Strategies for Numeracy Across the Curriculum

Presented by Michelle Walker-Glenn

Thursday, Dec. 4, 2008

Overview

Workshop Objectives and Expectations Introduction Rationale and Definition: Numeracy Numeracy Strategies Across the Curriculum Leadership Strategies for Numeracy Across

the Curriculum

Workshop Objectives1. Familiarize participants with Strategies for Numeracy

Across the Curriculum2. Understand the rationale for emphasizing numeracy

across the curriculum3. Understand the relationship between numeracy and

literacy4. Develop a working definition of numeracy5. Receive overview training on specific numeracy

strategies that can be used by teachers in all content areas

6. Develop training strategies to introduce school staff and administration to the implementation of numeracy strategies

Why is Numeracy Important?

“To function in today’s society, mathematical literacy (what the British call “numeracy”) is as essential as verbal literacy. These two kinds of literacy, although different, are not unrelated. Without the ability to read and understand, no one can become mathematically literate. Increasingly, the reverse is also true: without the ability to understand basic mathematical ideas, one cannot fully comprehend modern writing such as that which appears in the daily newspapers.”

-- National Research Council, 2001

Mathematical literacy…a serious problem in the U.S. 78% of adults cannot explain how to compute

the interest paid on a loan 71% cannot calculate miles per gallon on a

trip 58% cannot calculate a 10% tip for a lunch

bill

(Philips, 2007)

U.S. Department of Education 2008

The Final Report of the National Mathematics Advisory Panel

“Children’s goals and beliefs about learning are related to their mathematics performance. Experimental studies have demonstrated that changing children’s beliefs from a focus on ability to a focus on effort increases their engagement in mathematics learning, which in turn improves mathematics outcomes: When children believe that their efforts to learn make them “smarter,” they show greater persistence in mathematics learning. Teachers and other educational leaders should consistently help students and parents to understand that an increased emphasis on the importance of effort is related to improved mathematics performance.”

U.S. Department of Education 2008

The Final Report of the National Mathematics Advisory Panel

“Mathematics performance and learning of groups that have traditionally been underrepresented in mathematics fields can be improved by interventions that address social, affective, and motivational factors. Recent research documents that social and intellectual support from peers and teachers is associated with higher mathematics performance for all students, and that such support is especially important for many African American and Hispanic students.”

U.S. Department of Education 2008

The Final Report of the National Mathematics Advisory Panel

“The achievement gap between students of differing ethnic and socioeconomic groups can be significantly reduced or even eliminated if low-income and minority students increase their success in high school mathematics and science courses.”

(Evans et al., 2006)

Effort Based vs. Ability Based Approach Effort makes a difference. Academic

ability can be grown. It is not how smart the child is, but how hard he or she works that determines success. All students are held to high expectations and offered opportunities to take challenging courses.

Students learn at different rates and may not reach proficiency at the same time. A mistake is not an inability to perform, but a learning opportunity . For that reason, students may re-do work and retake tests.

Effort based teachers are not necessarily unrealistic about their students’ capabilities, but they are unwilling to give up on them. Students are provided extra help—during school, in the summer, and before-and after-school.

Students of high ability receive the highest marks and are selected to take the most challenging courses. Students perceived with less ability are put in classes with lower expectations. Any academic deficiencies students have are attributed to low ability.

Since time is the constant in learning, students that fail to finish assignments, score well on tests, or learn key concepts by the “due dates” receive failing marks with no second chances.

Extra help opportunities are entirely the responsibility of the student. If they take advantage of them, that’s good; but no structure exists to ensure that students who need extra help get it.

Effort Based vs. Ability Based Approach Students can be motivated to come

to the belief that their effort is worthwhile, even if they do not believe it at the time they enter school.

Students are provided with extensive and specific feedback through the learning process to make connections in their understanding and continue to learn.

Teachers explicitly teach students how to exert effective efforts in learning—study skills, time management, problem solving, and note-taking.

Students have the responsibility to motivate themselves. If they do not believe they can do well in school, they probably won’t.

Feedback to students is limited, often occurring only in the form of a numerical grade or letter grade.

Teachers assume that students should have these skills by the time they reach their classroom.

Taken from “Masters for Motivation” by Jonathan Saphier. Chapter 5 in On Common Ground:The Power of Professional Learning Communities by Dufour, Eaker, & Dufour

3 Reasons Why Numeracy is Important… Economy/Employability

“I advise my students to listen carefully the moment they decide to take no more mathematics courses. They might be able to hear the sound of closing doors.”

--James Caballero, 1991

National SecurityNational Security Agency – www.nsa.gov

Democracy“To develop an informed citizenry and to

support a democratic government, schools must graduate students who are numerate as well as literate.”

--Lynn Arthur Steen, 1999

Why is Numeracy important for ALL students? “A strong grounding in HS mathematics

through Algebra II or higher correlates powerfully with access to college, graduation from college, and earning in the top quartile of income from employment.”

The correlation is even stronger for African American and Hispanic students!

Transforming Traditional Mathematics Instruction intoInstruction with an Emphasis on Mathematical Literacy

Area of Mathematics

Traditional Perspective Mathematical Literacy

Perspective

Arithmetic Adding, subtracting multiplying, and dividing

Units and conversions, measurements and tolerances, estimates and accuracy

Numbers Place value, digits Notation and coding, index numbers and averages, employment indices

Geometry Properties of circles and triangles, areas and volumes

Shapes and measurements in three dimensions to organize data, global positioning systems

Statistics Means, medians, standard deviations Visual displays of quantitative ideas, random

trials, confidence intervals

Logic Mathematical rigor, deductive proof Hypotheses, conjectures, causality and correlation, statistical inference

Probability Calculating combinations Estimating and comparing risks, chance, and randomness

Applications Solving word problems Collecting, organizing and interpreting data; allocating resources and negotiating

differences

Proof Logical deduction Counter examples, scientific reasoning, legal standards, beyond a reasonable doubt

Technology Doing arithmetic on calculators, graphing calculators

Spreadsheets, statistical packages, presentation

software, Internet

What is Numeracy?

“At homeness” with numbers Appreciation of mathematics Confidence in math Reason Mental math ability Use symbols Sense of numbers Use mathematical models Interpret data Read and interpret graphs ……

Verbal Literacy and Numeracy

SREB’s Definition of Numeracy• The ability to interpret and understand numeric

symbols and relationships

• The ability to communicate and represent mathematical concepts in a variety of ways

• The development of mathematical culture and way of thinking and looking at the world in a mathematical way

• Appreciation for aesthetics, history and application of math

Source: SREB, 2007

Activity: Defining Numeracy

1. What are some characteristics of a numerate person (student)?

2. What are some examples of innumeracy in our society?

3. What does good teaching of numeracy look like?

4. What does poor teaching of numeracy look like?

Adding It Up (National Research Council)

UNDERSTANDING (conceptual understanding)—comprehension of mathematical concepts, operations, and relations, knowing what mathematical symbols, diagrams and procedures mean.

COMPUTING (procedural fluency)—Skill in carrying out procedures such as adding, subtracting, multiplying and dividing flexibly, accurately, efficiently, and appropriately.

APPLYING (strategic competence)—Ability to formulate, represent, devise strategies and solve mathematical problems using concepts and procedures appropriately.

REASONING (adaptive reasoning)—Capacity for logical thought, reflection, explanation, and justification, extending something known to something not yet known.

ENGAGING (productive disposition)—Habitual inclination to see mathematics as sensible, useful, and worthwhile, coupled with a belief in diligence and one’s own efficacy. Mathematics is useful and doable if one works at it.

Adding it UpNational Research Council(2001)

UnderstandingConceptual Understanding Strand

1/3

Understanding Conceptual Understanding Strand

1/2 of 1/3

ComputingProcedural Fluency Strand

1/2 x 1/3 = 1/6

ApplyingStrategic Competence Strand

“Charles went to the kitchen and saw that there was some pudding left in the pan. He noticed that about 1/3 of the pudding was left in the pan. He ate 1/2 of the remaining pudding. What fraction of the original pudding did he not eat?

ReasoningAdaptive Reasoning

1/2 plus 1/3 does not equal 2/5. Explain why this statement is true.

OR…

"Five out of four people have trouble with fractions.“(Steven Wright)

Explain how this quote is an example of irony.

EngagingProductive Disposition Strand

“What good are fractions?”

Why Teach Numeracy “Across the Curriculum”?

Learning is about making connections Brain research supports the need for connected

learning

Organization of Guidebook…

1. IntroductionRationale and definitions

2. Strategies for Improving Numeracy Across the Curriculum

Seven strategies

3. Leadership for Numeracy Across the Curriculum

Leadership activities, self-assessements, planning tools

What can all teachers do NOW to enhance

Numeracy? Be a good role model. Showcase the way you use mathematics in your professional life as well as your specific content area.

Make mathematics an integral part of daily instruction. Strive to make a connection during each class.

Provide time in class for students to work on mathematics that relates to instructional objectives for your content area.

Incorporate logical reasoning and problem solving opportunities daily, as it relates to your content.

Provide resources for students such as calculators, rulers, scale models, graphic organizers, charts, graphs, statistical data, etc., to enable students to experience mathematical connections to various topics across the curriculum.

Create and/or gather samples of mathematical connections to your specific content area. Share newspaper articles, magazine articles, and professional journal articles that show how mathematics is utilized in your academic discipline.

Allow students choice about their completion of assignments that incorporate mathematics and problem solving.

Source: Adapted from SREB, 2003

Invite students to incorporate data and data analysis as part of writing to authentic audiences for authentic reasons about which they truly care.

Provide students with prompt feedback about content as well as mathematical reasoning, when appropriate.

Avoid teaching computation in isolation. It should be addressed in the context of students’ own authentic problem solving.

Analyze student work to determine instructional implications and make adjustments in instruction to address areas of need.

Look at student work with an eye for logical reasoning, use of multiple representations, incorporation of data, and use of graphs that make cross-curricular connections.

Read professional literature about incorporating mathematical concepts into your specific content area.

Focus on improving each student’s knowledge and ability to apply mathematical thinking and reasoning skills across content areas rather than just developing computational skills in isolation.

Avoid sharing any personal “math phobias” or a personal dislike of mathematics. Educators never boast of being illiterate, yet we often freely share that we are innumerate!

Source: Adapted from SREB, 2003

Numeracy Strategies – Jigsaw Activity Familiarize yourself with your assigned strategy (10 minutes).

Working with a partner or group, give a summary (3-5 minutes) of the strategy. Use chart paper if necessary. Give examples of how you could use this strategy in your classroom.

Strategy 1 – p. 12Strategy 2 – p. 15 Strategy 3 – p. 21 Strategy 4 – p. 23 Strategy 5 – p. 28 Strategy 6 – p. 33 Strategy 7 – p. 37

Activity: Are We Implementing Across the Curriculum? Read through the list of statements on p. 42 and put

a check mark next to those that you believe are true for your school.

For statements marked “not true”, discuss the “next steps” necessary to make these into true statements.

Generate a list of 3-5 immediate actions that can be taken to support increased numeracy across the curriculum

Be prepared to share your action steps with the group.

Activity: Numeracy Survey for School Leaders Complete the “Numeracy Survey for School

Leaders” p. 76 without putting your name on it. Be honest!

Crumple survey and toss into a pile in the center of the room.

Select a survey from the pile…not your own. Create human bar graph.

1. Is numeracy emphasized in your school improvement plan? Yes Somewhat No

2. Does the school collect data on numeracy indicators, such as the number of students in every class who meet each standard each month? Yes No

3. Does the school have formal goals for numeracy? Yes Somewhat No

4. Does the school have formal standards for numeracy practice? Yes No

5. Does the school faculty, in general, use research-based strategies for improving numeracy?

Yes Somewhat No

6. Does the school environment and school culture promote numeracy? Yes Somewhat No

7. Would a visitor walking through your school be able to see and understand that numeracy is a strong focus here?

Yes Somewhat No

8. Do you use common planning time to ensure that teachers collaborate on teaching strategies?

Yes No

9. If yes to the previous question, is that time used effectively. Yes Somewhat No

10. Are teachers and administrators frequently observed demonstrating the value of numeracy through real-life experiences?

Yes Somewhat No

11. Does your school have a numeracy coach? Yes Somewhat No

12. In your opinion, what percentage of students are capable of meeting national mathematics standards (i.e., NCTM), given the right instruction?

13. In your opinion, what percentage of your faculty accepts responsibility for increasing the mathematics achievement of all students in your school, even those students not in their classes?

14. Are numeracy practices rewarded in your school? Yes Somewhat No

Closing Activity…

Key Ideas… Next Steps…

What will you do differently tomorrow morning? What will you do differently next week/month? What will you do differently this school year?

Homework: Creating Lesson Plans with a Focus on Numeracy…Math Teachers: Work with non-math colleagues to develop 3

lesson plans in non-math content areas using the Numeracy Strategies (p. 12-37). Bring copies of your plans for the group and be prepared to share.

Non Math Teachers: Use Numeracy Strategies (p. 12-37) to develop 3 lesson plans that incorporate numeracy across the curriculum. Bring copies of your plans for the group and be prepared to share.

Non Teachers: Complete at least 1 leadership activity (p. 40-82) with a team. Be prepared to share the results of your activity.

Homework: Bring HSTW or MMGW 2008 Assessment Data

All Participants: Bring a copy of your schools HSTW or MMGW 2008 Assessment Data

High School Page 1 - Executive Summary Page 2 – Key Indicators of Student Achievement Page 4 – 2008 Mean Math Scores Page 7 – Percent Meeting Math Goals Page 11 – Percent Taking HSTW Rec. Math Curr. Page 15 – Emphasis on Numeracy Across the Curriculum Page 28 – Emphasis on Numeracy Across the Curriculum Pages 85-96 – Math Demographic Data Pages 216-217 – Teacher Survey on Challenging Math Content

Extra Credit for Math Teachers: Review all of the questions listed on a test or

quiz. Identify whether each question addresses:

Conceptual understanding Procedural fluency Strategic competence (applying to story problem) Adaptive reasoning (justifying answers/explaining) Productive disposition (what good is ___ ?)Do your assessments enable students to develop all

5 strands of the “rope”?

Thank You

Contact Information:

Michelle Walker-Glenn

shellw@cinci.rr.com

“A man is like a fraction whose numerator is what he is and whose denominator is what he thinks of himself. The larger the denominator, the smaller the

fraction.” – Leo Tolstoy