pwcs nontraditional education conference april 15, 2013 – pace west preparing for the math sol...

PWCS Nontraditional Education Conference

April 15, 2013 – PACE West

Preparing for the Math SOL Test

Carol KnightSupervisor of Mathematicsknightcj@pwcs.edu

Donna StofkoElementary Math Coordinatorstofkoda@pwcs.edu

Three Components of High Quality Math Instruction

“Teaching for conceptual understanding, developing children’s procedural fluency, and

promoting strategic competence through meaningful problem-solving investigations.”

Shellard, E. and P. S. Moyer. What Principals Need to Know about Teaching Math. Alexandria, Va.: National Association of Elementary School Principals and Educational Research Service, 2002.

Research-InformedInstructional Strategies

1. Active engagement2. Solving challenging problems3. Connecting ideas, concepts and skills4. Communicating mathematically5. Engaging students’ prior knowledge6. Using ongoing, distributed practice with appropriate,

timely feedback7. Using appropriate tools strategically8. Promoting students positive self-beliefs

Diane J. Briars, NCSM Conference, April 2012

Content Standards Number and Number Sense Computation and Estimation Geometry and Measurement Statistics and Probability Patterns, Functions, and Algebra

Process Standards Problem Solving Reasoning and Proof Communication Connections Representation

The Virginia Standards of Learning

“A major goal of the mathematics program is to help students become competent

mathematical problem solvers.” VDOE, 2009

“The content of the mathematics standards is intended to support the five goals for students”

- 2009 Mathematics Standards of Learning

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Five goals: We want students to…

• become mathematical problem solvers who• communicate mathematically; • reason mathematically;• make mathematical connections; and• use mathematical representations to model

and interpret practical situations

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Assessment Announcements

• Availability of multi-day testing• State-level performance analysis of 2012 Math

SOL Tests of all levels• Approximately 20 additional items were

added to the SOL Practice Items for each testGrades 3-8 (released March 22)End-of Course Algebra and Geometry (released in

November )

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Test Administration Options – Grade 3• Section Break

– Same day testing: classroom break (recommendation of at least a fifteen minute break)

– Two day Testing

Section break at the

midpoint

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Test Administration Options – Grades 4 - 7Grade 4 and 5:

– Same day testing: no classroom break– Same day testing: classroom break– Two day testing

Grade 6 and 7:– Same day testing: no classroom break– Same day testing: classroom break

Note: A student can take a supervised break at any time during testing, on any SOL test.

Section break between non-calculator

and calculator sections

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Assessment Resources

• Statewide Assessment Analysis for Spring 2012 SOL Mathematics Tests– Located at:

http://www.doe.virginia.gov/testing/sol/performance_analysis/index.shtml#math

– Note: All PWCS teachers need to watch this presentation and discuss it with their teams

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VDOE’s Analysis of Student Performance on the 2012 Math Tests

http://www.doe.virginia.gov/testing/sol/performance_analysis/index.shtml#math

Identify each picture that has a ratio of 2:3 for the number of triangles to the number of circles.

Suggested Practice for SOL 6.1

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Students need additional practice using replacement values toevaluate expressions with cube roots and square roots.

Suggested Practice for SOL A.1

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Suggested Practice for SOL 6.20

Students need additional practice graphing inequalities on thenumber line, particularly when the variable is on the right sideof the inequality.Graph each inequality.a)

b)

c)

d)

0 2 -2

0 2 -2

0 2 -2

0 2 -2

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SOL Practice Item and Guideshttp://www.doe.virginia.gov/testing/sol/practice_items/index.shtml#math

Practice SOL Items

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Practice SOL Items• SOL Practice Items and guides are available for grade

s 3-8, Algebra I, Geometry, and Algebra II• Grades 3-8 Practice Tool: Practice measuring with

the ruler, measuring angles with the protractor, using the four function calculator, and provides a grid for open practice with tools

• EOC Practice Tool: Practice with geometric constructions and provides a grid for open practice with tools

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Practice SOL Items and Guides• It is essential that students have experiences with the

Practice SOL Items prior to testing.

• Teacher use of the Practice Item Guides with students is STRONGLY recommended.

• Practice Item Guides provide:– Guided practice with tools– Information specific to TEI functionality– Information on item format

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I. Drag and Drop

• Students respond by dragging answers to another spot on the screen

• Used in reading , writing, mathematics, and science assessments.

“TEI-Like” Items in the Classroom

Drag and Drop:• Use of a paper cut out, index card, sticky note,

that can be manipulated to answer a question (sort and categorize, order, label, pull from word bank, etc.)

• Any matching item or activity

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“TEI-Like” Items in the ClassroomDrag and DropSOL 1.7b The student will determine the value of a collection of pennies, nickels, and dimes whose total value is 100 cents or less.

Use of matching

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“TEI-Like” Items in the ClassroomDrag and DropSOL 4.2a The student will compare and order fractions andmixed numbers.

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“TEI-Like” Items in the Classroom Drag and Drop

SOL A.2c Factor completely first-and second-degree binomials and trinomials in one or two variables.

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“TEI-Like” Items in the Classroom

Drag and Drop examples:• Complete sentences or phrases with text• Match a figure to a description (ray, line, line

segment, point)• Create change with money• Complete the pattern with a missing figure• Place justifications into a two-column proof• Match properties to equations

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II. Hot Spot

• Hot spot items contain hot spot zones which represent student answer options

• Hot spot items may requires students to choose one or more options

• Number line and coordinate plane items require students to respond by clicking on a number line or coordinate plane to plot one or more points. Only points plotted with the pointer tool are scorable responses.

• Used in reading, writing, math, and science assessments

“TEI-Like” Items in the Classroom

Hot Spot:• “Circle all of these that are ---”• “Circle the two of these that show---” • “Plot the points that---” • “Shade the part of the model that---”

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“TEI-Like” Items in the ClassroomHot SpotSOL 1.7b The student will determine the value of a collection of pennies, nickels, and dimes whose total value is 100 cents or less.

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“TEI-Like” Items in the Classroom Hot SpotSOL 4.2a The student will compare and order fractions andmixed numbers

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“TEI-Like” Items in the ClassroomHot SpotSOL 7.3b The student will add, subtract, multiply, and divideintegers.

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“TEI-Like” Items in the ClassroomHot SpotSOL A.2b The student will perform operations on polynomials,including adding, subtracting, multiplying, and dividingpolynomials.

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“TEI-Like” Items in the ClassroomHot SpotSOL A.2c Factor completely first-and second-degree binomials and trinomials in one or two variables.

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“TEI-Like” Items in the ClassroomHot Spot examples:• Select all fractions that are equivalent to a given number• Select all equations that have a certain parent function• Select all ordered pairs that are part of a relation with a

given domain or range• Select two names that describe a figure• Select the two equivalent values (the decimal and

fraction equivalents)• Select all factors of a polynomial when completely

factored

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“TEI-Like” Items in the ClassroomHot Spot True/False examples:• Which attributes are true of a rhombus?• Which descriptions are true for a z-score?• Which descriptions are false for a box-and-

whisker plot?• Which descriptions of the graph of a function

are false?

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“TEI-Like” Items in the ClassroomHot Spot: Use of true/falseG.9 The student will verify characteristics of quadrilaterals and use properties of quadrilaterals to solve real-world problems.

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“TEI-Like” Items in the ClassroomHot Spot: Number Line and Coordinate Plane • For number lines and coordinate grids, having students plot points on

paper is the same content skill required for the online test• Number line examples:

– plot the solution to an absolute value equation– plot the probability of an event– plot an integer greater than a certain value

• Coordinate plane examples:– plot two points that lie on the line perpendicular to a given line– plot the inverse of a function– plot a table of values– plot two points to make a line

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“TEI-Like” Items in the ClassroomHot spot: Use of ShadingShading examples:• Shade sections of a whole to represent a fraction or

decimal• Shade a section of a Venn diagram• Shade the solution to a system of inequalities on a

coordinate plane• Shade the figure that represents a rotation of a figure

on a coordinate plane

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“TEI-Like” Items in the ClassroomHot Spot: Shading

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III. Fill-in-the-blank

• Some response boxes limit the characters that may be typed into it

• Students should carefully follow directions to give answer in the form requested (as a fraction in simplest form, as a decimal rounded to a given place, etc.)

• No item requires a student to correctly spell a word

• Used in math and science assessments

Test Development• TEI: Fill-in-the-Blank Items

Frequently asked question:

Will a student be marked wrong for not spelling a word correctly in fill-in-the-blank items?

Currently, there are no items that require students

to spell a word to correctly answer a question. Students do not need to enter words. May require letters, numbers, and/or characters.

ABC x<3 1/2 3R439

Test Development

• TEI: Fill-in-the-Blank ItemsFrequently asked question:

Do students have to give an exact answer for FIB items that require them to use a ruler or protractor?

There is a range of acceptable answers for certain items, depending on the type of measure required.

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Test Development• TEI: Fill-in-the-Blank Items

Frequently asked question: Can students enter a decimal equivalent when asked specifically for a fraction?

Acceptable character keys are controlled for student responses. In this case, the decimal would not be an allowable character.

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“TEI-Like” Items in the ClassroomFill in the blank:• Give students the opportunity to give an open

response, and give parameters, such as “in simplest form,” “as a decimal number,” “as an improper fraction,” “rounded to the nearest—”

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IV. Bar Graphs / Histograms

• Require students to graph data by indicating the height or length of one or more bars or intervals

• Used in math and science assessments

“TEI-Like” Items in the ClassroomBar Graphs/Histograms:• The creation on paper or with manipulatives of bar

graphs, line plots, picture graphs, etc. matches the experience online

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Recommendation:Increased Rigor in Daily Instruction

• Consider the level of cognitive demand that instructional activities require

• Consider the engagement level of the activity• Reflect on the kinds of questions that you are

asking students• Let students struggle with the mathematics

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Level of Cognitive Demand in Activities

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Level of Cognitive Demand in ActivitiesLe

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Level of Cognitive Demand in ActivitiesLe

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Simplify.

Is the value of this expression more or less than 1? How do you know?

Write a real-world problem using this expression.

Effective Questioning When Kids Struggle

• Ask students what they know• Ask about their approach to solve• Ask them where they ran into trouble• Ask them why• Restate what they’ve said• Ask them to reflect on possible other routes

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Effective Questioning and Discourse • Ask students to justify and explain their thinking• Have students share their problem solving

approaches with others• Ask them to explain others’ approaches in their

own words• Ask them to evaluate others’ approaches (error

analysis)• Ask them “what if” questions

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Recommendation:Interventions should include instruction on solving word problems that is based on common underlying structures.

Part-Part-Whole Problem Structure

Lynette has 4 fiction and 3 nonfiction books. How many books does she have?

Part Part

Whole

4 fiction 3 non-fiction

All Books

Singapore Bar Models

Mary made 686 biscuits. She sold some of them. If 298 were left over, how many biscuits did she sell?

686

298?

Rosa has 336 shells. She keeps 72 of the shells for herself and divides the remainingshells evenly among 6 friends. How many shells does Rosa give each of her friends?

Multi-Step

Why use these structures?

Key word strategies don’t work.• No development of meaning-making• No building of structures for more advanced learning

(decimals, fractions, algebra)• Many problems do not have key words• Students use key words inappropriately• Multi-step problems are impossible to solve with key

words.

Meet Marissa

School Bus Problem:

There are 295 students. School buses hold 25 students. How many buses are needed for all of the students?

RecommendationIntervention materials should include opportunities for students to work with visual representations of mathematical ideas and interventionists should be proficient in the use of visual representations of mathematical ideas.

Visual Representations

13 x 14 = 12

Visual Representations

What fraction of the balloons are yellow?

1 1 1

4 3 12

Area Model - Open Array(Algebra I - binomials)

Visual Representations that Connect to Related Concepts

3a

2a

5

7 3521a

10a

(3a + 5) (2a + 7) 6a2 + 21a + 10a + 35

6a2 + 31a + 35

Area Model - Open Array(4th grade)

70

30

8

5

2100

40

240

350

(70 + 8)(30 + 5)2100 + 350 + 240 + 40 = 2,730

Summer Professional DevelopmentElementary Offerings

• MAT 705 Math Instructional Leadership Academy (July 22 – 25) • MAT 284.9 An Orientation to the New Math Textbook for

Teachers of Grades K – 2 (2-hour sessions June 19, 24, 26, July 29, 30, August 22, 23, 27)• MAT 217.1 Math Navigator Training (August 9)• MAT 217.2 Assessing Math Concepts Training (August 19)• MAT 218.45 Making Sense of Fractions in Grades 4 and 5

(June 20-21 and August 13-14)• MAT 250.2 Building Number and Number Sense through Math

Models and Performance-based Assessment: Teaching and Assessing Virginia’s 2009 K-2 Mathematics Standards of Learning (GMU) (Dates to be announced – 90 recertification hours)

Summer Professional DevelopmentSecondary Offerings

• MAT 705 Math Instructional Leadership Academy (July 22 – 25) • MAT 217.1 Math Navigator Training for 3 – 8 (August 9)• MAT 313 Developing Algebraic Reasoning in Middle School

(June 20-28 – course is worth 45 recertification hours))• MAT 400 Algebra I Content Academy (June 24-28 course is

worth 30 recertification hours)• MAT 345 Developing Rational Numbers and Proportional

Reasoning through Math Models and Performance-based Assessment: Teaching and Assessing Virginia’s 2009 6-8 Mathematics Standards of Learning (GMU) (Dates to be announced – worth 90 recertification hours)

What Support is Needed?• Please reflect on the information you have

received today.• What support do you feel you and/or your

school is going to need this year? …next year?