assessment: enhanced learning and teaching chapter 4 to accompany helping children learn math cdn...

Assessment: Enhanced Learning and Teaching

Chapter 4Chapter 4

To accompany Helping Children Learn Math Cdn Ed, Reys et al.©2010 John Wiley & Sons Canada Ltd.

Assessment

• If an assessment target is clear and standing still, all students will reach it.

-Richard J. Stiggins (assessment expert)

Guiding Questions1. 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?

What is Learning?

• Defining learning is complicated.– Curricular Perspective: Learning is defined as the

acquisition of knowledge, skills, attitudes, values and experiences

– Cognitive Perspective: Learning is defined as the active process of formulating new and more complex understandings of the world.

Bloom’s Taxonomy

• Six-level classification system that uses observed student behaviour to infer the level of cognitive achievement.

• Moves from the general and concrete to the complex and abstract.

• The six levels are:• Knowledge• Comprehension• Application• Analysis• Evaluation• Synthesis

I.C.E. Model• Helps cue teachers about the kids of questions or

activities that help students think more deeply about their learning.

Two Types of Assessment

1. Formative 2. Summative

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.

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.

Four Phases of Assessment

Plan Assessment

GatherEvidence

InterpretEvidence

Use Results

Assessment Standards for School MathematicsNational Council of Teachers of Mathematics, 1995

Shifts in Classroom Assessment

• Making instructional decisions• Monitoring students' progress• Evaluating students' achievement

Assessment Standards for School MathematicsNational Council of Teachers of Mathematics, 1995

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 planningAssessment Standards for School MathematicsNational Council of Teachers of Mathematics, 1995

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

Assessment Standards for School MathematicsNational Council of Teachers of Mathematics, 1995

Assessment Standards for School Mathematics

• Shifts in evaluating 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

Assessment Standards for School MathematicsNational Council of Teachers of Mathematics, 1995

Ways to Assess Students’ Abilities and Dispositions

• Observation• Questioning• Interviewing• Performance tasks• Self-assessment and peer assessment

Ways to Assess Students’ Abilities and Dispositions (cont.)

• Work samples• Portfolios• Writing• Teacher-designed written tests

Sample Holistic Rubric

Sample Observation Guide

Observations

Figure 4-6 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.

Sample Student Self-Assessment

Figure 4-10 Sample student self-assessment “letter to myself” written at 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.

Self-Assessment Questions

Figure 4-8 Self-assessment questions for problem solving

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. )

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

Communicating Assessment Information

• Teachers have three main audiences to whom assessment will be communicated:– To students– To parents or guardians– To school administration

Assessment Practice

Given the problem

A class of 19 children is going on a field trip. 5 children can ride in each car. How many cars

will be needed?

How would you evaluate the following responses?

Assessment Examples (cont.)Student Problem Solving Sample

Alex: Third Month of Grade Three

Ben: Third Month of Grade Three

Assessment Examples (cont.)Student Problem Solving Sample

Carl: Third Month of Grade Three

Assessment Examples (cont.)Student Problem Solving Sample

Andrea: Fifth Month of Grade Four

Assessment Examples (cont.)Student Problem Solving Sample

Amy: Fifth Month of Grade Four

Assessment Examples (cont.)Student Problem Solving Sample

Copyright

Copyright © 2010 John Wiley & Sons Canada, Ltd. All rights reserved. Reproduction or translation of this work beyond that permitted by Access Copyright (The Canadian Copyright Licensing Agency) is unlawful. Requests for further information should be addressed to the Permissions Department, John Wiley & Sons Canada, Ltd. The purchaser may make back-up copies for his or her own use only and not for distribution or resale. The author and the publisher assume no responsibility for errors, omissions, or damages caused by the use of these programs or from the use of the information contained herein.