Writing to Learn with Quantitative Information

“Once students understand HOW things are said, they can better understand WHAT is being said, and only then do they have a chance to know WHY it is said”

–Robert Jamison “Learning the Language of Mathematics”

Short In-Class Exercise

Choose a “meaty” graph from your field that is either ambiguous or supports several potential conclusions about the data.

Provide the chart or graph and, if applicable, the data set

Pose open “writing to learn” questions for free write (in class) or homework. Examples might include:

What is this graph arguing? What conclusions can you draw from this data? What conclusions are suggested but not fully supported by this

graph/chart alone? (If applicable) Write out 1-2 other conclusions that might be

supported by the data set.

Example Chart

Example Graph

Numeracy (or Quantitative Literacy)

Teaching Quantitative Reasoning

Learning (Skill Development)Most K–12 math classes

Arithmetic / algebra / geometry

Context-light (or –free)

Acquisition (Application)Social/physical science classes

Argument from evidence, sources

Context-intensive

Writing-intensive

Literacy

A Literacy Analogy:

Quantitative ReasoningTeaching Critical Reasoning

Learning (Skill Development)Early-grades English classes

Structure / spelling / grammar

Context-light (or –free)

Acquisition (Application)Humanities/Social science classes

Argument from evidence, sources

Context-intensive

Writing-intensive

Quantitative Reasoning Is…Sophisticated reasoning using elementary mathematics

The core set of “math” skills need not extend past the college-freshman level.

Understood and argued in a variety of written, graphical, and appropriate mathematical formats

Ultimately, reasoning – and hence writing – takes center stage, followed by visual aids, followed by data and charts, and finally algebra.

(This is a bit like an “upside-down math class.”)

A “habit of mind” and a “conspiracy” across disciplinesQR is a lens through which topical questions may be asked and answered across the curriculum, through whatever context is appropriate to the discipline.

Quantitative Literacy (“Case”)

Quantitative literacy stresses the use of mathematical and logical tools to solve common problems. QL is inseparable from its context (17). Quantitative literacy can be understood and expressed in a variety of written, graphical, and mathematical formats.

The Quantitative Literacy Design Team (part of the National Council on Education and the Disciplines) breaks quantitative literacy into the following components:

Elements (Confidence, logic, sensibility, interpretation)

Expressions (In public, personal, and professional spheres)

Skills (Basic algebra, statistics, modeling, etc.)

What Is It?

Elements of QR (“Case” 8)

Confidence with Mathematics

Cultural Valuation / Appreciation

Interpretation of Data

Logical Thinking

Informed Decision-Making

Mathematics in Context

Number Sense / Estimation

Practical (Applied) Skills

Prerequisite Knowledge

Where Is It?

Expressions of QR (“Case” 10)

Public Citizenship / Government Cultural Roles, History, Scientific Method

Personal Finances (Debts, Accounts, Investments,

Mortgages…) Personal Health (Treatments, Insurances, Studies…)

Professional Small Business Management / Data Analysis Statistical Quality Control Scheduling, Budgeting, Inventory Planning, …

What’s It Made Of?

Skills of QR (“Case” 16)

Arithmetic, esp. Proportions and Percentages

Basic Algebra, through Exponents/Logs

Data Interpretation / Representation

Basic Statistics / Sampling and Chance

Logical Reasoning

Computer Skills (Excel, SPSS, Maple, etc.)