# Instruction and Assessment Analysis and Design August 1_ 2012 by hcj

VIEWS: 5 PAGES: 41

• pg 1
```									        Increased Rigor in the
2009 Mathematics Standards of Learning

January 2013

Michael Bolling, Director
Office of Mathematics and Governor’s Schools
What is “Rigor”?
• Is it:
– Assigning more mathematics problems?
– Issuing zeroes for incomplete work?
– Weeding out students from honors classes?
• Or rather:
– Providing challenging content through effective
instructional approaches that lead to the
development of cognitive strategies that students
can use when they do not know what to do next.
•                          2
What is “Rigor”?
• What is “Rigor”?
• Increased Rigor of the 2009 Mathematics
Standards of Learning
• New Assessments that Reflect the Increased
Rigor of the Standards
• Instructional Rigor

3
What is “Rigor”?
• Rigor requires active participation from both
teachers and students.
• Rigor asks students to use content to solve
complex problems and to develop strategies
that can be applied to other situations, make
connections across content areas, and
ultimately draw conclusions and create
solutions on their own.

4
What is “Rigor”?
• Rigor requires students to not only learn the
foundational knowledge of the mathematics,
but to apply it to real-world situations.
• Rigor requires teachers to create a learning
environment where students use their
knowledge to create meaning for a broader
purpose.
• Rigor requires students learn how to develop
alternative strategies if their first attempts are
unsuccessful.
5
Increased Rigor in the
2009 Mathematics Standards of Learning

• Explicit content changes
– Movement of content between and among grade levels
– Increased content expectations

6
Increased Rigor in the
2009 Mathematics Standards of Learning

• Explicit content changes
– Movement of content between and among grade levels
– Increased content expectations

7
Explicit Content Changes
• 2001 SOL 3.8 The student will solve problems
involving the sum or difference of two whole
numbers, each 9,999 or less, with or without
regrouping, using various computational methods,
including calculators, paper and pencil, mental
computation, and estimation.
• 2009 SOL 3.4 The student will estimate solutions to
and solve single-step and multistep problems
involving the sum or difference of two whole
numbers, each 9,999 or less, with or without
regrouping.
8
Explicit Content Changes

• 2001 SOL 7.22 The student will
– b) solve practical problems requiring the solution
of a one-step linear equation.
• 2009 SOL 7.14 The student will
– b) solve practical problems requiring the solution
of one- and two-step linear equations.

9
Explicit Content Changes

• 2009 SOL 6.10 The student will
– c) solve practical problems involving area and
perimeter
• 2001 SOL 7.7 The student, given appropriate
dimensions, will
– b) apply perimeter and area formulas in practical
situations.
• 2009 SOL 8.11 The student will
– solve practical area and perimeter problems
involving composite plane figures.
10
Explicit Content Changes

• 2001 SOL A.1 The student will solve multistep
linear equations and inequalities in one
variable …
• 2009 SOL A.5 The student will solve multistep
linear inequalities in two variables …

11
Increased Rigor in the
2009 Mathematics Standards of Learning

• Explicit content changes
– Movement of content between and among grade levels
– Increased content expectations

12

• Describing mean as “fair share” in grade 5
• Describing mean as “balance point” in grade 6
• Modeling one-step linear equations in grade 5
• Modeling multiplication and division with
• Percent increase/decrease in grade 8
These examples do not provide a
13

• Standard deviation, mean absolute deviation,
and z-scores in Algebra I
• Equations of circles in Geometry
• Normal distributions and the Standard Normal
curve in Algebra II
• Permutations and combinations in Algebra II

These examples do not provide a
14
Increased Rigor in the 2009 Mathematics
Standards of Learning Assessments

• Increased rigor reflective of the SOL
• Comprehensive interpretation of SOL and
Curriculum Framework
• Additional ways for students to
demonstrate understanding

15
Increased Rigor in the 2009 Mathematics
Standards of Learning Assessments

• Increased rigor reflective of the SOL
• Comprehensive interpretation of SOL and
Curriculum Framework
• Additional ways for students to
demonstrate understanding

16
Increased Rigor Reflected in SOL Assessments

OLD

Increased Rigor Reflected in SOL Assessments

NEW

Increased Rigor Reflected in SOL Assessments

OLD

Increased Rigor Reflected in SOL Assessments

NEW

Increased Rigor Reflected in SOL Assessments

OLD

Algebra 1         21
Increased Rigor Reflected in SOL Assessments

OLD

NEW

Algebra 1        22
Increased Rigor in the 2009 Mathematics
Standards of Learning Assessments

• Increased rigor reflective of the SOL
• Comprehensive interpretation of SOL and
Curriculum Framework
• Additional ways for students to
demonstrate understanding

23
SOL, Curriculum Framework,
and SOL Assessments
“The Curriculum Framework serves as a guide for
Standards of Learning assessment development.
Assessment items may not and should not be a
verbatim reflection of the information presented
in the Curriculum Framework.
Students are expected to continue to apply
knowledge and skills from Standards of Learning
presented in previous grades as they build
mathematical expertise.” – 2009 Mathematics Curriculum Framework

24
Comprehensive Interpretation
of the SOL and Curriculum Framework
SOL 3.11
The student will-
a) tell time to the nearest minute, using
analog and digital clocks; and
b) determine elapsed time in one-hour
increments over a 12-hour period.

25
Comprehensive Interpretation
of the SOL and Curriculum Framework
Under Essential Knowledge and Skills, the third bullet says:
• When given the beginning time and ending time,
determine the elapsed time in one-hour increments
within a 12-hour period (times do not cross between
a.m. and p.m.).
There are three elements in this type of problem: a
beginning time, an ending time, and the amount of time
that has elapsed. If given ANY two of these three
elements, the students should be able to find the missing
piece.

26
Comprehensive Interpretation
of the SOL and Curriculum Framework
G.12 The student, given the coordinates of the center of a circle
and a point on the circle, will write the equation of the circle.

Using the Curriculum Framework bullets and their converses,
students can be given combinations of the following and
– the coordinates of the center
– the diameter
– the coordinates of a point on the circle
– the equation of a circle
27
SOL, Curriculum Framework,
and SOL Assessments
“The Curriculum Framework serves as a guide for
Standards of Learning assessment development.
Assessment items may not and should not be a
verbatim reflection of the information presented
in the Curriculum Framework.
Students are expected to continue to apply
knowledge and skills from Standards of Learning
presented in previous grades as they build
mathematical expertise.” – 2009 Mathematics Curriculum Framework

28
Comprehensive Interpretation
of the SOL and Curriculum Framework
Use of Prior Knowledge:
• Even and odd numbers are taught in grade 2
(SOL 2.4), so numbers on a spinner in a grade
3 item can be referenced as even or odd (the
chance that a spinner will land on an even
number…).

29
Comprehensive Interpretation
of the SOL and Curriculum Framework
Use of Prior Knowledge:
• Stem-and-leaf plots are taught in grade 5 (SOL
5.15) and can be used to display data sets in
Algebra I (SOL A.9).
• Solving multistep equations are taught in
grade 8 (SOL 8.15) and Algebra I (SOL A.4),
and this skill can be used to find missing
measures throughout many of the geometry
standards.
30
Increased Rigor in the 2009 Mathematics
Standards of Learning Assessments

• Increased rigor reflective of the SOL
• Comprehensive interpretation of SOL and
Curriculum Framework
• Additional ways for students to
demonstrate understanding

31
Demonstrate Understanding
Addition of non-multiple choice items called
technology-enhanced items (TEI):
 Fill-in-the-blank
 Drag and drop
 Hot-spot: Select one or more “zones/spots”
to respond to a test item; i.e. select answer
option(s), shade region(s), place point(s) on
a grid or number line
 Creation of bar graphs/histograms
32
Example of Fill-in-the-Blank
Examples of Drag and Drop
Examples of Hot Spot
Examples of Hot Spot
Examples of Hot Spot
Creation of Graphs
How Can Teachers Achieve and
Maintain Instructional “Rigor”?
• Engage students in the learning process,
providing relevant activities and tasks that
require a high level of cognitive demand
• Ask high-leverage questions that require
students to think, process, and communicate
• Require students to justify their thinking and
reasoning

39
How Can Teachers Achieve and
Maintain Instructional “Rigor”?
• Provide instruction that requires students to
– become mathematical problem solvers that
– communicate mathematically;
– reason mathematically;
– make mathematical connections; and
– use mathematical representations to model
and interpret practical situations
Virginia’s Process Goals for Students
40
Mr. Michael Bolling – Michael.Bolling@doe.virginia.gov
Director, Office of Mathematics and Governor’s Schools,

Dr. Deborah Wickham – Deborah.Wickham@doe.virginia.gov
Mathematics Specialist, K-5

Mrs. Christa Southall – Christa.Southall@doe.virginia.gov
Mathematics Specialist

41

```
To top