mathematics

Virginia Warfield

Virginia Warfield is a mathematics topic covered in the lgStudy science library. This page brings together a partial reference excerpt, illustrations, worked examples, real-world applications and a short study plan, so you can understand Virginia Warfield rather than just read about it. In short: Virginia "Ginger" Patricia McShane Warfield is an American mathematician and mathematical educator. She received the Louise Hay Award from the Association for Women in Mathematics in 2007.

Key takeaways

Virginia Warfield belongs to mathematics; place it in that map before memorising details.
Learn the definition first, then one example that makes the definition concrete.
Connect Virginia Warfield to a quantity you can measure, compute or draw — that is where exam questions come from.
Reproduce the core statement of Virginia Warfield from memory before moving on to harder problems.

Reference excerpt

Virginia "Ginger" Patricia McShane Warfield is an American mathematician and mathematical educator. She received the Louise Hay Award from the Association for Women in Mathematics in 2007.

Education Warfield's father was mathematician Edward J. McShane. She received her Ph.D. in mathematics from Brown University in 1971. Her doctoral advisor was Wendell Fleming and the title of her dissertation was A Stochastic Maximum Principle.

Career While making contributions to the field of stochastic analysis after her Ph.D., Warfield became more and more engrossed by the problems of mathematics education. She worked with Project SEED, a highly regarded mathematics program whose goal was to promote sense-making mathematical activities for fourth through sixth graders. She addressed issues of teacher preparation and enhancement. She collaborated with the French mathematician Guy Brousseau, a pioneer in the “didactics of mathematics,” the scientific study of issues in mathematics teaching and learning. She has been an active member of the Association for Women in Mathematics (AWM). She has chaired the Education Committee, has served as Education Column Editor for the AWM Newsletter, and was elected as a Member-at-large to the Executive Committee. She has been a member of the Mathematical Association of America’s committees on Professional Development and Mathematical Education of Teachers.

Books Warfield is the author of the book Invitation to Didactique (self-published, 2007, and Springer Briefs in Education, 2014) and the co-author of Teaching Fractions through Situations: A Fundamental Experiment (with Guy Brousseau and Nadine Brousseau, Springer 2013).

References

Illustrations

Worked examples

Example 1 — a first encounter with Virginia Warfield

Start with the simplest possible case. Write down what Virginia Warfield claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In mathematics, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to Virginia Warfield before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about Virginia Warfield ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of Virginia Warfield

In research: Virginia Warfield appears in mathematics research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry: Engineering practice reuses Virginia Warfield in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom: Virginia Warfield is common in secondary-school and first-year university syllabi. It links to neighbouring topics 20th-century American mathematicians, 20th-century American women mathematicians, 21st-century American mathematicians, so understanding it makes those chapters shorter.
In everyday life: Look for Virginia Warfield outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.

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How to study Virginia Warfield in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what Virginia Warfield means in your own words.
Compare your version with the excerpt and mark what you missed.
Work through the three examples above with pen and paper.
Explain Virginia Warfield out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Virginia Warfield in simple terms?

Virginia "Ginger" Patricia McShane Warfield is an American mathematician and mathematical educator. She received the Louise Hay Award from the Association for Women in Mathematics in 2007.

Why does Virginia Warfield matter?

Because it connects several mathematics ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study Virginia Warfield?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on Virginia Warfield.