Evaluations may focus on progress in student learning (student evaluation), the effectiveness of school programs (program evaluation), and the effectiveness of the curriculum (curriculum evaluation). Teachers also reflect on the effectiveness of their instruction (teacher self-evaluation). In Student Evaluation: A Teacher Handbook (1991) the difference between the various forms of evaluation is explained.
The evaluation of student progress has a strong influence on both teaching and learning. Since the two main purposes of assessment are to help in making instructional decisions and to monitor student progress, assessment should be integrated into instruction. It helps to determine whether the teacher's intended meaning is the same as the student's constructed meaning and if it is not, the teacher can change the instruction to bring them together. If used appropriately, evaluation can promote learning, build confidence, and develop students' understanding of themselves.
To support formal school-based program evaluation activities, the Department has developed the Saskatchewan School-Based Program Evaluation Resource Book (1989) to be used in conjunction with an inservice package.
It involves gathering information and making judgments or decisions based on the information collected, to determine how well the curriculum is performing. The principal reason for curriculum evaluation is to plan improvements to the curriculum. Such improvements might involve changes to the curriculum document and/or the provision of resources or inservice to teachers.
Curriculum evaluation is described in greater detail in Curriculum Evaluation in Saskatchewan (Revised 1994).
Teachers refine their skills through reflecting upon elements of their instruction which includes evaluation. The following questions may assist teachers in reflecting on their evaluations of student progress.
It is also important for teachers, as professionals, to engage in self-evaluation. Teachers should take stock of their professional capabilities, set improvement targets, and participate in professional development activities. Some ways teachers can address their professional growth are by: reflecting on their own teaching; reading professional documents (e.g.: articles, journals, and books); attending workshops, professional conferences, and courses; and, developing networks with other professionals in their fields.
To enhance understanding of the evaluation process, it is useful to distinguish between the terms "assessment" and "evaluation". These terms are often used interchangeably causing some confusion over their meaning. Assessment is a preliminary phase in the evaluation process. In this phase, various techniques are used to gather information about student progress. Evaluation is the weighing of assessment information against some standard (such as a curriculum learning objective) in order to make a judgment. This may then lead to decision and action.
There are three main types of student evaluation: diagnostic, formative, and summative.
Diagnostic evaluation is used to determine where instruction should begin and usually occurs at the beginning of the school year or before a unit of instruction. Its main purposes are to identify students who lack prerequisite knowledge, understanding, or skills, so that remedial help can be arranged; to identify gifted learners to ensure they are being sufficiently challenged; and, to identify student interests.
It may consist of teacher-designed tests, informal discussions, and tasks that incorporate the pre-requisite skills or concepts. Diagnostic evaluation provides information essential to teachers in designing appropriate programs for students.
Formative evaluation is an ongoing classroom process that keeps students and educators informed of students' progress towards program learning objectives. It provides teachers with valuable information upon which instructional modifications can be made. Analysis of work samples, observation, interviews, checklists, and teacher-made tests are ways of collecting data for formative evaluation. This type of evaluation helps teachers understand the degree to which students are learning the course material and the extent to which their knowledge, understandings, skills, and attitudes are developing. Students are provided direction for future learning and are encouraged to take responsibility for their own progress.
Summative evaluation occurs most often at the end of the unit of study. Its primary purposes are to determine what has been learned over a period of time, to summarize student progress, and to report on progress to students, parents, and educators.
It is a formal evaluation and students are informed in advance of the timing, method, and specific knowledge, skills, or behaviours being evaluated. Evaluation techniques include testing, analysis of work samples, interviews, checklists, and projects.
Seldom are evaluations strictly formative or summative. For example, summative evaluation can be used formatively to assist teachers in making decisions about changes to instructional strategies or other aspects of students' learning programs. Similarly, formative evaluation may be used to assist teachers in making summative judgments about student progress. However, it is important that teachers make clear to students the purpose of assessments and whether they will later be used summatively.
Typically, teachers conduct all three types of evaluation during the course of the school year.
Evaluation can be viewed as a cyclical process including four phases: preparation, assessment, evaluation, and reflection. The evaluation process involves the teacher as a decision maker throughout the four phases.
In the preparation phase, decisions are made that identify what is to be evaluated, the type of evaluation (diagnostic, formative, or summative) to be used, the criteria against which student learning outcomes will be judged, and the most appropriate assessment techniques with which to gather information on student progress. Two main questions in this phase are "What do I want the students to know and be able to do?" and "What are valuable ways to ascertain whether they understand and can perform these activities?". The teacher's decisions in this phase form the basis for the remaining phases and may be made in consultation with the student.
During the assessment phase, the teacher identifies information-gathering strategies, collects student products, constructs or , selects instruments administers them to the student, and collects the information on student learning progress. The evidence gathered should link directly with the decisions made in the first phase. The teacher needs to ask questions like "What kinds of tasks can guide instruction and help monitor students' progress?" and "What are some important aspects to consider in choosing tasks?". The identification and elimination of bias (such as gender and cultural) from the assessment techniques and instruments, and the determination of where, when, and how assessments will be conducted are examples of important considerations for the teacher.
During the evaluation phase, the teacher interprets the assessment information and makes judgments about student progress. Teachers need to reflect on the assumptions they bring to the interpretation of evidence gathered. Based on the judgments or evaluations, teachers make decisions about student learning programs and report on progress to students, parents, and appropriate school personnel.
The reflection phase allows the teacher to consider the extent to which the previous phases in the evaluation process have been successful. Specifically, the teacher evaluates the utility and appropriateness of the assessment strategies used. Such reflection assists the teacher in making decisions concerning improvements or modifications to subsequent teaching and evaluation.
All four phases are included in diagnostic, formative, and summative evaluation processes and are represented in Figure 1.
Since evaluation is an integral part of the curriculum, Saskatchewan Education has developed the following guiding principles to provide a framework to assist teachers in planning for student evaluation.
Specific assessment strategies are selected or devised to gather information related to how well students are achieving the learning objectives of the curriculum. The assessment strategies used at any given time will depend on several factors such as the type of learning outcomes (knowledge, understanding, skill, attitude, value, or process), the subject area content, the instructional strategies used, the student's level of development, and the specific purpose of the evaluation.
The foundational objectives and the learning objectives for the curriculum become the criteria for assessing students. Although these objectives should be attainable by the majority of students, that is not true for all. In addition, some students may not reach full potential because they are not challenged but are allowed to remain at the acceptable "average". The Adaptive Dimension recognizes that the needs of all students must be considered in order for effective teaching and learning to occur. Therefore, adaptations to instruction or procedures may be required. Evaluation must be made in a context that is significant and similar to the learning environment; e.g.: students still at the concrete stage in operations with integers should have manipulatives available and should have their skills evaluated by observing them using the manipulative rather than by giving them a traditional written test. In the choice of objectives and evaluation strategies, the teacher should consider the individual needs of students.
Learning mathematics is a cumulative process that occurs as experiences contribute to understanding. A numerical grade offers only a glimpse of a student’s knowledge. If the goal of assessment is to obtain a valid and reliable picture of a student's understanding and achievement, evidence must come from a variety of sources. These sources may include oral presentations, written work, observations, or various combinations of these. Examples of written work include projects, homework assignments, journals, essays, quizzes, and exams. Records of a student's progress may include anecdotal records, portfolios, and mathematical journals. Rating scales and observations checklists are also helpful devices to record evidence of a student’s continued growth in understanding. The advantage of using several kinds of assessments is that a student’s understanding can be continuously monitored. In addition, because students differ in their perceptions and thinking styles, it is crucial that they are given the opportunity to demonstrate their individual capabilities. A single type of assessment can frustrate students, diminish their self-confidence, and make them feel anxious about mathematics.
The assessment of a student's mathematical knowledge includes his/her ability to solve problems, to use the language of mathematics, to reason and analyze, to comprehend the key concepts and procedures, and to think and act in positive ways. Assessment should also examine the extent to which students have integrated and made sense of mathematical concepts and procedures and whether they can apply these concepts and procedures to situations that require creative and critical thinking.
Understanding concepts and their interrelationships is essential to interpreting a situation and deriving an appropriate plan of action. Knowing what procedures are appropriate and how to execute them is essential to carrying out the plan successfully.
Progress in problem solving should be assessed systematically, deliberately, and continually. Methods for assessing a student's ability to solve problems include observing the student solving problems individually, in small groups, or in class discussions. Other methods include listening to students discuss their problem-solving processes and analyzing tests, homework, journals, and essays. A rating scale is useful for assessing a student's problem-solving skills. It may include rating a student's willingness to engage in problem solving, the use of a variety of strategies, facility in finding the solution to problems, and consistency in verifying the solution.
Assessment of a student's ability to communicate mathematically includes the meaning she/he attaches to the concepts and procedures of mathematics. It also involves his/her ability in talking about, writing about, understanding, and evaluating mathematical ideas. In assessing a student's ability to communicate, attention should be given to the clarity, precision, and appropriateness of mathematical terms and symbols. Teachers should ask questions regularly. Discussion is also a excellent means of judging a student's ability to function as a critical participant in small groups or in the class as a whole. Much of the assessment of communication skills can be done by oral and informal methods.
The assessment of a student's ability to use computers and software, such as word processors, spreadsheets, graphing, and geometry programs is also important. A student's ability to structure and present information with the use of technology can be assessed by determining if a student can use a spreadsheet or graph to simulate a situation and provide evidence for a conclusion.
An understanding of mathematical concepts involves more than mere recall of definitions and recognition of examples. It also encompasses a broad range of abilities. Assessment must include the aspects of conceptual understanding by focusing on a student's ability to discriminate between relevant and irrelevant attributes of a concept by selecting examples and non-examples, to represent concepts in various ways, and to recognize their various meanings. Observational checklists, anecdotal records, or written reports may be used to assess such conceptual understanding.
Learning mathematics also includes developing a positive attitude towards mathematics. The assessment of a student's attitude requires information about her/his thinking and actions in a wide variety of situations. Encourage students to reflect on their own thinking. Students' attitudes are reflected in how they ask and answer questions, work on problems, and approach new mathematics. Observations, homework assignments, written work such as extended projects, journals, and oral presentations are all excellent ways to assess a student's attitude towards mathematics.
The mathematics curriculum incorporates a number of instructional strategies and methods. Each one suggested has been chosen to facilitate the learning objectives effectively. Teachers should choose the most appropriate assessment techniques for what they have taught and how they have taught it. Mathematics involves more than just finding the correct answer to the problem. The strategy, the procedure used to solve it, and the communicative skill employed in convey understanding are also important. Evaluation identifies for the students, as well as their parents, those aspects of learning that are valued. For example, if we evaluate students on their computational skills and not on their knowledge of geometry, we could easily conclude that computation is more important than geometry.
Some assessment techniques are better suited for providing certain kinds of information than others. The techniques teachers use will depend upon the purpose of the assessment. For example, if a teacher wishes to assess the knowledge the students have gained, a quiz or test using objective items would provide the necessary evidence of student learning. However, should the teacher wish to assess problem-solving skills, a performance test with specific criteria listed on a rating scale or checklist as a recording instrument may prove of more value. Should information on student attitude or work involvement be the purpose of the assessment, anecdotal records may the best device. With processes that students would use in performing tasks, a teacher may choose to observe students during performance assessments or presentations and record the information on checklists or rating scales listing specific areas to be assessed. Teachers do not necessarily need to assess all students every class. For example, a teacher may prepare anecdotal records for five students per class.
Examples of how instructional strategies and assessment techniques may be applied to this curriculum can be found throughout the guide. These suggestions are not meant to be prescriptive. They are offered as examples of how a teacher may use a range of assessment techniques to assess student progress in a variety of different areas. Also provided are numerous templates that may be used or adapted for student assessment.
For further information on the various assessment strategies and types of instruments that can be used to collect and record information about student learning, refer to Student Evaluation: A Teacher Handbook (1991).
An important aspect of organizing an evaluation plan is managing the records that are kept.
The following ideas for record keeping and organizing for assessment have been adapted from Student Evaluation: A Teacher Handbook Follow-up Inservice (1993). These tips may assist any teacher when considering how an evaluation program may be organized.
Traditional grading systems often use a narrow focus on whether an answer is right or wrong. With holistic scoring, grades can be based on a student's total ability, content knowledge, and process rather than on the percentage of correct answers. Criteria can be determined for a rubric that can be used to score the work but can also communicate to students what the score means and how they can improve their performance. A score that indicates to the students a grading of their understanding, solution, and explanation is much more valuable than a single score. During the course of the year, these scores can be monitored and a clear picture of the student's progress in specific areas of mathematical thinking can be created.
The grades given should be fair, objective, and an accurate reflection of the student's achievement. Grading is a judgmental, and therefore, subjective process, hence teachers must be cautious not to evaluate only a small part of the student's knowledge, skills, and abilities.Informing Students and Parents or Guardians about Evaluation
"Best evaluation practice" stipulates that students know at the outset what will be assessed, how it will be assessed, why it is to be assessed, when it will be assessed, and how the assessment will contribute to an evaluation of their progress.
Students should know criteria, performance levels, and what constitutes high quality work. This enables them to evaluate their own work and know what the expectations are.
Whenever possible, this information should also be communicated to parents or guardians.
Evaluation is the reflective link between what ought to be and what is, and therefore, it is an essential part of the educational process. Evaluation procedures should provide positive and supportive feedback to students and should assist in making good decisions about the next steps in their learning and instruction. Regard students as active participants and encourage the development of self-appraisal. The main purposes for evaluating are to facilitate student learning and to improve instruction. By continuously evaluating student progress, school programs, curriculum, and the effectiveness of instruction and evaluation, these purposes will be realized.
Several resources listed in Mathematics 6-9: A Bibliography provide more detail and suggestions regarding evaluation in mathematics. In addition, a variety of templates that could be used are provided in the section Templates for Assessment and Evaluation, in the next document."
The templates represent some examples of the various types of evaluation and assessment the teacher might employ. The teacher is encouraged to peruse curriculum guides from other subject areas in order to obtain a more comprehensive set of evaluation templates. In addition, the teacher may adapt any of the templates to accommodate his/her students.