Assessment is an important and critical part of the mathematics classroom. Fair assessment is one of the components of the Pennsylvania Standards Aligned System (SAS) and is a process used before, during, and after instruction to provide feedback and to adjust ongoing teaching and learning to improve student achievement. Since the main goal of the mathematics classroom is to provide the students with experiences in order to build and then to apply mathematical ideas, there is a need to systematically evaluate whether pupil learning has been achieved (Curriculum Development Centre, 2003). As the mathematics classroom becomes more focused on students, assessment now emphasizes the processes of learning in both the cognitive and affective domains for the purpose of improving teaching and learning (Quek & Fan, 2009; Stiggins, 2007).
As part of the SAS, Pennsylvania has identified four types of assessment used to gather information about student learning: Formative, Benchmark, Diagnostic, and Summative. When used together, the different types of assessment will produce the information needed to provide an effective and efficient educational experience.
As defined in Pennsylvania, formative assessments include classroom-based assessment that allows teachers to monitor student understanding and to adjust their instructional practice in order to meet the individual needs of the students. Ongoing assessment is an integral part of daily effective instructional routines.
Formative assessments can consist of formal instruments or informal observations. Formative assessments should involve frequent opportunities for both teachers and students to assess their understanding and progress over time. Mathematical activities or problems given to students can be designed to make student thinking public, and therefore, observable by teachers. Based on the results, the teachers can identify and address instructionally the students’ misconceptions and skill needs and at the same time improve their teaching skills. Group work and class discussions provide students with the opportunity to ask each other questions and to assess and revise their own thinking. Teachers can use this information to make necessary instructional adjustments, such as re-teaching, delivering alternative instructional approaches and intervention, or offering additional opportunities for practice. Effective teachers seamlessly integrate formative assessment strategies into their daily instructional routines.
Formative assessment can be used to adapt instructional practices to meet individual student needs, as well as provide individual students with corrective feedback that allows them to reach defined goals and targets.
Examples of formative assessment include:
Benchmark Assessments are designed to provide feedback to both the teacher and the student about how a student is progressing towards demonstrating proficiency on age and/or grade level standards. Well designed benchmark assessments and standards aligned assessments:
Examples of benchmark assessments include:
Diagnostic assessments are used to determine, prior to instruction, a student’s strengths, needs, knowledge and skills. The results permit the instructor to re-mediate student deficits and adjust instruction and curriculum to meet each pupil’s unique needs.
Examples of diagnostic assessments include:
Summative assessments help to make an overall judgment of progress at the end of a defined period of instruction. Summative assessments may occur at the end of a chapter or unit, grade, or course, the end of the school year, or are administered at certain grades for purposes of state or local accountability.
The PSSA, PSSA-Modified, or PASA are used as state summative assessments and are designed to produce clear data on the student’s accomplishments at key points in his or her academic career. The results of the state summative assessments also help a school system determine what is working for all students and what adjustments need to be made.
If the results of state summative assessments are reported with reference to standards and individual students, they can be used as diagnostic tools by teachers to plan instruction and guide the leadership team in developing strategies that help improve student achievement.
Examples of summative assessments include: