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What is Assessment?
“The process of gathering evidence about a student’s knowledge of, ability to use, and disposition toward mathematics and of making inferences from that evidence for a variety of purposes (NCTM, 1995, p. 3)." In Principles to Actions, NCTM defined

assessment, in the context of effective mathematics instruction, as a “process whose primary purpose is to gather

data that support the teaching and learning of mathematics.” (p. 89)


Why do we Assess?

NCTM (1995) put forward that assessment serve four distinct functions in school mathematics:

1. Monitoring students’ progress to promote student learning

2. Making instructional decisions to modify instruction to facilitate student learning

3. Evaluating students’ achievement to summarize and report students demonstrated understanding

     at a particular moment in time

4. Evaluating programs to make decisions about instructional programs


Teaching that requires students to demonstrate a variety of skills and competencies is extremely important.

Teachers cannot just assume that learning has taken place. There has to be some way to assess if learning has 

taken place. There has to be some way to assess if learning has taken place. However, we have to give students a

fair chance of doing well on assessments. To do this, teachers need to have clear instructional objectives that

communicate exactly what the student should be able to do at the end of the lesson, important conditions under

which the learner will be expected to perform the competencies, how the student will be assessed and what

constitutes acceptable performance.


Once instructional objectives have been communicated clearly to students they know how to assess themselves and what they need to focus on during the lesson. Therefore,  I would post clear instructional objectives somewhere students can see at the beginning of every lesson. Students also must know how they will be assessed. Teachers must have different ways to assess student learning. There are two types of assessment,


A variety of assessment tools can be used to do so. Some of the assessment tools that can be used are test, quizzes, research papers, creative projects and presentations in which kids teach other kids. Pre-test and posttest serve as a great assessment tools as well. Ongoing assessments can also be used in the form of exit slips and post-test serve as a great assessment tools as well.

Why should we Assess?
“A good assessment strategy provides students with the opportunity to demonstrate how they understand essential concepts.” (EMSM, p. 80) Teachers need to assess both procedural skills and conceptual thinking. Teachers need to assess both content standards and standards for mathematical practice from the Common Core State Standards (If your school uses the common core standards). In Principles and Standards for School Mathematics (2000), NCTM asserted that assessment should “support the learning of important mathematics and furnish useful information to both teachers and students.” (p. 22)

What are the types of Assessments/Tests/Task?

Summative Assessment is an assessment OF learning. “Serves the purposes of accountability, or of ranking, or of certifying competence” (NCTM Research Brief, p. 1) }“Summative evidence offers evidence used to make inferences about what students have achieved – what they know and are able to do – at a specific point in time.” (Romagnano, 2006, pp. 14) Examples: FSA, Final exam for a course, SAT or ACT, FTCE

Formative Assessment is an assessment FOR learning. “Serves the purpose of promoting pupil’s learning” (NCTM Research Brief, p. 1) “An assessment functions formatively to the extent that evidence about student achievement is elicited, interpreted, and used by teachers, learners, or their peers to make decisions about the next steps in instruction that are likely to be better than the decisions they would have made in the absence of that evidence.” (William, 2011; p. 43)   }“Formative assessment is diagnostic; the evidence is used to guide subsequent instruction and support continued learning.” (Romagnano, 2006, pp. 14) Examples: Exit slip, peer review, classroom discussions or questions, teacher feedback with expected student action.

Three processes are central to considering formative assessment (Wiliam and Thompson, 2007):

•Establishing where learners are in their learning

•Establishing where they are going

•Establishing how to get there


These processes lead to five “Key Strategies” (NCTM Research Brief, 2007)

1.Clarifying, sharing, and understanding goals for learning and criteria for success with learners

2.Engineering effective classroom discussions, questions, activities, and tasks that elicit evidence of students’ learning

3.Providing feedback that moves learning forward

4.Activating students as owners of their own learning

5.Activating students as learning resources for one another

Benchmark Assessments are intended to be something between formative and summative assessments. They are fixed assessments, evaluating students against specific grade-level standards and learning goals rather than simply taking a quick pulse of understanding. “In assessment, benchmarks are descriptions or models of specific performance standards. The highest benchmark is an exemplar, a model of outstanding performance. An anchor paper is a sample of a student’s work that has met a particular benchmark.” (Romagnano, 2006, pp. 8-9)

Standardized Tests are given under identical conditions for all test takers. (Romagnano, 2006) 

Norm-referenced Tests report students’ scores relative to those of a previously chosen and tested reference group (Romagnano, 2006)

Standards-referenced [or criterion-referenced] Tests reports scores based on predetermined performance standards.” (Romagnano, 2006, p. 15)

Closed Tasks are tasks that have one path to a single correct answer. (Romagnano, 2006) 

Open-middled Tasks are tasks that have more than one path to a single correct answer. (Romagnano, 2006) 

Open-ended Tasks are tasks with more than one correct answer. (Romagnano, 2006) 

Ways to Score Assessments/Tests/Task?

Using a Rubric. “A rubric is the set of rules for scoring students’ work on constructed-response tasks. Generic rubrics provide general guidelines that may be applied to a wide variety of tasks. Specific rubrics are for use with specific tasks.” (Romagnano, 2006, p. 16)

Using a Holistic Score. “A holistic score is a single score based on the overall quality of the evidence provided by a student’s response. Analytic scoring of a student’s performance on an assessment item begins by identifying two or more aspects or dimensions of that performance to be assessed separately. A score is then assigned for each of these aspects of dimensions.”

(Romagnano, 2006, p. 17)

Using a Grade. “A grade is a number, letter, or other symbol used to summarize how the body of assessment evidence gathered for a student up to a point in time compares to the set of expectations for the student at that time. … Evaluation is the process of using judgment to determine the value of assessment evidence.” (Romagnano, 2006, p. 19)

Other Definitions related to Assessment from Romagnano

Mathematics Assessment is the process of making inferences about the learning and teaching of mathematics by collecting and interpreting necessarily indirect and incomplete evidence.” (Romagnano, 2006, p. 3)

“A construct is a mathematical concept or set of concepts learned by students. Mathematics assessment is designed to gather evidence about constructs.” (Romagnano, 2006, p. 4)

Measurement error is due to the lack of complete precision of the assessment process. Sampling error results from the differences between a sample and the population from which it is drawn.” (Romagnano, 2006, p. 4)

Alignment is used to describe the extent to which mathematics curriculum, instruction, and assessment are mutually supportive.” (Romagnano, 2006, p. 6)

Content standards are the mathematical strands that compose the school mathematics curriculum.” (Romagnano, 2006, p. 7)

Performance standards are the achievement expectations to which students are held. Performance standards specify what students are expected to know about each of the content standards at specific times.” (Romagnano, 2006, p. 8)

“Test score equating establishes a relationship that permits the comparison of scores on different tests.” (Romagnano, 2006, p. 18)

“A cut score is a point on a scoring scale where performance is judged to move from one level to the next.” (Romagnano, 2006, p. 19)

“Assessment is fair if the assessment tasks are not biased, if all students have had equal opportunities to learn the content being assessed, and if all students are treated equally by the assessment process. … An assessment task is biased is it produces evidence with systematic errors.” (Romagnano, 2006, p. 10)

Authentic assessment uses reliable evidence to make valid inferences.” (Romagnano, 2006, p. 13)

Valid uses of assessment evidence produce meaningful inferences about students’ mathematical knowledge.” (Romagnano, 2006, p. 10)

“Assessment is reliable if it produces accurate and consistent evidence. Reliability is a description of the precision of assessment.” (Romagnano, 2006, p. 9)

“The stakes of an assessment refer to the consequences of inferences made.” (Romagnano, 2006, p. 10)

What sites can I use for Assessment?

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