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QUESTIONING STRATEGIES FOR THE SECONDARY MATH CLASSROOM Richard Roper Secondar y Mathematics Specialist Region 15 ESC [email protected] netxv.net 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 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 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 _________? 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 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 _____? 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 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 …….? 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 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? 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 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? 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 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 ….? 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 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 char t 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 cer tain 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 m athematical in nature and m ay consist of t he number of dots on each side of t he domino or both. 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? 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. 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. 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. TYPES OF RESPONSE STRATEGIES Wait Time Think Pair Share Random Calling Class Survey More than one Answer Devil’s Advocate 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. 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. 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.