Foundations of Education and Instructional Assessment/Performance Assessment and Rubrics/Elementary Math

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Performance Assessment—Elementary MathEdit

By Taylor Smith

Learning Targets:Edit

1. After reading this article the student will have a better understanding of how to implement Performance-Based Assessment in an Elementary Mathematics lesson.

2. After reading this article the student will have a better understanding of a holistic rubric vs. an analytic rubric.

What is Performance-Based Assessment?Edit

Performance Assessment is especially important in mathematics as there are many processes involved in coming to a correct answer. There are many levels in mathematics to build on. For example understanding addition helps you understand subtraction Understanding multiplication helps you better understand division and so on. Students must always “show their work” so the teacher knows they understand the process to getting there.

The best way to decide how to implement performance assessment in a mathematics lesson is to fully understand performance assessment.

“Performance-based assessments ‘represent a set of strategies for the…application of knowledge, skills, and work habits through the performance of tasks that are meaningful and engaging to students’”(Brualdi, 1998). .

This sort of assessment helps the teacher by providing information about how the student applies knowledge as well as creating “additional learning experiences for the students (Brualdi, 1998)”

Steps to take when implementing Performance-based assessmentEdit

The first step in implementing performance-based assessment is to define the purpose of the assessment. The skill to be assessed, the level at which students should be performing, and the type of knowledge to be assessed are some of the things that need to be defined initially (Brualdi, 1998).

The next step is choosing an activity with which to assess. The two types of assessment that could be used are formal and informal (Brualdi, 1998). During an informal assessment the student does not realize they are being assessed (Brualdi, 1998). For example, if a unit on long division was being taught, after instruction, the teacher would give some problems to be worked on in the classroom. While students are working on these problems the teacher would walk around and check their work to see how well they understood the lesson. In doing this the teacher would either write down or make a mental note of what students did not understand so it could be reviewed.

During a formal assessment the student is aware they are being assessed (Brualdi, 1998). For example, during a unit on long division the teacher could give a pre-test after instruction. Students would complete the pre-test and then they could exchange papers and be graded by their peers. After grading the teacher could ask what questions were missed and then go over those problems step by step.

The next step would be to create a performance rubric (Brualdi, 1998). “As opposed to most traditional forms of testing, performance-based assessments don’t have clear-cut right or wrong answers. Rather, there are degrees to which a person is successful or unsuccessful (Brualdi, 1998)”. This is especially true for mathematics. Once again we will use long division as an example. If the student understands the process of long division but in doing the problem makes a multiplication or subtraction error, does that make the answer 100% incorrect? No it does not. This is where designing scoring rubrics for your classroom comes into play.

Holistic vs. Analytic RubricsEdit

“Rubrics are…formally defined as scoring guides, consisting of specific pre-established performance criteria, used in evaluating student work on performance assessments (Mertler, 2001)”. .

There are two types of rubrics which can be used: holistic and analytic (Mertler, 2001). A holistic rubric scores the process as a whole where the analytic rubric scores separate parts or steps of a problem and then totals the score (Mertler, 2001).

Holistic rubrics are normally used when there is room for error as long as the overall outcome is correct. They can be used when there the answer is somewhat definitive (Mertler, 2001). Holistic rubrics provide limited feedback to the student as it is an overall answer that is required and are mostly used for summative purposes (Mertler, 2001).

“Analytic rubrics are usually preferred when a fairly focused type of response is required; that is, for performance tasks in which there may be one or two acceptable responses and creativity is not an essential feature of the students’ responses (Mertler, 2001)”. The use of analytic rubrics can result in several scores which can slow down the grading process (Mertler, 2001). Click this link to see a general example of an analytic mathematics rubric.[1] This generic math rubric is a great example of something that could be re worked to use for a specific math subject.


In elementary mathematics it is imperative students are assessed formatively as well as summatively. Once again, there are so many facets of math that build on to one another. Something that is not understood or missed by a student can affect them throughout life. During my elementary years I did not grasp measurement and to this day, at almost thirty years old I still have trouble with measurement. It is minor but if something important is missed it could have a dangerous domino effect on your student’s future education.

Multiple Choice:Edit

1. What is the first step in implementing performance based assessment?

   (a) Create a Rubric
   (b) Choose an activity
   (c) Define a purpose
   (d) Decide which type of rubric to use

2. In which assessment is the student aware they are being evaluated?

   (a) Formal
   (b) Analytic
   (c) Holistic
   (d) Informal

3. If you are a 4th grade teacher and you want to informally evaluate your students understanding of long division you would:

   (a) Give them a pre test
   (b) Walk around the classroom while they are doing a worksheet and assess what they understand and don’t understand
   (c) Ask them if they have any questions about long division
   (d) Give a post test

4. Which type of rubric would be best used to assess a students understanding of long division?

   (a) Analytic
   (b) Formal
   (c) Informal
   (d) Holistic

Answers: (c), (a), (b), (a)


Brualdi, Amy (1998). Implementing performance assessment in the classroom. Practical Assessment, Research & Evaluation, 6(2). Retrieved March 20, 2009 from

Mertler, Craig A. (2001). Designing scoring rubrics for your classroom. Practical Assessment, Research & Evaluation, 7(25). Retrieved March 20, 2009 from