Assessment, as opposed to being a singular, one-dimensional measurement, is a complex process dependent upon an entire network of practices. It presumes a variety of strategies and procedures and requires multiple indicators and sources of evidence. Since no single assessment can completely describe or measure what one has learned or understands, adequate assessment only comes from multiple assessment measures.
When the term traditional assessment is used, what is usually meant is summative assessment. Summative assessments seek to determine what students know at the end of a chapter, unit, or series of lectures on a topic. Tests are just one of the tools used in traditional assessment, although they often receive the most attention and are the most pervasive. This is due to factors such as the ease with which they can be administered and scored and the fact that they enable teachers to judge students’ progress quickly and easily.
Traditional assessments such as tests are often graded and returned to students with a number and/or a letter grade at the top. Unfortunately, this number or letter grade often becomes more important than the learning the assessment was intended to measure. Even when comments and feedback are provided in addition to the letter or score, students assume that what matters in the end is the grade.
Traditional assessments are most frequently used to evaluate students, rank them, and assign a final grade. Traditional assessments generally involve the use tests, quizzes, and homework as the means for evaluation.
Content, skills, and attitudes addressed
Due to the often very short class periods and to the perceived need to include as many topics and concepts as possible, traditional assessments, especially tests and quizzes, often ask very superficial, procedural questions that require quick, unreflective responses. Traditional assessments ask “how, when, and where” questions but rarely ask “why.” Many traditional assessments mimic the questions asked in homework and are often taken straight from the textbook. Often very little attention is given to the design of assessment items; for example, the types of responses the questions will elicit, whether the questions have multiple points of entry, and what the questions will afford the instructor in terms of insights into student understanding.
The biggest strength of traditional assessments is the ease with which they can be designed and scored. Some textbooks include sample tests or test banks from which the instructor can choose appropriate questions. These features greatly reduce the time and effort needed to create appropriate tests. The grading of these types of tests is again facilitated with the help of the textbook publishers. If sample tests and a test bank are included, the answers are included as well. Thus there is no need to work out any of the problems or design thoughtful answers to any of the questions as those things have already been done.
The scoring of traditional assessments is further eased when the assessments use a multiple-choice format. Also, there is a perceived degree of objectivity in traditional assessments, especially when assessments have only one right answer. This perceived objectivity is further strengthened when the answer is the main, if not only, goal.
Traditional testing methods involve students working alone and are characterized by individual competition: competition for grades, against personal standards, and even for attention. This leads to a solitary experience and squelches the self-affirming possibility of shared interaction (Helmericks, 1993). This type of competition may encourage a few top students to succeed, but for the majority of students, a competitive environment is detrimental to their learning.
From an affective perspective, traditional tests often invoke feelings of anxiety severe enough to substantially limit their performance (Kulm, 1994). It is possible that anxiety surrounding test-taking can serve to motivate students to rise to the challenge; however, it is much more likely that this kind of anxiety will interfere with thinking and eventually compel students to give up. Many times formal testing situations such as these cause students who doubt their abilities to perform even worse than they are normally capable of performing.
Finally, the time limit inherent in traditional testing situations restricts the types of questions one can ask; the majority of questions are procedural and encourage rote and superficial learning. These types of questions send the message to students that if you do not know the answer immediately, you cannot solve the problem. It is impossible to give careful thought to a problem, or use any of the many heuristic strategies helpful in solving problems when you only have a few minutes to do so.
Very few need explicit examples of traditional assessments; for most of us, we have had years of experience with and exposure to traditional assessments. As mentioned, traditional assessments often include tests, quizzes, homework, problem sets and final exams.
Instead of disjointed tests that often only measure low-level knowledge, many authors suggest using assessment measures that emphasize the interconnections, coherence, and understanding among skills, concepts, and procedures, as well as among knowledge, abilities, and dispositions. Although these things can be measured using traditional assessments, due to the nature of the questions on traditional assessments, they rarely are.
Alternative assessments have multiple purposes. Some examples include providing students with additional opportunities to learn, using assessments to guide future instruction, providing students with feedback intended to enhance learning, and emphasizing what is important. Like traditional assessments, alternative assessments are also used to evaluate student understanding and assign grades.
Content, skills, and attitudes addressed
Alternative assessments provide instructors with a broader, more genuine picture of student learning. They allow one to assess students’ ability to reason and analyze, apply their knowledge to novel situations, demonstrate their understanding of the connections between concepts, and communicate their understanding in multiple ways.
The major strength of alternative assessments is the amount of information that can be gathered about student understanding, especially when students are required to explain, describe, or justify their answers. Requiring students to provide more than just an answer provides an opportunity for increased insight into student understanding. Students, too, learn more when they are required to explain, describe, or support their thinking.
These explanations can then encourage instructors to use alternative assessments formatively, which means the results of the assessment are used to adapt teaching to meet students’ needs (Black & Wiliam, 1998). In other words, the results of the assessments guide instruction with the goal of enhancing learning. Alternative assessments can also provide opportunities for enhanced and continued learning of the students, especially when they allow for communication between students.
Alternative assessments generally take more time than traditional assessments, both in their design and in their evaluation. In some cases, the time required exceeds the benefits, especially in large lecture classes, where the number of students is just too great to successfully implement certain alternative assessments.
Another weakness is the considerable amount of knowledge required to successfully design alternative assessments. It is much easier to take a problem or question from a textbook than to design a question that allows for multiple points of entry, assesses higher order thinking, is cognitively complex, and elicits answers that provide insight into student understanding.
Alternative assessments come in a wide variety of forms. Since the forms can vary greatly, a short pro and con statement of each type is included in each example.
Direct observation is one of the best ways to evaluate students’ thinking processes while solving problems. According to Lester (1996) “observing and questioning students while they are engaged in mathematics activities can yield invaluable information not only about their skill, but also about their thinking processes, their attitudes, and their beliefs” (p. 4). Although a paper and pencil test provides some insight into student knowledge, it does not offer the opportunity for the “aha” moments to be witnessed; the teacher cannot see where connections were made solely by marks made on the student’s paper.
Observations can be done while circulating around the room, taking nothing away from the process of teaching and in fact, making the evaluation process part of learning. This integration of assessment and instruction is the only way to truly assess higher order thinking according to some authors (e.g., Badger, 1996; Kulm, 1994; McMullen, 1993; Nagasaki & Becker, 1993; Zessoules & Gardner, 1991). Observations can also be done during office hours, which is probably a more common place for observations to occur since few instructors have the flexibility or time to circulate.
Pros: An incredible amount of information can be gleaned from a relatively small amount of time spent attending to individual students.
Cons: As mentioned, few instructors have the freedom to circulate around the classroom observing their students at work—the time taken away from teaching important content may seem to be too great a sacrifice.
Using open-ended problems
Open-ended questions can vary from simply asking a student to explain their work to requiring them to formulate hypotheses, identify possible explanations, state conjectures, create new problems or extend existing problems, and make generalizations. These problems are usually very carefully developed and furnish a context in which each student can rely on his or her own strengths to solve the problems, thereby generating a variety of approaches to the problem to compare and contrast. The ability to incorporate knowledge from a variety of resources such as formal knowledge, previously learned concepts and skills, and general common sense makes open-ended problems valid means for measuring connections between knowledge bases.
Pros: Easily incorporated into many different assessments, such as tests, take-home exams, group projects, and homework.
Cons: Difficult and time-consuming to write truly high-quality open-ended questions that go beyond tacking on a “why” at the end of a question.
Self-assessment, an essential component of formative assessment, requires students to monitor their own progress in learning and be active in critically examining their own knowledge, both of which further students’ reflection of their own thinking. To be most effective, the desired goal, evidence about one’s present condition, and some understanding of a way to close the gap between the two, needs be made explicit to students. Asking students to assess their own work alters their perception of themselves as active learners and challenges them to become thoughtful judges of their own work. Students can learn a great deal when assessing their own work, especially when they revisit previously difficult problems and see how the concepts inherent in those problems may inform more recent questions (Carroll & Carini, 1991).
According to Zessoules & Gardner (1991), “as students take on increased responsibility for their own learning and assessment, their growing awareness and ownership of their development enables them to make use of the process of assessment as a tool for learning” (p. 63). Students who have the ability to “know how much they know, to judge the quality of this knowledge, and to know what they need to do in order to learn more” (Kenney & Silver, 1993, p. 236) are considered to be powerful learners, a trait highly regarded in any educational system.
Pros: Encourages students to become more committed to, active in, and effective regarding their learning.
Cons: Requires the instructor to be very clear about what the learning goals really are, and explicitly state where they want students to be and how students can actually get there.
Journals provide another resource for finding out what students think. They can be a daily record of problem solving activities, descriptions of solutions to problems as though one were describing to someone else how it was done, or descriptions of what they have learned. They can act as an outlet for students’ feelings, attitudes, and beliefs, giving teachers greater insight into their students. They can also encourage metacognitive behavior by having students write about concepts they understand or do not understand. Further, they provide students the opportunity to write in the language of the discipline in an informal way, which can act as a precursor to writing more formally.
Journals also can be used to increase student refection, which is a critical component in successful problem solving. Writing reflections often solidifies understandings through the process of putting into words exactly what students are thinking. This habit of reflection “has the power to boost the silent and mechanistic approach to assessment into an active, vivid discourse between teachers and students” (Zessoules & Gardner, 1991, p. 58). When students regularly write in journals they often come to value the act of reflecting on their work—what they have been learning, what is difficult or challenging for them, and how they can use previous learning challenges to help them at the present time (Kenney & Silver, 1993; Lester & Kroll, 1996). This reflection allows them to become aware of which of their behaviors facilitate and which inhibit their learning.
Journals also inform the teacher what his or her students took from the instruction given them. What students learn may not coincide with what the teacher thought they would learn and journals offer a means for informing the teacher of any discrepancies between what was thought to be taught and what the students actually learned.
Pros: Allows very in-depth insight into student knowledge and understanding, student strengths and weaknesses, as well as student beliefs and attitudes.
Cons: Very time-consuming, not only for students to write, but especially for instructors to read.
In general, portfolios, also called performance assessments, consist of a collection of student work over time. They might include work such as tests, quizzes, homework problems, notes from a journal, descriptions of investigations, and solutions for problems—any written work that exemplifies the student’activities. Often students select which of these samples are included and sometimes are required to include a cover sheet stating the main topics, what was learned, why specific items were chosen for inclusion, evidence of progress, and areas of needed work (Alper, Fendel, Fraser, & Resek, 1993).
Pros: Gives a more complete picture of what a student knows and encourages teachers to focus on the connections inherent in a subject when it is viewed over time.
Cons: Very time-consuming to pour through even one student’s portfolio, let alone 30 or 300.
Not only is sharing ideas conducive to greater understanding but it also reduces anxiety in testing situations. Research has also shown that collaborative test taking promotes continued learning (Helmericks, 1993; Lehman, 1995; Vockell, 1994; Webb, 1995). One of the standards from NCTM’s Assessment Standard for School Mathematics (1995) states that assessment should enhance learning, and learning involves being able to reason and communicate. “Even a small amount of collaboration may influence a students’ understanding and performance” (Webb, 1995, p. 247). According to Webb (1995), developing new understanding by building on other students’ ideas is a form of learning, as well as is giving explanations that encourage the explainer to justify statements, recognize misconceptions, reevaluate thinking, and clarify thoughts. Every one of these aspects of collaborative testing has great potential for increasing student learning, especially for those students who are not served by traditional assessment practices. Many ways of implementing collaborative testing exist. I have named and will highlight a few that have been successfully implemented in college classrooms.
One collaborative testing technique has all students take a test in small groups, each completing his or her own test. One test is then randomly chosen from the group to be graded with the understanding that all students in the group will receive the same grade. The benefit of this approach is that it encourages students to work together, to be aware of what others are doing, and to make sure all their group members really understand the problems and solutions, as anyone’s test could be the one scored.
Pros: Requires you to grade only one third (if groups of three are used) of the normal
number of tests.
Cons: Competitive students may be less than thrilled to be dependent upon the work of others and may require some guidance in working collaboratively.
Another technique has all group members solve one problem together and write a single solution. They then individually answer questions about the group solution and solve two similar problems—a problem that is parallel to the group problem and one that extends it (Kroll, Masingila, & Mau, 1996). This affords the opportunity for an individual score to be calculated, as well as the group score.
A variation on this bases each student’s grade on the sum of the group score and the average of the individual scores, resulting in the same grade for each group member (Raymond, 1994). Again, this encourages students to commit to the learning of their group members, making sure that everyone truly understands the problems and solutions, as each group member’s score is dependent upon the learning of everyone else.
Another variation on the grading of this includes additional points if all group members score above a certain criteria. Thus on the individual portion of the test, everyone’s score increases if all group members reach the required level. This changes the dependency upon others for each student’s score to a commitment to the learning of all group members, creating a “one for all and all for one” kind of atmosphere.
Pros: Students have the benefit of learning while taking the group portion of the test while maintaining a level of individual accountability.
Cons: Fewer concepts can be tested, as the three questions are parallel in structure.
Yet another version is the group take-home exam (Brunner, 1999). Group members are given 7–10 days to complete the exam, hand in one solution signed by all, and all receive the same grade. I have found in situations like this that having group members anonymously grade all other members, including themselves, is a means for determining whether everyone contributed equally.
A variation on this is the group oral take-home exam (Crannell, 1999). In this situation, the written work that is handed in is only used to clarify points; otherwise, the students are graded entirely on their understanding of the material as they present it. This also allows students to learn from their mistakes, to the extent that “they get feedback even as they present their results, and since they have debated the results with their teammates, they care about the answer” (Crannell, 1999, p. 144).
Pros: The longer time frame allows for high level, conceptual problems on the test and students can learn a great deal when researching the answers to such problems.
Cons: Unless answers are given orally, it is very difficult to determine if all group members contributed equally or what each group member knows individually.
Another example uses a group retake (Roberts, 1999; Vockell, 1994). After taking an individual test, everyone retakes the same test in groups, using the retake as yet another opportunity for immediate feedback. In addition, since they just invested a good deal of time thinking about the problems individually, students are able to gain a much deeper understanding of the material.
Pros: Students get immediate feedback and develop greater understanding.
Cons: The number of tests doubles, thus doubling the time necessary for testing and grading.
A final example switches the order of the previous variation. Students take a test collaboratively and then are required to retake a similar, but different, test individually. This again encourages students to thoroughly understand the group’s answers, as they will be required to display further evidence of their understanding on an individual posttest.
Pros: The collaborative portion of the testing acts as an opportunity for learning, while the individual component allows for individual accountability.
Cons: The number of tests doubles, thus doubling the time necessary for testing and grading.
Student writing can be a very effective way to get information about student understanding in a very short amount of time. This information can be used immediately to adjust teaching in the effort of increasing student understanding. Many ways of using student writing exist. Again, I have named and will highlight a few that have been successfully implemented in college classrooms.
Students are required to hand in questions regarding that week’s reading at the beginning of each week. They can be as simple as questions that clarify or questions that ask for full explanations of connections. This technique forces students to actually do the readings and come to class better prepared. It also informs the teacher of incomplete understandings and areas of confusion.
A broader version of this simply does not restrict the questions to being from the readings. They could also be from homework, in class, or general questions about the mathematics. It is important in this case to make a note that they are not to be procedural questions, such as “How do you do number 5?” but that they are to help the student clarify a concept.
Pros: A great deal of information can be communicated through a question and this can quickly be used to adjust instruction accordingly.
Cons: Unless students read the text very carefully, they may not know what their questions are until they really get into the material.
Another technique is called the one-minute paper (even though you really need about three minutes) (Bressoud, 1999). In the last three minutes of class, the students are to write the answers to two questions: 1) What was the most important point made in class today? and, 2) What unanswered question do you still have? The teacher can have the responses be anonymous or signed, depending if he or she thinks the students will be hesitant to write honest questions or if the teacher desires information on individual students.
Pros: Again, great deal of information can be communicated through the answers to these two simple questions and this can be used to adjust instruction accordingly.
Cons: Frequently it is difficult to give up the last three minutes, as often we are trying to point out one last thing before class is over.
A variation on this theme is to have students name five significant points that were made in class (Bressoud, 1999). This can be especially useful in determining the range of understanding and perceptions of classroom events. Not only does the teacher keep abreast of where the students are in their understanding, this method serves as a means for keeping attendance up when students are required to include their names.
Pros: Allows instructors to quickly determine whether or not the students were attending to the real important points in the lesson.
Cons: Students may not be able to list even one main point if they are feeling lost or confused about the material.
Another way to use writing is to begin class with a writing task (Miller, 1999). Prompts can be distributed immediately to students as they enter class or be displayed at the front of the room. The goal is to offer the students a non-threatening way to write about their understanding—or lack thereof—of the content or current concepts they are learning. Again, they should elicit students’ conceptual understanding of a topic as opposed to reciting formulas or performing routine computations.
Pros: Allows instructors to quickly assess the understanding of their students.
Cons: May take up more time than you may like, as students often need a fair amount of time to answer the question.
Homework can also be used as the site for writing. Having students write what they are thinking on their homework as they are solving problems can be very enlightening both for them and for the teacher. Also, including emotions and frustrations in their writing, for example expressing their frustration when they are stuck can act as a vent, possibly opening the student up to new ideas of how to move forward and get unstuck (Mason, Burton, & Stacey, 1985).
Pros: Often helps students to answer problems and clues the instructor into the questions students may have.
Cons: Grading homework takes long enough without a narrative attached.
Another way to use homework is to design the questions in a true-false-explain format (Barnett, 1999). Barnett suggests writing questions that address the most important aspects of the concept and that are most likely to be misunderstood. Giving students two to four statements on the same concept, with the requirement that they have to not only determine whether they are true or false, but also defend that position, clarifies relationships among elements within a concept.
Pros: Regular use of these types of questions can provide a teacher with instructional feedback, as well as serve as a mechanism to encourage student reflection on concepts.
Cons: Time-intensive to write multiple questions of this sort, to answer these types of questions, and even more time-consuming to read through and grade.
One question I have frequently asked professors is “Why do you assess your students?” For many, it is not a question about which they have thought deeply. For most of us, the bottom line is that we have to give our students a grade. But there are many other reasons for assessing our students. We assess students because we want to find out what, and to what extent, they have learned what we hoped to have taught them. We assess students because we want them to know where they stand. We assess to give them feedback on their progress. We assess to determine how effective our teaching is. But we can use assessment for other purposes as well. We can use assessment to provide additional learning opportunities, as in the case of collaborative testing. We can use assessment to guide our teaching, as in the case of formative assessment. We can use assessment to diagnose misconceptions, while observing our students. We can use assessment to find out what questions our students have, through various types of student writing.
Although assessment is usually thought of in summative terms, many other purposes exist, and all have the potential for enhancing student learning. Traditional tests can enhance learning when the questions are carefully crafted to expose student understanding and misunderstandings. Alternative assessments can enhance learning by requiring students to communicate the interconnections and coherence among concepts and procedures. Thinking of assessment as a means for enhancing student learning aligns assessment with instruction. We teach in order for our students to learn. We can assess with the goal of increasing that learning.
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