Montana Mathematics Content Standards, Benchmarks, and

Performance Descriptors

2/6/2010

Purpose:

• To become familiar with: o the Montana Mathematics Standards, gain

understanding of the benchmarks and Essential Learning Expectations

o the Montana Mathematics Performance Descriptors

o the Vision for Montana Mathematics and how it translates into a district, a school and a classroom

2/6/2010

Montana Board of Public EducationStandards Revision 2005-2010

• The Montana Board of Public Education is charged with the responsibility of leading a process of standards revision pursuant to Administrative Rules of Montana 10.54.2503.

• The Office of Public Instruction facilitates this process in partnership with Montana educators and the Montana public.- Board of Public Education Statement of Purpose -

• Assure Montana citizens that its public schools are providing all children of our great state with challenging academic expectations.

• Revised standards provide a framework to help guide local curriculum and instruction.

2/6/2010

The 2008-2009 Mathematics Standards

Review Process

November 2008 – March 2009, the Office of Public Instruction convened a committee of K-16 mathematics educators from across the state to review and revise the K-12 Montana Mathematics Content Standards and Performance Descriptors. The committee was charged by the Board of Public Education to revise standards based on the following criteria. Standards will:

• be academic in nature and content specific.• be challenging and rigorous.• be clear, understandable and free of jargon.• be measurable.• address diversity, specifically fulfilling the commitment to

implementing MCA 20-1-501, Indian Education for All.

2/6/2010

Our team of diverse and hard-working individuals, through respect and communication, will meet our goal of improving Montana students’ mathematical education by revising the Montana Mathematics Content Standards by March 1st, 2009, while ensuring everyone has a voice and understanding that at times will have to agree to disagree.

Criteria for Benchmarks • clear statements of expectations for a proficient student • specific and significant • appropriate learning progression • challenging• manageable for instruction within the time frame • provide opportunity to learn prior to assessing • Contains no gaps, overlaps or redundancy

The 2008-2009 Mathematics Standards Review Process (cont’d)

2/6/2010

Number Sense & Operations

Algebraic & Functional Reasoning

Geometric Reasoning

Data Analysis

2/6/2010

HOW WELL

DOING THE MATH

NEARING PROFICIENCY

ADVANCED PROFICIENT

NOVICE

Performance Descriptors

2/6/2010

Mathematical Rigor

In the Montana Mathematics Content Standards, rigor is a process where students:

• approach mathematics with a disposition to accept challenge and apply effort;

• engage in mathematical work that promotes deep knowledge of content, analytical reasoning, and use of appropriate tools; and

• emerge fluent in the language of mathematics, proficient with the tools of mathematics, and empowered as mathematical thinkers.

A Vision for Montana Mathematics

2/6/2010

Building with Toothpicks 

 Use a pattern to determine the perimeter of the fifth shape in this sequence. Explain your solution.

A Learning Experience to Exemplify Montana Mathematics Standards

A Learning Experience to Exemplify Montana Mathematics Standards

2/6/2010

Building with Toothpicks 

• Describe how you would determine the perimeter of the nth shape. Write a word sentence and a formula.

• Remove the toothpicks from inside the shape and determine the area of the fifth shape. Explain your solution.

• Describe how you would determine the area of the nth shape. Write a word sentence and a formula.

 

Groups• Read the standard and determine what big

ideas described within the standard fit the Toothpick Problem.

• Select Benchmarks the Toothpick Problem addresses.

• Give evidence to justify your selection.

Connection to Standards, Benchmarks and Essential Learning Expectations

2/6/2010

Five Mathematical Processes

1.Mathematics does not exist in isolation. 2.Mathematics does not follow a single fixed

path. 3.Mathematics is not a private enterprise. 4.Mathematics is not free of context.5.Mathematics is about doing, not simply

knowing.

Vision for Montana Mathematics describes and explains what this means for Montana

2/6/2010

Five Mathematical Proficiencies

1. Conceptual Understanding2. Procedural Fluency3. Strategic Competence4. Adaptive Reasoning5. Productive Disposition

Vision for Montana Mathematics describes and explains what this means for Montana

2/6/2010

Five Montana Principles

1. All students can successfully learn mathematics.2. Mathematical processes are fundamental

companions to content. 3. Mathematics is a human endeavor with scientific,

social, and cultural relevance.4. Technology is integral to learning mathematics.5. Mathematics education is for the future, not for

today.

Vision for Montana Mathematics describes and explains what this means for Montana

2/6/2010

Standards-Based Education

1. Determine the essential learning expectations utilizing the Montana Mathematics Standards

2. Design lesson, activity, and/or problems that will teach the essential learning expectations

3. Design the formative assessments that will determine if essential learning has occurred

Brainstorm and share how to accomplish Standards-Based Mathematics Education in your classroom, your school and your district

2/6/2010

Questions?

2/6/2010

Thank you!

For more information on the Montana Mathematics Standards please contact:

Jean HowardMathematics Curriculum SpecialistMontana Office of Public InstructionPO Box 202501Helena, MT 59620-2501Telephone: (406) 444-0706E-mail: jhoward@mt.govhttp://www.opi.mt.gov/Math/Index.html

2/6/2010