1. CHAPTER 5 Creating Assessment for Learning
Elementary and Middle School Mathematics Teaching Developmentally
Ninth Edition
Van de Walle, Karp and Bay-Williams
Developed by E. Todd Brown /Professor Emeritus University of Louisville

2. Integrating Assessment into Instruction
NCTM Principles and Standards (2010) stress two main ideas
Assessment should enhance student learning
Assessment is a valuable tool for making instructional decisions
These ideas aligns with assessment of learning- students evaluated on what they know at a given moment
These ideas aligns with assessment for learning- students continually evaluated so instruction targeted to gaps

3. Assessment Standards for School Mathematics
The Mathematics Standard. Assessment should reflect the mathematics that all students need to know. The Learning Standard. Assessment should enhance mathematics learning. The Equity Standard. Assessment should promote equity. The Openness Standard. Assessment should be an open process. The Inference Standard. Assessment should promote valid inferences about mathematics learning. The Coherence Standard. Assessment should be a coherent process.

4. What Is Assessment?
Gather evidence and make learning visible of student knowledge, flexibility in applying that knowledge and disposition and attitudes toward mathematics.
Should not be separate from instruction
Incorporate critical mathematical practices and processes
Summative assessments are cumulative
Formative assessments are to check students development
identify where learners are
identify the goal for learners
identify a path for reaching the goal

5. What Should Be Assessed?
Conceptual Understanding and Procedural Fluency
— how the student understands essential concepts while doing mathematics
Strategic Competence and Adaptive Reasoning
— skills represented in the five NCTM process standards
__ eight standards for Mathematical Practices ( CCSS)
Productive Dispositions
— ability to persevere and confidence and beliefs about their own mathematics abilities

6. Formative method 1-Observations
Anecdotal notes
Checklists
Question probes
Systematic plan for gathering evidence during and after portions of the lesson.

7. Formative method 2-Interviews
Diagnostic interviews provide a means for getting in-depth information you cannot get in any other way
Hearing students’ descriptions of strategies
Probe their understanding
Identify strengths and gaps
Examples-
Which is greater: 7/8 or 7/7?
Are the two numbers underlined the same? 6, 561

8. Formative method 2-Interviews cont.
Flexibility is key to diagnostic interviews.
Overall plan with an easier and a more challenging task
Materials available that match those students have used during instruction
Probing questions
How would you explain this to a second
grader?
Can you explain what you just did?
Why did you solve it that way?

9. Formative method 3-Tasks
Any written product, including problem-based tasks, journal entries, student self-assessment and tests
Problem-based tasks’ critical components
Focus on important mathematics concept or skill
Stimulate connection of students’ prior knowledge
Allow multiple solution methods and variety of tools
Opportunities for students to correct themselves along the way
Occasions for students to confront misconceptions
Encourage student reasoning and thinking
Opportunities to use mathematical processes and practices
Generate data for instructional decision making

10. Formative method 3-Tasks cont. Translation template

11. Rubrics and Their Uses
Analyzing problem-based learning through formative and summative assessment provides large amounts of information.
A rubric with a scale based on predetermined criteria serves two important functions
Permits students to see what is central to excellent performance
Provides scoring guidelines for teacher to use in analyzing student performance

12. Generic Rubrics identify broad categories of performance

13. Try this one
The Whole Set (Grades 3–4) Learning Goals: (1) Determine a whole, give a fractional part (using a set model). (2) Make sense of quantities and their relationships in a context . Mary counted 15 cupcakes left from the whole batch that her mother made for the picnic. “We’ve already eaten two fifths,” she noted. How many cupcakes did her mother bake? Discuss strategies used to solve the task.

14. Example of an Observation Rubric
Determining performance indicators is always a subjective process. Here is one example.

15. Rubric Performance Indicators
Determining performance indicators is a subjective process based on a given standard and learning targets as well as your professional judgment. Indicators should be shared ahead of time with students so you convey what is expected. Example of a rubric for the Whole Set problem 3 Determines the correct answer or uses an approach that would yield a correct answer if not for minor errors. Explanations and reasoning are weak. Giving correct results and reasoning for number eaten but an incorrect result for the total baked is a level 3 performance. 4 Determines the total number baked and uses words, pictures, and numbers to explain and justify the result and how it was obtained. Demonstrates a knowledge of fractional parts and the relation to the whole.

16. Writing as an Assessment Tool
Writing integrates instruction and assessment Writing provides a window to student perceptions and thinking Writing for early learners is drawings and markings Writing is a script for students that have trouble verbalizing their thinking Writing is a valuable tool to share with parents at conferences.

17. Written Communication Methods
Student journals
Clear, well-defined purpose
Provide writing prompts
I think the answer is..
Explain to a student in class (who was absent) what you learned
What was the most interesting mathematics idea you learned today…
Writing for early learners

18. Student Self-Assessment
Methods-
Pre-assessments
Exit slips
Quick two questions at the end of instruction
Open-ended writing prompt
Questionnaire
Students must know why they are doing the self-assessment. Promotes students being active versus passive learners.

19. Tests
Tests need to go beyond requiring students to demonstrate only procedural knowledge. Tests need to be designed so they match the goals of the instruction.
Test considerations
Permit calculators
Permit students to use manipulatives and drawings
Include opportunities for explanation
Use open-ended questions

20. Thoughts about high stakes Tests
External tests need to be a part of your assessment plan Teach the big ideas in the mathematics curriculum that are aligned to state and local standards Identify the broad conceptual foundations in the standards and select problem-based tasks that foster this understanding

21. Thoughts on Grading A grade
is a statistic to communicate to others an achievement level
accuracy and validity dependent on information used to generate the grade, professional judgment of the teacher and alignment of assessment with goals and objectives of the instruction
should be used with other information about a student’s work (problem-solving processes, attitudes, and beliefs)
What gets graded by teachers is what gets valued by students?

22. Freebies! WooHoo!
Tomorrow ONLY (2/9)