strategies for numeracy across the curriculum1

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Strategies for Numeracy

Across the CurriculumPresented 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 Objectives

1. Familiarize participants with Strategies for Numeracy Across the Curriculum

2. Understand the rationale for emphasizing numeracyacross the curriculum

3. Understand the relationship between numeracy and

literacy4. Develop a working definition of numeracy

5. Receive overview training on specific numeracystrategies that can be used by teachers in all content

areas6. Develop training strategies to introduce school staff and

administration to the implementation of numeracystrategies



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 relatedto their mathematics performance. Experimental studieshave demonstrated that changing children’s beliefs from

a focus on ability to a focus on effort increases their engagement in mathematics learning, which in turnimproves mathematics outcomes: When children believethat their efforts to learn make them ―smarter,‖ they showgreater persistence in mathematics learning. Teachers

and other educational leaders should consistently helpstudents and parents to understand that an increasedemphasis on the importance of effort is related toimproved mathematics performance.‖






―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.‖






―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. Academicability can be grown. It is not how smartthe child is, but how hard he or she worksthat determines success. All students areheld to high expectations and offeredopportunities to take challenging courses.

Students learn at different rates and maynot reach proficiency at the same time. Amistake is not an inability to perform, buta learning opportunity . For that reason,students may re-do work and retaketests.

Effort based teachers are not necessarily

unrealistic about their students’capabilities, but they are unwilling to giveup on them. Students are provided extrahelp—during school, in the summer, andbefore-and after-school.

Students of high ability receive thehighest marks and are selected to takethe most challenging courses. Studentsperceived with less ability are put inclasses with lower expectations. Anyacademic deficiencies students have areattributed to low ability.

Since time is the constant in learning,students that fail to finish assignments,score well on tests, or learn key conceptsby the ―due dates‖ receive failing markswith no second chances.

Extra help opportunities are entirely theresponsibility of the student. If they takeadvantage of them, that’s good; but nostructure exists to ensure that studentswho need extra help get it.



Effort Based vs. Ability Based Approach

Students can be motivated to cometo the belief that their effort isworthwhile, even if they do notbelieve it at the time they enter school.

Students are provided withextensive and specific feedbackthrough the learning process tomake connections in their understanding and continue tolearn.

Teachers explicitly teach students

how to exert effective efforts inlearning—study skills, timemanagement, problem solving, andnote-taking.

Students have the responsibility tomotivate themselves. If they do notbelieve they can do well in school,they probably won’t.

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

Teachers assume that students

should have these skills by the timethey reach their classroom.

Taken from ―Masters for Motivation‖ by Jonathan

Saphier. Chapter 5 in On Common Ground:ThePower of Professional Learning Communities byDufour, 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 Security

National Security Agency – www.nsa.gov

Democracy

“To develop an informed citizenry and tosupport 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 quartileof income from employment.‖

The correlation is even stronger for African

American and Hispanic students!



Transforming Traditional Mathematics Instruction into

Instruction with an Emphasis on Mathematical Literacy

Area of

Mathematics

Traditional Perspective Mathematical Literacy

Perspective

Arithmetic Adding, subtracting multiplying, anddividing

Units and conversions, measurements andtolerances, 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 numericsymbols 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 (conceptu al und erstanding ) —comprehension of mathematical concepts, operations, and relations, knowing whatmathematical symbols, diagrams and procedures mean.

COMPUTING (proc edural f luency ) —Skill in carrying out procedures suchas adding, subtracting, multiplying and dividing flexibly, accurately,efficiently, and appropriately.

APPLYING (strategic comp etence) — Ability to formulate, represent,

devise strategies and solve mathematical problems using concepts andprocedures appropriately.

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

ENGAGING (produc t ive dispos i t ion) —Habitual inclination to seemathematics as sensible, useful, and worthwhile, coupled with a belief indiligence and one’s own efficacy. Mathematics is useful and doable if one

works at it.



Adding it Up

National Research

Council(2001)



Understanding Conceptual Understanding Strand

1/3



Understanding

Conceptual Understanding Strand

1/2 of 1/3



Computing Procedural Fluency Strand

1/2 x 1/3 = 1/6



Applying Strategic 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?



Reasoning Adaptive 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.



Engaging Productive 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. Introduction

Rationale and definitions

2. Strategies for Improving Numeracy Across

the CurriculumSeven strategies

3. Leadership for Numeracy Across the

CurriculumLeadership 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 connectionduring each class.

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

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

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

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

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

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 howyou could use this strategy in your classroom.

Strategy 1 – p. 12


Strategy 3 – p. 21Strategy 4 – p. 23






Activity: Are We Implementing Across the

Curriculum?

Read through the list of statements on p. 42 and puta check mark next to those that you believe are truefor your school.

For statements marked ―not true‖, discuss the ―nextsteps‖ necessary to make these into truestatements.

Generate a list of 3-5 immediate actions that can betaken to support increased numeracy across thecurriculum

Be prepared to share your action steps with thegroup.



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 thecenter 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 teachingstrategies?

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 3lesson plans in non-math content areas using the NumeracyStrategies (p. 12-37). Bring copies of your plans for thegroup and be prepared to share.

Non Math Teachers: Use Numeracy Strategies (p. 12-37) todevelop 3 lesson plans that incorporate numeracy acrossthe curriculum. Bring copies of your plans for the group andbe 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 MMGW2008 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 CurriculumPages 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

[email protected]

“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

mailto:[email protected]

mailto:[email protected]

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