sara arizmendez cassie arquette karl spendlove. team effort ◦ math teachers need to be aware of...

Sara ArizmendezCassie ArquetteKarl Spendlove

Team Effort◦ Math teachers need to be aware of the content standards

and how they will be tested◦ Math teachers should be using problems similar to those

on the NHSPE on classroom assignments and tests◦ Math teachers should require students to take notes, and

include vocabulary and notation in the notes and classroom tests

◦ Math teachers should integrate memory aids and problem solving strategies into student notes

◦ Math teachers should link new concepts and skills to prior knowledge and/or real-world applications

◦ Math teachers should use a long-term memory review to help students prepare for high-stakes tests

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It is the responsibility of all teachers to prepare our students for the Math NHSPE, not to teach the test.

Teachers: Provide standards-based instruction Components of an Effective Lesson Teacher Expectancies

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Overview of theNevada High School

Proficiency Exam (NHSPE)

Content Standard 2.0: Patterns, Functions, and Algebra

7 8 9-12

2.7.1 E/S

Use and create tables, charts, and graphs to extend a pattern in order to describe a linear rule, including integer values.

2.8.1 E/S

Find the missing term in a numerical sequence or a pictorial representation of a sequence.

2.12.1 E/S

Use algebraic expressions to identify and describe the nth term of a sequence.

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2.7.2 I/S

Evaluate formulas and algebraic expressions for given integer values.Solve and graphically represent equations and inequalities in one variable with integer solutions.

2.8.2 I/S

Evaluate formulas and algebraic expressions using rational numbers (with and without technology).Solve and graphically represent equations and inequalities in one variable, including absolute value.

2.12.2 E/S

Isolate any variable in given equations, inequalities, proportions, and formulas to use in mathematical and practical situations.

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Content Standard◦ 1.0: Numbers, Number Sense, and Computation◦ 2.0: Patterns, Functions, and Algebra◦ 3.0: Measurement◦ 4.0: Spatial Relationships, Geometry, and Logic◦ 5.0: Data Analysis

Grade Level Theme

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E = Enduring I = Important to know and do W = Worth being familiar with L = Local level only S = State level

All questions marked with an “S” will be tested on the Nevada High School Proficiency Exam (NHSPE)

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C1 – Number Sense and Operations C2 – Algebra and Functions C3 – Measurement and Geometry C4 – Data Analysis, Statistics, and

Probability

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C1 – Number Sense and Operations C2 – Algebra and Functions C3 – Measurement C4 – Geometry C5 – Data Analysis, Statistics, and

Probability

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A1: Conceptual Understanding◦ Students are asked to recognize, select,

identify, or compare◦ Question does not involve computation

A2: Procedural Knowledge◦ Students are asked to convert, use, determine,

graph, or apply◦ Question usually requires only one step to solve

A3: Problem Solving◦ Students are asked to solve, apply, evaluate,

analyze, or differentiate◦ Question asks students to solve “real-world”

and/or multi-task problems

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C1 C2 C3 C4Total Items

A1 0 6 4 3 13 22%

A2 2 9 6 6 23 38%

A3 4 6 8 6 24 40%

Total Items

6 21 18 15 60100%

10% 35% 30% 25% 100%

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Testing Matrix for classes Testing Matrix for classes of 2011 and earlier of 2011 and earlier

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C1 C2 C3 C4 C5Total Items

DOK1 6 7 3 4 7 27 45%

DOK2 3 9 4 5 6 27 45%

DOK3 0 1 2 1 2 6 10%

Total Items

9 17 9 10 15 60100%

15% 28% 15% 17% 25% 100%

Testing Matrix for 2010 (class of Testing Matrix for 2010 (class of 2012) 2012)

Passing Score is 304 for class of 2011 and earlier.This usually equates to 40 questions correct out of 60.

Students should be aware that their goal is a passing score… NOT a perfect score!

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Passing Score for class of 2012 and later will be set next spring.

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There is no penalty for incorrect answers, so students should fill in an answer for every problem.

LEAVE NO BLANKS!!

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Analyzing theNevada Math Standardsand CCSD Curriculum

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Classroom Strategies

•Long Term Memory Review Activities

•Memory Aids

•Test-Taking Strategies

Put the answer sheet aside. Do not bubble in until the test is completed.

Use graph paper for your scratch paper Organize your scratch paper in squares –

each square should have an answer and/or a check mark, question mark, or x.

Tear out the formula sheet

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Write in the test booklet◦ Label and/or draw on the pictures they provide◦ Measure the diagrams to check your answer◦ Circle important information and “clue” words◦ Cross out answers that don’t make sense

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Problem Solving◦ Read the problem like a story, then look for the

math◦ Write down important facts◦ Use “nice” numbers◦ Work backwards from the answers◦ Draw pictures, write an equation, look for a

pattern◦ Check your formula sheet◦ Be sure to answer the question that was asked

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Attend available tutoring sessions Get several good nights of sleep Wake up early the day of the test Wear comfortable clothes Eat a good breakfast Bring mints to the test Bring something personal to the test

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Vocabulary and NotationThere is no more single important factor that affects student achievement than vocabulary and notation.

Examples of words to emphasize◦ Common words used in questions (evaluate,

estimate, simplify, solve, consecutive, precise, etc.)

◦ Words for mathematical operations (sum, perimeter, difference, less than, product, area, number of ways, quotient, ratio, etc.)

◦ Geometry terms – provide memory aids◦ Words with multiple meanings (range, degree,

tangent, etc.)

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STUDENTS HAVE AN UNLIMITED AMOUNT OF TIME TO COMPLETE THE NHSPE, AS LONG

AS THEY ARE ON TASK

Encourage students to take short “breaks” every 20 minutes to clear their minds.

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◦ Sample proficiency exams◦ Practice worksheets◦ Item Specification Sheet◦ ACCES software – create your own!◦ RPDP practice materials – www.rpdp.net◦ CPD practice materials – www.ccsd.net/cpd ◦ NV Dept of Education – www.doe.nv.gov ◦ www.supermathtutor.com

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Depth of KnowledgeOverview

DOK is a scale of cognitive demand intended to describe the complexity of thinking required to complete a task, answer a question, or solve a problem

Adapted from the model used by Norman Webb, University of Wisconsin, to align standards with assessments

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The Nevada Department of Education believes that DOK levels not only provide for a greater depth and breadth of learning, but also meet the requirements of academic rigor required by No Child Left Behind by ensuring that assessment items are as cognitively demanding as the expectation of the content standard.

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The Nevada Department of Education has adopted and modified Norman Webb’s DOK levels to replace the present ability levels (A1, A2, and A3) on state assessments

These DOK levels will be incorporated into all of Nevada’s state assessments by 2010

DOK is a tool to ensure that teachers are teaching to the depth and breadth of the standards.

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Level 1 - Recall and Reproduction•Basic recall of concepts, definitions, facts, and processes•Answering a Level 1 item can involve following a simple, well-known procedure or formula.•Simple skills and abilities or recall characterize DOK 1

Level 1 - Recall and Reproduction•Basic recall of concepts, definitions, facts, and processes•Answering a Level 1 item can involve following a simple, well-known procedure or formula.•Simple skills and abilities or recall characterize DOK 1

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Level 2 – Basic Application of Skills and Concepts•Includes the engagement of some mental processing beyond recalling or reproducing a response•Requires students to make some decisions as to how to approach a problem or task•Implies more than one mental or cognitive process/step

Level 2 – Basic Application of Skills and Concepts•Includes the engagement of some mental processing beyond recalling or reproducing a response•Requires students to make some decisions as to how to approach a problem or task•Implies more than one mental or cognitive process/step

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Level 3 - Strategic Thinking •Requires deep understanding as exhibited through planning, using evidence, and more demanding cognitive reasoning•The cognitive demands are complex and abstract•Requires students to justify their response •May have more than one possible answer

Level 3 - Strategic Thinking •Requires deep understanding as exhibited through planning, using evidence, and more demanding cognitive reasoning•The cognitive demands are complex and abstract•Requires students to justify their response •May have more than one possible answer

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Level 4 - Extended Thinking•Requires high cognitive demand and is very complex•An investigation or application that requires time to research, think or process multiple conditions of the problem•Includes non-routine manipulations or connections across disciplines/ content areas/ multiple sources•Due to the cognitive complexity, requires an extended period of time•NOT TESTED ON THE CRT or HSPE

Level 4 - Extended Thinking•Requires high cognitive demand and is very complex•An investigation or application that requires time to research, think or process multiple conditions of the problem•Includes non-routine manipulations or connections across disciplines/ content areas/ multiple sources•Due to the cognitive complexity, requires an extended period of time•NOT TESTED ON THE CRT or HSPE

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DOK 1- Describe the order of operations. (Simple recall)

DOK 2- Describe the difference between graphing linear equations and inequalities. (Requires cognitive processing to determine the differences in the two relations’ graphs)

DOK 3- Describe how unknown measures of sides and angles in a triangle can be determined. (Requires understanding of different techniques for solving triangles and when they can be used)

DOK levels are NOT a measure of difficulty

Ex: What is the definition of parallel? (DOK 1 – recall)

If you know the definition, then it is not difficult.

Ex: What is the definition of eccentricity? (DOK 1 – recall)

If you do not know the definition, this is a difficult question, but that alone does not change the DOK level.

◦ It is possible to have a “difficult” Level 1 question.

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DOK levels can be cumulative◦ An item/standard written to DOK 3 often

contains DOK 1 and DOK 2 level demands

DOK 1 + DOK 1 ≠ DOK 2◦ DOK levels are not additive. That is, a

DOK 2 activity is not created by repetitive DOK 1 activities

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DOK 1Apply a Formula

**HSPE Instructional Materials 2009 grade (H)

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DOK 2Retrieve information from a table, graph, or figure and use it to solve a problem requiring multiple steps.

**HSPE Instructional Materials 2009 grade (H)

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DOK 3Perform a procedure with multiple steps and multiple decision points.

**HSPE Instructional Materials 2009 grade (H)

Recall and Reproduction

(DOK 1)

Skills and Concepts/ Basic

Reasoning (DOK 2)

Strategic Thinking/ Complex Reasoning

(DOK 3)

Extended Thinking/ Reasoning

(DOK 4)

Find the next three terms in the following pattern: 2/7, 4/7, 6/7, 8/7. …

Draw the next figure in the following pattern:

Find the next three terms in the pattern and determine the rule for the following pattern of numbers:

1, 4, 8, 11, 15, 18, 22, 25, 29, …

Find the next three terms in the pattern, determine the rule for finding the next number in the pattern, and make or find a model for the pattern:

1, 1, 2, 3, 5, 8, 13, 21, 34, …

Students will extend patterns, find the missing term(s) in a pattern or describe rules for patterns (numbers, pictures, tables, words) from real-world and mathematical problems.

Professional Development Opportunities

Resources◦www.RPDP.net◦InterAct®

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Ed Link > Curriculum & Prof Dev > Textbooks & Instructional Resources > Depth of Knowledge

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Item Writing 101

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Stem:The part of the item that presents the question or problem to be answered.

Answer Choices

Distracters:The incorrect answer choices.

Correct Answer

What is the capital of Nevada?

A. RenoB. Las VegasC. Virginia CityD. Carson City*

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**HSPE Instructional Materials 2009 grade (H)

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We thank you for all that you do for our students in CCSD!