“How to Solve It” (first published in 1945) is a small volume by mathematician George Pólya describing methods of problem solving. The book suggests the following steps when solving a mathematical problem:
1. Understand the problem.
2. Devise a plan to solve it.
3. Carry out the plan.
4. Revise and extend: look back on your work.
Yonkoma manga (4コマ漫画, “four cell manga” or 4-koma for short), a comic strip format, generally consists of gag comic strips within four panels of equal size ordered from top to bottom.
And also:
Traditionally, yonkoma follow a structure known as kishōtenketsu. This word is a compound formed from the following Japanese kanji characters:
Ki (起): The first panel forms the basis of the story; it sets the scene.
Shō (承): The second panel develops upon the foundation of the story laid down in the first panel.
Ten (転): The third panel is the climax, in which an unforeseen development occurs.
Ketsu (結): The fourth panel is the conclusion, in which the effects of the third panel are seen.
What is the best way to educate, to teach and learn? Ideally, students shouldn’t merely memorize facts and recall them on demand, although retaining well accepted knowledge is important. Certainly, students need mental structures to organize these facts, so that they form associated groups of categories and classification. Additionally, methods are needed for accepting and rejecting facts, and procedures for organizing facts, although facts may often be revisited for truth, or to reorganize them, and so on.
Benjamin Bloom et al. developed a taxonomy for educators of six mental aspects for the acquisition of knowledge, which was revised later into six cognitive actions or processes by L. Anderson, B. S. Krathwohl and others. These six actions form a sort of food pyramid for knowledge, so that lower actions form a broader base for higher ones. Both taxonomies sort a dimensional hierarchy of knowledge operated by these aspects or actions from concrete to abstract: Factual, Conceptual, Procedural, and Metacognitive (the last added when revised).
In the revised taxonomy, “Remember” is the lowest cognitive action, described by “remember facts and basic concepts,” which deals with the Factual and Conceptual. Above it is “Understand,” described by “explain ideas or concepts,” and I imagine an idea can be a fact. Next is a procedural action “Apply: use information in new situations,” and in fact all six actions are procedural by being actions. At the top of the pyramid is “Analyze,” “Evaluate,” and “Create”. The Metacognitive dimension (“thinking about thinking”) is for thinking about these six actions and these four dimensions, as to how they are related and differ.
These taxonomies are well considered and there are many resources to investigate.
Anderson, L., Bloom, B. S., Krathwohl, D., & Airasian, P. (2000). Taxonomy for learning, teaching and assessing: A revision of Bloom’s Taxonomy of Educational Objectives (2nd ed.). New York: Allyn & Bacon, Inc.
Anderson, L. W., Krathwohl, D. R., Airasian, P. W., Cruikshank, K. A., Mayer, R. E., Pin- trich, P. R., … & Wittrock, M. C. (2001). A taxonomy for learning, teaching, and assessing: A revision of Bloom’s taxonomy of educational objectives, abridged edition. White Plains, NY: Longman.
A Yojijukugo (四字熟語) is a unit of four kanji characters that usually represents an idiomatic saying in Japanese. It is itself a yojijukugo, even though it isn’t idiomatic, since the term can also broadly refer to a non-idiomatic phrase of four characters.
Shunkashūtō (春夏秋冬) is a nice one that means the four seasons of the year, and so is a fourfold written in four kanji characters.
Eshajōri (会者定離) is hopefully appropriate, meaning “every meeting must involve a parting”.
Why Evolution is True is a blog written by Jerry Coyne, centered on evolution and biology but also dealing with diverse topics like politics, culture, and cats.