Tag Archives: Education

Four Dimensions of Knowledge

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.

Further Reading:


Bloom’s Taxonomy

Revised Bloom’s Taxonomy


Bloom’s Taxonomy Revised


Pedagogy of book and chapter organization

Click to access Anderson-and-Krathwohl_Revised-Blooms-Taxonomy.pdf

Click to access krathwohl.pdf

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.




Concepts, Theory-Theory of






Four Things

I’ve heard that learning English isn’t easy, but I don’t really remember my own experience of doing so. Learning the difference between these four indefinite pronouns is just one of the many things to know, and seems to be a common grade school poster to hang up in the classroom.

  • Anything
  • Something
  • Everything
  • Nothing

Some use these four words together in a clever sentence or epigram, but today I’ve got nothing except this sad little diagram. I hope it is of some use to someone.

I also see this is done with anybody, somebody, everybody, and nobody, and there are some cute little stories out there too! Plus here’s another diagram.

Further Reading:






Education is Not a Product

A recent meme popular in education:

  • Education is not a product.
  • Students are not customers.
  • Professors are not tools.
  • The University is not a factory.

I’m not sure who originally came up with this interesting saying.

Examining the anti-analogy, you have “customers buy products made in a factory with tools”. Perhaps a better fourfold would be to change this to “workers use tools to make products in a factory”, so you could say “Students are not workers.” But then you lose the capitalistic “consumer culture” geist.

Or you could say the Professors are (not) factory workers and the Students are (not) the raw material. As a homework assignment, write an essay or develop a mathematical theory comparing this anti-analogy fourfold (or a close derivative thereof) to Aristotle’s Four Causes. Please show your work.

Further Reading:

Note the similarity with some of the elements of the following (which also reminds me for the Four Causes):




The Rigor-Relevance Framework

The Rigor-Relevance Framework is a fourfold developed by the International Center for Leadership in Education (www.leadered.com). It is an instrument to aid in planning and evaluation for teachers and their students. It is composed of

  • Acquisition: Low rigor and low relevance
  • Application: Low rigor and high relevance
  • Assimilation: High rigor and low relevance
  • Adaptation: High rigor and high relevance

Rigor (from low to high) is said to be based on the six levels of Bloom’s Taxonomy of Thinking (knowledge, comprehension, application, analysis, synthesis, evaluation; or revised as remember, understand, apply, analyze, evaluate, create).

Relevance (from low to high) is said to be based on Daggett’s Application Model (knowledge in one discipline, apply in discipline, apply across disciplines, apply to real-world predictable situations, apply to real-world predictable situations).

There seems to be quite a bit of information associated with this center so I’ll need to look at it some more!

Further Reading:




Compare to other learning cycles (I thought I had more than one…)


Also I’d like to compare this with Whitehead’s Criteria of Metaphysical Theories






Science, Technology, Engineering, and Mathematics

STEM: Science, Technology, Engineering, and Mathematics. We often hear that these areas of education and expertise are critical for the development of our modern society. To attract students to these fields, banners and logos are full of bright colors and crisp graphics. In comparison, above is my rather dull diagram. Not very enticing, is it?

Some are now adding Arts to the four, giving STEAM. I think the Arts are important of course, but fives don’t go with my oeuvre.

In addition, I give you a diagram with Chinese substituted for English (科學 技術 工程 數學).

Further Reading: