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

2. 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

3. 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

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

5. 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

6. 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

7. 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

8. 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

9. 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

10. 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

11. 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

12. 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

13. 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

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

15. 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

16. 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

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

18. Sample Scoring Scale
Figure 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

19. 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

20. 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

21. 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

22. 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

23. 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

24. 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

25. 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

26. 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