mathematics

Patricia D. Shure

Patricia D. Shure 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 Patricia D. Shure rather than just read about it. In short: Patricia D. Shure is an American mathematics educator.

Key takeaways

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

Reference excerpt

Patricia D. Shure is an American mathematics educator. With Morton Brown and B. Alan Taylor, she is known for developing "Michigan calculus", a style of teaching calculus and combining cooperative real-world problem solving by the students with an instructional focus on conceptual understanding. She is a senior lecturer emerita of mathematics at the University of Michigan, where she taught from 1982 until her retirement in 2006.

Education and career Shure did both her undergraduate and graduate studies at the University of Michigan, earning a bachelor's degree in 1958 and a master's degree in 1960. After working as a secondary school teacher for two decades, she returned to Michigan in 1982 as coordinator for mathematics and science in the Coalition for the Use of Learning Skills. She also became a lecturer in mathematics, and later a senior lecturer.

Mathematics education At Michigan, she played a key role not just in teaching mathematics, but in training the other instructors and graduate students there to be good teachers of mathematics. Her work on calculus reform began in 1992; it was based in part on the "Harvard calculus" project led by Andrew M. Gleason, and her instructor training materials have been widely used at other universities. With Gleason and others, she became the author of a widely used precalculus textbook, Functions Modeling Change: A Preparation for Calculus (Wiley, 2000; 5th ed., 2017). The program she initiated at Michigan continues in successful use there.

Recognition In 2001 the Association for Women in Mathematics gave Shure their Louise Hay Award for her contributions to mathematics education. In the same year she became the AWM/MAA Falconer Lecturer, speaking on "The Scholarship of Learning and Teaching: A Look Back and a Look Ahead".

References

Worked examples

Example 1 — a first encounter with Patricia D. Shure

Start with the simplest possible case. Write down what Patricia D. Shure 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 Patricia D. Shure 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 Patricia D. Shure 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 Patricia D. Shure

In research: Patricia D. Shure 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 Patricia D. Shure 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: Patricia D. Shure 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 Patricia D. Shure 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 Patricia D. Shure in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what Patricia D. Shure 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 Patricia D. Shure out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Patricia D. Shure in simple terms?

Patricia D. Shure is an American mathematics educator.

Why does Patricia D. Shure 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 Patricia D. Shure?

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 Patricia D. Shure.