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Instruction and Assessment Analysis and Design August 1_ 2012

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Instruction and Assessment Analysis and Design August 1_ 2012 Powered By Docstoc
					        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

• Content additions



                          6
         Increased Rigor in the
 2009 Mathematics Standards of Learning


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

• Content additions



                          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

• Content additions



                          12
                 Content Additions

• Properties in elementary grades
• 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
  fractions in grade 6
• Percent increase/decrease in grade 8
       These examples do not provide a
       comprehensive listing of content additions.
                               13
                 Content Additions

• 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
       comprehensive listing of content additions.
                               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

                  Grade 3
Increased Rigor Reflected in SOL Assessments




                                       NEW




                  Grade 3
Increased Rigor Reflected in SOL Assessments




                                     OLD

                  Grade 4
Increased Rigor Reflected in SOL Assessments




                                      NEW

                  Grade 4
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
  asked to find other parts:
   – the coordinates of the center
   – the radius
   – 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
      Additional Ways for Students to
       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



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