Assessments

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AssessmentsAssessments

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Assessment for MathematicsAssessment for MathematicsNCTMNCTM

Purpose of Assessment

The NCTM Assessment Principle

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Purposes of AssessmentPurposes of Assessment

To evaluate the effectiveness of your teaching

To monitor the progress of studentsTo help make instructional decisionsTo evaluate students’ achievementTo evaluate programs

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NCTM Assessment PrincipleNCTM Assessment Principle

Assessment should support the learning of important mathematics and furnish useful information to both teachers and students.

Assessment should be more than merely a test at the end of instruction to gauge learning. It should be an integral part of instruction that guides teachers and enhances students’ learning.

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Teachers should be continually gathering information about their students through questions, interviews, writing tasks, and other means.

They can then make appropriate decisions about such matters as reviewing material, re-teaching a difficult concept, or providing something more or different for students who are struggling or need enrichment.

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To be consistent with the Learning Principle, assessments should focus on understanding as well as procedural skills.

Because different students show what they know and can do in different ways, assessments should also be done in multiple ways, and teachers should look for a convergence of evidence from different sources.

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Teachers must ensure that all students are given an opportunity to demonstrate their mathematics learning.

For example, teachers should use communication-enhancing and bilingual techniques to support students who are learning English

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Assessments – Educational Assessments – Educational MeasuresMeasures

Teachers – to determine students’ progress in learning specific knowledge or skills

Students – to ascertain if they are learning what they are being asked to learn

Parents – to determine how well their children are doing in school

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Assessments – Educational Assessments – Educational MeasuresMeasures

Principals – to determine how well their students are learning

School psychologists – to assess students’ particular strengths and needs

School counselors – to guide students in choosing courses of study and careers

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Assessments –Educational Assessments –Educational MeasuresMeasures

Lawmakers and policymakers – to set educational priorities and allocate resources

Research and evaluation directors – to collect data to extend general knowledge about educational processes or help evaluate the effectiveness of particular schools programs.

News reporters – to report on the quality of schooling Lawyers – to argue for or against appropriateness and

legality of particular educational practices

Measurement and Assessment in Schools (Worthen, B., et. al., 1998)

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AssessmentsAssessments

StateNationalInternational

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State and National State and National AssessmentsAssessments

Connecticut Assessments

– Connecticut Mastery Tests (CMTs)

– Connecticut Academic Performance Test (CAPT)

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National and International National and International AssessmentsAssessments

Advanced PlacementScholastic Aptitude Tests (SATs)National Assessment of Educational

Progress – “The Nations Report Card”Trends in International Math and Science

Study(TIMMS)

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Connecticut AssessmentsConnecticut Assessments

Connecticut Mastery Tests (CMTs) have been administered since 1985

Limited English proficient (LEP) may be exempt from taking the tests

Language arts(reading, writing, listening, and mechanics of language) and mathematics

Given in Spring for grades 3 to 8– www.cmtreports.com/

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Connecticut Academic Connecticut Academic Performance Test (CAPTPerformance Test (CAPT))

Since 1994 All Grade 10 students Tested on science, math, reading, and writing Part of testing system that provides a logical

progression from assessing specific objectives at the lower grades to integration and application of skills at high school level

http://www.captreports.com

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National Assessment of National Assessment of Educational Progress (NAEP)Educational Progress (NAEP)

Department of Education“The Nations Report Card”Group comparison by race and ethnicity,

gender, type of community, and regionhttp://nces.ed.gov/nationsreportcard/

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Trends inTrends inInternational Math and International Math and

Science Study (TIMMS)Science Study (TIMMS)TIMMS is an educational research project

investigating student achievement in mathematics and science in about 40 countries around the world

Objective is to measure and interpret differences in national educations systems to improve the teaching and learning of mathematics and science worldwide

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TIMSS – How did the United TIMSS – How did the United States do?States do?

http://nces.ed.gov/timss/

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Connecticut Mastery TestsConnecticut Mastery Tests

For grades 3 to 8 given in Spring…

http://www.cmtreports.com

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2007 CMT Grade 3 Results by Content 2007 CMT Grade 3 Results by Content Strand Mathematics ConnecticutStrand Mathematics Connecticut

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2007 CMT Grade 52007 CMT Grade 5Results by Content Strand Mathematics Results by Content Strand Mathematics

ConnecticutConnecticut

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2007 CMT Grade 5 2007 CMT Grade 5 Results by Content Strand Mathematics Results by Content Strand Mathematics

Hartford,ConnecticutHartford,Connecticut

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2007 CMT Grade 5 2007 CMT Grade 5 Results by Content Strand Mathematics Results by Content Strand Mathematics

Avon,ConnecticutAvon,Connecticut

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CMT Mathematics Grade 3 Test BlueprintCMT Mathematics Grade 3 Test Blueprint

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CMT Mathematics Grade 4 CMT Mathematics Grade 4 Test BlueprintTest Blueprint

Building Assessment into Building Assessment into InstructionInstruction

Monitoring your teachingMonitoring student progressMaking instructional decisionsEvaluating student achievementEvaluating programs.

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What Should Be Assessed?What Should Be Assessed?

Concepts Mathematical ProcessesDispositionsProcedures

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Authentic/Alternate Authentic/Alternate AssessmentAssessment

Assess student understanding by promoting student discussion– How are students involved in the lesson activity?– How successful are they?

Include presentations and require that all students participate– Ensure that all students take an active part in the

presentation

Authentic/Alternate Authentic/Alternate AssessmentAssessment

Involve students in the development of rubricsInterview your studentsMake writing about math a routine not a

special occasionFind a way for your students to communicate

math outside of classAssign self assessments for students to monitor

their progress

Writing to LearnWriting to Learn

1. How is assessment different than testing? 2. What are at least four purposes of assessment? 3. How can a learning task or problem be an

assessment task? 4. What is the difference between scoring and

grading? 5. Do you think that teaching to the test is a good

method of raising scores on high-stakes tests? What do you think is the best way to raise scores??

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Questions Used ToQuestions Used To• evaluate & diagnose

• discover students interests

• motivate students’ learning

• give practice in expression

• emphasize important point

• provide review—drill or practice

• show agreement & disagreement

• develop students’ ability to think

• uncover students’ mental process

• find out something one did not know

• obtain the attention of wandering minds

• find out whether students knows something

• show relationships, such as cause & effect

• help students organize & interpret materialsBased on information found in: Victor, E. & Kellough, R.D. Science for the Elementary & Middle School, pgs. 68-70. Prentice Hall: Columbus, Ohio

Types of QuestionsTypes of Questions

Based on information found in: Victor, E. & Kellough, R.D. Science for the Elementary & Middle School, pgs. 70-71. Prentice Hall: Columbus, Ohio

Convergent-Thinking• low-order, recall, one answer questions—aka: narrow & closed• What are the five types of questions?• use to start discussions

Cueing• after 3-9 second wait, used to cue students• Do you recall the quadratic equation we learned?

Clarifying & Probing• student to go beyond simple or quick response• you understand student’s ideas, feeling, thought processes• What I hear you saying is that you prefer to work alone. Is this correct? Why do you

think/feel you work better alone?• strong positive correlation with student learning & development of metacognitive

skills

Evaluative• compels students to place a value on something• Should points be given for informal assignments?

Divergent-Thinking• higher-order, call for analysis, synthesis, evaluation— aka: broad, reflective,

thought & open-ended questions• What measures could you take to increase your learning in this class?

Questioning DosGive students’ sufficient “think time”• minimum wait time of 3-9 seconds

Listen to students’ responses• clue to their understanding—you know when they need clarification or have

misconceptions• informal, assessment tool.

Ask for clarification• whether responses accurate or inaccurate Why?• also ask other students to respond Do you agree?• careful probing can reveal misunderstandings Involve more students• calling on volunteers teaches other students they don’t have to participate• ensure involvement: surveys, draw names at random, check names off list, etc.• develop system to help you assess individual students’ Use open-ended questions• closed questions ask recall of isolated facts• open-ended questions call for analysis, evaluation, creativeness & involve everyone in

discussion

Accept all answers• questioning or ridiculing students’ responses makes them anxious & unwilling to respond in

future• remain neutral• reduce “verbal rewards” & sanctions • praise effort not “accuracy” of response

Questioning Don’tsDon’t ask leading questions or answer own questions• when greeted with silence, use wait time or rephrase question• avoid leading questions: Don’t you think that . . . ? or Wouldn’t you agree that . . . ? • use questions to find out what students know & stimulate more questions

Avoid multiple questions• multiple questions confuse students & complicate issues—How many different kinds of light bulbs are

there? How do they work? Which is the most energy efficient?• ask only one question at a time Do not use questions to discipline students• Don’t use sarcastic questions to confront students’ misbehavior—Isn’t it about time you stopped fooling

around?• never ask questions to embarrass or punish students Steer clear of the “boys club” • female elementary teachers ask boys more questions (and probe their responses more often) than

they do girls• solution: record & analyze class discussion or ask someone to count number of times you call on

male/female• if you have a problem, call on girl, boy, girl, boy

Avoid falling into a rut• vary way you ask questions & how students respond• start with fact/definition recall questions, progress to explanation, analysis, hypothesis, prediction

questions• use Bloom’s Taxonomy to explore higher levels

Examples of Authentic Examples of Authentic Assessment TasksAssessment Tasks

Does the graph y = x squared ever intersect the graph y = x squared = 2? What are some ways that you could test your idea?

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Examples of Authentic Examples of Authentic Assessment TasksAssessment Tasks

Tell me everything that you can about these two triangles

45 degree

s

2 units

2 u

nits

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RubricsRubrics

A rubric is a framework that can be designed or adapted by the teacher for a particular group of students or a particular mathematical task (Kulm, 1994).

http://school.discoveryeducation.com/schrockguide/assess.html

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Documents

Assessments