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Assessment: The Good, The Bad, The Ugly

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Questions to think about How do you assess students performance in mathematics? How does performance on tests compare to daily performance in terms of importance? What role does partial credit have in mathematics? What does data-driven instruction mean to you?

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Formative Assessment (Assessment in the middle???) How do we collect evidence of student performance in the midst of a lesson?

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Interviews A sequence of questions – Broad to more specific during follow up questions Good rule of thumb – Question something they know – Question something they know a little bit about – Question something that stretches them

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Interviews A few types of questions – Questioning for an answer – Questioning for a procedure – Questioning for an explanation – Questioning for mathematical thinking For the Sharing Cookies task come up with one of each type of question…

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Observations Observe and record – Clipboard – Notebook – Index Cards Two approaches – Thorough observation – Drive-by observation

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Observations What issues do we have observing students in your classroom?

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Good assessments come from good tasks!

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Kathy Richardson Assessment Lets take a look at the packet

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Higher-level thinking assessments You have 36 yards of fencing to build a pen for your dog. – What are the possible dimensions of a rectangular pen that you could build? – What are the areas of the various pens?

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Components of this task for assessment? Understanding of area Understanding of perimeter Understanding corner counts for 2 yards Show work Use of manipulatives Appropriate picture drawn Multiple representations (> than one way)

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Looking at Student Work Evidence that they understand? How can we help?

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Rubrics Dog Pen Problem – If you were to score students out of 10 points, what would you give points for? – As a group come up w/ a grading scheme (out of 10 points)

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Arranging Tiles Take six plastic square tiles How many different ways can you arrange the six tiles so that each tile is sharing a side with at least one other tile?

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Approaches?

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Different arrangements

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Folding the arrangements Which of the arrangements will fold up into a cube? Why do you think that? Using some paper and scissors lets explore some of these arrangements

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Concluding the Arranging Cubes task Assessment?

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Various Types of Assessment Norm-referenced – Purpose Compare students performance to other students – Format Multiple choice – Scoring Compared to other students scores (percentiles) 99 th percentile = scored better than 99% of other students – Can all students score in the 99 th percentile? – Examples Iowa Test of Basic Skills Stanford 9 Test

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Creating Assessments Norm-referenced – Iowa Test of Basic Skills (ITBS) – NC EOG tests Norming makes it difficult for all students to pass – Scores naturally increase over time due to norming

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Norming Tests When tests are renormed – Math, Reading, Approx. 50% are passing (levels 3 and 4) Bar gets radically adjusted to even out the percent that passes Statistically- norming helps to avoid a ceiling effect where most pass

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Types of Assessments Criterion-referenced – Purpose Measures students mastery of standards and criteria – Format Typically multiple choice exams – Scoring Based on percentage correct E.g., 400 possible points, >300 = advanced, = proficient Can all students be proficient? – Examples Most State assessments (GA, VA, NC in )

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High-stakes testing What happens to a child if he/she fails an EOG test? What happens to a school if their student performance on EOG tests are not adequate?

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NCLB: AYP Annual Yearly Progress (AYP) – Target goals assess progress Goals increase in , In percent proficiency is expected. – AYP is measured by subgroups (e.g., ethnicity, gender, disability) Students tend to fit in more than one subgroup – E.g., African-American male with a learning disability fits into 3 subgroups

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Assessment Questions Multiple choice – Question (stem) – Answer choices Typically three to four choices In numerical or alphabetical order Wrong answers are plausible (common errors) Multiple-Multiple Choice – Question – Answer choices More than one choice can be correct

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Can multiple choice questions… Assess students higher-order thinking skills? – Why or why not? – How can you compose multiple choice questions that extend beyond recall of basic knowledge?

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Creating Assessments High-level multiple choice tests?

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What happens when you double the length of the side of a square? A) double area B) double perimeter C) quadruple area D) quadruple perimeter

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Assessment Questions Performance-based – Purpose Assess students ability to perform or complete tasks related to concepts and skills – Format Tasks- multiple-choice, short answer, multi-part – Scoring Rubric based Scores are compared: pre-test, post-test; benchmarks Can all students score above the benchmark? – Examples Illinois State Mathematics Exam Balanced Assessment in Mathematics (last weeks module)

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Creating Assessments Performance-based – Merging between higher-order thinking skills and content Actions- analyzing, evaluating, explaining, synthesizing How do these levels of thinking align to constructivist beliefs about teaching and learning?

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Writing Effective Standards-based Items Multi-step problems…. – Susan has three fish and Tommy has four fish. The next day, Susan gets two more fish and Tommy gets one more fish. How many fish do each have? – There are six cookies in each pack and four crackers in each bag. If I have nine packs of cookies and eight bags of crackers, how many of each do I have?

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Writing Effective Standards-based Items What-if problems… – A square is 3 inches on each side. If I tripled the length of each side what happens to the area? It doubles It is nine times greater It quadruples It triples

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Writing Effective Standards-based Items What-if problems… – I have six counters. What if I shared those counters between myself and a friend? Each friend gets two Each friend gets three Each friend gets four Each friend gets six

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Writing Effective Standards-based Items Working backwards… – I go fishing every day during my five-day vacation. Each day I caught one more fish than I did the day before. If I caught a total of 20 fish, how many fish did I catch on day 1? 1 fish 2 fish 3 fish 4 fish

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Writing Effective Standards-based Items Missing part tasks… (CGI) – Some students were playing freeze tag at recess. Six of them stopped playing. Nine of them kept playing. How many were playing at the beginning?

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In your grade level groups… Pick a standard (suggested…the one from your lesson plan) Write eight assessment tasks (2 of each) – Multi-step – What if – Working backwards – Missing part

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