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Common Core State Standards in Mathematics

Standards-Based Assessment and Grading

CCSS in Mathematics

Standards define what students should understand and be able

to do.

Common Core: Overview of Mathematics

Standards for Mathematical Content 50%K-8 presented by grade levelOrganized into domains that progress over several

gradesGrade introductions give 2-4 focal points at each

grade level

Standards for Mathematical Practice 50%Carry across all grade levelsDescribe habits of a mathematically expert student

CCSS Domain Progression

k 1 2 3 4 5 6 7 8

  Geometry

Measurement and Data Statistics and Probability

Number and Operation in Base 10 The Number System

Operations and Algebraic Thinking Expressions and Equations

Counting and

Cardinality    Number and Operations - -

Fractions

Ratios and Proportional Relationships

Functions

Habits of a Mathematically Expert Student

The Common Core proposes a set of Mathematical Practices that all teachers should develop in their students:

1. Make sense of problems and persevere in solving them

2. Reason abstractly and quantitatively

3. Construct viable arguments and critique the reasoning of others

4. Model with mathematics

5. Use appropriate tools strategically

6. Attend to precision

7. Look for and make use of structure

8. Look for and express regularity in repeated reasoning

Common Core/STEM Connection

View the standards through a lens of inquiry-based instruction

Focus on cross-curricular connections, problem solving, & content area literacy

Real-world application and analysis of content knowledge

Student-centered learning environment

6 Instructional Shifts in CCSS Math

FocusCoherenceFluencyDeep UnderstandingApplicationDual Intensity

Rigor

The CCSSM Require a Balance of:

Solid conceptual understanding Procedural skill and fluency Application of skills in problem solving situations

This requires equal intensity in time, activities, and resources in pursuit of all three.

Revised Bloom’s Taxonomy

Higher-Order Thinking:

CreatingGenerating new ideas, products, or ways of viewing things Designing, constructing, planning, producing, inventing

EvaluatingJustifying a decision or course of actionChecking, hypothesizing, critiquing, experimenting, judging

AnalyzingBreaking information into parts to explore understandings and

relationshipsComparing, organizing, deconstructing interrogating, finding

Revised Bloom’s Taxonomy

ApplyingUsing information in another familiar situationImplementing, carrying out, using, executing

UnderstandingExplaining ideas or conceptsInterpreting, summarizing, paraphrasing, classifying,

explaining

RememberingRecalling informationRecognizing, listing, describing, retrieving, naming

finding

Traditional Gradingversus

Standards-Based Grading

Traditional Grade Book

Final Grade is based upon the following:

Homework QuizzesTestsProjectsParticipation

Standards-Based Grading

Grading that references student achievement to specific topics

within each subject area.

Standards-referenced system

Formative Assessment

Student achievement will be positively affected if

standards-based reporting is rooted in a clear-cut

system of formative assessment.

Formative Assessment

Tasting the Soup

Formative Scores vs. Summative Scores

Formative Scores = scores that are recorded in the interest of providing information to students and teachers about the progression of learning.

Summative Scores = scores that are derived at the end of a grading period and represent a student’s final status at a particular point in time.

Instructional Feedback = assessments may be scored but are not recorded and are used to help inform students about areas of improvement and teachers about the progression of individual students or an entire class.

The Need for a New Scale

75% or

4,3,2,1

Consider the FollowingTypes of Content in Three Sections of an

Assessment

 

Section A: Ten multiple-choice items that are factual in nature but important to the topic.Section B: Four short constructed-response items that require students to explain principles or give examples of generalizations as presented in class.Section C: Two short constructed-response items that require students to make inferences and applications that go beyond what was presented in class.

Points for Section A: ____Points for Section B: ____Points for Section C: ____Total: ____

Points to

Section A

Points to

Section B

Points to

Section C

Total Points for Student (Final Score)

Teacher 1

40 40 20 60Teacher 2

20 40 40 40Teacher 3

60 20 20 70Teacher 4

70 20 10 80Teacher 5

20 20 60 30Assume: A particular student has exhibited the followingpattern of scores: he or she answered all the items correctly in section A, two of the four items in B correctly, and neither of the two items in section C.

Rubric-Based Approach

“rubrica terra” or red earth

Today the term rubric usually applies to a

description of knowledge or skill for a specific topic.

Designing a Scale

Identify a learning goalIdentify simpler and more complex content

A scale is an attempt to create a continuum that articulates distinct

levels of knowledge and skill relative to a specific topic.

A Generic Scale

Score 4

More complex content

Score 3

Target learning goal

Score 2

Simpler content

Score 1

With help, partial success at score 2.0 content and score 3.0 content

Score 0

Even with help, no success

Science – Learning Goal 1:

Students will be able to differentiate heritable

traits from non-heritable traits in real-world

scenarios.

Science – Learning Goal 1

Score 4.0

Students will be able to discuss how heritable traits and non-heritable traits affect one another.

Score 3.0

Students will be able to differentiate heritable traits from non-heritable traits in real-world.

Score 2.0

Students will be able to recognize accurate statements about isolated examples of heritable and non-heritable traits.

Score 1.0

With help, partial success at score 2.0 content and score 3.0 content

Score 0.0

Even with help, no success

Student Friendly Scale

Scale 4.0

We should be able to talk about how the traits we inherit and the traits we develop on our own are related to one another. For example, a person born in a family that has always lived near the equator might have darker skin and enjoy warm-weather hobbies such as swimming or scuba diving, but someone born in a family that has always lived in a cold climate might have fair skin and enjoy cold-weather hobbies such as skiing or ice skating.

Scale 3.0

We should be able to tell the difference between traits we inherit from our parents and traits we develop on our own. For example, Michael Phelps is such a good swimmer partly because of how tall he is and how wide his wingspan is (traits he inherited) and partly because he practiced really hard and did what his coach told him to (things he chose to do).

Scale 2.0

We should be able to talk about the traits we get from our parents and the traits we develop on our own. For example, we cannot change the traits we get from our parents, such as height or eye color, but we can change the traits we develop, such as patience or work ethic.

Science – Trimester Grade

Standard 1: 2.5Standard 2: 2.0Standard 3: 3.0Standard 4: 3.5Science Grade = 2.75

Ms. Westbrook’s First Grade Class

Resources

Common Core State Standards-Mathhttp://www.k12.wa.us/Mathematics/Standards.aspx

For Families and Communitieshttp://www.k12.wa.us/CoreStandards/Families/default.aspx

Parent Roadmaps to the CCSS-Mathematics

http://www.cgcs.org/Page/244

The Mathematics Standards-How they were developed. (You Tube video)

http://www.youtube.com/watch?v=dnjbwJdcPjE&feature=c4-overview-vl&list=PL913348FFD75155C6