Chapter 9 ~~~~~ Mathematical Assessment

2 Basic Components Mathematics Content : understanding of the mathematical processes Content : understanding of the mathematical processes Operations : written and oral calculation skills from counting to solving multi-digit equations Operations : written and oral calculation skills from counting to solving multi-digit equations Application: ability to use practical math skills Application: ability to use practical math skills Problem solving : reading, comprehending and solving computation of word problems Problem solving : reading, comprehending and solving computation of word problems Consumer skills : real-life vocational, survival skills Consumer skills : real-life vocational, survival skills

3 NCTM Supported Assessment Focus Recommended Assessment Domains: Recommended Assessment Domains: Dispositions towards mathematics Dispositions towards mathematics Ability to translate from one mode of representation to another Ability to translate from one mode of representation to another Ability to express mathematical ideas by speaking, writing, demonstrating, and depicting them visually. Ability to express mathematical ideas by speaking, writing, demonstrating, and depicting them visually.

4 NCTM Revised Standards’ Focus Promoting active involvement of students Promoting active involvement of students Cooperative learning – peers work together to develop meaningful solutions to math problems Cooperative learning – peers work together to develop meaningful solutions to math problems Increased emphasis on having students evaluate their own mathematical performance Increased emphasis on having students evaluate their own mathematical performance

5 Common Math Problems Oral language problems Oral language problems Cultural-linguistic difficulties Cultural-linguistic difficulties Cognitive factors Cognitive factors Emotional factors Emotional factors Ineffective instruction Ineffective instruction Poor reading skills Poor reading skills Poor abstract or symbolic thinking Poor abstract or symbolic thinking Failure to use common sense Failure to use common sense Information processing problems Information processing problems

6 Types of Informal Math Assessment Math Probes – quick, efficient, time samples of skills assessing accuracy and fluency Math Probes – quick, efficient, time samples of skills assessing accuracy and fluency Error Analysis – identifies types of math errors and why student is making errors, used to determine whether a pattern exists Error Analysis – identifies types of math errors and why student is making errors, used to determine whether a pattern exists Oral Math Interview- students’ thought processes described aloud Oral Math Interview- students’ thought processes described aloud Math Task Analysis- used to determine how each step in a task is accomplished Math Task Analysis- used to determine how each step in a task is accomplished

7 Types of Informal Math Assessment – cont. Math Scope and Sequence Analysis – guide to determine the skills covered (scope) and the order of presentation (sequence) in a curriculum Math Scope and Sequence Analysis – guide to determine the skills covered (scope) and the order of presentation (sequence) in a curriculum Math Inventory – determines skills and concepts that are mastered, emerging, or undeveloped Math Inventory – determines skills and concepts that are mastered, emerging, or undeveloped Math Journal Writing – evaluates ability to reflect on and record skills and concepts. Math Journal Writing – evaluates ability to reflect on and record skills and concepts. Performance-based Assessment – apply knowledge in real-life situations Performance-based Assessment – apply knowledge in real-life situations

8 Types of Informal Math Assessment – cont. Math Portfolio – student work collected over time Math Portfolio – student work collected over time Math Self-Assessment – student can reflect on and assess own skills Math Self-Assessment – student can reflect on and assess own skills Peer Assessment - compare work with others and gain insight Peer Assessment - compare work with others and gain insight Life Skills Assessment – kindergarten to 12 th grade practical math skill competency Life Skills Assessment – kindergarten to 12 th grade practical math skill competency