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?