mathematics

Mathetics

Mathetics 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 Mathetics rather than just read about it. In short: Mathetics is the science of learning. The term was coined by John Amos Comenius (1592–1670) in his work Spicilegium didacticum, published in 1680.

Key takeaways

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

Reference excerpt

Mathetics is the science of learning. The term was coined by John Amos Comenius (1592–1670) in his work Spicilegium didacticum, published in 1680. He understood Mathetics as the opposite of Didactics, the science of teaching. Mathetics considers and uses findings of current interest from pedagogical psychology, neurophysiology and information technology.

The Journal of Mathetics In 1962, The University of Alabama's Mathetics Foundation began publication of The Journal of Mathetics. However, only two issues were ever printed, the first in January and the second in April. The contents of the first issue included:

p. 7 THE TECHNOLOGY OF EDUCATION – domain theory, operant span, long division p. 75 EFFECTING THE USE OF EFFICIENT STUDY HABITS – SQ3R, stimulus control, graph paper p. 87 THE CONTROL OF EATING – obese, disposition to eat, weight loss p. 111 THE PROGRESS PLOTTER As A REINFORCEMENT DEVICE – reading rate, mathetical, delayed auditory feedback

Mathetics in literature Seymour Papert, MIT mathematician, educator, and author, explains the rationale behind the term mathetics in Chapter 5 (A Word for Learning) of his book, The Children's Machine. The origin of the word, according to Papert, is not from "mathematics," but from the Greek, mathēmatikos, which means "disposed to learn." He feels this word (or one like it) should become as much part of the vocabulary about education as is the word pedagogy or instructional design. In Chapter 6 of The Children's Machine, Papert mentions six case studies, and all six have their own accompanying learning moral and they all continue his discussion of his views of mathetics. Case study 2 looks at people who use mathematics to change and alter their recipes while cooking. His emphasis here is the use of mathematical knowledge without formal instruction, which he considers to be the central mathetic moral of the study. Papert states "The central epistemological moral is that we all used concrete forms of reasoning. The central mathetic moral is that in doing this we demonstrated we had learned to do something mathematical without instruction – and even despite having been taught to proceed differently" (p. 115). Papert's 1980 book, Mindstorms: Children, Computers, and Powerful Ideas, discusses the mathetic approach to learning. By using a mathetic approach, Papert feels that independent learning and creative thinking are being encouraged. The mathetic approach can be summarized as "learning by doing." Many proponents of the mathetic approach feel that the best, and maybe the only, way to learn is by self-discovery.

References

Mathetics: The technology of education TF Gilbert – Journal of Mathetics, January 1962

External links Research and information about Mathetics Database with literature about Mathetics in several languages Archived 2022-12-23 at the Wayback Machine (closed?) The Journal of Mathetics

Worked examples

Example 1 — a first encounter with Mathetics

Start with the simplest possible case. Write down what Mathetics 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 Mathetics 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 Mathetics 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 Mathetics

In research: Mathetics 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 Mathetics 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: Mathetics is common in secondary-school and first-year university syllabi. It links to neighbouring topics Didactics, Learning, so understanding it makes those chapters shorter.
In everyday life: Look for Mathetics 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 Mathetics in 20 minutes

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

Frequently asked questions

What is Mathetics in simple terms?

Mathetics is the science of learning. The term was coined by John Amos Comenius (1592–1670) in his work Spicilegium didacticum, published in 1680.

Why does Mathetics 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 Mathetics?

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 Mathetics.