3 Assessment for Mathematics NCTM Purpose of AssessmentThe NCTM Assessment Principle
4 Purposes of Assessment To evaluate the effectiveness of your teachingTo monitor the progress of studentsTo help make instructional decisionsTo evaluate students’ achievementTo evaluate programs
5 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.
6 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.
7 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.
8 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
9 Assessments – Educational Measures Teachers – to determine students’ progress in learning specific knowledge or skillsStudents – to ascertain if they are learning what they are being asked to learnParents – to determine how well their children are doing in school
10 Assessments – Educational Measures Principals – to determine how well their students are learningSchool psychologists – to assess students’ particular strengths and needsSchool counselors – to guide students in choosing courses of study and careers
11 Assessments –Educational Measures Lawmakers and policymakers – to set educational priorities and allocate resourcesResearch 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 schoolingLawyers – to argue for or against appropriateness and legality of particular educational practicesMeasurement and Assessment in Schools (Worthen, B., et. al., 1998)
13 State and National Assessments Connecticut AssessmentsConnecticut Mastery Tests (CMTs)Connecticut Academic Performance Test (CAPT)
14 National and International Assessments Advanced PlacementScholastic Aptitude Tests (SATs)National Assessment of Educational Progress – “The Nations Report Card”Trends in International Math and Science Study(TIMMS)
15 Connecticut Assessments Connecticut Mastery Tests (CMTs) have been administered since 1985Limited English proficient (LEP) may be exempt from taking the testsLanguage arts(reading, writing, listening, and mechanics of language) and mathematicsGiven in Spring for grades 3 to 8
16 Connecticut Academic Performance Test (CAPT) Since 1994All Grade 10 studentsTested on science, math, reading, and writingPart 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
17 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
18 Trends in International Math and Science Study (TIMMS) TIMMS is an educational research project investigating student achievement in mathematics and science in about 40 countries around the worldObjective is to measure and interpret differences in national educations systems to improve the teaching and learning of mathematics and science worldwide
27 Building Assessment into Instruction Monitoring your teachingMonitoring student progressMaking instructional decisionsEvaluating student achievementEvaluating programs.
28 What Should Be Assessed? ConceptsMathematical ProcessesDispositionsProcedures
29 Authentic/Alternate Assessment Assess student understanding by promoting student discussionHow are students involved in the lesson activity?How successful are they?Include presentations and require that all students participateEnsure that all students take an active part in the presentation
30 Authentic/Alternate Assessment 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
31 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??
32 Questions Used To evaluate & diagnose discover students interests motivate students’ learninggive practice in expressionemphasize important pointprovide review—drill or practiceshow agreement & disagreementdevelop students’ ability to thinkuncover students’ mental processfind out something one did not knowobtain the attention of wandering mindsfind out whether students knows somethingshow relationships, such as cause & effecthelp students organize & interpret materialsBased on information found in: Victor, E. & Kellough, R.D. Science for the Elementary & Middle School, pgs Prentice Hall: Columbus, Ohio
33 Types of Questions Convergent-Thinking Cueing Clarifying & Probing low-order, recall, one answer questions—aka: narrow & closedWhat are the five types of questions?use to start discussionsCueingafter 3-9 second wait, used to cue studentsDo you recall the quadratic equation we learned?Clarifying & Probingstudent to go beyond simple or quick responseyou understand student’s ideas, feeling, thought processesWhat 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 skillsEvaluativecompels students to place a value on somethingShould points be given for informal assignments?Divergent-Thinkinghigher-order, call for analysis, synthesis, evaluation— aka: broad, reflective, thought & open-ended questionsWhat 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 Prentice Hall: Columbus, Ohio
34 Questioning Dos Give students’ sufficient “think time” minimum wait time of 3-9 secondsListen to students’ responsesclue to their understanding—you know when they need clarification or have misconceptionsinformal, assessment tool.Ask for clarificationwhether responses accurate or inaccurate Why?also ask other students to respond Do you agree?careful probing can reveal misunderstandingsInvolve more studentscalling on volunteers teaches other students they don’t have to participateensure involvement: surveys, draw names at random, check names off list, etc.develop system to help you assess individual students’Use open-ended questionsclosed questions ask recall of isolated factsopen-ended questions call for analysis, evaluation, creativeness & involve everyone in discussionAccept all answersquestioning or ridiculing students’ responses makes them anxious & unwilling to respond in futureremain neutralreduce “verbal rewards” & sanctionspraise effort not “accuracy” of response
35 Questioning Don’ts Don’t ask leading questions or answer own questions when greeted with silence, use wait time or rephrase questionavoid 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 questionsmultiple 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 timeDo not use questions to discipline studentsDon’t use sarcastic questions to confront students’ misbehavior—Isn’t it about time you stopped fooling around?never ask questions to embarrass or punish studentsSteer clear of the “boys club”female elementary teachers ask boys more questions (and probe their responses more often) than they do girlssolution: record & analyze class discussion or ask someone to count number of times you call on male/femaleif you have a problem, call on girl, boy, girl, boyAvoid falling into a rutvary way you ask questions & how students respondstart with fact/definition recall questions, progress to explanation, analysis, hypothesis, prediction questionsuse Bloom’s Taxonomy to explore higher levels
36 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?
37 Examples of Authentic Assessment Tasks Tell me everything that you can about these two triangles45 degrees2 units2 units
38 RubricsA 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).