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Cover art goes here. Artwork provided in a separate fi le! Secondary_Math_PM_FM.indd i Secondary_Math_PM_FM.indd i 6/6/2011 5:18:10 PM 6/6/2011 5:18:10 PM Secondary_Math_PM_FM.indd ii Secondary_Math_PM_FM.indd ii 6/6/2011 5:18:10 PM 6/6/2011 5:18:10 PM P A R T I C I P A N T ’ S M A N U A L SECONDARY MATHEMATICS Secondary_Math_PM_FM.indd iii Secondary_Math_PM_FM.indd iii 6/6/2011 5:18:10 PM 6/6/2011 5:18:10 PM © 2010 The New Teacher Project, Inc. All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means electronic, mechanical, photocopied, recorded, or otherwise, without the prior written permission of the publisher. Every effort has been made to contact copyright holders of material reproduced in this book. Any omissions will be rectifi ed in subsequent printings if notice is given to the publisher. Bilingual Education Early Childhood Education Elementary Education Elementary Special Education English as a Second Language Foreign Language Generalist Education Middle School Mathematics Music Secondary English Language Arts Secondary Mathematics Secondary Science Secondary Social Studies Secondary Special Education Visual Arts About The New Teacher Project The New Teacher Project (TNTP) helps school districts and states fulfi ll the promise of public education by ensuring that all students—especially those from high-need communities—get excellent teachers. A national nonprofi t organization founded by teachers, TNTP is driven by the knowledge that although great teachers are the best solution to educational inequality, the nation’s education systems do not suffi ciently prioritize the goal of effective teachers for all. In response, TNTP develops customized programs and policy interventions that enable education leaders to fi nd, develop, and keep great teachers and achieve reforms that promote effective teaching in every classroom. Since its inception in 1997, TNTP has recruited or trained approximately 37,000 teachers—mainly through its highly selective Teaching Fellows™ programs—benefi ting an estimated 5.9 million students. TNTP has also released a series of acclaimed studies of the policies and practices that affect the quality of the nation’s teacher workforce, most recently including The Widget Effect: Our National Failure to Acknowledge and Act on Differences in Teacher Effectiveness (2009). Today TNTP is active in more than 40 cities, including Baltimore, Chicago, Denver, New Orleans, New York, and Oakland. For more information, please visit www.tntp.org. Teaching for Student Achievement, General Education and Special Education The New Teacher Project’s pre-service training program, Teaching for Student Achievement (TfSA), is currently in its fi fth edition. The training, which is designed specifi cally with the needs of novice teachers in mind, is based on the essential knowledge and skills that new teachers need in order to have an immediate impact on the success of their students. The conceptual framework is informed by the latest pedagogical research as well as TNTP’s own fi eld-based research of program participants. Over the last several years of development, TNTP has integrated the best practices of its most successful candidates with those of other successful teachers in high-need schools to create a training program with two central goals for participants: (1) to make immediate academic progress with all students; and (2) to close the achievement gap. Teachers who participate in the TfSA curriculum receive a Guidebook, our central text for the training experience. The Guidebook is available in both general education and special education versions, and serves as a resource to teachers during the training experience and beyond. Teaching for Results Teaching for Results seminars are designed to maximize a new teacher’s effectiveness through a focus on data- driven instructional planning and delivery that aims to close the achievement gap for all students. Each title in the series is grounded in an inquiry process through which course participants learn research-based instructional strategies specifi c to a content area and are taught to constantly evaluate the effi cacy of those strategies against authentic student performance data. This process encourages new teachers to make real-time adjustments to their instructional practice with the goal of increasing student achievement. Titles Offered in the Teaching for Results Series: Secondary_Math_PM_FM.indd iv Secondary_Math_PM_FM.indd iv 6/6/2011 5:18:11 PM 6/6/2011 5:18:11 PM ©2010 The New Teacher Project iii Table of Contents PARTICIPANT Orientation Session ............................................................................... 1 Handout OS.1: Personal and Course Goals ..............................................................2 Handout OS.2: Center 1—Content .............................................................................4 Handout OS.3: Center 2—Assessment .................................................................... 17 Handout OS.4: Center 3—Instruction .....................................................................39 Handout OS.5: Strategic Design ...............................................................................48 Handout OS.6: Strategic Design Unit Planning Template ....................................49 Handout OS.7: Unit Plan Self-Assessment ..............................................................55 Handout OS.8: Unit Plan Components ....................................................................56 Handout OS.9: Successes, Goals, and Challenges in My Classroom .................. 61 Session 1: Introduction to Secondary Mathematics ...........................63 Handout 1.1: Free Write Refl ection ..........................................................................64 Handout 1.2: Preparing for College in Secondary Mathematics ..........................65 Handout 1.3: Graphic Organizer for Preparing for College in Secondary Mathematics ................................................................ 76 Handout 1.4: Secondary Mathematics Content Domain Graphic ........................ 81 Handout 1.5: Applying the Content Domain Graphic ............................................82 Handout 1.6: The Secondary Mathematics Content Domain ...............................83 Handout 1.7: Examining Standards .........................................................................85 Handout 1.8: Sample: How Is the Mathematics Domain Addressed in Instruction? .....................................................................................86 Handout 1.9: How Is the Mathematics Domain Addressed in Instruction? .......90 Handout 1.10: Instructional Strategies Log ............................................................93 Module 1: Foundations for Teaching Mathematics Session 2: Setting Up for Success .........................................................97 Handout 2.1: Developing a Vision of Success .........................................................98 Handout 2.2: 40 Developmental Assets for Adolescents Ages 12–18 ..................99 Handout 2.3: Assessment of 40 Developmental Assets ...................................... 102 Handout 2.4: Characteristics of Adolescents ....................................................... 108 Handout 2.5: Mathematics Confi dence Questionnaire ....................................... 110 Handout 2.6: 10 Ways to Increase Mathematics Confi dence .............................. 111 Handout 2.7: Developing Routines for Confi dence .............................................. 113 Handout 2.8: “I Can …” ............................................................................................ 115 Handout 2.9: Student Goal-Tracking Template .....................................................117 Handout 2.10: Four-Point Rubric for Assessing Specifi c Mathematics Skills .. 118 Handout 2.11: Understanding Knowledge for Teaching ......................................120 Handout 2.12: The Content Domain as Knowledge for Teaching ...................... 121 (continued) Secondary_Math_PM_FM.indd iii Secondary_Math_PM_FM.indd iii 6/6/2011 5:18:11 PM 6/6/2011 5:18:11 PM iv Table of Contents Table of Contents (continued) Handout 2.13: Self-Assessment ..............................................................................122 Handout 2.14: Setting Professional Goals .............................................................124 Session 3: Engaging in the Cycle of Inquiry ......................................127 Handout 3.1: Setting Big Goals for Students ........................................................128 Handout 3.2: Assessment Practices That Improve Teacher and Student Performance .......................................................................129 Handout 3.3: Assessment Inventory ...................................................................... 135 Handout 3.4: What Data Do You Have? .................................................................138 Handout 3.5: The Inquiry Process .........................................................................139 Handout 3.6: Inquiry Process Walk-Through ....................................................... 140 Handout 3.7: Inquiry Process Implementation ..................................................... 143 Handout 3.8: Identifying a Focus Class ................................................................ 145 Handout 3.9: MDTP Diagnostics Overview .......................................................... 146 Handout 3.10: Which Assessment Do I Use? ........................................................ 150 Handout 3.11: How Do I Administer the MDTP Assessment? ............................ 154 Handout 3.12: Sample Student Directions for MDTP .......................................... 155 Handout 3.13: Sample MDTP Test Results Report .............................................. 157 Handout 3.14: Forming Ground Rules ................................................................... 169 Handout 3.15: The Inquiry Process, Step One: Diagnose ....................................171 Handout 3.16: Objectives Checklist ....................................................................... 173 Session 4: Overview of Teaching Standards ......................................175 Handout 4.1: About the National Council of Teachers of Mathematics .............176 Handout 4.2: NCATE/NCTM Standards ................................................................ 179 Handout 4.3: NCTM and the Content Domain ..................................................... 187 Handout 4.4: Sample Geometry Standards........................................................... 188 Handout 4.5: Sample NCTM Standards and State Standards ............................ 189 Handout 4.6: NCTM Standards and State Standards .......................................... 191 Handout 4.7: Sample Unit Plan ............................................................................... 192 Handout 4.8: Unit Plan ............................................................................................ 194 Handout 4.9: Sample: Aligning NCTM Standards to Your Professional Goals ............................................................................ 196 Handout 4.10: Exit Slip ............................................................................................ 197 Module 2: Problem Solving, Proof, and Communication in Mathematics Session 5: Using Data to Drive Instruction I .....................................199 Handout 5.1: Navigating Your Score Report .........................................................200 Handout 5.2: Sample MDTP Test Results Report ................................................206 Handout 5.3: Practice Analyzing Class-Wide Patterns ....................................... 212 Handout 5.4: Analyzing Your Class-Wide Patterns ...............................................214 Secondary_Math_PM_FM.indd iv Secondary_Math_PM_FM.indd iv 6/6/2011 5:18:11 PM 6/6/2011 5:18:11 PM ©2010 The New Teacher Project v Handout 5.5: Common Errors with Basic Skills .................................................. 216 Handout 5.6: Lowest Scoring Item Analysis ......................................................... 219 Handout 5.7: Example Identifying Student Strengths and Gaps ........................ 221 Handout 5.8: Identifying Student Strengths and Gaps ........................................222 Handout 5.9: Student Grouping .............................................................................223 Handout 5.10: Setting Goals ...................................................................................224 Handout 5.11: Teaching Plan for Mathematics .....................................................226 Handout 5.12: Incorporating Peer Feedback into Teaching Plan ......................228 Handout 5.13: Creating Effective Questions for Inquiry Groups .......................230 Handout 5.14: Data Analysis Protocol Notes ........................................................233 Session 6: Mathematical Problem Solving .........................................235 Handout 6.1: Evaluating My Teaching Plan ..........................................................236 Handout 6.2: Article on Problem Solving .............................................................237 Handout 6.3: Problem-Solving Article Discussion ..............................................248 Handout 6.4: How Is Problem Solving Addressed in Instruction? ....................249 Handout 6.5: The RICE Problem-Solving Method ...............................................252 Handout 6.6: Practice with the RICE Method ......................................................253 Handout 6.7: Problem of the Day Routine .............................................................254 Handout 6.8: Problem of the Day Routine Example Problem ............................255 Handout 6.9: Problem-Solving Pitfalls ..................................................................256 Handout 6.10: Critical Foundations for Algebra ..................................................258 Handout 6.11: Key Concepts in Algebra and Number Sense ..............................260 Handout 6.12: The Uses of Variables .....................................................................262 Handout 6.13: The Four Uses of Variables ............................................................263 Handout 6.14: Problem-Solving Skills for College Readiness ............................264 Handout 6.15: Problem-Solving Strategies Overview .........................................265 Handout 6.16: Sample Strategy Implementation PLANNING Sheet ..................269 Handout 6.17: Sample Strategy Implementation REFLECTION Sheet .............. 271 Handout 6.18: Evaluation Criteria for Strategy Implementation Planning Sheet................................................................................. 272 Handout 6.19: Strategy Implementation PLANNING Sheet................................ 273 Handout 6.20: Strategy Implementation REFLECTION Sheet ........................... 276 Session 7: Mathematical Reasoning and Proof ..................................279 Handout 7.1: Strategy Debrief Group Process ......................................................280 Handout 7.2: Mathematical Reasoning as Equity ................................................ 281 Handout 7.3: Reading Guide for Mathematical Reasoning as Equity ...............288 Handout 7.4: Reasoning and Sense Making .........................................................290 Handout 7.5: Reading Guide for Reasoning and Sense Making .........................296 Handout 7.6: Reframing Mathematical Concepts ................................................297 Handout 7.7: Problem-Solving Practice .................................................................299 Handout 7.8: Problem-Solving Practice—Full Examples ..................................300 Handout 7.9: Aspects of Encouraging Reasoning in the Mathematics Classroom ..........................................................................................304 (continued) Secondary_Math_PM_FM.indd v Secondary_Math_PM_FM.indd v 6/6/2011 5:18:11 PM 6/6/2011 5:18:11 PM vi Table of Contents Handout 7.10: Problem-Solving Examples (Resource) .......................................305 Handout 7.11: Types of Reasoning ......................................................................... 315 Handout 7.12: Formal Proofs in Geometry ............................................................316 Handout 7.13: Formal Proofs in Calculus ..............................................................317 Handout 7.14: Practice Using Diagrams to Aid Proofs ....................................... 318 Handout 7.15: Reasoning and Proof Strategies Overview .................................. 319 Handout 7.16: Strategy Implementation PLANNING Sheet ................................322 Handout 7.17: Strategy Implementation REFLECTION Sheet ............................325 Session 8: Literacy and Communication in Mathematics ................. 327 Handout 8.1: Strategy Debrief Group Process ......................................................328 Handout 8.2: Learning Mathematical Language in the Zone of Proximal Development .................................................................329 Handout 8.3: Learning Mathematical Language ...................................................335 Handout 8.4: The Need for Language Instruction in the Mathematics Classroom ...........................................................................................336 Handout 8.5: Tools for Socratic Seminars .............................................................338 Handout 8.6: Mathematics Vocabulary to Be Taught Explicitly .........................340 Handout 8.7: Mathematics Literacy Strategies ......................................................342 Handout 8.8: Mathematics Writing Prompts .........................................................348 Handout 8.9: Communicating About Measurement .............................................350 Handout 8.10: Number Sense and Communication ..............................................354 Handout 8.11: Communicating About Algebra ...................................................... 355 Handout 8.12: Mathematical Literacy and Communication Strategies Overview ........................................................................358 Handout 8.13: Strategy Implementation PLANNING Sheet.................................365 Handout 8.14: Strategy Implementation REFLECTION Sheet ............................368 Handout 8.15: Objectives Checklist ........................................................................ 371 Module 3: Connections, Representation, and Applications in Mathematics Session 9: Using Data to Drive Instruction II ...................................373 Handout 9.1: Strategy Debrief Group Process ..................................................... 374 Handout 9.2: Analyzing Your Class-Wide Patterns .............................................. 375 Handout 9.3: Lowest Scoring Item Analysis ......................................................... 376 Handout 9.4: Sample Data Set: First Administration .......................................... 377 Handout 9.5: Sample Data Set: Second Administration ..................................... 378 Handout 9.6: Example Identifying Student Strengths and Gaps ....................... 379 Handout 9.7: Identifying Student Strengths and Gaps ........................................380 Handout 9.8: Findings and Refl ections ................................................................. 381 Handout 9.9: Student Grouping .............................................................................382 Handout 9.10: Setting Goals ...................................................................................383 Table of Contents (continued) Secondary_Math_PM_FM.indd vi Secondary_Math_PM_FM.indd vi 6/6/2011 5:18:11 PM 6/6/2011 5:18:11 PM ©2010 The New Teacher Project vii Handout 9.11: Respond Plan for Mathematics ......................................................385 Handout 9.12: Exit Slip ............................................................................................389 Session 10: Mathematical Connections ..............................................391 Handout 10.1: Revisiting Professional Goals ........................................................392 Handout 10.2: Overview of Mathematical Connections .....................................394 Handout 10.3: Mathematical Connections and the Content Domain ................396 Handout 10.4: Connecting Measurement to the Standards ................................397 Handout 10.5: Connecting Measurement to Other Subjects ..............................399 Handout 10.6: Topics in Discrete Mathematics .................................................... 401 Handout 10.7: Discrete Mathematics .....................................................................403 Handout 10.8: Connecting Discrete Mathematics to State Standards (Examples) .....................................................405 Handout 10.9: Connecting Discrete Mathematics to My Classroom .................406 Handout 10.10: How Is Discrete Mathematics Addressed in Instruction? ............407 Handout 10.11: Connecting Mathematics to the Real World .............................. 410 Handout 10.12: Mathematical Connections Strategies Overview ...................... 421 Handout 10.13: Strategy Implementation PLANNING Sheet ..............................423 Handout 10.14: Strategy Implementation REFLECTION Sheet..........................426 Session 11: Mathematical Representation .........................................429 Handout 11.1: Strategy Debrief Group Process ....................................................430 Handout 11.2: Dienes on Manipulatives ................................................................ 431 Handout 11.3: Cognitive Scaffold for Dienes on Manipulatives .........................435 Handout 11.4: Representation in Number Sense .................................................437 Handout 11.5: Representations of Integer Mathematics .....................................438 Handout 11.6: Manipulatives and Number Sense ................................................439 Handout 11.7: Manipulatives in Geometry ............................................................443 Handout 11.8: Discovering the Pythagorean Theorem .......................................445 Handout 11.9: Algebra Tiles as Pictorial Representations of Variable Expressions ................................................................. 447 Handout 11.10: Reproducible Algebra Tiles ..........................................................448 Handout 11.11: Factoring and Foiling with Algebra Tiles ..................................449 Handout 11.12: Online Resources for Mathematical Representations ..............450 Handout 11.13: Written Representations in Mathematics ................................... 451 Handout 11.14: Connecting Verbal and Graphic Representations .....................453 Handout 11.15: Mathematical Representations Strategies Overview ............... 461 Handout 11.16: Strategy Implementation PLANNING Sheet ..............................466 Handout 11.17: Strategy Implementation REFLECTION Sheet ..........................469 Session 12: Technology for Mathematics ...........................................471 Handout 12.1: Strategy Debrief Group Process ................................................... 472 Handout 12.2: General Principles for Evaluating Technology ........................... 473 Handout 12.3: WebQuests: Technology for Students with Disabilities ............. 476 (continued) Secondary_Math_PM_FM.indd vii Secondary_Math_PM_FM.indd vii 6/6/2011 5:18:12 PM 6/6/2011 5:18:12 PM viii Table of Contents Handout 12.4: WebQuest: Technology for Exploration and Reinforcement .... 477 Handout 12.5: WebQuest: Technology for Dialogue and Presentation ............. 478 Handout 12.6: Meaningful Incorporation of Calculators .................................... 479 Handout 12.7: Understanding Algebra Through Graphing Calculators ............480 Handout 12.8: Using the Graphing Calculator to Find a Best-Fit Line .............485 Handout 12.9: Using Computer Spreadsheets to Solve Equations ....................489 Handout 12.10: Find the Formula Using a Spreadsheet to Solve a Pattern ......499 Handout 12.11: Refl ecting on Graphing Calculators and Spreadsheets ............505 Handout 12.12: Technology Resources by Content .............................................508 Handout 12.13: How Is Technology Addressed in Instruction? ..........................511 Handout 12.14: Technology Strategies Overview .................................................514 Handout 12.15: Strategy Implementation PLANNING Sheet .............................. 519 Handout 12.16: Strategy Implementation REFLECTION Sheet .........................522 Session 13: Project-Based Learning ...................................................525 Handout 13.1: Strategy Debrief Group Process ...................................................526 Handout 13:2: What Is Project-Based Learning (PBL)?...................................... 527 Handout 13.3a: Overview of Multiple Intelligences in the Classroom ..............529 Handout 13.3b: Multiple Intelligences Self-Assessment......................................533 Handout 13.3c: Understanding Your Intelligences ..............................................537 Handout 13.4: Using Multiple Intelligences for PBL and Mathematics .............538 Handout 13.5: Project Criteria Checklist ..............................................................539 Handout 13.6: Sample Project ................................................................................540 Handout 13.7: Steps for Designing a Project ........................................................ 552 Handout 13.8: Designing a Project ........................................................................555 Handout 13.9: PBL Resources ................................................................................ 557 Handout 13.10: Objectives Checklist .....................................................................559 Module 4: Closing Session 14: Responding to Student Needs .........................................561 Handout 14.1: Project-Based Learning Debrief ....................................................562 Handout 14.2: Tuning Protocol ..............................................................................563 Handout 14.3: Student Study ..................................................................................565 Handout 14.4: Understanding Mathematics Diffi culties .....................................566 Handout 14.5: Strategies for Addressing Disabilities in Mathematics .............. 570 Handout 14.6: Summary: Diffi culties in Understanding Mathematics.............. 575 Handout 14.7: Case Studies in Mathematics Disabilities .................................... 576 Handout 14.8: Analyzing the Case Studies ........................................................... 577 Handout 14.9: Intervention Plan ............................................................................ 578 Handout 14.10: Exit Slip .......................................................................................... 579 Table of Contents (continued) Secondary_Math_PM_FM.indd viii Secondary_Math_PM_FM.indd viii 6/6/2011 5:18:12 PM 6/6/2011 5:18:12 PM ©2010 The New Teacher Project ix Session 15: Closing Session ................................................................581 Handout 15.1: Sentence and Question Stems for Feedback ...............................582 Handout 15.2: Analyzing Student Progress in the Content Domain .................583 Handout 15.3: Synthesizing Strategy Implementation Planning and Refl ection Sheets .....................................................................584 Handout 15.4: Managing for Success .....................................................................587 Handout 15.5: Management Strengths and Weaknesses.....................................590 Handout 15.6: Setting Professional Growth Goals ..............................................592 Teaching for Results: Secondary Mathematics References: Teaching for Results 2010 .......................................593 Secondary_Math_PM_FM.indd ix Secondary_Math_PM_FM.indd ix 6/6/2011 5:18:12 PM 6/6/2011 5:18:12 PM Course Overview Overview The Secondary Mathematics seminar is designed to help new teachers increase their effi cacy as content area teachers of secondary mathematics. This course will systematically guide teachers in gaining new insights on the way secondary mathematics content is organized to understand better what students are expected to know and be able to do at each grade level. A comparison of the organization of the content area—referred to as a content domain—to the local and state standards and any local curricular resources such as textbooks or district pacing guides will empower teachers to examine critically the tools they have been given to ensure student mastery and to determine if there are particular areas of study that will need to be supplemented with the teacher’s own repertoire of instructional strategies. To aid in this process, the course is set up so that participants are exposed to an extensive bank of content-specifi c instructional strategies. Teachers are also asked to assess constantly student performance in relation to standards and expectations of content mastery through a course routine called the inquiry process. With a clear picture of where students are, and where they need to be to achieve at high levels, teachers are best equipped to effectively and effi ciently plan, teach, reteach when warranted, and make changes to their instructional practice to ensure measurable results in their efforts to close the achievement gap. The interaction between the areas of focus mentioned above, which can be parsed into three broad components of content, assessment, and instruction, lies at the heart of the course. Each experience in this course aims to help teachers become more effective at understanding and delivering the content for which their students must master, administering and utilizing assessment tools and data to inform instruction to move students toward standards mastery, and ultimately toward closing the achievement gap. Course goals are listed below and provide measurable descriptions of the knowledge and skills participants will be able to demonstrate by the end of the Secondary Mathematics course. x Course Overview Secondary_Math_PM_FM.indd x Secondary_Math_PM_FM.indd x 6/6/2011 5:18:12 PM 6/6/2011 5:18:12 PM ©2010 The New Teacher Project xi (continued) The Secondary Mathematics seminar is organized around the following course outcomes aligned to the three key course themes of content, assessment, and instruction. The ultimate goal of this course is to equip teachers with the skills and habits of mind to help them close the achievement gap. By the end of the course, participants will Content � develop depth of understanding about content and pedagogy to effectively make mathematics content accessible to students � critically analyze the unique topics, structures, and vocabulary of secondary mathematics content to make connections across topics while planning and delivering instruction Assessment � implement various assessments (diagnostic, formative, summative) to collect data about and monitor progress of student achievement Instruction � make instructional choices to modify or supplement curriculum to meet standards and achieve big goals for a diverse group of learners � facilitate opportunities for students to develop connections between mathematics skills, concepts in the domain, and real-world applications COURSE GOALS: Secondary_Math_PM_FM.indd xi Secondary_Math_PM_FM.indd xi 6/6/2011 5:18:12 PM 6/6/2011 5:18:12 PM xii Course Overview We believe that high-quality teachers can and must close the achievement gap. Participants are responsible for ensuring that all of their students meet or exceed grade-level standards. It is critical that participants adjust their instruction to increase the academic achievement of students who are performing below grade level to help them catch up, as well as bolster the academic achievement of students who are currently meeting minimum grade level expectations. To help ensure that what is learned in the course is being integrated into the daily work of teaching to close the achievement gap, participant competencies for each course theme are presented below along with digestible and accessible reminders of how to achieve the goals on a daily basis. Those reminders are referred to as key messages throughout the course. Teaching for Results: Competencies Key Messages It is your responsibility to understand deeply the content you teach in order to make learning meaningful to all students. Each of the core subjects you teach has a unique organizational structure, vocabulary, and requirements. Understanding these elements will help you make connections for your students between skills and knowledge, as well as within and between content areas. Most important, you will be able to help your students generalize and apply knowledge to new and complex academic tasks. Assessment is a key component to closing the achievement gap. Teachers need to use ongoing assessments to be highly effective in the classroom. You will need to monitor student progress carefully, critically analyze results, and make immediate and careful changes to your own teaching practices to achieve measurable progress in student performance. You need to understand how to select effective assessments so that you can continuously document student progress toward meeting or exceeding grade-level standards by the end of the school year. You will invest students in their academic development by being transparent about their performance, sharing results, and providing them with the ongoing assessment tools they need to understand and drive their own academic success. Teachers must choose instructional strategies carefully to maximize their impact on student achievement. Your instructional choices should support student mastery of standards, be informed by student achievement data, and be differentiated to meet student needs. This will help ensure that your efforts in the classroom will lead toward academic achievement for every student. Your curriculum is a tool, but whether your students make gains is up to you. No curriculum on its own will be effective for all students. CONTENT ASSESSMENT INSTRUCTION Course Overview (continued) Secondary_Math_PM_FM.indd xii Secondary_Math_PM_FM.indd xii 6/6/2011 5:18:12 PM 6/6/2011 5:18:12 PM ©2010 The New Teacher Project xiii (continued) Course Assessments For each competency there is a related assignment or series of assignments that enables participants to demonstrate mastery of the competencies upon which this course is grounded. These assignments comprise the course assessments. Some assignments are completed during the sessions, while others are given as homework. Note that there are multiple assignments required as part of this course, not all of which are part of the course assessments. Some of the assignments are formative in nature, while the assignments that comprise the course assessments are meant to be capstone assignments related to each competency. A full list of assignments can be found in the syllabus. Secondary_Math_PM_FM.indd xiii Secondary_Math_PM_FM.indd xiii 6/6/2011 5:18:12 PM 6/6/2011 5:18:12 PM

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