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Rick Billstein, U of Montana. “You can’t fatten a hog by weighing it.” so said a farmer to a governor at a public hearing In order to explain in plain language the dilemma of educational assessment. To be useful to society, assessment must advance education, not merely record its status. Assessment is a way of measuring what students know and expressing what students should learn. (Measuring What Counts, MSEB, 1993)

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Rick Billstein, U of Montana The primary purpose of assessment is to improve student performance through credible feedback, not merely to give grades via simple tests.

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Rick Billstein, U of Montana Assessment is the process of gathering information about students -what they know and can do. The key question is assessment is: How can we find out what students are learning? Evaluation is the process of interpreting and making judgments about assessment information. By itself, assessment data is neither good or bad. It simply mirrors what is going on in the classroom. The key question in evaluation is: Are students learning what we want them to learn? (Authentic Assessment, Diane Hart, 1994)

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Rick Billstein, U of Montana The Content Principle Assessment should reflect the mathematics that is most important for students to learn. The Learning Principle Assessment should enhance mathematics learning and support good instructional practice. The Equity Principle Assessment should support every student’s Opportunity to learn important mathematics. (Measuring What Counts, MSEB, 1993)

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Rick Billstein, U of Montana Important mathematics must shape and define the content of assessment. Appropriate tasks emphasize connections within mathematics, embed mathematics in relevant external contexts, require students to communicate clearly their mathematical thinking, and promote facility in solving non-routine problems. (Measuring What Counts, MSEB, 1993)

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Rick Billstein, U of Montana There can be no equity in assessment as long as excellence is not demanded of all. If we want excellence, the level of expectation must be set high enough so that with effort and good instruction, every student will learn important mathematics. (students need feedback even if it is harsh- e.g. sports) (Measuring What Counts, MSEB, 1993)

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Rick Billstein, U of Montana Assessment in writing provides a good analogy for math. We do not measure writing skills by testing only grammar, spelling, and vocabulary. To assess writing teachers must ask students to actually write: sentences, paragraphs, and essays. In math, we should assess students by asking them to engage in real math - to solve problems, make conjectures, and make convincing arguments. (Measuring What Counts, MSEB, 1993)

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Rick Billstein, U of Montana The Roles of Assessment A. to measure performance, i.e. “to enable students to show what they know, understand, and can do.” B. to exemplify the performance goals C. to drive classroom learning activities WYTIWYG (What You Test Is What You Get) (Assessment for Improvement, Hugh Burkhardt, 2004)

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Rick Billstein, U of Montana …it is through our assessment That we communicate most clearly to students Which activities and learning outcomes we value. -- David Clark

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Rick Billstein, U of Montana Assessments Matter The content of a test affects what students study and what teachers teach, and the form of the assessment affects how they approach the task. Teachers have discovered, for example, that if they want their students to become better writers, they must make better writing count in the classroom; they must teach it and assess it authentically. If teachers want students to acquire skills in solving math problems, or communicating their math ideas, they must both teach and assess those skills. (A Collection of Performance Tasks and Rubrics, Middle School Mathemtics, Charlotte Danielson, 1997)

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Rick Billstein, U of Montana Mathematics assessment must reflect what is important for students to learn, rather than what is easy to assess.

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Rick Billstein, U of Montana Reform Mantra Assess what we value, and value what we assess. Move beyond: * “Test what is merely easy and uncontroversial to test and grade ”Teach, test, and hope for the best.” (Grant Wiggins workshop, 2005) ]

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Rick Billstein, U of Montana Alternative assessment includes any type of assessment in which students create a response to a question rather than choose a response from a given list. (multiple choice, true-false, matching). Alternative assessments can include: Short answer questions Essays Performances Oral presentations Demonstrations Exhibitions Portfolios

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Rick Billstein, U of Montana Performance assessment has one enormous drawback; it is time consuming to do, both in design and to work into classroom instruction time. Even teachers who are committed to the practice of performance assessment find that they don’t have time to design good performance tasks, to try them out with students, and perfect them for later use. Furthermore, most teachers do not learn to design performance tasks and scoring rubrics as part of their professional preparation. (A Collection of Performance Tasks and Rubrics, Middle School Mathematics, Charlotte Danielson, 1997)

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Rick Billstein, U of Montana New assessments will require new kinds of scoring guides and ways of reporting students performance that more accurately reflect the richness and diversity of mathematical learning than do the typical single number scores of today. (Measuring What Counts, MSEB, 1993)

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Rick Billstein, U of Montana Open-ended Problems Open-ended questions enable teachers to see more clearly what all of their students know and understand. Such questions allow each child to respond at his/her level in a way that is meaningful. This can give teachers a window into students thinking and sometimes even open a door! (Open-ended Questions in Elementary Mathematics, Dyer, Moynihan, 2000)

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Rick Billstein, U of Montana For making day-to-day decisions, the teacher is the best person to assess mathematics learning, and the classroom is the best context in which to do so. When an assessment measure is well aligned with -and integrated into- the system of mathematics teaching and learning, preparing students to perform well should involve little more than teaching the mathematics program well. (Cathy Seeley, NCTM News Bulletin, Sept. 2005)

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Rick Billstein, U of Montana Education is slow to change Education is slow to change, but testing is slower. (McLean, 1990)

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Rick Billstein, U of Montana Chicago Research Assignments were related to the degree to which they required “authentic” intellectual work: “Students who received assignments requiring more challenging intellectual work also achieved greater than average gains on the Iowa Test of Basic Skills in reading and mathematics, and demonstrated higher performance in reading, mathematics, and writing on the Illinois Goals Assessment Program …”

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Rick Billstein, U of Montana Chicago Research contin. “Contrary to some expectations, we found high-quality assignments in some very disadvantaged Chicago classrooms, and (found) that all students in these classes benefited from exposure to such instruction. We conclude, therefore, (that) assignments calling for more authenic intellectual work actually improve student scores on conventional tests. (p. 29) (www.consortiumchicago.org/publications)

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Rick Billstein, U of Montana STEM Project STEM Project Assessment Methods Classroom Observations Oral Discussions Class Presentations Open-Ended Questions Extended Problem Solving Enhanced Multiple Choice Questions Written Tasks and Tests Projects Explorations Take-home Tests Homework Journals Group Work Portfolios Tests Student Interviews Summative Tests Standardized Achievement Criterion-Referenced Tests

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Rick Billstein, U of Montana What Gets Assessed Gets Attended To!!! The questions that students are asked determine the learning that occurs. KEYS The task The criteria used to assess the task Student self-assessment

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Rick Billstein, U of Montana Student Self Assessment The first type of student use of a scoring rubric should be for students to evaluate their own work. Most teachers find that for the most part students are quite hard on themselves, in some cases more so than their teachers would be. Clear performance descriptors will help in keeping evaluations consistent, but students frequently reveal a genuine concern for maintaining high standards, even when evaluating their own work. Peer assessment: If students have used a rubric to evaluate their own work, they will be generally be able to provide feedback to their peers in the same spirit. When this happens, the classroom becomes a true community of learners. ( A Collection of Performance Tasks and Rubrics, Middle School Mathemtics, Charlotte Danielson, 1997)

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Rick Billstein, U of Montana Open-ended problems are not necessarily better than well-defined tasks. The mere labels “performance assessment” and “open-ended” do not guarantee that a task meets sound educational principles. For example, open-end problems can be interesting and engaging but mathematically trivial. Performance tasks can be realistic and mathematically appropriate but out of harmony with certain students’ cultural backgrounds. (Measuring What Counts, MSEB, 1993)

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Rick Billstein, U of Montana California Learning Assessment System (CLAS) Mathematics Rubric 4. Fully accomplishes the purpose of the task Shows full grasp and use of the central mathematical ideas(s) Recorded work communicates thinking clearly using some combination of written, symbolic, and/or visual means 3. Substantially accomplished the purpose of the task Shows essential grasp of the central mathematical ideas(s) Recorded work in large part communicates the thinking 2. Partially accomplishes the purpose of the task Shows partial but limited grasp of the central mathematical idea(s) Recorded work may be incomplete, misdirected or not clearly presented 1.Little or no progress toward accomplishing the purpose of the task Shows little or no grasp of the central mathematical ideas(s). Recorded work is barely (if at all) comprehensible

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Rick Billstein, U of Montana Introduction of the E 2 to the class ｷ Discuss the due date. ｷ Make sure everyone understands the problem. ｷ Check in each day with the class to check progress and help with any questions. ｷ Offer to look at student work in progress. ｷ This may be a good time for peer assessment. Handing in the E 2 to the class ｷ Self assess together in class. ｷ Give students time to share parts of their solution. ｷ Give students time to rework parts of their project and hand it in later. Strategies for Managing MATHthematics Assessment

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Rick Billstein, U of Montana Grading the projects ｷ Allow about as long to return papers as the students had to work on them. ｷ Try to hand papers back in about a week. ｷ Grading gets easier and easier with practice! ｷ Use the criteria and get an idea of what should constitute each level in each area of assessment. ｷ Look at the teacher ’ s notes for ideas about grading.

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Rick Billstein, U of Montana Suggested profiles of A, B, C ｷ Do not total the points on the criteria. ｷ Use your own judgment about A-, B+, etc. A - High standards B - Good, but lacking in some areas C - Developing response ｷ Remember that every problem does not elicit every criterion. Returning the papers ｷ Whole group feedback o Illustrate a variety of solutions and approaches. o Highlight exceptional responses. ｷ Individual feedback o Monitor student progress on the criteria. o Compare self-assessment to the teacher ’ s assessment. o Give help or explanations about the student ’ s own responses or grade.

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Rick Billstein, U of Montana Tips for the Teacher when Assessing Student Work using MathThematics

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Rick Billstein, U of Montana

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