Posted in Mathematics education

Bloom’s Taxonomy and iPad Apps

The original Bloom’s taxonomy include KnowledgeComprehension, Analysis, Synthesis, and Evaluation. I was introduced to this when I was in college and I must admit it was not of much help to me in planning my math lessons. I just couldn’t fit it. The pyramid image was not of help at all and I think even created the now much ingrained deductive method of teaching. I think teachers must have unconsciously looked at it as a food pyramid so they give a dose of those of knowledge-acquisition activities first before providing activities  that will engage students in higher-level processes

 

Lorin Anderson, a former student of Bloom, revisited the cognitive domain in the learning taxonomy in the mid-nineties and made some important changes: changing the names in the six categories from noun to verb forms and slightly rearranging them. The new taxonomy reflects a more active form of thinking of Creating, Evaluating, Analyzing, Understanding, and Remembering. I also like the inverted pyramid as long as it is not viewed like there is a strict hierarchy of the categories. In fact in my own experience I just make sure that all these are covered in a lesson as much as possible. The way to do this is to teach mathematics through problem solving or engage students in mathematical investigations. Still, the best framework will still be one tailored to mathematics. For me its my list of Mathematical Habits of Mind.

Revised Bloom's Taxonomy

In searching for Bloom’s taxonomy I came across the image below – Bloom’s taxonomy for iPad. It’s a collection of iPad apps classified according to Bloom’s taxonomy.  I found it cute so I’m including it here. This will come in handy once I have my own iPad and start creating math lesson for this device.

There is also such a thing as Learning Pyramid which compares how we learn things and the retention rate in our brain after 2-3 weeks.

Click here for source of image of Bloom’s Taxonomy for iPads.

Posted in Trigonometry

Algebra test items: Trigonometric Functions

This is my third post on constructing test items based on TIMSS Assessment Framework. My first set of examples is about assessing understanding of zeros of polynomial function and the second post is about graphs of rational functions. Of course there are other frameworks that may be used for constructing test item like the Bloom’s Taxonomy. However, in my experience, Bloom’s is not very useful in mathematics, even its revised version.  The best framework so far for mathematics is that of TIMMS’s which I summarized here.

Here are three examples of trigonometry test questions using the three different cognitive levels:  knowing facts, procedures and concepts, applying, and reasoning.

Knowing

If  cos2(3x-3) = 5 , what is the value of 1-sin2 (3x-3) equal to?

a. 0

b. 1

c. 3

d. 4

e. 5

Applying

Given the graphs of f and g, sketch the graph of f+g.

Reasoning

Which of the following functions will have the same set zeroes as function g, given that g(x) = sin kx and f(x) = k?

a. f+g

b. fg

c. fg

d. g/f

e. gof