete puzzle and discuss with your table group the progression of the goal
How will this learning trajectory support students’ understanding of procedural skills and fluency in the Content Strand: Operations and Computation?
How will this tool (content strand development) support teachers understanding of students’ mathematical learning?