Structured Questioning

for algebra & mathematical reasoning

Objective: Students will use a structured approach to algebra by asking questions that compare what they can see to what they think they know.

Reformatted: January 2010

 

Background:

I arrived in a non-tracking urban high school to find a classroom where the range in skill levels from the lowest to highest student in each class was greater than four years. The higher performing students performed at about grade level. The middle students vacillated between doing one problem right and the very next problem wrong. The lower performing students crossed their arms and claimed they just couldn't do it. Many of the students openly admitted they simply memorize material just long enough to pass the chapter test, then they forget it. This lessons was used to get them to focus on their own awareness and thinking.

Purpose:

We obviously needed students to recognize that learning involves much more than short term memorization. I recognized that I needed to offer an approach that worked at three different levels. Here's how I worded the purpose for the students:

  1. Top students: By successfully asking questions you become independent of the teacher, and move ahead of what he is teaching, and become the master of your own learning.
  2. Middle students: By asking questions you will correct your mistakes when you are not sure and develop better techniques for remembering.
  3. Bottom students: By asking questions to distinguish between what you do and don't understand you communicate your strengths & difficulties to a teacher, or tutor, so that they may help you. You will stop saying, "I don't understand!" which is not a question and does not tell a person how to help you!

Approach:

Start by coaching the students with at-level problems in the following structured sequence of questions:

  1. What do I see?
  2. What do I understand or believe about what I see?
  3. What do I not know or understand about what I see?
  4. How can I figure out, find out what I don't understand?

Focus on distinguishing between: "what I see," "what I believe," and "what I don't understand." Gradually raise the problem level (e.g. use trig functions, summation symbols, etc.) above the common skill level of the class to get them to focus on how the questions may lead them towards a solution.

Require lower performing students to introduce all questions by stating what they see. Require students who claim they did not do the homework, because they didn't understand it to write out their answers to the structured questions for each problem they can't do. Discuss what can be learned from those answers. Have mid-level students compare what they see in similar problems.

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Example:

For students who have just practiced solving using factoring and the quadratic equation, give a problem such as: x3 - x2 = 6x . Coach answering (Of course, answers will vary with skill level):

What do I see?

  • I see: x3, x2, 6x,
  • a variable on both sides the "=",
  • there are 3 terms each with an "x"

What do I understand or believe about what I see?

  • I believe that I am looking for the value of "x"
  • I should get the equation into the form " = 0"
  • Factoring has solved equations with x2.

What do I not know or understand about what I see?

  • I don't know what to do with that x3

How can I figure out, find out what I don't understand?

  • I can compare this problem to how I solved problems with "x2"
  • I can ask somebody, "what do I do when the problem has x3 in it?"

Observations:

The structured questions approach has made it easier for me to go over material by stopping at each step and asking, "What do we see?" and "What do we already understand about that?" For example, when working with a problem that had complex fractions I was able to say, "We see a fraction which has fractions being subtracted in the numerator." "We believe that we may subtract fractions by finding a common denominator, so let's do that to the fractions in the numerator."

At the very same time, our English / Social Studies teacher, facing the same frustrations, changed her lessons to "Who? What? Where? When? Why? How?"

Some students expressed being uncomfortable with this approach. They wanted to go back to having me show them steps to memorize. But is memorizing real learning? Even worse is memorizing until the test, then forgetting, as many of the students have acknowledged they do, real learning?

On one advanced problem a few students said, "I don't understand anything!" So we went through the structured questions as a class, and determined that they understood almost every part of the problem except for one unknown symbol (S). At that point, it was obvious they could look it up, ask someone to explain what that symbol meant.

By the end of the year a noticeable increase in math standardized test scores did occur.


 
 

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