CAAT Follow Up Meeting #3 Proportional Reasoning

Coaching CadreBreathitt/Jackson/EstillApril 10, 2013

Jennifer McDanielJennifer.mcdaniel@clay.kyschools.us

InstructionGuiding QuestionWhat factors promote (or discourage) students involvement in thinking about and developing an understanding of content?

Motivation in the Math ClassroomIn pairs discuss:What, ideally, does student involvement in learning mathematics look and feel like fromyour perspective as a teacher?the perspective of your students?Research on MotivationInvolvement is more than being physically on-taskFocused concentration and care about things making senseIntrinsically motivated to persistCognitively engaged and challenged

Two areas of focus:Cognitive Demand of Mathematical Tasks Discourse Strategies

ReferencesHenningsen & Stein (1997). Mathematical tasks and student cognition. Journal for Research in Mathematics Education, 28(5), 524-549.Turner et al. (1998). Creating contexts for involvement in mathematics. Journal of Educational Psychology, 90(4), 730-745.Mathematical TasksWhat is cognitive demand?Focus is on the sort of student thinking required.Kinds of thinking required:MemorizationProcedures without ConnectionsRequires little or no understanding of concepts or relationships.Procedures with ConnectionsRequires some understanding of the how or why of the procedure.Doing MathematicsLower levelHigher levelHand Out for reference5Examples of Mathematical Tasks (1)MemorizationWhich of these shows the identity property of multiplication?A) a x b = b x aB) a x 1 = aC) a + 0 = aProcedures without ConnectionsWrite and solve a proportion for each of these:A) 17 is what percent of 68?B) 21 is 30% of what number?Too much of a focus on lower level tasks discourages student involvement in learning mathematics.Examples of Mathematical Tasks (2)Procedures with ConnectionsSolve by factoring: x2 7x + 12 = 0Explain how the factors of the equation relate to the roots of the equation. Use this information to draw a sketch of the graph of the function f(x) = x2 7x + 12. Doing MathematicsDescribe a situation that could be modeled with the equation y = 2x + 5, then make a graph to represent the model. Explain how the situation, equation, and graph are interrelated.Higher level tasks, when well-implemented, promote involvement in learning mathematics.Characteristics ofHigher-Level Mathematical TasksHigher-level tasks require students to

do more than computation.extend prior knowledge to explore unfamiliar tasks and situations.use a variety of means (models, drawings, graphs, concrete materials, etc) to represent phenomena.look for patterns and relationships and check their results against existing knowledge.make predictions, estimations and/or hypotheses and devise means for testing them.demonstrate and deepen their understanding of mathematical concepts and relationships.Recall: The Border ProblemWithout counting 1-by-1 and without writing anything down, calculate the number of shaded squares in the 10 by 10 grid shown.Determine a general rule for finding the number of shaded squares in any similar n by n grid.Talk PartnersDiscuss with your talk partner examples of students Doing Mathematics within your classroom, grade level, or school setting. Be prepared to share with the entire group.

Discourse Strategies (less involvement): I-R-EInitiation-Response-Evaluation (I-R-E)Ask a known-answer questionEvaluate a student response as right or wrongMinimize student interaction through prescribed turn takingEstablish the authority of the text and teacherExamplesWhat is the answer to #5?What are you supposed to do next?What is the reciprocal of 3/5? 5/3. Very good!That is exactly what the book says.11Discourse Strategies (less involvement): ProceduresProceduresGive directionsImplement proceduresTell students how to think and actExamplesListen to what I say and write it down.Take out your books and turn to page 45.

12Discourse Strategies (less involvement): Extrinsic SupportExtrinsic SupportSuperficial statements of praise (focus is not on the learning goals and objectives)Threats to gain complianceExamplesYou have such neat handwriting.These scores are terrible. I was really shocked.If you dont finish up you will stay after class.13Discourse Strategies (more involvement): Intrinsic SupportIntrinsic SupportView challenge/risk taking as desirableRespond to errors constructivelyComment on students progress toward the learning goals and objectivesEvoke students curiosity and interestExamplesThat's great! Do you see what she did for #5?This may seem difficult, but if you stay with it you'll figure it out.Good. You figured out the y-intercept. How might we determine the slope here?Discourse Strategies (more involvement): NegotiationNegotiationAdjust instruction in response to studentsModel strategies students might useGuide students to deeper understandingExamplesWhat information is needed to solve this problem?Try to break the problem into smaller parts.Here is an example of how I might approach a similar problem.15Discourse Strategies (more involvement): Transfer ResponsibilityTransfer responsibilitySupport development of strategic thinkingEncourage autonomous learningHold students accountable for understandingExamplesExplain the strategy you used to get that answer.You need to have a rule to justify your statement.Why does Normas method work?16Talk PartnersDiscuss with your talk partner methods of encouraging math talk or student discourse in your classroom, grade level, or school setting. Please be prepared to share with the entire group.

EffectiveQuestioningHow do we expect students to answer questions?http://www.youtube.com/watch?v=Boxsh_onY5E 19

How can quality questioning transform Classrooms?Reference for all slides in power point:Quality Questioning: Research-Based Practice to Engage Every Learner(Jackie Acree Walsh & Beth Dankert Sattes)

Focus QuestionsHow can effective questioning help transform a traditional, teacher-centered classroom into a student-centered, inquiry-oriented community of learners?

What are the connections between quality questions and student learning and achievement?

Why are there gaps between what we know about effective questioning and what we do in classrooms? How many questions do- Teachers ask in a 30 minute period?Students ask in a 30 minute period?Teachers estimated they would ask 15 questions and that 15 would be the desired rate.

Teachers estimated that their students were asking about 10 questions, which would be below their desired target of 15.

Actual observations :Teachers asked an average of 50.6 questions and their students posed only 1.8 questions!Research about Current Practice and Implications for ChangeTeachers ask many questions.Most teacher questions are at the lowest cognitive level-known as fact, recall, or knowledge.Not all students are accountable to respond to all questions. Teachers frequently call on volunteers, and these volunteers constitute a select group of students.Teachers typically wait less than one second after asking a question before calling on a student to answer(wait time 1). They wait even less time (usually 0 seconds) before speaking after a student has answered (wait time 2).Teachers often accept incorrect answers without probing; they frequently answer their own questions.Students ask very few content-related questions. What does effective questioning look like in the classroom?

Students asking QuestionsTeachers take up to two-thirds of the classroom talk time. Students are talk-deprived (Alvermann et al., 1996)

Student discussion increase retention as much as 50%. (Sousa, 2001)

25What does effective questioning look like in the classroom?

Questioning NormsExamples of Questioning Norms:We all need time to reflect on past experiences if we are to gain new understandings.We all need time to think before speakingWe all need time to think out loud and complete our thoughts.We learn best when we formulate and answer our own questions.We learn from one another when we listen with attention and respect.When we share talk time, we demonstrate respect, and we learn from one another.

Take Home MessageThere is a gap between best practice and current practice when it comes to questioning.

Teachers seem to know what constitutes best practice but we arent always good monitors of our own performance. Questions for ReflectionJigsaw with 4 reflection questions29The important thing is to not stop questioning.-Albert Einstein

30From CHETL TO TPGESCHETLLearning ClimateClassroom Assessment and Student ReflectionInstructional Rigor and Student EngagementInstructional RelevanceContent Knowledge

TPGESPlanning and PreparationClassroom EnvironmentInstructionProfessional ResponsibilitiesStudent Growth (For Consideration)

Reflecting on Instructional Practices:How you can strengthen the ways student involvement and motivation are promoted and supported in your classes?

Write 3-5 statements about specific strategies youd like to work to improve.Examples: I give students tasks that require them to think about mathematical relationships and concepts.I provide feedback to students that promotes further thinking and improved understanding.I allow opportunities for students to be an authority in mathematics.

Identify where you are now and where you want to be.http://www.jennyray.net/tpges-resources.html

www.reneeyates2math.com

CHETL & TPGES RESOURCES

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The arrows point to places I have had conflicts with the statements provided. My facial expressions are so hard to control!!! In some iEPs the statement says to call on the student first. So I point this out as a possible conflict. Questioning Summer 201234Habits Are Hard to BreakA teacher with 20 years of experience will have asked something like 1.2 million questions in her career. And when youve done something the same way, over a million times, its quite difficult to start doing it another way.

Wiliam (2003)35Random thoughts Whether the students are working independently or working in small groups, effective questioning can take the class to new heights. Take time to allow students to think and formulate responses. The goal is for students to generate content related questions instead of all questions coming from the teacher. Often, questioning reveals student misconceptions. We want all students to feel comfortable demonstrating their level of understanding and develop the ability to formulate their own questions to guide their learning. We need a classroom climate that fosters the idea that there may be more than one way to solve a problem and we all have something to offer when it comes to the class discussion. Even if a student is incorrect, important misconceptions can be uncovered and discussed. It is powerful when these conversations are student driven.

Observation PlanYates formAdministrationPeer-to-PeerConnections to TPGES

Reasons for student disengagement from classroom questioning:Teachers do not require engagement.There is no intrinsic pressure to be engaged because of the disconnect between the students world and classroom curriculum.Fear; students do not want to take risks in front of peers and the teacher.Goal is to just get through school, and the easiest path is to just show up and go through the motions.How can I become a better questioner?Working in groups of 3, prepare one power point slide/question with answers/suggestions for each of the following:How can we convince all students that their answers matter to us?How can we engage all students in coming up with their own answers to each of our questions?How can we promote equitable participation of all students in classroom questioning?How can I become a better questioner?What one word sums up what you have learned about effective questioning?What are 1 to 3 things with respect to effective questioning that you will do differently/better this school year?Enter a reminder in the calendar on your phone.Set the alarm to remind you!How can I become a better questioner?

The important thing is to not stop questioning.-Albert Einstein

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AssessmentFormative Assessment Taskswww.mathshell.org

What are FALs?

Lessons designed to move students away from simply getting the answers and toward learning the mathematics that they need to solve the problem.Formative Assessment Lessons43Clarifying and sharing learning intentions and criteria for successEngineering effective discussion, questions, activities, and tasks that elicit evidence of learningProviding feedback that moves students forward Activating students as instructional resources for one anotherActivating students as owners of their own learning5 Strategies of Formative Assessment44Completed 2/3 of the way through a unit.Completely scripted (They are not intended to be changed.)Students are grouped according to pretest/misconceptions or by abilityMost take 2-3 daysScaffold learning (all students are expected to show growth, but do not all reach the same level of understanding)Key Characteristics of a FAL45Problem SolvingConcept DevelopmentTypes of a FAL46Begins with a taskEncourages students to formulate questions and reason logicallyGiven sample student work showing different approaches with mistakesCritique and improve the workRevise their original approach or change itCommunicates and reflects on resultsVideohttp://map.mathshell.org/static/draft/pd/modules/3_Problem_Solving/html/videos_d1.htm

Problem Solving Characteristics47Begins with a task or pre-assessmentStudents are exposed to feedback questionsInvolved in a learning activity (small group)Class discussion (whole group)Post-Test to measure growthVideohttp://map.mathshell.org/static/draft/pd/modules/2_Concept_Lessons/html/videos_e1.htm

Concept Development Characteristics48Work through the FAL as a student to make sure it fitsComplete the pre-assessment 2-3 days prior to completing the activityUse results to group kids according to misconceptionsMeet as a math team to develop feedback questions based on pre-assessmentsProcess of a FAL49Frame the lessonStudents complete the process according to script-individual-collaborative-whole groupPost-assessment/reflectionTeacher uses results to guide instruction for the remainder of the unitProcess of a FAL contd.50MAP Assessment Task TypesThe task types indicate the breadth and depth of CCSS mathematical practices assessed by the task. Novice tasks involve only MP2 and MP6 and do so at a low level. Apprentice tasks add MP3 and MP7 but, because of the guidance within the task, do so at a comparatively modest level. Expert tasks aim to cover the full range of practices.

Make sense of problems and persevere in solving them

Reason abstractly and quantitatively

Construct viable arguments and critique the reasoning of others

Model with mathematics

Use appropriate tools strategically

Attend to precision

Look for and make use of structure

Look for and express regularity in repeated reasoning Mathematical PracticesActivityCard SortMathematical PracticesHow did we do SMP-1. DSMP-2. HSMP-3. ASMP-4. ESMP-5. BSMP-6. FSMP-7. CSMP-8. GCurriculumIntegrating FAL Lessons and TasksWhere are you now?

Where would you like to be?

What might be some strategies to close the gap?ReflectionsIMPACT GoalsObservation PlansGoals for upcoming yearIMPACT GoalsI (Instruction)-Learn about effective strategies and activities for you classroom

M (Mathematics)- Strengthen and expand your subject area expertise

P (Problem Solving)-Explore and create tasks to help students become better critical and creative thinkers

A (Assessment)- Experience and discuss effective uses of formative and summative assessment

C (Content)-Identify and align resources designed to satisfy content requirements

T (Technology)- Gain hands-on experience using technology as a tool for teaching and learning mathematics.

Observation PlanYates formAdministrationPeer-to-PeerConnections to TPGES