mathematics

Harold R. Jacobs

Harold R. Jacobs 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 Harold R. Jacobs rather than just read about it. In short: Harold R. Jacobs (born 1939), who authored three mathematics books, both taught the subject and taught those who teach it.

Key takeaways

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

Reference excerpt

Harold R. Jacobs (born 1939), who authored three mathematics books, both taught the subject and taught those who teach it. Since retiring he has continued writing articles, and as of 2012 had lectured "at more than 200" math conferences. His books have been used by some homeschoolers and has inspired followup works.

Biography Jacobs was born in North Hollywood and while in high school "realized that he wanted to become a teacher." The 1939-born educator began "in the late 1960s" what became his first book, originally published in 1970, as an attempt to address the needs of "those students who had not done well in mathematics." His works helped inspire other educators to extend areas such as "inquiry-based learning." He chaired a high school math department in California for 12 years.

Works (1970): Mathematics: A Human Endeavor (revised 1982, 1994) A student workbook for this was subsequently written by Susan Knueven Wong. The 1994 edition was (re)titled as Mathematics, a Human Endeavor: A Textbook for Those Who Think They Don't Like the Subject. Jacobs' approach, described as ahead of its time, was to introduce concepts in an entertaining yet practical way. Jacobs' description of the mathematics of billiards inspired a teacher to write a simulation in the Logo educational computer programming language to help improve both his understanding and his teaching. (1974): Geometry: Seeing, Doing, Understanding (revised 1987, 2003). The 2003 edition makes reference to computer software such as The Geometer's Sketchpad. Even before this edition, the Teacher's notes for Geometry was used for developing new ways of teaching. One instructor credited the book's success to being "mathematically very sound" yet using a "little by little" approach. (1979): Elementary Algebra (revised 2016) The style of gently introducing new topics ahead of time, with details in a subsequent chapter, while accepted in homeschooling, has those who disagree for its use in classrooms. several articles for Encyclopædia Britannica and The Mathematics Teacher. The three books were published by W. H. Freeman and Company, and "overhead transparencies for" classroom use were subsequently developed. The Elementary Algebra text has attracted interest by homeschoolers, particularly when used in conjunction with an independently produced set of DVDs offering 36 hours of educational instruction.

References

Worked examples

Example 1 — a first encounter with Harold R. Jacobs

Start with the simplest possible case. Write down what Harold R. Jacobs 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 Harold R. Jacobs 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 Harold R. Jacobs 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 Harold R. Jacobs

In research: Harold R. Jacobs 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 Harold R. Jacobs 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: Harold R. Jacobs is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1939 births, 20th-century American writers, 21st-century American writers, so understanding it makes those chapters shorter.
In everyday life: Look for Harold R. Jacobs 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 Harold R. Jacobs in 20 minutes

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

Frequently asked questions

What is Harold R. Jacobs in simple terms?

Harold R. Jacobs (born 1939), who authored three mathematics books, both taught the subject and taught those who teach it.

Why does Harold R. Jacobs 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 Harold R. Jacobs?

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 Harold R. Jacobs.