Questioning.

  When I went through teacher training, we were taught to ask the student "What is the next step?"  since solving equations was a process.  As we know, things have changed so our method of questioning should be changing but if you are like me, its not.

What are the best types of questions we should be asking our students now.  There are 8 recommendations of types  questions for the classroom.

1.  Use fewer information gathering type questions such as "What is the area formula for a trapazoid."  These have a time and place but do not require higher level thinking.

2. Ask questions which require students to explain, elaborate, or clarify their thinking.  These are probing questions needed to uncover student understanding.

3. Allow students time to answer.  Students need at least 10 seconds to gather and formulate their answers and ELL students require even more time. Research indicates teachers usually allow fewer than 5 seconds to answer.

4. Ask students to make their thinking visible by connecting mathematical ideas with relationships such as connecting arrays with multiplication.

5. Take time to encourage students to reflect and justify their answers.  This forces students to stop and explain their thinking process so as to understand the material better.

6. Avoid guiding the conversation to a predesignated  conclusion.  When you do this, you ignore students who may need to go elsewhere to get to the conclusion.

7. Try focusing your questions on the needs of the students.  These questions will probe, assess, and it encourages students to express their thinking.

8. Encourage students to ask questions of each other. You will have to help students learn the types of questions which are better asked by them rather than "Did you get the answer?" "No?"  "Time for the teacher." 

These are suggested by the National Council of Teachers of Mathematics but I stumbled across a paper in which the person suggested writing questions which were non-computational but could spark conversation so the teacher could gauge their back ground knowledge and understanding.  The teacher sets up the situation with four possible answers.  Each of the answers connects with the situation but is not the whole answer.

Imagine that you are sky-diving. The graph of your speed as a function of time, from

the time you jumped out of the plane to the time you achieve terminal velocity is most likely

a)Increasing concave down.

b)Decreasing concave down.

c)A straight line with positive slope.

d)Increasing concave up.

 

Notice there are no numbers, just concepts and situations where students have to justify their answer.

Let me know what you think.  I'm interested to hear. Have a good day.