In the cases where the definition of the assessment type did not seem self-explanatory, I have included a brief definition.
By goal: Formative and Summative
Formative assessment – Ongoing diagnostics, used for adjustments to teaching and learning.
Summative assesssment – Gives feedback on total progress and proficiency.
I would use formative assessment in a situation that requires monitoring. For instance, I would use a lot of formative assessment as a new teacher, to monitor my own effectiveness as a teacher. I would use it in a situation where I’m designing a new unit and want to know its effectiveness. I would also use formative assessment in a situation where a student is standing out in some way, either struggling, excelling or in some other way not fitting in with the majority of students.
I would use summative assessment in two circumstances. One is to get an overall evaluation of understanding at the end of a unit, end of term, or something similar. The other is as a preassessment to get an idea of what level of proficiency students have before beginning to teach a new topic.
By neutrality: Objective and Subjective
Everyone would like to feel they are objective in assessment, but even in mathematics, absolute objectivity is probably not possible. There are always choices about what material should be on an assessment, and how it should be presented. In constructive response questions there is ambiguity in what constitutes a completely correct answer, and what the fairest scoring is for answers that are partially correct. The best I can do is to learn from student feedback about what they think is objective, and then search for a workable compromise between their perception, my own perception, and departmental standards.
By the entity doing it: Self-assessment, Peer assessment, Another person assessment, Automatic (computer) assessment
I would use self-assessment in situations where I want to get students more involved in their own learning. This is ideal in middle school, when the concept of owning the course can generate some excitement. I would also use it in a situation where I wanted student feedback in order to assess the effectiveness of my own teaching.
Peer assessment seems, in most cases, more suited to the humanities. However, in instances where there are group projects with presentations to the class, peer assessment would be a good tool. It is worthwhile for students to know how effective their presentations were on the other students, and affirming to be reminded what their peers learned from their presentations.
Third party assessments might be suitable in some special cases. For instance, if a student has done a research project about the uses of mathematics in insurance, having the student’s work assessed by an actuary would make sense.
Automatic assessment could be used in on-line self-study units, for students to self-check how well they have absorbed new material. If they do not do well on the assessment, they should be redirected to reread the material and try the assessment again before moving on.
By response: Constructed-response and Selected-response
My own preference is for constructed response. This allows students both to be creative, and truly demonstrate how well they understand something. Selected-response has its advantages though. One is that in many cases, the amount of teacher time available simply does not allow for the considered grading necessary for constructive response assessments. Another advantage of selected-response is in situations where students are inundated with information. Selected-response may help them sort through information rather than be overwhelmed by it.
By mind properties: Ability and Performance
Ability assessment has its place, but I wouldn’t use it very often. However, there are cases where it could be helpful. For instance, to try to get a better understanding of a student who is in an outlier. The student may be underperforming because he has not been placed in a suitable class. To help investigate suspicions like these, I would use an ability assessment.
My guess would be that performance assessment is not used very much in mathematics classes. However, I think this is a shame, as it could be a good outlet for student creativity. Someone with an interest in drawing, theater, or storytelling could be given an opportunity to showcase some of their skills, whereas they do not normally have such an opportunity.
A performance assessment that I like to use is having students present a research project to the class. Students often become self-motivated when working on their own projects, and they enjoy sharing what they have learned with others. It is a good opportunity for them to develop the research and communication skills.
By contextualization: Authentic and Standardized
Authentic assessment is an assessment that resembles a real life situation.
The tendency is to use standardized assessment, because these are more readily available. However, I prefer using a mix of both types. Students need to be able to handle both problems that are realistic (authentic) and also abstractions of realistic problems (standardized). The use of authentic assessment also has the advantage of stimulating student interest by tieing learning to the real world.
Campbell, B. and Campbell, R. (2009). Mindful Learning. Thousand Oaks, CA: Sage.