Inquiry In Instruction [I 3 ] HS-MASS III

Inquiry In Instruction [I3] HS-MASS III Michigan Mathematics & Science Center Network

History of HS-MASSHigh School Mathematics and Science Success HS-MASS I 2006 – 2007 High School Content Expectations Michigan Merit Examination Teaching Strategies for Charts, Tables, and Graphs HS-MASS II 2007 – 2008 High School Clarification Documents Formative and Summative Assessment The Language of Mathematics (Vocabulary) HS-MASS III (I3) 2009 Inquiry In Instruction Creating a Classroom Culture of Inquiry Designing Mathematical Lessons to Foster Inquiry

What has changed since HS-MASS I? 1. High School Content Expectations • First rolled out in 8/06, changes occurred & new version presented in11/07 • Clarification Documents: www.mi-math-companion.wikispaces.com 2. MME • Assessment Design • Contributing Components • AYP Targets • Pre & Post MME Algebra II HSCEs

Inquiry In InstructionOutcomes • Identify key elements of an inquiry based approach to teaching. • Change current practices to become more inquiry based in nature. • Develop lessons and investigations that exemplify the key elements of inquiry instruction. • Implement knowledge and pedagogical skills related to formative assessment to support inquiry learning.

Inquiry In Instruction Requirements of participants • Mathematics & Science teachers: 8 - 12 • Complete pre & post teacher survey • Develop lessons to be taught to at least one math class • Administer pre & post student assessment • Complete a questionnaire • Attend all I3 sessions

Goals, Activities & Timeline Day 1 (2/18) Goal: Develop an understanding of math inquiry and how it looks in the classroom. Identify at least one target math lesson. Day 2 (3/3) Goal: Deepen the understanding of math inquiry. Develop one inquiry-based lesson to be implemented in at least one math class. Complete the lesson-design template to be shared with your colleagues. Day 3 (Evening Session – 4/22) Goal: Reflect upon the complexities of inquiry-based teaching and learning.

Inquiry In Instruction (I³) Teacher Pre-Survey Student Packet - SAMPI Handouts-

Inquiry in Instruction (I3) Growing the Innovators of Tomorrow: Michigan Students’ Thoughts on Learning Mathematics Melendy Lovett Educational & Productivity Solutions Texas Instruments Incorporated MCTM Luncheon Address October 15, 2005 - Video Clip - 8

Inquiry In Instruction (I3) • What is Inquiry in Instruction ? • What does it look like in mathematics? • Where do I stand in the process? • How can I change my classroom practices?

Describe or Define (in your own words): Facts/Characteristics: Non-Examples: Examples: Using the Frayer Model to Represent Inquiry • Complete with a partner • You will be revisiting/revising as needed Inquiry

Inquiry Consensograph • Determine your “level” of understanding using information below: 1 – Have little understanding of Inquiry in Math instruction 2 – Understand Inquiry in Math instruction but not implemented in classroom. 3 – Have used inquiry in Math instruction 4 – Inquiry in Math instruction is regularly used in my classroom. • Place your level (using numbers 1 – 4) on a post-it • Place post-it on blank chart paper on the wall

Introduction to Inquiry

Engage Evaluate Explore Elaborate Explain The 5E Learning Cycle Learning involves making sense of 1) prior experiences, and 2) new first-hand explorations.

Essential Components of Inquiry (5E Model) • Engage • Stimulate student thinking to access prior knowledge • Explore • Students scaffold new knowledge, investigate, and organize • Explain • Students analyze their data • Students support ideas with evidence • Elaborate or Extend • Students draw conclusions based on information they acquire • Evaluate • Students defend their conclusions • Students dialogue with other students and the teacher in learning

The 5-E Learning Cycle: Match the Student Activity with the 5-E Stage: • Engage • Explore • Explain • Elaborate and • Evaluate ___ Student demonstrates an understanding of the concept or skill. ___ Student shows interest in the topic. ___ Student applies explanations and skills to a new but similar situation. ___ Student listens critically as other students explain their answers or solutions. ___ Student records observations and ideas.

The 5-E Learning Cycle: Match the Student Activity with the 5-E Stage: • Engage • Explore • Explain • Elaborate and • Evaluate _E_ Student demonstrates an understanding of the concept or skill. _A_ Student shows interest in the topic. _D_ Student applies explanations and skills to a new but similar situation. _C_ Student listens critically as other students explain their answers or solutions. _B_ Student records observations and ideas.

The 5-E Learning Cycle: Match the Teacher Activity with the 5-E Stage: • Engage • Explore • Explain • Elaborate and • Evaluate ___ Teacher creates interest and generates curiosity. ___ Teacher expects students to use formal definitions and explanations provided previously. ___ Teacher asks students for justification (evidence) and clarification. ___ Teacher redirects students’ investigations by asking probing questions. ___ Teacher allows students to assess their own learning.

The 5-E Learning Cycle: Match the Teacher Activity with the 5-E Stage: • Engage • Explore • Explain • Elaborate and • Evaluate _A_ Teacher creates interest and generates curiosity. _D_ Teacher expects students to use formal definitions and explanations provided previously. _C_ Teacher asks students for justification (evidence) and clarification. _B_ Teacher redirects students’ investigations by asking probing questions. _E_ Teacher allows students to assess their own learning.

The 5-E Learning Cycle: Are the following examples of student behaviors … “C” Consistent with the 5-E Instructional Model, or “I” Inconsistent with the 5-E Instructional Model: ____ Student asks, “Is this the ‘right’ answer?” ____ Student works with little or no interaction with others. ____ Student discusses alternatives with others. ____ Student draws conclusions from “thin air,” i.e. ignores previous information. ____ Student accepts explanations without justification. ____ Student answers open-ended questions using evidence and previously accepted explanations. ____ Student uses previously-recorded observations in explanations. ____ Student asks “Why did this happen?” ____ Student offers only memorized definitions or explanations. ____ Student uses previous information to ask questions and propose solutions. ____ Student seeks and offers no more than one solution to a problem.

The 5-E Learning Cycle: Are the following examples of student behaviors … “C” Consistent with the 5-E Instructional Model, or “I” Inconsistent with the 5-E Instructional Model: _I__ Student asks, “Is this the ‘right’ answer?” _I__ Student works with little or no interaction with others. _C_ Student discusses alternatives with others. _I__ Student draws conclusions from “thin air,” i.e. ignores previous information. _I__ Student accepts explanations without justification. _C_ Student answers open-ended questions using evidence and previously accepted explanations. _C_ Student uses previously-recorded observations in explanations. _C_ Student asks “Why did this happen?” _I__ Student offers only memorized definitions or explanations. _C_ Student uses previous information to ask questions and propose solutions. _I__ Student seeks and offers no more than one solution to a problem.

The 5-E Learning Cycle: Are the following examples of teacher behaviors … “C” Consistent with the 5-E Instructional Model, or “I” Inconsistent with the 5-E Instructional Model: _____ Teacher provides premature answers to students’ questions and states conclusions. _____ Teacher encourages students to explain concepts in their own words. _____ Teacher leads students step-by-step to a solution. _____ Teacher acts as a “consultant” for students. _____ Teacher generates interest and curiosity, and raises questions. _____ Teacher does not solicit students’ explanations. _____ Teacher asks open-ended questions such as “What evidence do you have?” _____ Teacher lectures. _____ Teacher refers students to existing evidence and asks “What do you already know?” _____ Teacher tests vocabulary words and isolated facts. _____ Teacher reminds students of alternate explanations.

The 5-E Learning Cycle: Are the following examples of teacher behaviors … “C” Consistent with the 5-E Instructional Model, or “I” Inconsistent with the 5-E Instructional Model: __I__ Teacher provides premature answers to students’ questions and states conclusions. __C_ Teacher encourages students to explain concepts in their own words. __I__ Teacher leads students step-by-step to a solution. __C_ Teacher acts as a “consultant” for students. __C_ Teacher generates interest and curiosity, and raises questions. __I__ Teacher does not solicit students’ explanations. __C_ Teacher asks open-ended questions such as “What evidence do you have?” __I__ Teacher lectures. __C_ Teacher refers students to existing evidence and asks “What do you already know?” __I__ Teacher tests vocabulary words and isolated facts. __C_ Teacher reminds students of alternate explanations.

Essential Components of Mathematical Inquiry • Conjecturing • Students are presented with a problem and make predictions • Constructivism • Students scaffold new mathematical knowledge • Connections • Students make connections to prior knowledge • Students make connections to various mathematical principles • Conclusions • Students draw conclusions based on information they acquire • Communication • Students defend their conclusions • Students dialogue with other students and the teacher in learning 23

Simplified Inquiry Model • Starts with a question • Involves an investigation • Results shared

Another Model • Ask • Investigate • Create • Discuss • Reflect

Inquiry Lesson Cycle • Introduce Lesson • Build the Foundation • Conduct Exploration • Analyze Data • Justify Conjectures/Solutions • Present Findings/Summarize Understandings Connect to Next Lesson

Inquiry : “Families of Functions” Creating a Poster Your poster will include: • Your name • The equation • Word description of your equation • Table of values • Graph of your function • List of anything you notice

Mathematics Inquiry : “Finding Proof” Case Study in a Geometry Classroom - Annenberg Video - www.learner.org

Finding ProofSome Considerations • How does this approach to finding proof compare with traditional methods? • Value of extending a problem over several days? • Consider use of history in the study of mathematics. - Discuss with your group -

Reminders for next session 1. Give the student pre-test. 2. Bring in the completed student pre-test. 3. Come with a lesson that you will modify at the next session.

3 – 2 – 1 Out On an index card from one of the boxes, please write down: 3 Things you learned today 2 Formative assessments used today 1 Question/Comment you have Please place the card on the table as you leave… Thank you!

Inquiry In Instruction [I 3 ] HS-MASS III