1. What should be assessed?
1.1. "Assessments can provide students with opportunities to demonstrate how they understand essential concepts"
1.2. "Procedural fluency should also be assessed. This fluency includes understanding the procedure"
1.3. "The skills represented in the five process standards of Principles and Standards and the eight Standards for Mathematical Practice from the Common Core State Standards should also be assessed."
1.3.1. Problem Solving, Reasoning, Communication, Connections, Representations
1.4. "Collecting data on students’ ability to persevere, as well as their confidence and belief in their own mathematical abilities, is also important."
2. Assessment Methods
2.1. Observations
2.1.1. Annactodal Notes
2.1.1.1. "The act of professional noticing is a process where you observe learners through a focus on three phases: (1) attending, (2) interpreting, and (3) deciding"
2.1.1.1.1. "That means you attend to everything such as if the child is nodding his head, using fingers to count, creating appropriate models or using strategies that are clearly described and defended. Then you interpret those gestures, comments, drawings and actions by making notes of students’ strengths and the level of sophistication of their conceptual understanding. The last step is noting decisions for subsequent instructional actions."
2.1.2. Checklists
2.1.2.1. "To focus your attention, a checklist with several specific processes, mathematical practices, or content objectives can be devised"
2.1.3. "First, information that may have gone unnoticed is suddenly visible and important. Second, observation data gathered systematically can be combined with other data and used in planning lessons, providing feedback to students, conducting parent conferences, and determining grades."
2.1.4. "Depending on what evidence you may be trying to gather, several days to two weeks may be required to complete observations on how each student is progressing on a standard. "
2.1.4.1. "Shorter periods of observation will focus on a particular cluster of concepts or skills or on particular students."
2.1.4.2. "Over longer periods, you can note growth in mathematical processes or practices, such as problem solving, modeling, or reasoning. "
2.2. Questioning
2.2.1. "Probing student thinking through questioning can provide useful data and insights that could inform instruction. Also, your use of questions helps students get past being “stuck” and promotes their ability to think for themselves"
2.3. Interviews
2.3.1. "Interviews, particularly diagnostic interviews, are a means of getting in-depth information about an individual student’s knowledge of concepts and strategy use to provide needed navigation. Interviews are a blending of observations with questioning."
2.3.1.1. "There is no one right way to plan or structure a diagnostic interview. In fact, flexibility is a key ingredient. You should, however, have an overall plan that includes an easier task and a more challenging task in case you have misjudged the starting point."
2.4. Tasks
2.4.1. Problem based Tasks
2.4.1.1. "Problem-based tasks are tasks that are connected to actual problem-solving activities used in instruction. High quality tasks permit every student to demonstrate their abilities. They also include real-world or authentic contexts that interest students or relate to recent classroom events."
2.4.2. Transitional Tasks
2.4.2.1. "Using four possible representations for concepts, students are asked, for example, to demonstrate understanding using words, models, numbers and word problems. As students flexibly move between these representations, there is a better chance that a concept will be integrated into a rich web of ideas."
2.4.3. Writing
2.4.3.1. "journals, exit slips, or other formats about tasks provides a unique window to students’ perceptions and ways that they are thinking about an idea. Students’ writing can make sense of problems, express early ideas about concepts, unearth confusion, connect representations, or even clarify strategy use"
3. Communicating Grading and Shaping Instruction
3.1. Grading
3.1.1. "A grade is a statistic used to communicate to others the achievement level that a student has attained in a particular area of study. The accuracy or validity of the grade is dependent on the evidence used in generating the grade, the teacher’s professional judgment, and the alignment of the assessments with standards."
3.1.2. "Among the many components of the grading process, one truth is undeniable: What gets graded by teachers is what gets valued by students. Using observations, interviews, exit slips, journals, and rubric scores to provide feedback and encourage a pursuit of excellence must also relate to grades"
3.2. Shaping
3.2.1. "This process includes shifting from one approach or strategy development to another, pointing out examples or counterexamples to students, or using different materials and prompts. Knowing how to shape the next steps in instruction for an individual when the content is not learned is critical if you are going to avoid “covering” topics and move toward student growth and progress. If instead you just move on without some students grasping the learning objectives, “students accumulate debts of knowledge (knowledge owed to them)” "
3.2.2. "Summative assessment scores on high-stakes tests are often of little utility in creating instructional next steps to help students progress . But the formative assessment process described throughout this book can help."
4. Formative
4.1. "assessment for learning) includes tools that check the status of students’ development during instructional activities, preassess, or attempt to identify students’ naïve understandings or misconceptions related to the standards they are learning"
4.2. Three key Components: "(1) Identify where learners are; (2) identify the goal for the learners; and (3) identify paths to reach the goal."
5. Summative
5.1. "cumulative evaluations that take place usually after instruction is completed (assessment of learning). They commonly generate a single score that measures overall progress towards content and practice/process standards"
6. Rubrics
6.1. Generic
6.1.1. "Generic rubrics identify broad categories of performance and therefore can be used for multiple assignments."
6.2. Task-Specific
6.2.1. "Task-specific rubrics include specific statements, also known as performance indicators, that describe what students’ work should look like at each rubric level and, in so doing, establish criteria for acceptable performance on that particular task"
7. Self Assessment
7.1. "a key strategy in effectively incorporating the formative assessment process into instruction is the activation of students as “owners of their own learning". Students’ abilities to self-regulate as active participants in their own learning process has shown to be a predictor of mathematics achievement in the intermediate elementary grades"
8. Tests
8.1. "Tests can be designed to find out what concepts students understand and how their ideas are connected. Tests should go beyond just knowing how to perform an algorithm and instead require the student to demonstrate a conceptual basis for the process. Additionally, tests should explore how students have internalized concepts by requiring explanation of students’ thinking, application of ideas to new situations and flexibility by permitting multiple correct answers."
8.2. Improving Preformance of High Stakes Tests
8.2.1. "The best advice for succeeding on high-stakes tests is to teach the big ideas in the mathematics curriculum that are aligned with your required state standards. Students who have learned conceptual ideas in a manner focused on relational understanding and who have learned the processes and practices of doing mathematics will perform well on tests, regardless of the format or specific objectives."