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
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 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
10 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
11 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 (Worthen, B., et. al., 1998)
13 State and National Assessments Connecticut Assessments – Connecticut Mastery Tests (CMTs) – Connecticut Academic Performance Test (CAPT)
14 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)
15 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/ www.cmtreports.com
16 Connecticut Academic Performance 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 http://www.captreports.com
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 http://nces.ed.gov/nationsreportcard/
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 world Objective is to measure and interpret differences in national educations systems to improve the teaching and learning of mathematics and science worldwide
19 TIMSS – How did the United States do? http://nces.ed.gov/timss/
20 Connecticut Mastery Tests For grades 3 to 8 given in Spring… http://www.cmtreports.com
Building Assessment into Instruction Monitoring your teaching Monitoring student progress Making instructional decisions Evaluating student achievement Evaluating programs. 27
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?? 31
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 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 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 ’ 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 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—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 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? 36
Examples of Authentic 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 http://school.discoveryeducation.com/schro ckguide/assess.html 38