CHAPTER 4 Assessment: Enhanced Teaching and Learning Reys/ Lindquist/ Lamdin/ Smith, Helping Children Learn Math, 10th Edition, © 2012

Assessment Assessment should support the learning of important mathematics and provide useful information to teachers and students. (NCTM, 2000, p.22) Reys/ Lindquist/ Lamdin/ Smith, Helping Children Learn Math, 10th Edition, © 2012

Focus Questions 1. How are assessments of learning (summative assessment) and assessments for learning (formative assessment) alike and different—in characteristics and in when or how they are used? 2. How do the four phases of classroom assessment help teachers inform their instruction? 3. What different methods can teachers use to gather information about their students’ abilities, dispositions, and interests, and what do each of these methods communicate to students about what is valued in teaching and learning mathematics? Reys/ Lindquist/ Lamdin/ Smith, Helping Children Learn Math, 10th Edition, © 2012

Two Types of Assessment 1. Summative 2. Formative Reys/ Lindquist/ Lamdin/ Smith, Helping Children Learn Math, 10th Edition, © 2012

Summative Assessment Assessment of Learning - Summative assessment provides evidence of student achievement for purposes of public reporting and accountability. Ex. tests, end-of year exams, standardized tests. Master 4-1: Two Types of Assessment Reys/ Lindquist/ Lamdin/ Smith, Helping Children Learn Math, 10th Edition, © 2012

Formative Assessment Assessment for Learning – Formative Assessment documents students’ achievement as well as guides instructional decisions and helps students learn. Ex. homework, in-class assignments, performance assessments, teacher observations, classroom tests. Master 4-1: Two Types of Assessment Reys/ Lindquist/ Lamdin/ Smith, Helping Children Learn Math, 10th Edition, © 2012

Four Phases of Assessment Plan Assessment Gather Evidence Interpret Use Results Master 4-3: Purposes and Phases of Assessment Assessment Standards for School Mathematics National Council of Teachers of Mathematics, 1995 Reys/ Lindquist/ Lamdin/ Smith, Helping Children Learn Math, 10th Edition, © 2012

Four Purposes of Assessment Making Instructional Decisions Monitoring Students' Progress Evaluating Students' Achievement Evaluating Programs Assessment Standards for School Mathematics National Council of Teachers of Mathematics, 1995 Master 4-3: Purposes and Phases of Assessment Reys/ Lindquist/ Lamdin/ Smith, Helping Children Learn Math, 9th Edition, © 2009

Assessment Standards for School Mathematics Shifts in Making Instructional Decisions toward: integrating assessment with instruction using evidence from a variety of assessment formats and contexts using evidence of every student's progress toward long- range goals in instructional planning Master 4-2: Assessment Shifts Assessment Standards for School Mathematics National Council of Teachers of Mathematics, 1995 Reys/ Lindquist/ Lamdin/ Smith, Helping Children Learn Math, 10th Edition, © 2012

Assessment Standards for School Mathematics Shifts in Monitoring Students’ Progress toward: assessing progress toward mathematical power communicating with students about performance in a continuous, comprehensive manner using multiple and complex assessment tools students learning to assess their own progress Master 4-2: Assessment Shifts Assessment Standards for School Mathematics National Council of Teachers of Mathematics, 1995 Reys/ Lindquist/ Lamdin/ Smith, Helping Children Learn Math, 10th Edition, © 2012

Assessment Standards for School Mathematics Shifts in Assessing to Evaluate Students’ Achievement toward: comparing students’ performance with performance criteria assessing progress toward mathematical power certification based on balanced, multiple sources of information profiles of achievement based on public criteria Master 4-2: Assessment Shifts Assessment Standards for School Mathematics National Council of Teachers of Mathematics, 1995 Reys/ Lindquist/ Lamdin/ Smith, Helping Children Learn Math, 10th Edition, © 2012

Ways to Assess Observation Questioning Interviewing Performance Tasks Self-Assessment and Peer Assessment Master 4-4: Ways to Assess Reys/ Lindquist/ Lamdin/ Smith, Helping Children Learn Math, 10th Edition, © 2012

Ways to Assess Work Samples Portfolios Writings Teacher-Designed Written Tests Standardized Achievement Tests Master 4-4: Ways to Assess Reys/ Lindquist/ Lamdin/ Smith, Helping Children Learn Math, 9th Edition, © 2009

Sample Observation Guide Reys/ Lindquist/ Lamdin/ Smith, Helping Children Learn Math, 10th Edition, © 2012

Observations Figure 4-4 Flip cards for recording classroom observations. Cards can be arranged alphabetically or by classroom seat assignments, whatever will help you find the right card quickly. Reys/ Lindquist/ Lamdin/ Smith, Helping Children Learn Math, 10th Edition, © 2012

Sample Student Self-Assessment Figure 4-8 Sample student self-assessment “letter to myself” written t the beginning of the year. Students can compare this letter with a letter written at the end of the year to show their growth over the school year. Reys/ Lindquist/ Lamdin/ Smith, Helping Children Learn Math, 10th Edition, © 2012

Self-Assessment Questions Figure 4-6 Self-assessment questions for problem solving Reys/ Lindquist/ Lamdin/ Smith, Helping Children Learn Math, 10th Edition, © 2012

Sample Scoring Scale Figure 4-10 A scale for scoring problem solving. (Source: Reprinted with permission from “How to Evaluate Progress in Problem Solving,” copyright 1987 by the National Council of Teachers of Mathematics. All rights reserved. ) Reys/ Lindquist/ Lamdin/ Smith, Helping Children Learn Math, 10th Edition, © 2012

Keeping Assessment Records It is important to keep both informal and formal records of students’ learning and their dispositions toward mathematics. Examples of Assessment: Checklists Student Files Class Records Master 4-5: Keeping Records and Communicating about Assessment Reys/ Lindquist/ Lamdin/ Smith, Helping Children Learn Math, 10th Edition, © 2012

Communicating Assessment Information Teachers have three main audiences to whom assessment will be communicated: To Students To Parents or Guardians To School Administration Master 4-5: Keeping Records and Communicating about Assessment Reys/ Lindquist/ Lamdin/ Smith, Helping Children Learn Math, 10th Edition, © 2012

Assessment Problem. If a class of 19 children go on a field trip and 5 children can ride in each car, how many cars will be needed? Reys/ Lindquist/ Lamdin/ Smith, Helping Children Learn Math, 10th Edition, © 2012

Assessment (cont’d) Student Problem Solving Sample Alex: Third Month of Third Grade Master 4-6: Problem Solving Sample Reys/ Lindquist/ Lamdin/ Smith, Helping Children Learn Math, 10th Edition, © 2012

Ben: Third Month of Third Grade Assessment (cont’d) Student Problem Solving Sample Ben: Third Month of Third Grade Master 4-7: Problem Solving Sample Reys/ Lindquist/ Lamdin/ Smith, Helping Children Learn Math, 10th Edition, © 2012

Assessment (cont’d) Student Problem Solving Sample Carl: Third Month of Third Grade Master 4-8: Problem Solving Sample Reys/ Lindquist/ Lamdin/ Smith, Helping Children Learn Math, 10th Edition, © 2012

Assessment (cont’d) Student Problem Solving Sample Andrea: Fifth Month of Fourth Grade Master 4-9: Problem Solving Sample Reys/ Lindquist/ Lamdin/ Smith, Helping Children Learn Math, 10th Edition, © 2012

Amy: Fifth Month of Fourth Grade Assessment (cont’d) Student Problem Solving Sample Master 4-10: Problem Solving Sample Amy: Fifth Month of Fourth Grade Reys/ Lindquist/ Lamdin/ Smith, Helping Children Learn Math, 10th Edition, © 2012