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Friday, February 26, 2010

Philosophy on Assessment in Math Education

What is the most important part of teaching? 

Many people may say that it is the teaching. But in reality, isn't it the learning? Along those line, I feel that assessing what has been learned is most crucial. But assessing student understanding is the most complex part of the teaching cycle.

Teachers must be fair and respectful when assessing students. I believe all students need to be assessed by the same standards. All students should be assessed by all methods, not different methods due to level or activity. In assessing a student, I will use both formal and informal methods of assessment. I also want to consider whether my assessments (which my students always consider to be "tests") are formative or summative. Do they inform and influence what/how I teach or do they inform me on what my students know? Finally, assessment does not always need to be considered "formal". Informal observations are just as valid, and in many instances, even more valid, then a higher stakes "test".

That being said, the use of tests and quizzes are indispensable to the assessment of mathematics education. But in too many classes, tests are the only form of assessment in math. I believe that in addition to tests, students should be able to apply the knowledge they possess at a higher level in "real world" projects. These projects allow the teacher not only to assess the mathematical component, but also the logical thought process as well as the ability to work in a group.

In addition to the periodic checks that tests and projects can provide, portfolios allow students together with teachers to assess their knowledge and progress over time. The problem with portfolios is finding the time to analyze them efficiently and usefully. I actually believe portfolios are good for the student and his/her family, but not as useful for the teacher who has too many students to begin with. With both the student and the teacher making decisions about which items of work will become artifacts, both can see how the student's knowledge has changed. Portfolios allow students to demonstrate change over time, rather than just a static item from one day.

Overall, I feel that each student needs to be assessed in several different methods. This allows the teacher to provide a fair and unbiased view of how well the student has learned the material.

As a teacher, I will use several types of assessment to make sure that all students are informed of their progress. Assessment is the teachers most difficult task, yet the most crucial.


Matt Townsley said...

I couldn't agree more that students need to be assessed in multiple ways. A portfolio, test, and project view of *each* student's understanding of the many topics/big ideas assessed in a secondary math class is ideal. But is it reality? It is realistic to have this individualized approach for all 120 students? I'm not trying to be pessimistic, merely realistic. I have ~70 students at any given time (4x4 block schedule...teach 3 classes), regularly put in 50+ hour weeks and still can't realistically individualize instruction, let alone formal assessments for my students. This is reality for me and so many other educators in secondary schools. With that in mind, I'm wondering what a realistic compromise would be...smaller class sizes for all? improving the written assessments we give to create more of a "real world" flavor? I look forward to more of your thoughts in this area as it's one I've wrestled with for a while.

ERKO said...


I totally agree with you: portfolios are held up high in the education world, but are incredibly time consuming and not always as useful as they are thought to be. The assessment of the portfolio is difficult in the best of conditions. I think a portfolio is most useful as a source of supporting evidence for judgements on student understanding. It is also potentially a very useful tool for self assessment and family participation. I do not believe that they are a plausible substitution for other assessments. If there are contrasting opinions on this, I would love to hear them.

Matt Townsley said...

You're right...the only contrasting opinions I've heard are from folks who don't have 70-120 students or who haven't ever been in the classroom. :)

Your last statement in the original post sums it up, "Assessment is the teachers most difficult task, yet the most crucial." This is really tough stuff!