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

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

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.

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

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

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

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

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?

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

Formative method 3-Tasks cont. Translation template

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

Generic Rubrics identify broad categories of performance

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.

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

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.

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.

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

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.

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

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

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?