Process and Content Standards in Mathematics: Thoughts and Reflections

V2CTM - Valley of Virginia Council of Teachers of Mathematics

November 13, 2012

Michael Bolling, Acting Director, Office of Mathematics and Governor’s Schools

memorable teacher

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Curve of Change Implementation

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Past PracticeDenial

Anger

Fear

Depression

Understanding

Acceptance

Progress

VDOE Professional Development Focus

2009

•Specific SOL changes (content)

2010

•Vertical articulation of the SOL and areas of greatest challenge (content and pedagogy)

2011

•Process goals (standards) in mathematics

2012

•Using formative assessments (performance tasks) to inform instruction

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“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…for students to

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

and interpret practical situations

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Virginia’s Process Goals for Students• Mathematical Problem Solving• Mathematical Communication• Mathematical Reasoning• Mathematical Connections• Mathematical Representations

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Direct Instruction

Modeling

Cooperative Learning

Kinesthetic Learning

Graphic Organizers

Independent Work

Scaffolded Instruction

Differentiation

Problem Solving

Communication

Reasoning

Connections

Multiple Representations

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Store A Store B Store C

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A recipe requires ½ cup of butter to make a dozen cookies.

•If you have 3 ¾ cups of butter, do you have enough to make at least 4 cookies for each of the 24 students in your math class? Explain why or why not.

•Show at least two different ways to solve the problem.

•You compare the price of butter from different store ads. If the original price of butter for a 1 pound pack is $3.99 at all three stores, explain which store has the best price to make your cookies the most affordable:

Standards of Learning• 6.4 The student will demonstrate multiple

representations of multiplication and division of fractions.

• 6.2 The student willa) investigate and describe fractions, decimals and percents

as ratios;b) identify a given fraction, decimal or percent from a

representation; c) demonstrate equivalent relationships among fractions,

decimals, and percents; and compare and order fractions, decimals, and percents.

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Vertical Articulation Documents

Assessment Types• Formal

– Formative (prior to or during instruction)– Summative (following instruction)

• Informal– Listening– Questioning– Observing

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Formative Assessment• ‘Assessment FOR learning’• Checking in on understanding and on the

formation of learning• Diagnostic in nature – should lead to changes

in instruction• Class tasks, homework, quizzes, benchmark

tests• Includes a lot of student feedback

Summative Assessment• ‘Assessment OF learning’• Typically provides a level of student

performance (grade)• Tests, projects, simulation tests• Less student feedback

Format of Assessment Items• Multiple choice• Open response

– Short response• Fill in the blank• Solve, simplify• Explain why/justify

– Open-ended • doesn’t have a predefined answer• synthesizes multiple concepts

Instruction, Assessment, and Backwards Design1. What are the content objectives that

students should master?2. How will we assess the content?3. What instructional experiences will we

provide that will assist ALL students to access and master the content?

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Purpose of assessment Improve student learning• Checking for student understanding, growth,

and progress• Determining common misunderstandings• Determining common errors• Informing instructional and assessment

decisions (currently and in the future)

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Instructional and Assessment Resources• Standards of Learning & Curriculum Framework• Testing blueprints• SOL Practice Items and Tools Practice and Guides• SOL Institutes (2009, 2010, 2011, 2012 coming soon)• Instructional Videos• ESS Sample Lesson Plans• Technical assistance documents A.9 AII.11 • Vocabulary resources• Statewide Analysis presentations

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We, as teachers, should be…• Engaging students in the learning, providing

relevant and rigorous activities and tasks• Asking high-leverage questions – make

students work harder than you• Requiring students to communicate their

thinking and listen carefully to them• Making students justify their thinking• Using multiple models

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Proce

ss G

oals!

We, as teachers, should be…• Using formative assessments to learn about

the level of student understanding to reflect on and change your own teaching

• Collaborating to develop a deeper understanding of what needs to be taught and how it should and could be assessed

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Be the teacher that makes a child remember you.

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