Math Tasks According to Bloom

Bloom's Taxonomy is a classification of learning objectives within education. Each subsequent level within Bloom's model represents progressive levels of higher order thinking skills. This entry focuses on mathematics tasks at each of the cognitive level of Bloom's taxonomy. First, I will provide a quick review of each of the Bloom's levels and then I will provide math tasks at each of the levels.

1. Knowledge - This level focuses on learning terms, facts, methods, procedures, concepts.
   
2. Comprehension - This level focuses on understanding uses and implications of terms, facts, methods, procedures, concepts.
3. Application - This level focuses on practicing theory, solving problems, and using information in the new situations.
4. Analysis - This level focuses on analyzing structure, recognizing assumptions, and breaking down material into parts.
5. Synthesis - This level focuses on putting information together into new and creative ways.
6. Evaluation - This level focuses on setting standards, judging with purpose, and accepting / rejecting ideas based on the standard criteria.

Here are examples of mathematics tasks at each of Bloom's levels:


Knowledge

• Identify the thousandths place for the number 123.456789
• From a given data set, identify the mode, mean, median, and range
  

Comprehension

• Explain how to convert between fractions, decimals, and percents
• Classify polygons by regularity, line symmetry, and concavity
  

Application

• How do you calculate the percent of a given whole?
• Solve for the area of a rectangle using the formula area = length x width
  

Analysis

• What methods can be used to compare and order fractions?
• What factors do you consider when formulating a plan for problem solving?
  

Synthesis

• Describe some patterns that you recognized in the construction of Pascal's Triangle.
• What predictions can you make from the given graph?
  

Evaluation

• Describe how to solve a problem using the 4 step method.
• Justify your reason for using the strategy you selected.

Certainly, the Bloom's levels can sometimes seem "fuzzy" and a given task can be applied to different levels within Bloom's Taxonomy. But the above examples give a good overview of how mathematics skills can be used at each of the levels.