Assessment: The Good, The Bad, The Ugly

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?

Formative Assessment (Assessment in the middle???)

• How do we collect evidence of student performance in the midst of a lesson?

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

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…

Observations

• Observe and record– Clipboard– Notebook– Index Cards

• Two approaches– Thorough observation– Drive-by observation

Observations

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

Good assessments come from good tasks!

Kathy Richardson Assessment

• Let’s take a look at the packet

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?

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)

Looking at Student Work

• Evidence that they understand?

• How can we help?

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)

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?

Approaches?

Different arrangements

Folding the arrangements

• Which of the arrangements will fold up into a cube?

• Why do you think that?

• Using some paper and scissors let’s explore some of these arrangements

Concluding the Arranging Cubes task

• Assessment?

Various Types of Assessment• Norm-referenced– Purpose

• Compare students’ performance to other students

– Format• Multiple choice

– Scoring• Compared to other students’ scores (percentiles)• 99th percentile = scored better than 99% of other students

– Can all students score in the 99th percentile?

– Examples• Iowa Test of Basic Skills• Stanford 9 Test

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

Norming Tests

• When tests are renormed – Math, 2005-2006. Reading, 2007-2008

• 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

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, 200-299 = proficient• Can all students be proficient?

– Examples• Most State assessments (GA, VA, NC in 2011-2012)

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?

NCLB: AYP

• Annual Yearly Progress (AYP)– Target goals assess progress • Goals increase in 2007-08, 2010-11 • In 2013-14 100 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

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

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?

Creating Assessments

• High-level multiple choice tests?

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

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 week’s module)

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?

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?

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

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

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

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?• 3• 9• 12• 15

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