Assessments

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Assessment for Mathematics NCTM

 Purpose of Assessment  The NCTM Assessment Principle 3

Purposes of Assessment

 To evaluate the effectiveness of your teaching  To monitor the progress of students  To help make instructional decisions  To evaluate students’ achievement  To evaluate programs 4

NCTM 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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NCTM Assessment Principle

 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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NCTM Assessment Principle

 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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NCTM Assessment Principle

 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 8

Assessments – Educational Measures

 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 9

Assessments – Educational Measures

 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 10

Assessments –Educational Measures

    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

al., 1998) (Worthen, B., et. 11

Assessments

 State  National  International 12

State and National Assessments

 Connecticut Assessments – Connecticut Mastery Tests (CMTs) – Connecticut Academic Performance Test (CAPT) 13

National and International Assessments

 Advanced Placement  Scholastic Aptitude Tests (SATs)  National Assessment of Educational Progress – “The Nations Report Card”  Trends in International Math and Science Study(TIMMS) 14

Connecticut 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 Performance Test (CAPT

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 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 Educational Progress (NAEP)

 Department of Education  “The Nations Report Card”  Group comparison by race and ethnicity, gender, type of community, and region  http://nces.ed.gov/nationsreportcard/ 17

Trends in International Math and

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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 18

TIMSS – How did the United States do?

 http://nces.ed.gov/timss/ 19

Connecticut 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 Strand Mathematics Connecticut

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2007 CMT Grade 5 Results by Content Strand Mathematics Connecticut

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2007 CMT Grade 5 Results by Content Strand Mathematics Hartford,Connecticut

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2007 CMT Grade 5 Results by Content Strand Mathematics Avon,Connecticut

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CMT Mathematics Grade 3 Test Blueprint

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CMT Mathematics Grade 4 Test Blueprint

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Building Assessment into Instruction

 Monitoring your teaching  Monitoring student progress  Making instructional decisions  Evaluating student achievement  Evaluating programs.

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What Should Be Assessed?

 Concepts  Mathematical Processes  Dispositions  Procedures 28

Authentic/Alternate Assessment

 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 Assessment

 Involve students in the development of rubrics  Interview your students  Make writing about math a routine not a special occasion  Find a way for your students to communicate math outside of class  Assign self assessments for students to monitor their progress

Writing 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 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 materials Based on information found in: Victor, E. & Kellough, R.D.

Science for the Elementary & Middle School

, pgs. 68-70. Prentice Hall: Columbus, Ohio

Types of Questions

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?

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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— Columbus, Ohio

aka

: broad, reflective, thought & open-ended questions •

What measures could you take to increase your learning in this class?

Based on information found in: Victor, E. & Kellough, R.D.

Science for the Elementary & Middle School

, pgs. 70-71. Prentice Hall:

Questioning Dos Give 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 • develop system to help you assess individual students ’ ’ t have to participate • ensure involvement: surveys, draw names at random, check names off list, etc.

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 respons e

Questioning Don ’ ts Don’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— • ask only one question at a time

How many different kinds of light bulbs are there? How do they work? Which is the most energy efficient?

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 level s

Examples of Authentic Assessment 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

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Assessment Tasks

Tell me everything that you can about these two triangles 45 degree s 2 unit s 37

Rubrics

 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/schro ckguide/assess.html

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