1 What is the area of the above rectangle? Warm - up 4 cm 6 cm Draw two different rectangles whose areas are the same as the one above.

2 The students will learn appropriate questioning techniques to enhance learning and for motivating students. Classroom Questioning

3 “always the beautiful answer who asks a more beautiful question.” e.e. cummings Introduction

4 What do you think is a fair number of questions for a teacher to pose in a class period? Motivation One to two HUNDRED!* When does a teacher have time to think? * Research findings by Romiet Stevens

5 Knowledge questions – Bloom’s Taxonomy of Educational Objectives Verbs – define, describe, identify, label, list, match, name, reproduce, state, etc. Write two sample questions that demonstrate this area of educational objectives. ask students to recall, recognize, or remember things. Models - What is the definition of pi? List three ways in which to prove triangles congruent.

6 Comprehension questions - Bloom’s Taxonomy Verbs – compare, decide, defend, describe, explain, give, illustrate, interpret, paraphrase, reorder, restate in your words, select, etc. Write two sample questions that demonstrate this area of educational objectives. require students to mentally manipulate knowledge by organizing, arranging, and restating. Models - Illustrate the sine of 45 degrees. Give an example of a scalene triangle.

7 Application questions – Bloom’s Taxonomy challenge students to apply a rule, algorithm, or process to a problem. Verbs – apply, change, classify, compute, demonstrate, develop, employ, manipulate, modify, produce, etc. Write two sample questions that demonstrate this area of educational objectives. Models - How is ( ) an example of ( )? Use ( ) to solve ( )?

8 Analysis questions - Bloom’s Taxonomy Verbs – apply, change, classify, compute, demonstrate, develop, employ, manipulate, modify, produce, etc. Write two sample questions that demonstrate this area of educational objectives. Models - Select two methods for solving quadratic equations that will always work. Make a tree diagram to illustrate the different types of quadrilaterals. require students to pull things apart; identify motives; reasons, and causes; make inferences, generalizations, and conclusions; and generate evidence to refute or support a position.

9 Synthesis questions - Bloom’s Taxonomy Verbs - assemble, compose, create, design, explain, organize, rearrange, reconstruct, tell, write, etc. Write two sample questions that demonstrate this area of educational objectives. Models - Create a mathematical operation that is commutative but not associative. Compose a story of two fractions who meet and are added together. encourage students to think creatively, to produce original statements and predictions, or to solve problems that have more than one solution.

10 Evaluation questions - Bloom’s Taxonomy Verbs - appraise, compare, critize, defend, discriminate, evaluate, justify, priortize, summarize, support, etc. Write two sample questions that demonstrate this area of educational objectives. Models - Justify the use of a base 10 number system in this computer, binary age. Defend the title given to Gauss as the “Prince of Mathematics”. require students to express reasoned opinion, judge the merits of an idea, hypothesis, or solution to a problem.

11 Bloom’s Taxonomy Students will tend to approach your class as a knowledge-based subject if you present them with an overabundance of knowledge-level questions and they will approach you class at a higher level of thinking if you use high level thinking questions. Perhaps the most important thing about Bloom’s Taxonomy is that research shows that “students tend to read and think based on the types of questions they anticipate receiving from the teacher.” TF

12 What is the area of the above rectangle? Rectangle Investigation 4 cm 6 cm Draw two different rectangles whose areas are the same as the one above. Draw all possible rectangles whose areas are the same as the one above.

13 Quiet Techniques - Some Questioning Techniques Raise your hands Write a response in your notebook Thumbs up/thumbs down If the answer is (a) show one finger; (b) two fingers; etc.

14 Non-quiet Techniques - Some Questioning Techniques Ask students to pair and agree on a response. Have students prepare a response with the teacher commenting that she will call on three students to respond. Use “Think, Pair, and Share”.

15 Questioning Sequence Hand out the “Questioning Sequence” from Making Every Minute Count, Dave Johnson and based on Madeline Hunter’s work. Discuss this sequence.

16 Questioning Sequence When you ask a question and get a student response be sure to always give some kind of response to the student. Praise – “Yes, you are on the right track!” When you ask a question and get a student response be sure to always give some kind of response to the student. Praise – “Yes, you are on the right track!” Encouragement – “I like how you used the definition of absolute value in your answer.” When you ask a question and get a student response be sure to always give some kind of response to the student. Praise – “Yes, you are on the right track!” Encouragement – “I like how you used the definition of absolute value in your answer.” Criticism – “No, that’s incorrect. You forgot to carry the two.” When you ask a question and get a student response be sure to always give some kind of response to the student. Praise – “Yes, you are on the right track!” Encouragement – “I like how you used the definition of absolute value in your answer.” Criticism – “No, that’s incorrect. You forgot to carry the two.” Remediation – “ Tom, that is not quite right, what does PEMDAS mean?” TF

17 Questioning Sequence Although most teachers typically respond with “Okay,” “Good,” “Nice job,”, “Cool,” or perhaps an occasional “Wow!”, a more powerful response is to use the student’s answer as part of a follow-up question. This action – Recognizes that the teacher was actually listening to the student. Provides an opportunity for the student to clarify her answer. Provides motivation to keep the conversation going. Celebrates the student’s participation in the lesson. TF

18 Please elaborate. Follow-up Questions to Ask Dave Johnson How did you decide that? Can you justify that? Give us your insight into arriving at that answer. How did you reason? What steps did you take? To a person in the street who doesn’t speak “math,” tell how you decided that was correct. continued

19 Is there another way one could arrive at that answer? Follow-up Questions to Ask Does that work with negative numbers? What do you believe you must add to Brian’s answer to cover all cases? I want everyone to think about Brian’s response and be prepared to repeat, in your own words, his response. Have you seen that before in this class?

20 Pause for a Cause Pass out the handout on pausing during questioning sessions from “Motivation Counts” by Dave Johnson. Discuss it briefly.

21 Thought, John Dewey said, begins with questions. Certainly, much student thinking and learning begins with teachers asking better classroom questions. SUMMARIZE/CONCLUSION

22 Handouts Pass out the handout on “Self- evaluation on Questioning” from “Motivation Counts” by Dave Johnson.

23 Assignment Read Chapter 5 and Chapter 7, Posamentier.