Rick Billstein, U of Mont ana . “You can’t fatten a hog by weighing it.” so said a farmer to a governor at a so said a farmer to a governor at a public hearing public hearing In order to explain in plain language In order to explain in plain language the dilemma of educational the dilemma of educational assessment. assessment. To be useful to society, assessment To be useful to society, assessment must advance education, not merely must advance education, not merely record its status. record its status.
Transcript
Rick Billstein, U of Montana
.“You can’t fatten a hog by weighing
it.”
so said a farmer to a governor at a public hearingso said a farmer to a governor at a public hearingIn order to explain in plain language the dilemma In order to explain in plain language the dilemma of educational assessment. of educational assessment.
To be useful to society, assessment must advance To be useful to society, assessment must advance education, not merely record its status.education, not merely record its status.
Assessment is a way of measuring what studentsknow and expressing what students should learn.
(Measuring What Counts, MSEB, 1993)
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.
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)
Rick Billstein, U of Montana
The Content PrincipleThe Content Principle
Assessment should reflect the mathematics that ismost 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)
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)
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)
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 assesswriting teachers must ask students toactually write: sentences, paragraphs, and essays.
In math, we should assess students byasking them to engage in real math - to solve problems, make conjectures, and make convincing arguments.
(Measuring What Counts, MSEB, 1993)
Rick Billstein, U of Montana
The Roles of AssessmentA. 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)
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
Rick Billstein, U of Montana
Assessments MatterThe 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)
Rick Billstein, U of Montana
Mathematics assessment
must reflect what is
important for students to learn,
rather than what iseasy to assess.
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)
]
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 questionsEssaysPerformancesOral presentationsDemonstrationsExhibitionsPortfolios
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)
Rick Billstein, U of Montana
New assessments will require new kinds of scoring guides and ways ofreporting students performance that more accurately reflect the richness and diversity of mathematical learning than do thetypical single number scores oftoday.
(Measuring What Counts, MSEB, 1993)
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)
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)
Rick Billstein, U of Montana
Education is slow to changeEducation is slow to change,
but
testing is slower.testing is slower.(McLean, 1990)
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 …”
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 workactually improve student scores on conventional tests. (p. 29)
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
Rick Billstein, U of Montana
Student Self AssessmentThe 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)
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)
Rick Billstein, U of Montana
California Learning Assessment System (CLAS)
Mathematics Rubric
4. Fully accomplishes the purpose of the taskShows 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
Rick Billstein, U of Montana
Introduction of the E2 to the classｷｷ Discuss the due date.ｷｷ Make sure everyone understands the problem.ｷｷ Check in each day with the class to check progress
and help with any questions.ｷｷ Offer to look at student work in progress.ｷｷ This may be a good time for peer assessment.
Handing in the E2 to the classｷｷ Self assess together in class.ｷｷ Give students time to share parts of their solution.ｷｷ Give students time to rework parts of their project
and hand it in later.
Strategies for Managing MATHthematics Assessment
Rick Billstein, U of Montana
Grading the projectsｷｷ Allow about as long to return papers as the students
had to work on them.ｷｷ Try to hand papers back in about a week.ｷｷ Grading gets easier and easier with practice!ｷｷ Use the criteria and get an idea of what should
constitute each level in each area of assessment.ｷｷ Look at the teacher’s notes for ideas about grading.
Rick Billstein, U of Montana
Suggested profiles of A, B, Cｷｷ Do not total the points on the criteria.ｷｷ Use your own judgment about A-, B+, etc.
A - High standardsB - Good, but lacking in some areasC - Developing response
ｷｷ Remember that every problem does not elicit every criterion.
Returning the papersｷｷ Whole group feedbacko Illustrate a variety of solutions and approaches.o Highlight exceptional responses.ｷｷ Individual feedbacko 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.
Rick Billstein, U of Montana
1. Read the entire student work before you begin to
assess it.
2. Have a Math Thematics t eacher assessment sheets handy.
3. Do not spend a tremendous amount of time scoring one
criteri a. .
4. Keep your written comment s to students at a minimum.
5. Record calculation errors on the bott om of the Math Thematics Assessment Sheet.
Tips for the Teacher when Assessing Student Work using
