Math Standards
description
Transcript of Math Standards
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Math Standards
James & Tammy ParsonsMetro Nashville Public Schools
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How to access today’s materials:
http://public.me.com/flyparsons
James’ email: [email protected]
Tammy’s email: [email protected]
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What are Standards?
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A Standards-Based Education System
Standards help ensure students learn what is important, rather than allowing textbooks to dictate classroom practice.
Student learning is the focus – aiming for a high and deep level of student understanding that goes beyond traditional textbook-based or lesson-based instruction.
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A standards-based system:
measures success based on student learning (the achievement of standards) rather than compliance with rules and regulations.
aligns policies, initiatives, curriculum, instruction, and assessments with clearly defined academic standards.
consistently communicates and uses standards to focus on ways to ensure success or all students.
uses assessment to inform instruction.
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Standards-based systems increase student achievement.
Students generally learn better in a standards-based environment because everybody’s working towards the same goal.
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In standards-based systems: Teachers know what the standards are and choose
classroom activities and teaching strategies that enable students to achieve the standards.
Students know the standards, too, and can see scoring guides that embody them. The students can use them to complete their work.
Parents know them and can help students by seeing that their homework aligns with the standards.
Administrators know what is necessary to attain the standards and provide professional development, resources and materials to ensure that students are able to reach the prescribed standards.
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Differences Between Standards-Based and Norm-Referenced Systems
Norm-Referenced Believe some students
are naturally smarter than others.
Content subject matter varies with different groups of students.
Assessments compare what students know to what other students know.
Standards-Based Believe virtually all
students can “get smart” through effort.
Content subject matter is the same for all groups of students.
Assessments compare what students know to standards and benchmarks.
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Differences Between Standards-Based and Norm-Referenced Systems
Norm-Referenced No objective criteria to
deploy resources – students who need the most often get the least.
Professional development episodic – one-time workshops.
Standards-Based Resources are deployed
as needed for all students to meet standards – students who need more get more.
Professional development focuses on improving instruction so all students meet standards.
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About the Math Standards
These are the same across all grades.1. Process2. Number & Operations3. Algebra4. Geometry & Measurement5. Data Analysis, Probability, and Statistics
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•GLE/CLE (Grade/Course Level Expectations): represent the fundamental goals for student learning that are used by teachers as the principal guide for instructional planning in that grade/course. These are the instructional targets for that grade/course. (GLEs are used in K–8; CLEs are used in Grades 9–12.)
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Checks for Understanding: are suggestions for assessing student learning. These formative/summative checks provide information about whether a student has met a particular Grade or Course Level Expectation. Formative assessments are typically embedded within a lesson. (Checks for Understanding are denoted by the checkmark symbol (√).) Checks for Understanding are resources to help the teacher determine if students are mastering what they are expected to learn.
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SPI (State Performance Indicators): are the basis for student accountability and are used by the state to prepare standardized test items aligned with corresponding Grade or Course Level Expectations. SPIs are not instructional targets. (There are no SPIs in Grades K–2.)
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Process Standard – connected to NCTM process standards. Embeds communication, proof, reasoning, historical development of mathematics, and modeling into one standard. GLEs are same across K–8 grade bands, but the checks for understanding and SPIs differ.
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Understanding the Codes
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Jefferson County Public Schoolshttp://jc-schools.net/dynamic/math/math.html
Other website resources:http://Illuminations.nctm.orgwww.portaportal.comwww.internet4classrooms.comhttp://www.thinkfinity.org/home.aspx
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INTRODUCTION TO WEBB’S DEPTH-OF-KNOWLEDGE LEVELS
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Item Difficulty vs.
Cognitive Complexity
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DOK is a reference to the cognitive demand that must occur to answer a question, perform a task, or generate a product. Adding is a mental process. Knowing the rule for adding is the
intended outcome that influences the DOK.
Once someone learns the “rule” of how to add, 4 + 4 is DOK 1 and is also easy.
Adding 4,678,895 + 9,578,885 is still a DOK 1 but may be more “difficult.”
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BLOOM’S TAXONOMY WEBB’S DEPTH OF KNOWLEDGE
KNOWLEDGE “The recall of specifics and universals,
involving little more than bringing to mind the appropriate material”
Recall – Recall of a fact, information, or procedure (e.g., What are 3 critical skill cues for the overhand throw?)COMPREHENSION
“Ability to process knowledge on alow level such that the knowledge
can be reproduced or communicatedwithout a verbatim repetition.”
APPLICATION“The use of abstractions in
concrete situations.”
Basic Application of Skill/Concept – Use of information, conceptual knowledge, procedures, two or more steps, etc. (e.g., Explain why each skill cue is important to the overhand throw. “By stepping forward you
are able to throw the ball further.”)
ANALYSIS“The breakdown of a situation into
its component parts.”
Strategic Thinking – Requires reasoning, developing a plan or sequence of steps; has some complexity; more than one possible
answer; generally takes less than 10 minutes to do (e.g., Design 2 different plays in basketball and explain what different skills are needed
and when the plays should be carried out.)
SYNTHESIS AND EVALUATION“Putting together elements & partsto form a whole, then making value
judgments about the method.”
Extended Thinking – Requires an investigation; time to think and process multiple conditions of the problem or task; and more than 10
minutes to do non-routine manipulations (e.g., Analyze 3 different tennis, racquetball, and badminton strokes for similarities, differences, and
purposes. Then, discuss the relationship between the mechanics of the stroke and the strategy for using the stroke during game play.)
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Webb’s Depth of Knowledge levelsLevel 1 Recall and ReproductionLevel 2 Skills & ConceptsLevel 3 Strategic ThinkingLevel 4 Extended Thinking
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Level 1 Recall Level 1 Recall
Requires simple recall of such information as a fact, definition, term, or performance of a simple process or procedure. A student answering a Level 1 item either knows the answer or does not.
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List the numbers from 0-5. Locate or recall facts about squares. Describe the attributes of a cube. Determine the perimeter or area of
rectangles given a drawing or labels Identify basic rules for participating in
simple games and activities
Level 1 Examples
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Level 2 Basic Application of Skills & Level 2 Basic Application of Skills & ConceptsConcepts
Involves some mental skills, concepts, or processing beyond habitual response. Students must make some decisions about how to approach a problem or activity. Keywords distinguishing a Level 2 item include classify, organize, observe, estimate, collect data, and compare data.
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Compare fractions and decimals Identify and summarize the steps for solving a
problem Explain the cause-effect of a given set of data Predict/estimate a logical outcome based on
information in a chart or graph Explain how good work habits are important at
home, school, and on the job Classify plane and three dimensional figures Describe qualitative change (the older you get,
the taller you get)
Level 2 Examples
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Level 3 Strategic ThinkingLevel 3 Strategic ThinkingRequires reasoning, planning, using evidence, and thinking at a higher level than the previous two levels. The complexity results because the multi-step task requires more demanding reasoning.
An assessment item that has more than one possible answer and requires
students to justify the response they give would most likely be a Level 3.
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Compose and decompose geometric figures to find area/perimeter of irregular figures
Analyze or evaluate various representations of data
Solve a multiple-step problem and provide support with a mathematical explanation that justifies the answer
Explain, generalize or connect mathematical ideas to solve problems and interpret solutions
Level 3 Examples
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Level 4 Extended ThinkingLevel 4 Extended ThinkingRequires complex reasoning, planning, developing, and thinking, most likely over an extended time. Cognitive demands are high, and students are required to make connections both within and among subject domains.
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Apply and adapt a variety of appropriate strategies to problem solving, including estimation, and reasonableness of solutions.
Level 4 Examples
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Extended ThinkingThe cognitive demands of the task should be high and the work should be complexStudents should be required to make several connectionsDesigning and conducting experimentsMaking connections between a finding and related conceptsCombining and synthesizing idea into new concepts
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Task Comparison ThinkingCollecting data samples Recall
Organizing the data in a chart Skills/concepts
Using the chart to make and justify predictions
StrategicThinking
Developing a generalized model from the data and applying it to a new situation
ExtendingThinking
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Verbs and DOK
The Depth of Knowledge is NOT determined by the verb, but the context in which the verb is used and the depth of thinking (cognitive demand) required.
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Level 3- Describe a model that you might use to represent the relationships of the areas of squares and triangles. (requires deep understanding of area and a determination of how best to represent it)
Level 2- Describe the difference between squares and triangles. (requires cognitive processing to determine the differences in the two types of figures)
Level 1- Describe two attributes of a square. (simple recall)
Same verb—three DOK levels
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Reflect…
• Depth of Knowledge is a scale of cognitive demand.• DOK requires looking at the assessment item/standard-not student work-in order to determine the level. DOK is about the item/standard-not the student.• The context of the assessment item/standard must be considered to determine the DOK-not just a look at what verb was chosen.
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Click here:
Screen Shot
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Teacher frustrated over Standards
Click on Teacher
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Activities 2nd Grade
Multiplication Face Cards Number Roads Make a Dollar Game Gorilla Lunch Menu Circle Handout Pattern Block – Equivalent Fractions
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Activities
How Does It Grow Balancing Act Math Machines How Far Create a House Number Mary Had a Little Lamb
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Activities
More than One Story Which is Which Birthday Graph Unlikely/Likely Events How big is your foot?
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KWL Chart
K W LWhat I Have
LearnedWhat I Know What I Want
To Know
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Activities (5-8)
Hallways and Bedrooms Quadrilateral Sort Triangle Triangles What’s Your Angle? Tangram Values Polygon PizzasGLE Search
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Activities (5-8) A PIN for Mr. Mitchell Remove OneGLE Search
Walk the Graph Graphic Stories Building with Toothpicks Exploring Houses Table for 63, please
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A Standards-Based Education System
Standards-based education is a process for planning, delivering, monitoring and improving academic programs in which clearly defined academic content standards provide the basis for content in instruction and assessment.
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Segment 7
Transforming Instruction Through Standards
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Implications for Instructional ChangeDirections
Individually read and highlight Traditional instructional aspects in BLUE Transformative aspects in YELLOW.
Compare highlights with elbow partner. As a group, use your papers to complete
the laminated chart. Match each transformative aspect with its
traditional counterpart. Debrief with subsequent slides.
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Traditional vs. Transformative
Time is the variable: performance is constant
Goal: expect performance standards to be obtained by all students
Based on spiral learning
Time is constant; performance is the variable
Goal: expect normally distributed performance
Based on linear learning
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Traditional vs. Transformative
Less “coverage” yields more “higher order” cognition
Domains-driven curriculum
Long-term retention
More “coverage” yields less “higher order” cognition
Textbook-driven curriculum
Short-term memorization
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Traditional vs. Transformative
Concrete-to-abstract
Constructivist
Gifted students allowed time to linger on various topics
Abstract; no concrete basis
Traditionalist
Gifted students must keep up pace, potential for burnout
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Traditional vs. Transformative
Emphasis placed on raising underachievers’ performance levels
Socratic, discovery methods
Begins with the end in mind
Emphasis on maintaining timeline, underachievers separated
Lecture, dissemination
Rarely reaches the end
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Traditional vs. Transformative
Time frames collapsed
Teach inquiry
Integrated curriculum
High emphasis on time
Teach content
Segmented curriculum
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Segment 9
Making Standards User Friendly
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Working with two variable data Using multiple graphical representations Solve problems using visual representations Use sample data and proportional reasoning to make
predictions Use percentages to interpret circle graphs Evaluate experiment design Choose appropriate types of representations for data Move between concrete and abstract representations Use math ideas in multiple settings Understand and apply proportionality Write equations to solve problems using ratio and percent Use ratio and proportion to solve problems Express values as ratios, percents, and fractions
Standards-Based Instruction:A Melting Pot Approach
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What is it about this activity that relates to the idea of a melting pot?
Standards-Based Instruction:A Melting Pot Approach
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The Language of the Standards GLE:is a statement that defines what all students should know and be able
to do at the end of a given grade level. GLEs add further definition to the content standards and benchmarks.
Checks for Understanding: SPI: