Georgia Performance Standards 8th Grade Mathematics Day 2: Learning to Assess and Assessing to Learn

Contact Information Janet Davis 404-463-1736 jdavis@doe.k12.ga.us Massie McAdoo, Ph.D. 404-463-6924 mmcadoo@doe.k12.ga.us Peggy Pool 404-657-9063 ppool@doe.k12.ga.us Georgia Department of Education 1754 Twin Towers East Atlanta, Georgia 30334

Bloom on Mastery

Most students (perhaps over 90 percent) CAN master what we teach Most students (perhaps over 90 percent) CAN master what we teach. Our basic instructional task is to define what we mean by mastery of a subject and to discover methods and materials to help the largest proportion of our students reach it. Benjamin S. Bloom (1971)

Table Discussion What should we assess? Why should we assess? How should we assess?

According to Grant Wiggins… What is to be assessed must be clear and explicit to all students. NO MORE SURPRISES! Rubrics must accompany all major assignments and assessments.

A rubric is a set of rules that Shows levels of quality Communicates standards Tells students expectations for assessment task Is NOT a checklist (yes or no answers) Includes dimensions (criteria), indicators and a rating scale.

Essential Question 1 What should we assess?

Which question shows a better understanding of lines? 1. Given a slope of 5 and a y-intercept of 3, write the equation of the line. OR 2. A company that produces pens has n pens in stock at the beginning of a certain day. It produces these pens at a constant rate r for the entire day. If that day, pens have been produced at a greater constant rate, write an equation that can be used to determine the number of pens produced that day.

A TASK ? Joe and Sue own a chain of ice cream stores. They have found that they sell an average of 1500 cones per summer day when they charge $1.00 each and 1200 cones per summer day when they charge $1.25 each. a. Write these two pieces of data as ordered pairs. b. Find the slope of the line between these ordered pairs. c. Use the slope and an ordered pair to write an equation of the line. d. Use this equation to predict the number of cones the will be sell at $1.30 each.

Is This a Good Task? Decide whether this is or is not a good task. Justify your answer.

Criteria for Good Tasks Involves significant mathematics Can be solved in a variety of ways Elicits a range of responses Requires communication Stimulates best performance Lends itself to a scoring rubric

Standards Based Education Model GPS Stage 1 Identify Desired Results (Big Ideas) Enduring Understandings  Essential Questions  Skills and Knowledge (one or more) Standards Elements Stage 2 Determine Acceptable Evidence (Design Balanced Assessments) (To assess student progress toward desired results) All above, plus Tasks Student Work Teacher Commentary Participant’s Guide, page 8 Stage 3 Plan Learning Experiences and Instruction (to support student success on assessments, leading to desired results) All above

Looking for Big Ideas Big Ideas are key concepts. Look for ideas in key nouns found in the standards. M8A4. Students will graph and analyze graphs of linear equations and inequalities. K Standard Share the book, The Grouchy Ladybug.

From Understandings to Questions “Students will use linear algebra to represent, analyze and solve problems.” Why is it important to be able to represent data with lines? How can I analyze that data to make conclusions and predictions?

Skills and Knowledge KNOWLEDGE (declarative) SKILLS (procedural) Facts Concepts Generalizations Rules, Laws, Procedures Skills Procedures Processes A P L I C A T I O N Participant’s Guide, page 13 KNOWLEDGE (declarative) SKILLS (procedural)

Skills and Knowledge M8A4. Students will graph and analyze graphs of linear equations and inequalities. Graph of linear equations Slope as rate of change Equation of Line

Concept Development Abstract Semi- Abstract Semi- Concrete Concrete

Essential Question 2 Why should we assess?

The purpose of summative assessment is to prove achievement, and the purpose of formative assessment is to improve achievement. Pratt, 1980

Bungee Jumping Complete the task. Identify the standards addressed by this assignment. Specify the criteria of the assignment.

Bungee Jumping What could you learn about students based on their performance on this task?

Accountability The purpose of the Georgia Testing Program is to measure the level of student achievement of the standards identify students failing to achieve mastery of content provide teachers with diagnostic information assist school systems in identifying strengths and weaknesses in order to establish priorities in planning educational programs.

Testing CRCT Information

Essential Question 3 How should we assess?

Assessment vs. Grading Student 1 receives mostly As and high Bs in the beginning; but his/her performance drops off considerably, and s/he receives an F on the final performance test. Student 2 is erratic, receiving an equal number of As and Fs. Student 3 is clueless at the beginning, but by the last few sessions, s/he catches on and performs flawlessly on the final performance. His/her grades are, in order from the first test to the last, F, F, F, F, C, B, A, A, A.

WHICH STUDENT DO YOU WANT TO PACK YOUR PARACHUTE? WHY?

How should we assess? What assessment insights did you gain from this activity?

Assessing for Learning vs Grading Continuous process Provides feedback to improve student achievement May be formative or summative Provides a means of collecting evidence of student mastery of the standards Provides a photo album of student progress through which student growth can be observed Grading A means of assigning numerical or alphabetical grade to a student’s work to inform students, parents and other stakeholders May be formative or summative Provides an attempt to quantitatively describe student achievement Provides a snapshot of student progress

Performance Tasks & Assessments * often occur over time * result in a tangible product or observable performance * encourage self-evaluation and revision * require judgment to score * reveal degrees of proficiency based on criteria established and made public prior to the performance * sometimes involve students working with others

Multiple Representations Pictures Tables Words Symbols Graphs Demonstrate activities that can be used to support the given standard: Arrays (Pictures) Collections (Words) Repeated Addition (Symbols) Multiplication Table (Tables) Function/ Input-Output Chart (Graphs)

Types of Classroom Assessment Selected Response Constructed Response Performance Assessment Informal Assessment Multiple Choice True-False Matching Fill-in-the-blank (words, phrases) Essay Short answer (sentences, paragraphs) Diagram Web Concept Map Flowchart Graph Table Matrix Illustration Presentation Movement Science lab Athletic skill Dramatization Enactment Project Debate Model Exhibition Recital Oral questioning Observation Interview Conference Process description Checklist Rating scale Journal sharing Thinking aloud a process Student self-assessment Peer review

Matching Assessments with Standards ASSESSMENT FORMAT ACHIEVEMENT TARGET Selected Response Constructed Response Performance Tasks Informal Assessment Knowledge/ Informational Skills/Process Thinking and Reasoning Communication Other: Can assess mastery of specific elements of content knowledge Short answers allow students to apply content knowledge Not a good choice for this target; other options preferred Teacher can ask questions, evaluate answers, and infer mastery; but this may not be time-efficient Can assess application of some patterns of reasoning Can observe and evaluate skills as they are being performed Strong match when skill is oral communication Written descriptions of complex problem solutions can provide insight into reasoning proficiency. Can watch students solve some problems or examine some products and infer reasoning proficiency Can ask students to “think aloud” or can ask follow-up questions to probe reasoning Can observe and evaluate oral & written communication portions of performance tasks. Strong match with some communication skills, especially oral communication Can assess under-standing of the steps of a process, but not a good choice for evaluating most skills Not a good choice for this target; other options preferred. -Adapted from Marzano and Stiggins

Advantages of Using a Rubric Lowers students’ anxiety about what is expected of them Provides specific feedback about the quality of their work Provides a way to communicate expectations and progress Ensures all student work is judged by the same standard Disengages the “halo” effect and its reverse Leads students toward quality work.

Basic Rubric Template Scale Criteria Indicator Indicator Indicator

Bungee Jumping Create a rubric to assess the bungee jumping task as a culminating task for the unit on Equations of Lines.

Put that Rubric to Use Now to try your hand at assessing student work. You are to choose two of the “works” posted around the room and assess this work using the rubric that you have created.

Self-Assessment Setting a Goal

Field Assignment Redeliver Day 2. Use what you have learned today to create an assessment you will use with your students. Collect work samples to share with the group. Bring a copy of the assessment and student work samples of your task to Day 3. Bring resources to help you plan for instruction.

Days of Training Implementation Year One Implementation Year Two Day One: Standards, Content, and Curriculum Mapping Day Two:  Assessment Days Three and Four: Classroom Implementation Implementation Year Two Day Five: Differentiation Day Six: Examining Student Work Day Seven: On-line Survey We don’t have to do it all today!

Contact Information Janet Davis 404-463-1736 jdavis@doe.k12.ga.us Massie McAdoo, Ph.D. 404-463-6924 mmcadoo@doe.k12.ga.us Peggy Pool 404-657-9063 ppool@doe.k12.ga.us Georgia Department of Education 1754 Twin Towers East Atlanta, Georgia 30334