Bloom's Taxonomy

According to Bloom, one may classify a limited number of activities that affect the cognitive domain and involve knowledge and the development of intellectual skills. This domain is the one most relevant for the mathematics and a scientific study area since it includes the recall or recognition of specific facts procedural patterns, and concepts that serve in the development of intellectual abilities and skills. There are six major competence categories, which are listed in order below, starting from the simplest behavior to the most complex. These categories can also be thought of as degrees of difficulties and may be used to classify learning objects. Notice that, if a learning module tackles more of them, then the first ones must be mastered before the next ones can take place. Each competence is described by the maths skills demonstrated by it and by some keywords that are likely to appear in the learning module.

- Recall a definition or a theorem, basic knowledge of e.g. rules of derivation, trigonometric equivalences, terminology and major results in a certain area. Knowledge of values of constants like e. Question Cues: list, define, tell, describe, state, match, select, identify, show, label, collect, examine, tabulate, quote, name, what, etc.

2.Comprehension - Understand the meaning, translation, interpolation, and interpretation of instructions and problems. State a problem in one's own words. Understand a definition or a theorem and how they depend on other definitions, grasp the meaning of a certain symbolic expression, use abstract knowledge in concrete examples, derive and predict consequences of assumptions on mathematical objects e.g. given this function, describe its first and second derivative or write an algorithm to compute the greatest common divisor of two polynomials. Question Cues: summarize, describe, interpret, contrast, predict, associate, distinguish, estimate, differentiate, discuss, extend, give examples, give counter-example

3.Application - Use a theorem or more theorems to show properties of a mathematical object. Describe a concrete example in abstract terms. Apply a solving strategy to solve an exercise in a new domain. Questions Cues: apply, demonstrate, calculate, complete, illustrate, show, solve, examine, modify, relate, change, classify, experiment, discover

4.Analysis - Separates definitions and axioms and from theorems. Understands logical structures of proofs and complex mathematical domains. Recognizes hidden consequences following by initial assumptions and components of mathematical objects. Ability to classify abstract structures and objects, e.g. classify a conic. Question Cues: analyze, separate, order, explain, connect, classify, arrange, divide, compare, select, explain, infer

- Define a new structure from known elements and derive its properties. Generalize a theorem or prove a new theorem. Relate the results in a certain area to results in a different area. Question Cues: formulate, generalize, rewrite, combine, integrate, modify, rearrange, substitute, invent, what if?, compose

6.Evaluation - Compare and discriminate between ideas, assess value of theories, presentations and research. Be able to make hypotheses based on mathematical facts. Verify validity of mathematical claims. Judge usefulness of results. Question Cues: assess, decide, rank, grade, test, measure, recommend, convince, select, judge, explain, discriminate, support, conclude, compare, summarize


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