Talking writing and mathematical thinking and quantitative reasoning

Quantitative Skills, Thinking, and Reasoning A variety of resources that use quantitative thinking in the classroom are available through SERC websites.

From this directive, four assessment initiatives were developed. Two of these - writing and critical thinking - are familiar concepts to most educators. Two others - information technology literacy and quantitative reasoning - may be relatively new concepts, or at least relatively new terminologies.

The May,Dialogue Issue No. In this issue, an overview of quantitative reasoning will be presented. Often, quantitative reasoning QR is assumed to be synonymous with mathematics, and, indeed, the two are inextricably linked.

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Yet there are differences, one of which is that while mathematics is primarily a discipline, QR is a skill, one with practical applications. A mathematician might take joy in abstraction, but the well-educated citizen can apply QR skills to daily contexts: Moreover, while mathematics is often exclusive, frequently with a language of its own, QR is inclusive, its language plain and everyday.

In our information-rich - some might say information-overloaded - society, QR skills are especially important. We may no longer need to perform quantitative calculations by hand, but we do need to interpret them and judge their accuracy.

Few people are trained to work with complex mathematical concepts, but all educated citizens should be able to understand mathematics well enough to develop informed opinions about quantitative concepts.

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To illustrate the point, here are some test questions taken from a freshman Quantitative Reasoning Study Packet at Wellesley College. Answering them requires quantitative skills that most educators would agree all educated citizens should possess.

They also estimate that the party-goers left behind 40 tons of garbage. Given that a ton equals 2, pounds, how many pounds of garbage did the average party-goer leave behind? Assume that the investment would increase by the same proportion.

Did the number of injured skaters almost double, almost triple, or more than triple? QR is a state-mandated accountability measure While arguably not the most important reason to address QR as a component of a complete education, it is one of four state-mandated student learning outcomes.

As mentioned, writing, critical thinking, and information technological literacy are the others. Western Washington University is leading the state effort in developing an assessment of student learning in quantitative reasoning. We will be developing a plan for assessing QR on our campus and will provide a progress report to the Higher Education Coordinating Board later this year.

QR is a student learning outcome For most educators the more important reason to assess QR is that in order to become educated citizens students should graduate from college with some level of competence in quantitative reasoning.

Many students do not learn sophisticated math skills, but all should be able to use simple math tools to reason - to understand, interpret, critique, debunk, challenge, explicate, and draw conclusions. In short, college graduates should be able to evaluate the crush of quantitative data modern life throws at all literate citizens.

According to the Mathematical Association of America MAA 3the following quantitative literacy or QR requirements should be established for all students who receive a bachelor's degree: Interpret mathematical models such as formulas, graphs, table, and schematics, and draw inferences from them.

Represent mathematical information symbolically, visually, numerically, and verbally. Use arithmetical, algebraic, geometric, and statistical methods to solve problems.

Estimate and check answers to mathematical problems in order to determine reasonableness, identify alternatives, and select optimal results.

Recognize that mathematical and statistical methods have limits. At Wellesley, all freshmen are required to take a QR placement test. If they don't meet minimum standards, they must enroll in QRa course that brings them up to competency.

Once they have completed QR of if they have already passed the QR placement test students must, at some point in their academic career, take a QR overlay course, designed to "engage students in the analysis and interpretation of data in a scientific or social context.

Overlay courses are offered in the humanities, sciences, and social sciences. They have five basic goals note that these goals echo the Quantitative Literacy requirements established by the MAA.Features that contribute to an effective community of writers also apply to mathematics classrooms, where students use writing and talking "to make their mathematical thinking visible," according to Phyllis and David Whitin (Math 2).

3 Talking, Writing, and Mathematical Thinking ideas builds a willingness to live with the tentative and the provi-sional, an important dimension of a risk-taking stance (Lampert. Preview OVERVIEW. By talking, writing, and reasoning in math journals, students shift the emphasis of their work from finding the “right” answer to a metacognitive exploration of .

Writing in mathematics provides unique opportunities for students to engage in self-assessment and become critical of the mathematical writing of others, and it serves as a window for teachers to better understand the mathematical thinking of students.

Cognitive Functioning and Psychological Processing Definitions, Areas of Impact, and Recommended Strategies/Accommodations sequential and quantitative reasoning, and categorical reasoning. Quantitative reasoning- the ability to inductively and deductively reason with concepts involving mathematical relations and properties.

To improve your Logical Reasoning skills, it is important to differentiate between observations and inferences. Observation means using your senses such as hearing, seeing, smelling, touching to collect the required data or information.