Instruction and Assessment Analysis and Design August 1, 2012

Increased Rigor in the 2009 Mathematics Standards of Learning

January 2013

Michael Bolling, DirectorOffice of Mathematics and Governors Schools

1What 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.

#Many discussions relating to the definition of rigorSome people equate harder with rigorous

21/17/2013What is Rigor?What is Rigor?Increased Rigor of the 2009 Mathematics Standards of LearningNew Assessments that Reflect the Increased Rigor of the StandardsInstructional Rigor

#Rigor comes from a combination of things: increased content expectations and instructional and assessment experiences that require an increased level of cognitive demand. 3What 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.

#Rigor requires all members of the educational process, teachers and students, to be deeply involved in the learning process

41/17/2013What 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.

#Rigor requires meaningful and relevant application of content and facilitates their ability to develop strategies to solve problems based on what they know, even if it is in an unfamiliar setting.51/17/2013Increased Rigor in the 2009 Mathematics Standards of LearningExplicit content changes Movement of content between and among grade levelsIncreased content expectationsContent additions

#6Increased Rigor in the 2009 Mathematics Standards of LearningExplicit content changes Movement of content between and among grade levelsIncreased content expectationsContent additions

#72001 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.

Explicit Content Changes

#82001 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.

Explicit Content Changes

#92009 SOL 6.10 The student willc) solve practical problems involving area and perimeter2001 SOL 7.7 The student, given appropriate dimensions, willb) 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.

Explicit Content Changes

#102001 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

Explicit Content Changes

#11Increased Rigor in the 2009 Mathematics Standards of LearningExplicit content changes Movement of content between and among grade levelsIncreased content expectationsContent additions

#12Content AdditionsProperties in elementary gradesDescribing mean as fair share in grade 5Describing mean as balance point in grade 6Modeling one-step linear equations in grade 5Modeling multiplication and division with fractions in grade 6Percent increase/decrease in grade 8These examples do not provide a comprehensive listing of content additions.

#Content AdditionsStandard deviation, mean absolute deviation, and z-scores in Algebra IEquations of circles in GeometryNormal distributions and the Standard Normal curve in Algebra IIPermutations and combinations in Algebra IIThese examples do not provide a comprehensive listing of content additions.

#Increased Rigor in the 2009 Mathematics Standards of Learning AssessmentsIncreased rigor reflective of the SOLComprehensive interpretation of SOL and Curriculum FrameworkAdditional ways for students to demonstrate understanding

#15Increased Rigor in the 2009 Mathematics Standards of Learning AssessmentsIncreased rigor reflective of the SOLComprehensive interpretation of SOL and Curriculum FrameworkAdditional ways for students to demonstrate understanding

#16Increased Rigor Reflected in SOL Assessments

Grade 3OLD

#17Increased Rigor Reflected in SOL Assessments

Grade 3NEW

#18Increased Rigor Reflected in SOL Assessments

OLDGrade 4

#19Increased Rigor Reflected in SOL Assessments

Grade 4NEW

#Increased Rigor Reflected in SOL Assessments21

OLDAlgebra 1

#2122OLD

Algebra 1NEWIncreased Rigor Reflected in SOL Assessments

#22Increased Rigor in the 2009 Mathematics Standards of Learning AssessmentsIncreased rigor reflective of the SOLComprehensive interpretation of SOL and Curriculum FrameworkAdditional ways for students to demonstrate understanding

#23SOL, Curriculum Framework,and SOL AssessmentsThe 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

#24Comprehensive Interpretationof the SOL and Curriculum Framework

SOL 3.11 The student will-a) tell time to the nearest minute, using analog and digital clocks; andb) determine elapsed time in one-hour increments over a 12-hour period.

#25Comprehensive Interpretationof 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.

#26Comprehensive Interpretationof 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 circlethe equation of a circle

#27SOL, Curriculum Framework,and SOL AssessmentsThe 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

#28Comprehensive Interpretationof 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).

#29Comprehensive Interpretationof the SOL and Curriculum FrameworkUse 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.

#30Increased Rigor in the 2009 Mathematics Standards of Learning AssessmentsIncreased rigor reflective of the SOLComprehensive interpretation of SOL and Curriculum FrameworkAdditional ways for students to demonstrate understanding

#31Additional Ways for Students to Demonstrate UnderstandingAddition of non-multiple choice items called technology-enhanced items (TEI):Fill-in-the-blankDrag and dropHot-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 lineCreation of bar graphs/histograms

#32Example of Fill-in-the-Blank

#33Examples of Drag and Drop

#34Examples of Hot Spot

#35Examples of Hot Spot

#36Examples of Hot Spot

#37Creation of Graphs

#38How 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 demandAsk high-leverage questions that require students to think, process, and communicateRequire students to justify their thinking and reasoning

#How Can Teachers Achieve and Maintain Instructional Rigor?Provide instruction that requires students tobecome mathematical problem solvers thatcommunicate mathematically; reason mathematically;make mathematical connections; anduse mathematical representations to model and interpret practical situations

Virginias Process Goals for Students

#40Mr. Michael Bolling Michael.Bolling@doe.virginia.govDirector, Office of Mathematics and Governors Schools,

Dr. Deborah Wickham Deborah.Wickham@doe.virginia.govMathematics Specialist, K-5

Mrs. Christa Southall Christa.Southall@doe.virginia.govMathematics Specialist

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