Questioning Strategies for the Secondary Math Classroom

1. Questioning Strategies for the Secondary Math Classroom Richard Roper Secondary Mathematics Specialist Region 15 ESC richard.roper@netxv.net

2. Questioning….Why? • Bloom’s Taxonomy is a way of grouping student’s thinking into six classifications based on the complexity of their cognitive ability • Knowledge, Comprehension, Application, Analysis, Synthesis and Evaluation • From Noun to Verb • Verbs describe actions while nouns do not • Remembering, Understanding, Applying, Analyzing, Evaluating and Creating

3. Questioning Foldable • Fold across the solid line • Cut across the dotted line • The bottom two tabs will be “Remembering” and “Understanding” • The next two tabs will be “Applying” and “Analyzing” • The top two tabs will be “Evaluating” and “Creating” • The title at the top of the foldable will be “Revised Bloom’s Taxonomy” • Use this foldable to record notes for the next several slides

4. Remembering • Able to retrieve information learned • Able to recall and restate information • Able to reproduce algorithmic events • Question Stems for “Remembering” • What do you know about ….? • How did ___________ happen? • Who was the main character? • Can you define the word _________? • Identify the date of _________?

5. Possible Activities to help with Remembering • Fact charts • Write down known information • Repeat important information • Label visual aids • Identify important points • Use an Outline to denote

6. Understanding • Paraphrasing important passages • Interpreting … • Explanation of math/science algorithms • Rewording definitions into their own words • Question Stem for “Understanding” • How would you explain …..? • How would you rephrase….? • Can you summarize the given passage? • What was the main idea of the story? • Can you give details about the _____?

7. Possible Activities to help with Understanding • Retell a story in their own words • Give an example or a non-example • Allow them to come up with their own definitions of a word • Ask them to condense a paragraph into a single sentence • Summarize a sequence of events

8. Applying • Making connections • Relating key components of a short story • Solving semi-complex problems • Implementing a plan to …. • Demonstrate • Question Stems for “Applying” • How would you use …..? • What examples can you find for ……? • How would you demonstrate……? • What else could ______ have done in the story? • What would the result be if …….?

9. Possible Activities to help with Applying • Ask student to predict • Choose the best statement that applies • What would the result be if …. • Make a scrapbook or journal • Construct a model that demonstrates how something works

10. Analyzing • Sorting and organizing information • Categorizing data into useful groups • Compare and contrast ideas • Use of sequencing to make info relevant • Question Stems for “Analyzing” • How would you organize_______? • What are the properties of ______? • Why did _______ happen? • What ideas justify…..? • What are the important steps in the ________ process?

11. Possible Activities to help with Analyzing • Ask them what the facts are • Which statement is relevant • What conclusions can they come to • State your point of view • Prepare a report on a particular subject • Investigate the solution to a word problem

12. Evaluating • Supporting a position • Defending in a debate situation • Criticizing a point of view • Hypothesizing a mathematical concept • Question Stems for “Evaluating” • Do you agree or disagree with …..? • How do you feel about …..? • Which is better and which is worst? • Which solution is the best and why?

13. Possible Activities to help with Evaluating • Try to find the errors in a given statement • List a set of criteria to judge from • Pick a side and try to convince other of your point of view • Form a panel to discuss the views of a particular time period • Determine any inconsistencies in a system of equations

14. Creating • Designing/Developing • Generalizing a mathematical concept • Drawing conclusions from a writing sample • Inventing something used in a research project • Question Stems for “Creating” • What would happen if …..? • How can you arrange …..? • How would you improve it? • What do you think would happen if ….?

15. Possible Activities to help with Creating • Ask students to test their theories • State a rule to a given problem • Create a timeline in history • Use a math problem to another math situation • Compose a piece of music • Revise a passage to give a different plot

16. Dominoes Activity • Separate into two teams – divide the room • Group 1 can only ask Yes/No questions. • Group 2 can ask any questions. • All questions must be submitted in writing on the supplied chart paper. • The goal of the game is to correctly guess the mathematics rule that will involve one of the four main operations: addition subtraction, multiplication or division. • Each round will consist of asking one question to obtain information about the rule. • The rule is then applied to a certain domino. If the domino fits the rule, I will be placed on the red sheet of paper. If not, the domino will not be placed on the red sheet of paper. • One question per round. • To win, your group must correctly identify the rule. Hint: The rule will be mathematical in nature and may consist of the number of dots on each side of the domino or both.

17. Important Questioning Practices • What type of questions needs to be used? • How does the questions need to be introduced by the teacher? • How must a student interpret the questions to help lead them into a meaningful discussion? • How can basic knowledge lead to conceptual thinking? • How can conceptual thinking lead to procedural techniques? • How can procedural techniques lead to metacognitive thoughts and problem solving?

18. The Role of the Question • Questions needs to use to the depth and complexity of the instructional situation. • Questions should differentiate. • Questions should be introduced to add value to or contribute to the knowledge gained both for the student and for the whole group. • Questions should intrigue the whole group to participate. • Questions should encourage ownership.

19. The Role of the Teacher asking the Question • Become the facilitator of the discussion. • Use the appropriate question to level up on the Bloom’s list. • Build in important “Wait Time” to allow for full dissemination of the information. • Selection of student(s) to bring value to the discussion. • Get students to talk more than the teacher.

20. The Role of the Student • Students lead the discussion. • Students must adhere to the protocol. • Agree to disagree but with mutual respect. • Discussion needs to have added value. • Students work together to further learning process. • Obtain resources as needed.

21. Types of Response Strategies • Wait Time • Think Pair Share • Random Calling • Class Survey • More than one Answer • Devil’s Advocate

22. Less Effective Classroom Instruction • Mr. Turner works example problems on the board and expects student to recreate his work. • Students are given 50 ordered pairs and are expected to graph them all. • Students are given a set of numbers and expect to find mean, median and mode. • Mrs. Williams shows students where the formulas on the formula chart. • Students are working in groups with one person doing all the work while the others are observing. • Mr. Thompson requires that all students turn in their work at the end of the class period whether they are finished or not. • Mrs. Perez reads a passage out loud.

23. More Effective Classroom Instruction • Mr. Turner puts a problem on the board and starts a class discussion by asking “How could we solve this problem?” • Students are given 10 ordered pairs and are asked to determine if there is a correlation and to justify their answer. • Mrs. Perez asks students to read a short passage and facilitates a class discussion on what the theme of the passage was. • Mr. Thompson asks students to recreate a scene from a particular part in history? • Mrs. Williams asks students to investigate formulas from a formula chart and give examples of where a particular formula would be used.

24. Conclusion Effective questioning will have the most impact when the question(s) is well thought out in advance. Transitioning from traditional questioning methods to well-prepared, meaningful and thought provoking questions will require a great deal of patience. Educators, such as yourselves, must be persistent and perceptive while asking purposeful questions. Unhelpful traditional questions must be replaced by inquiry based questioning as a means to supplement effective instruction.