Explorations In Math

Wait, parents! I know, this sounds like something for teachers only, but read on. There’s useful information here for you, as well.

Let’s start with this question: What is Bloom’s Taxonomy? It’s a way of measuring the complexity of the questions and tasks teachers and parents pose to children. Using the taxonomy is a way to encourage children to higher levels of thinking. The important thing to keep in mind is that the first three levels are review of existing knowledge; the last three levels are where new learning occurs.  Those are the levels to strive for when discussing new learning. Here’s a summary of the six levels of questioning:

REVIEW (OLD LEARNING)

• Knowledge, the lowest level, is characterized by simple recall of facts:

-  What’s 9 + 8?

-  What’s 4 x 6?

• Comprehension includes compare and contrasting tasks:

-  Which is greater, 301 or 310?

-  What’s the definition of a square?

• Application involves solving problems and using knowledge:

-  If there are 7 days in a week, how many days are there in 3 weeks?

-  It’s 100 miles to grandma’s house. If we drive at 50 MPH, how long will

it take to get there?

-  Do you have enough money in your hand to buy a 50 cent cookie?

NEW LEARNING

• Analysis asks students to look for patterns and organize parts.

-  5,  10,  15,  20,  ??, 30,  ??

-  3 x 37 = 111,  6 x 37 = 222,  9 x 37 = 333,  12 x 37 = ???

• Synthesis is where new learning takes place, connecting existing knowledge and ideas to formulate new ones and to bring together knowledge and facts from different areas.

-  If  6 + 8 = 14, what would 8 + 6 equal?

-  If the formula for the area of a square is L x W, what would the formula

be for the area of a triangle, which is one half of a square?

- What would happen if…?

• Evaluation is assessing what has been presented, including one’s own ideas.

This is the highest level of thinking. It asks the child to think about and explain the reasoning that led to an answer. The most important math questions you can ask your child elicit this thinking:

-  Why do you think so?

-  Tell me how you did that.

-  Is there a better way to solve the problem?

The taxonomy, of course, applies across all subjects. A great opportunity for parents to use it is reading aloud to your children. Make sure some of the questions you ask as you read fall into the last three levels. For example: What might have happened if Alice had caught the White Rabbit? Why do you think the Red Queen is always so angry? If you were Alice, what would you do? These kinds of questions will stimulate thinking, and that’s what we want.  Want more? Click here.

Dave Gardner

Mathematician in Residence