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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.