An Introduction to Mathematics Curriculum Topic Study EMPOWERR Summer Institute July 27, 2011.

An Introduction to Mathematics Curriculum Topic Study

EMPOWERR Summer InstituteJuly 27, 2011

3 Goals for the CTS Intro Session

• (Learn about) To develop awareness of Curriculum Topic Study (CTS) as a tool you can use for connecting standards and research on learning to classroom practice.

• (Practice) To provide guided practice in using CTS.

• (Apply) To consider ways you might apply CTS to your work.

Bridging the Gap

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National Standards Research on Learning

Classroom PracticeState Standards

What is CTS?

A process that incorporates a systematic study of standards and research

A set of tools and collective resources for improving curriculum, instruction, assessment, and teacher content knowledge

An intellectually rigorous and engaging professional development experience

What CTS Is Not

CTS IS NOT:• A remedy for weak content knowledge• A collection of teaching activities• A description of “how to’s”• A quick fix• The end-all for professional development

Having State and National Standards Is Not Enough…

What has been missing is a systematic, scholarly, deliberate process to help educators intellectually engage with standards and research on student learning so they can make effective use of them. (Keeley, 2005)

CTS provides that “missing link”

A First Glance at the CTS Book• Pair up with someone at your table.• Open the CTS book at random. With your partner

or table group, do a quick scan of the page you opened to. What do you see that provides you with a “preview” of CTS?

• Mark the page with a sticky note.• Repeat 2-3 times to get an initial sense of what is

contained in the CTS book.• Share something you found that particularly

interests you and tell why.

Components of a CTS Study Guide

• CTS Sections and Outcomes• Selected Readings from CTS Resources• Web Site- Supplementary Material

http://www.curriculumtopicstudy.org/

The CTS Guide

• Each guide has 6 CTS sections (Left Column)o Purposes of the sections

I : Identify Adult Content Knowledge II : Consider Instructional Implications III : Identify Concepts and Specific Ideas IV : Examine Research on Student Learning V : Examine Coherency and Articulation VI : Clarify State Standards and District Curriculum

• Each section links to CTS sources and pre-vetted Readings (Right Column)

• Supplementary materials for each topic can be found at www.curriculumtopicstudy.org

CTS: The Swiss Army Knife of Curriculum, Instruction, and Assessment

Improve adult science literacy (I)

Improve knowledge of content teachers

teach (I)

Examine curricular and instructional considerations (II)

Identify difficulties and misconceptions (IV)

Identify “Big Ideas”, Concepts, Specific Ideas, and Skills (III)

Consider developmental

implications (II, IV)

Examine scope and sequence (III)

See connections and articulation within and

across topics (V)

Clarify state standards and district

curriculum (VI)

CTS Collective Resources- Experts at Your Fingertips 24/7

Indicates the resource is online

Indicates parts of the resource are online

Getting to Know the Resources

SciencePages 24-26

Science for All AmericansScience MattersBenchmarks for Science LiteracyThe National Science StandardsMaking Sense of Secondary ScienceAtlas of Science Literacy

MathematicsPages 27-30

Science for All AmericansBeyond NumeracyBenchmarks for Science LiteracyPrinciples and Standards for School MathematicsResearch CompanionAtlas of Science Literacy

Parallel Resources in Science CTS

Getting to Know the CTS Resources

Introduction to CTS Using K-12 Snapshots

The CTS Scaffold

Scaffold: The structure and supports that a teacher or more knowledgeable helper provides to allow a learner to perform a task he or she cannot yet perform independently. (Vygotsky, 1978; Dixon-Krauss, 1996; Wertsch,1991.)

Quick Summary of the CTS Scaffold

STEP 1: Scan and select the CTS category.

STEP 2: Scan the list of topics within the category that include the content you are examining.

STEP 3:Select the CTS guide you will use.

STEP 4: Determine which section(s) of the CTS guide will help you find the

information you need.

STEP 5: Select the resource(s) you will use, the grade span(s), and the readings.

STEP 6: Examine the reading for information relevant to your topic and

task.

STEP 7: Record your findings. If you do not find what you need, go back to Step 2 and repeat with another topic.

Quick Scaffold Practice Steps 1-3

“What kinds of experiences should I provide my middle school students when they are learning about percent?”

Category? Numbers and OperationsCTS Topic Guide?PercentPage Number of CTS Guide?Page 129

Quick Scaffold Practice- Step 4

“What kinds of experiences should I provide my middle school students when they are learning about percent?”

Section? Section IIOutcome?Consider Instructional Implications

Quick Scaffold Practice- Step 5

“What kinds of experiences should I provide my middle school students when they are learning about percent?”

Which resource, grade level, and page numbers do I read?Benchmarks (6-8)- Numbers, grade span essay, p 123and/or PSSM (6-8)-Number and Operations, p 215 Understanding Numbers, pp 215-217

What part of the page do I focus on?Just the essay, not the bullets!

More Quick Scaffold PracticeSteps 1-3

“What specific ideas about statistics should I focus on at the 3-5 grade level?”Category? Data AnalysisCTS Topic Guide?Statistical Reasoning or Summarizing DataPage Number of CTS Guide?Page 186 or 187

More Quick Scaffold Practice- Step 4

“What specific ideas about statistics should I focus on at the 3-5 grade level?”

Section? Section III (Could also include Section V and VI)Outcome?Identify Concepts and Specific Ideas

More Quick Scaffold Practice- Step 5

“What specific ideas about statistics should I focus on at the 3-5 grade level?”

Which resource, grade level, and page numbers do I read?Benchmarks (3-5) 9D Uncertainty pages 227-230; 9E Reasoning pages 232-234; 12E Critical Response Skills pages 298-300 PSSM (3-5) Data Analysis and Probability page 176 or 400

What part of the page do I focus on?Just the bulleted learning goals, not the essay.

More Quick Scaffold PracticeSteps 1-3

“What should adults know about mathematical equations? Category? AlgebraCTS Topic Guide?Expressions and EquationsPage Number of CTS Guide?Page 136

More Quick Practice- Step 4

“What should adults know about mathematical equations?

Section? Section IOutcome?Identify Adult Content Knowledge

More Quick Scaffold – Step 5

“What should adults know about mathematical equations?

Which resource, grade level, and page numbers do I read?Science for All Americans- Ch 9 pp 132-34 and/or Beyond Numeracy- Algebra, Some Basic Principles, pp 7-9

And Even More Practice- Steps 1-3

“I’m curious to see how the concepts and skills related to proportional reasoning develop from elementary grades through high school.”

Category? Integrated TopicsCTS Topic Guide?ProportionalityPage Number of CTS Guide?Page 198

And Even More Practice- Step 4

“I’m curious to see how the concepts and skills related to proportional reasoning develop from elementary grades through high school.”

Section? Section VOutcome?Examine Coherency and Articulation

And Even More Practice- Step 5

“I’m curious to see how the concepts and skills related to proportional reasoning develop from elementary grades through high school.”

What Atlas strand map will you use?Ratios and ProportionalityIs there a conceptual strand or strands within a map you should focus on?Parts and Wholes, Description or Comparison, and Computation

Last One!

“I wonder what difficulties or common misconceptions I should anticipate when students create and interpret graphs?”Category? Integrated TopicsCTS Topic Guide?Graphic RepresentationPage Number of CTS Guide?Page 196

Step 4?

“I wonder what difficulties or common misconceptions I should anticipate when students create and interpret graphs?”

Section? Section IVOutcome?Examine Research on Student Learning

Read and Examine Related Parts

Students of all ages often interpret graphs of situations as literal pictures rather than as symbolic representations of the situations. Many students interpret distance/time graphs as the paths of actual journeys. In addition, students confound the slope of a graph with the maximum or the minimum value and do not know that the slope of a graph is a measure of rate. When constructing graphs, middle-school and high-school students have difficulties with the notions of interval scale and coordinates even after traditional instruction in algebra. For example, some students think it is legitimate to construct different scales for the positive and the negative parts of the axes. Alternatively, students think that the scales on the X and Y axes must be identical, even if that obscures the relationship. When interpreting graphs, middle-school students do not understand the effect that a scale change would have on the appearance of the graph. Finally, students read graphs point-by-point and ignore their global features. This has been attributed to algebra lessons where students are given questions that they could easily answer from a table of ordered pairs. They are rarely asked questions about maximum and minimum values; intervals over which a function increases, decreases or levels off; or rates of change. (Benchmarks for Science Literacy page 351)

Related PartsStudents of all ages often interpret graphs of situations as literal pictures rather than as symbolic representations of the situations. Many students interpret distance/time graphs as the paths of actual journeys. In addition, students confound the slope of a graph with the maximum or the minimum value and do not know that the slope of a graph is a measure of rate. When constructing graphs, middle-school and high-school students have difficulties with the notions of interval scale and coordinates even after traditional instruction in algebra. For example, some students think it is legitimate to construct different scales for the positive and the negative parts of the axes. Alternatively, students think that the scales on the X and Y axes must be identical, even if that obscures the relationship. When interpreting graphs, middle-school students do not understand the effect that a scale change would have on the appearance of the graph. Finally, students read graphs point-by-point and ignore their global features. This has been attributed to algebra lessons where students are given questions that they could easily answer from a table of ordered pairs. They are rarely asked questions about maximum and minimum values; intervals over which a function increases, decreases or levels off; or rates of change. (Benchmarks for Science Literacy page 351)

Let’s Get Started!

CTS is like learning any new skill. It takes practice, perseverance, focus, time, and effort!

Eliciting Your Prior Knowledge

• Choose a snapshot that interests you.• Record your response to the question,

based only on your prior knowledge before using CTS.

• Save your response for later.

CTS Snapshot Practice

• Practice using the scaffold to answer the snapshot question. Do not take shortcuts this first time!

• Record notes from your reading that address the question (not the entire topic).

• Complete a reflection note.

Post your reflection note on the reflection wall charts. Begin another snapshot if you have time.

Reflection Wall

Examine your response to the snapshot question before doing CTS. How did you respond after doing a CTS?

Write a reflection on a Post-It note describing the value of using CTS to address your snapshot question. What new knowledge did you gain by doing the CTS?

Applying CTS to Our Work

• Turn to page 35 and examine the list of ways CTS can be applied to mathematics education.

• Turn to Chapter 4 on p 53 to scan examples of using CTS in content, curricular, instructional, and assessment contexts.

• Which of these applications do you think you might use CTS for (or do you have a new one)?

• Do a “Quick Write” on your thoughts about using CTS in our EMPOWERR work.

For Additional Information

• Visit the CTS web site at www.curriculumtopicstudy.org

• Contact: EMPOWERR Project Staff