Assessment

1. Assessment By Kelly Dau EDMA 658

2. Assessment should not merely be done to students; rather, it should also be done for students.NCTM 2000, p.22

3. The Assessment Principle Assessment should support the learning of important mathematics and furnish useful information to both teachers and students. NCTM 1995

4. NCTM Assessment Standards for School Mathematics • Reflect the mathematics that students should know and be able to do • Enhance mathematics learning • Promote equity • Be an open process • Promote valid inferences • Be a coherent process

5. Why do we assess? • Monitor student progress • Make instructional decisions • Evaluate student achievement • Evaluate programs

6. What should be assessed? • Concepts and procedures • Productive disposition • Mathematical processes • Problem solving • Reasoning • Communication

7. Measures of Open-Ended Problem-Solving Performance • Fluency • Flexibility • Originality

8. Use questions to reveal students’ mathematical thinking • Compute 5.2 x 4.3 • Draw a picture to show .7, and explain how you know that your picture shows the given decimal. • Do .3 and .30 name the same amount? • Explain your answer.

9. Jennifer divided 70 by a mystery number and got 2.63 for an answer. • Is the mystery number bigger or smaller than 70? • How do you know? • Without dividing, estimate which of the following has the SMALLEST quotient: • 4.9 / 0.003 • 4.9 / 0.03 • 4.9 / 0.3 • 4.9 / 3

10. Name a decimal that estimates the value of point A • Why did you give A that value? 0 A 1

11. Consider the role of rubrics in how students present their ideas. More than an assessment, rubrics can provide feedback to teachers, further students’ understanding, and encourage articulation of ideas.

12. Types of Rubrics • Holistic – describe the qualities of performance as a whole, judging overall performance with all processes given equal weight. • Analytic – assign scores to the essential traits or dimensions of the task allowing certain dimensions of the task to be given more weight if so desired. • Specific – created for only one task and have performance descriptors that address only that task. • General – use language that is not task specific.

13. Van de Walle Double-Sort Procedure • Sort student work into two categories: “got it” for work that essentially has the target concept or idea and “not yet” for work that contains misconceptions or incorrect procedures. • Take the “got it” work and sort it into two additional categories of “excellent” and “proficient.” • Take the “not yet” work and sort it into two categories of “marginal” and “unsatisfactory.” • Once the student work is sorted, look through the work in each category and note the common characteristics.

14. Double Sort Rubric These categories and related information describe a holistic double sort assessment.

15. Analytic Rubric An analytic rubric, which is not task-specific, scores the essential traits or dimensions of the task.

16. Task Specific Rubric - Holistic This partial example of a holistic rubric describes the qualities of a student’s performance as a whole.

17. Combined Analytic and Holistic Student friendly or student-created rubric.

18. What a difference a word makes! Formative assessments help identify students who need help when there is still time to help; but perhaps the definition should be expanded to “assessment for learning” to describe learning that happens in the classroom and involves students in every aspect of their own assessment.

19. Five Keys to Quality Formative Assessment • Clear purposes – clarifying, sharing, and understanding goals for learning and criteria for success with students • Clear targets – engineering effective classroom discussions, questions, activities, and tasks that elicit evidence of students’ learning • Sound design – providing feedback that moves learning forward • Effective communication – activating students as owners of their own learning • Student involvement – activating students as learning resources for one another

20. On-going Formative Assessments • Observation Tools • Anecdotal notes • Observation rubrics • Checklists for individual students • Checklists for full classes • Writing • Journals • Portfolios • Group projects • Diagnostic Interviews

21. So, where’s the technology? • Students today are growing up in a world with a variety of high-tech tools, but there is one day a year when most schools across the country revert to an era when whiteboards were blackboards—testing day! • For the most part, investments in technology have not led to fundamental changes in approaches to testing; mostly these investments have simply made old ways more efficient by replacing paper-based, multiple-choice, fill-in-the-bubble tests with computerized versions of the same. Overall, the types of skills tests measure, and what the test results can tell us, have remained essentially the same. • But don’t let that stop YOU! Use the technology you have available, focusing on supporting the learning of important mathematics and furnishing useful information to both teachers and students.

22. To put teachers in the position of deciding between what they believe best enhances their students’ learning and what is required to survive in the education system puts them in an untenable position. High stakes assessments must be closely linked to the goals teachers are being asked to achieve.

23. Remember, data collected through assessments is being used to: • Reveal a teacher who is putting forth great effort and shows improvement in teaching methods; • Identify a teacher who does not take assessment seriously; • Indicate teacher content knowledge; • Demonstrate a teacher’s strengths; • Show a teacher who, through challenges in classroom management techniques, cannot get the students to take the content seriously; and • Highlight a teacher who is working assiduously with her students and experiencing amazing progress!

24. While data can be an indicator of many things, it should be used to open doors and illuminate strategies and pedagogies to increase students’ learning and growth!

25. Mathematical Proficiency Five Strand Rope Model • Conceptual understanding refers to comprehension of mathematical concepts, operations, and relations; it is the functional grasp of mathematical ideas, it enables students to learn new ideas by connecting to ideas they already know.  • Procedural fluency is defined as skill in carrying out procedures flexibly, accurately, efficiently, and appropriately.  • Strategic competence is the ability to formulate, represent, and solve mathematical problems. • Adaptive reasoning refers to the capacity for logical thought, reflection, explanation, and justification. • Productive disposition is habitual inclination to see mathematics as sensible, useful, and worthwhile, coupled with a belief in diligence and one's own efficacy. 

26. What is Mathematical Proficency? Source: National Research Council (2001)

27. NCTM Assessment Standards

28. Mathematics Standard • Use NCTM and state/local standards to establish what mathematics students should know and be able to do and base assessments on those essential concepts and processes; • Develop assessments that encourage the application of mathematics to real and sometimes novel situations; • Focus on significant and correct mathematics.

29. Learning Standard • Incorporate assessment as an integral part of instruction and not an interruption or a singular event at the end of a unit of study; • Inform students about what content is important and what is valued by emphasizing those ideas in your instruction and matching your assessments to the models and methods used; • Listen thoughtfully to your students so that further instruction will not be based on guesswork but instead on evidence of students’ misunderstandings or needs.

30. Equity Standard • Respect the unique qualities, experiences, and expertise of all students; • Maintain high expectations for students while recognizing their individual needs; • Incorporate multiple approaches to assessing students, including the provision of accommodations and modifications for students with special needs.

31. Openness Standard • Establish with students the expectations for their performance and how they can demonstrate what they know; • Avoid just looking at answers and give attention to the examination of the thinking processes students used; • Provide students with examples of responses that meet expectations and those that don’t meet expectations.

32. Inferences Standard • Reflect seriously and honestly on what students are revealing about what they know; • Use multiple assessments (e.g., observations, interviews, tasks, tests) to draw conclusions about students’ performance; • Avoid bias by establishing a rubric that describes the evidence needed and the value of each component used for scoring.

33. Coherence Standard • Match your assessment techniques with both the objectives of your instruction and the methods of your instruction; • Ensure that assessments are a reflection of the content you want students to learn; • Develop a system of assessment that allows you to use the results to inform your instruction in a feedback loop.

34. Remember, we are required to… • Post two to three grades per week per content area • TEST fundamental concepts and processes (2-3 formative assessments to one summative) with documentation • GRADE our students on the results of these tests Standards-based or A B C D F model • Make measurable gains on MAPs and SBAs • And know that “YOU are being tracked”

35. Standards-based assessment needs to be accompanied by a clear set of grade-level goals so that teachers, parents, and the whole community can work together to help all children achieve those goals. Continuing informal assessment throughout the year can help teachers adjust their teaching and identify students who need additional help. Perhaps more such help might be available if money spent on comparison testing were allocated to help children learn?

36. Let’s Explore with Kathy! Kathy Schrock’s Guide to Everything: Assessment and Rubrics http://www.schrockguide.net/assessment-and-rubrics.html

37. References • Bay-Williams, Jennifer, John Van de Walle, and Karen S. Karp. Elementary and middle school mathematics, teaching developmentally. Seventh. MA: Allyn & Bacon, 2010. Print. • Kilpatrick, J., J. Swafford, and B. Findell. Adding it up: Helping children learn mathematics. National Academies Press, 2001. Print. • McGatha, Maggie, and Peg Darcy. "Rubrics at Play." Mathematics teaching in the middle school. 15.6 (2010): 328-336. Web. 18 Nov. 2012. <http://www.eric.ed.gov/ERICWebPortal/search/detailmini.jsp?_nfpb=true&_&ERICExtSearch_SearchValue_0=EJ878921&ERICExtSearch_SearchType_0=no&accno=EJ878921>. • Principles and Standards for School Mathematics. Fifth Printing 2008. Reston: National Council of Teachers of Mathematics, 2005. Print. • Schrock, Kathy. “Kathy Schrock’s Guide to Everything: Assessment and Rubrics.” http://www.schrockguide.net/assessment-and-rubrics.html • Stiggins, Rick, and Jan Chappuis. "What a difference a word makes." National Staff Development Council. 27.1 (2006): 10-14. Web. 18 Nov. 2012. <http://ati.pearson.com/downloads/What-a-difference-a-word-makes.pdf>. • Tucker, Bill. "Beyond the Bubble: Technology and the Future of Student Assessment.”  Education Sector Reports. (2009): 1-16. Web. 25 Nov. 2012. <http://www.educationsector.org/publications/beyond-bubble-technology-and-future-student-assessment>.