Types of Assessment:

Assessment Issues:

1. A rubric is an instrument that serves as a guideline for evaluating student work. While there have been a great deal of attention paid to use of scoring rubrics in mathematics assessment, oftentimes, there is little discussion of exactly what a rubric is.

2. Throughout this module, we will explore the various types of rubrics as they are applied to a mathematics context. Most important are the types of considerations we, as mathematics educators, must make in developing appropriate and effective rubrics. As we progress through the How far, how fast? How many, how much? module, we will examine these issues in light of the opening activities and the poster-building activities.

Formative Assessment: Informal assessment that occurs during the instructional period. As we teach, or as the students are doing an activity, how do we know if the students are understanding the intended concepts? Most often, this type of assessment comes from asking questions in class as they work and seeing their progress.

Summative Assessment: At the conclusion of a lesson, activity, or project, how do we evaluate a student’s work and understanding of the mathematics? Most often, we associate summative assessment with grades, test scores, project grades, etc.

Reminder:

Although any “grade” is before the “final” grade is a type of summative assessment, all of those grades serve a dual purpose—they give information about a students’ progress and understanding of topics covered. Thus, most “graded” work is also a type of formative assessment as well.

Holistic Rubric

• A scoring scheme that focuses on product completion rather than process components.
• If we give “all or nothing” credit, it is, in essence, a holistic type of grade.
• A popular example of a holistic rubric is: 0 points—no effort and no work done; 1 point—student attempted to do the work and partially completed the assignment or it is partially correct; 2 points—assignment completed and all work is correctly done.
• This is often used when the effort is more important than the correctness of individual parts of an assignment. Example: One might only grade specific problems given in homework, but will give a holistic grade to signify if the homework assignment was attempted and/or completed.

Analytic rubric

• A scoring scheme that focuses on the process and components of an assignment more than its attempt and completion.
• The goal is to analyze a problem, project, or assignment to decide the relative importance of each part of the task and to categorize these elements. Points are then assigned according to the level of sophistication or correctness in each category.
• Sample categories for an analytic rubric are: correctness of mathematical procedures, strategies for setting up a problem or solving a problem, the use of appropriate representations, effective communication of one’s understanding and strategies, etc.
• ISBE uses a three-category analytic rubric for extended-response items on the ISAT: Mathematical knowledge (procedure, correct solution), strategic knowledge (reasonableness, problem-solving strategies), and explanation (communication, justification).
• WHAT about our familiar term in mathematics education, “PARTIAL CREDIT”? Partial credit assigned on any one mathematics problem is an analytic rubric that focuses on ONE category: mathematics procedure.