PWCS Nontraditional Education
Conference
April 15, 2013 – PACE West
Preparing for the Math SOL Test
Carol Knight
Supervisor of Mathematics
knightcj@pwcs.edu
Donna Stofko
Elementary Math Coordinator
stofkoda@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-Informed
Instructional Strategies
1. Active engagement
2. Solving challenging problems
3. Connecting ideas, concepts and skills
4. Communicating mathematically
5. Engaging students’ prior knowledge
6. Using ongoing, distributed practice with appropriate,
timely feedback
7. Using appropriate tools strategically
8. Promoting students positive self-beliefs
Diane J. Briars, NCSM Conference, April 2012
The Virginia Standards of Learning
Content Standards
Process Standards

Number and Number Sense

Problem Solving

Computation and Estimation

Reasoning and Proof

Geometry and Measurement

Communication

Statistics and Probability

Connections

Patterns, Functions, and Algebra

Representation
“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
5
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
6
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 test
Grades 3-8 (released March 22)
End-of Course Algebra and Geometry (released in
November )
7
Test Administration Options – Grade 3
• Section Break
– Same day testing: classroom break
(recommendation of at least a fifteen minute break)
– Two day Testing
8
Test Administration Options – Grades 4 - 7
Grade 4 and 5:
– Same day testing:
– Same day testing:
– Two day testing
Grade 6 and 7:
– Same day testing:
– Same day testing:
no classroom break
classroom break
no classroom break
classroom break
Note: A student can take a supervised break at any time during testing, on any SOL
test.
9
Assessment Resources
• Statewide Assessment Analysis for Spring
2012 SOL Mathematics Tests
– Located at:
http://www.doe.virginia.gov/testing/sol/performa
nce_analysis/index.shtml#math
– Note: All PWCS teachers need
to watch this presentation and
discuss it with their teams
10
VDOE’s Analysis of Student
Performance on the 2012 Math Tests
http://www.doe.virginia.gov/testing/sol/performance_analysis/index.shtml#math
Suggested Practice for SOL 6.1
Identify each picture that has a ratio of 2:3 for the number
of triangles to the number of circles.
12
Suggested Practice for SOL A.1
Students need additional practice using replacement values to
evaluate expressions with cube roots and square roots.
13
Suggested Practice for SOL 6.20
Students need additional practice graphing inequalities on the
number line, particularly when the variable is on the right side
of the inequality.
Graph each inequality.
a)
-2
0
2
c)
-2
0
2
d)
-2
0
2
-2
0
2
b)
14
SOL Practice Item and Guides
http://www.doe.virginia.gov/testing/sol/practice_items/index.shtml#math
Practice SOL Items
16
Practice SOL Items
• SOL Practice Items and guides are available for
grades 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
17
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
18
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
20
“TEI-Like” Items in the Classroom
Drag and Drop
SOL 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
21
“TEI-Like” Items in the Classroom
Drag and Drop
SOL 4.2a The student will compare and order fractions and
mixed numbers.
22
“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.
23
“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
24
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---”
26
“TEI-Like” Items in the Classroom
Hot Spot
SOL 1.7b The student will determine the value of a collection of pennies,
nickels, and dimes whose total value is 100 cents or less.
27
“TEI-Like” Items in the Classroom
Hot Spot
SOL 4.2a The student will compare and order fractions and
mixed numbers
28
“TEI-Like” Items in the Classroom
Hot Spot
SOL 7.3b The student will add, subtract, multiply, and divide
integers.
29
“TEI-Like” Items in the Classroom
Hot Spot
SOL A.2b The student will perform operations on polynomials,
including adding, subtracting, multiplying, and dividing
polynomials.
30
“TEI-Like” Items in the Classroom
Hot Spot
SOL A.2c Factor completely first-and second-degree binomials
and trinomials in one or two variables.
31
“TEI-Like” Items in the Classroom
Hot 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
32
“TEI-Like” Items in the Classroom
Hot 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-andwhisker plot?
• Which descriptions of the graph of a function
are false?
33
“TEI-Like” Items in the Classroom
Hot Spot: Use of true/false
G.9 The student will verify characteristics of quadrilaterals and use
properties of quadrilaterals to solve real-world problems.
34
“TEI-Like” Items in the Classroom
Hot 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
35
“TEI-Like” Items in the Classroom
Hot spot: Use of Shading
Shading 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
36
“TEI-Like” Items in the Classroom
Hot Spot: Shading
37
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.
3R4
x<3
ABC
1/2
39
Test Development
• TEI: Fill-in-the-Blank Items
Frequently 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.
40
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.
41
“TEI-Like” Items in the Classroom
Fill 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—”
42
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 Classroom
Bar Graphs/Histograms:
• The creation on paper or with manipulatives of bar
graphs, line plots, picture graphs, etc. matches the
experience online
44
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
45
Level of Cognitive Demand in Activities
46
Level of Cognitive Demand
Level of Cognitive Demand in Activities
47
Level of Cognitive Demand
Level of Cognitive Demand in Activities
Write a real-world
problem using this
expression.
Is the value of this
expression more or
less than 1? How do
you know?
Simplify.
48
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
49
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
50
Recommendation:
Interventions should include instruction on
solving word problems that is based on common
underlying structures.
Part-Part-Whole Problem Structure
4 Part
fiction
Part
3 non-fiction
Whole
All
Books
Lynette has 4 fiction and 3 nonfiction books. How
many books does she have?
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 remaining
shells evenly among 6 friends. How many shells does
Rosa give each of her friends?
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?
Recommendation
Intervention 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
1 1 1
 
4 3 12
What fraction
of the balloons
are yellow?
Visual Representations that Connect to
Related Concepts
Area Model - Open Array
(4th grade)
30
5
Area Model - Open Array
(Algebra I - binomials)
8
2100
240
2a
350
40
7
(70 + 8)(30 + 5)
2100 + 350 + 240 + 40 = 2,730
5
3a
70
10a
21a
(3a + 5) (2a + 7)
6a2 + 21a + 10a + 35
6a2 + 31a + 35
35
Summer Professional Development
Elementary 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 Development
Secondary 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?