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Assessment and Evaluation in Mathematics
Evaluation and assessment in mathematics are extremely important, but only if done effectively and used properly. Assessment can tell teachers a lot about themselves, the students, and the instruction. Teachers can use assessment to see how the students are progressing and where more instruction is needed. Informal assessment also shows teachers what strategies are working and which need some improvement or need to be eliminated. Essentially, assessment is the backbone of the educational process.
The most important role of assessment is its aide in designing instruction. A teacher can tell which areas need to be discussed more by structuring an assessment so that all of the objectives are covered. When students perform poorly in one area the teacher knows that more instruction is needed. For example, in my high school Calculus course many students struggled with optimization. On the first exam of the optimization problems were worked into the material and people did very poorly on only those problems. Therefore, our teacher spent some more time on it and gave us extra problems to work on. The next two tests contained optimization problems along with the new material. Slowly our teacher could see an improvement in that area. I feel that it is increasingly more difficult for teachers to use assessment for this purpose because of the demands to cover a certain amount of material. In my aiding class the students were having considerable trouble with solving equations for a single variable. The teacher could only continue the instruction for an extra day because she had to keep up with the SOL schedule. Therefore, evaluation was not helping shape instruction.
Evaluation and assessment can be a complicated topic because it involves many different aspects. Assessment can be split into two parts, informal and formal assessment. Informal assessment occurs when the teacher watches students and evaluates them without giving them a test on the material. For example, if a teacher wants to know if the students are catching onto one particular topic she may listen to what the students are saying during group discussions. From this information the teacher can decide whether or not to spend more time on one topic. Formal assessment involves giving the students a test or assignment. Usually in mathematics formal assessment is a test given at the end of a section or chapter to determine students' mastery of the skills. I feel that teachers need to utilize both methods of assessment. If a teacher relies on one method they may not get the whole picture. For example, students may understand a concept, but the questions on the formal assessment may not accurately assess what they know. Therefore the teacher will think that the students do not understand when they really do. If the teacher had done some informal assessment she might have noticed that the students really do understand what is going on. Thus, I think that assessment would be inadequate if only one method was used.
There are also two types of evaluation, formative and summative. Formative evaluation occurs throughout the instructional period. Many times the teacher will give the students a quiz after a section or two of material to make sure that everyone is grasping an understanding. Summative evaluation, on the other hand, occurs at the end of a chapter or at the end of a course, depending on how the course is structured. A summative evaluation shows whether or not students understand everything that was covered. I feel that summative evaluations tend to be more general in nature since there is more material that needs to be covered. I do not think that a student should be judged by one summative evaluation at the end of a course. The is usually only a problem on one concept and if there is something about the problem that students struggle with it does not mean that they do not understand the concept. Many times too much emphasis is placed on summative and not formative evaluations. For example, with the new SOL's it is being considered that students will not pass a course unless they can pass the SOL test, no matter how they do in class. Therefore, the student is being judged by one summative evaluation. I think that both the formative and summative evaluations should be used to determine a student's understanding.
There are even different types of understanding. Students can understand both how to complete a problem and how to relate that concept to other areas. In mathematics many times, I feel that students are asked to know how to find the answer and the steps to get there rather then how the problem can be applied to other things. I remember in high school that everything we did emphasized the steps to completing a problem rather then applying the information to other areas. Therefore, when I reached college it was a challenge to switch gears and begin thinking about relating the information rather then being able to use the formula. I still feel that high schools are emphasizing the methods of doing a problem and part of the reason is the SOL's. Teachers do not have time to cover everything about a concept so they stick to what is on the SOL's, completing problems. Therefore, teachers are going to continue emphasizing methods until more time is allotted for everything else.
I feel that evaluation and assessment are very important parts of teaching and learning. They can lose their importance if they are not applied properly or if there are conflicting issues. The most important part of assessment is being able to use it to structure instruction. Students will greatly benefit if their education is based on what they are having trouble with and what they need to understand. All methods of evaluation and assessment need to be used in order to accurately determine where students need extra help and what they already understand. Hopefully with helpful evaluations and assessments students will benefit greatly from the educational experience.