Tag Archive | assessment

Assessing Mathematics Reflection – Blog About it PDR #4

Thinking back to high school, I can only think of being assessed in two different ways that were memorable: homework and written tests/exams.  Of this three, I would have to say the most memorable/vivid form of assessment for mathematics would have to be written tests/exams.  This brings thoughts mostly of good experiences that I have had with this form of assessment in my high school mathematics classes.  This is because in high school, I was one of those students who excelled at writing tests and exams.  Also, I never saw a problem with having such a limited variety of assessments because I never knew there were different ways to assess mathematics besides written tests/exams (and homework) until I enrolled in education math classes in university.

Online Portfolios

After the presentations in class on Tuesday, I realize now that there are two other ways that a few of my high school math teachers attempted to assess me: investigation and portfolios.  However, one of my teachers only attempted investigation once and the portfolios were very informal and not efficiently used.  It wasn’t until I had completed my presentation on portfolios that I realized one of my high school teachers had used this form of assessment.  This is because I had previously thought that portfolios were either only art portfolios or the professional kind of portfolios that contained your resume, cover letter, any awards/accomplishments, etc.  So basically, the type of portfolio that I could take into an interview, say for teaching, and show this to my future boss to help increase my chances of being hired.  Now, I am aware that there are different types of portfolios, including student portfolios, and what you can include can vary depending on what your purpose is and what you want your end goal to be.  A few other bits of information that I had learned about portfolios in a math class includes:

1. How you can use portfolios in math – create a portfolio for a famous mathematician, see a student’s thinking process and understanding, provide evidence to parents of their child’s learning and allow them to get involved with their students learning, and to upload assignments on (for online portfolios; this could include presentations, videos, and/or VoiceThreads).

2. What you can include in a portfolio – vocabulary words, videos/presentations, homework, tests/exams, reflections/journal entries, and/or any resources that the student found helpful with math.

3. Advantages – using portfolios in a math class can definitely be more advantageous than not in a math class.  These can be used for showing strengths and areas of improvement, best work, getting parents involved in students learning (for online portfolios), for checking students understanding of materials (through things like reflections), and they can be used as an end of unit/year review, assuming that homework and/or tests have been collected in this portfolio.

During presentations, I had learned about many more different methods of assessment, two in particular where I learned the most were: oral presentations and reports, and anecdotal records and checklists.

Oral Presentations and Reports

I already knew what oral presentations and reports were, but what I didn’t know about them is
1. When to use this method – when opinions need to be shared, at the conclusion of a research as a way of sharing findings, and after content has been explored or experienced.

2. When not to use this method -at the start of a unit or when time is of the essence.

3. Advantages of using this method – builds students communication and public speaking skills, allows creativity and personalization, integrating language skills, and it can be interactive.

4. Disadvantages of using this method – can be stressful for students who are shy, time consuming, can be biased and may not be completely accurate (teacher must mark everything at that time or he/she may forget something essential).

Thinking about this method, I’m not 100% convinced I would use this often in my classroom.  I suppose it is hard to tell until I become comfortable with the idea of it in math and can think of projects that my students can do that can include this method.

Anecdotal Records and Checklists

First of all, I had no idea what anecdotal records were (although I had a slight idea).  In Kelsey’s presentation, I learned that anecdotal records are written observations of what you see taking place in your classroom as students are working.  So, a few other things that I learned about anecdotal records and checklists are:

1. Advantages of this method – facilitate review of assessment and curriculum, provides cumulative information on student learning, and provides ongoing documentation of learning that may be shared with students, parents and teachers.

2. Disadvantages of this method – can be time consuming after class and requires planning and preparation.

3. When to use this method – use to assess the understanding of mathematical concepts and while students are working (both individually or in groups).

I would definitely use this method in my classroom.  In a way, I feel that it is something that we already do when planning our lessons and walking around checking on student work and understanding, just minus the writing notes down on a piece of paper or checklist.

 Purpose of performance-based assessment and  how they connect to ideas of assessment for/as/of/ learning.

From what I’ve learned, performance-based assessment checks a students skills and understanding rather than just checking if the student can compute a correct answer.  It can be used to check if students are at the appropriate achievement level and let you know that your class is ready to move on to other material.  Although many performance-based assessment methods can be time consuming, it is definitely worth the time to use because it checks these important things that simple testing cannot.

In my opinion, most of the performance-based assessment connects with the assessment as learning, although a few fit with assessment for and assessment of learning.  For example, entrance slips can be used as a diagnostic so it could be considered assessment for learning, interviews and anecdotal records and checklists check for student understanding throughout the unit/year, and rubrics and rating scales assess at the end so this is a form of assessment of learning.  However, any of these assessment methods can be manipulated to fit any of the assessment for/as/of learning; so really when you think about it, performance-based assessment connects with all the ideas of assessment and learning and it is definitely worth while to do as students can benefit greatly from this.


In my classroom, I would definitely use performance-based assessment to assess my students.  It provides much more detailed feedback that my students and myself can benefit from rather than just assessing students using tradition methods of testing and homework checks.  This assignment was definitely an eye opener of how different types of assessments can be used in math and for all of you math teachers out there, there are more ways to assess students than just testing! Don’t be afraid to try new things.  These assessment methods are definitely a great starting place at changing the perception of what a typical math classroom is.

ECS 350 Reader Response #2

For today’s reader response, I read chapter four of the Differentiated Instructional Strategies” by Gregory and Chapman.  This chapter was all about assessment and evaluation and the different types of assessment and evaluation.  Many ideas were introduced for different ways to assess and evaluate students.  A few of the ideas that I liked were the graffiti wall, mostly because I thought it was an interesting and more student engaging version of doing a KWL chart, and also the portfolios.

One of my “AHA” moments while reading this chapter was at the section discussing portfolios.  The main reason why I had an “AHA” moment at this part was because it reminded me of one of my teachers who had used this.  It was one of my high school math teachers and she mostly kept our tests, exams and homework in these portfolios.  One reason that I really liked this idea, both now and at the time, is because it displayed some of my work of what I was doing in the class and because it made for a really detailed review that covered all of the content.  Also, now with my new teaching experience and knowledge, I also like this idea because it’s something to show parents at conferences (so basically make it quite a bit easier for parent-teacher interviews) and because it’s a good way to see how a student has progressed and what they need to work on (or even what I need to work on if it’s a common error between quite a few students).

Another sort of “AHA” moment that I had while reading this chapter was the section discussing the type of feedback that we should give students.  I have never really thought of which type of feedback I should be giving my students but when I think of it, I probably would have just thought to just give a mixture of both the grade and the descriptive feedback.  However, I began to think that I shouldn’t when the textbook stated that students are still more focused on the grade if we give both so they don’t really improve.  Also if we only give the descriptive feedback, it’s been proven that students will improve up to 60% better.  I didn’t just cave in that easily to what the text was saying.  I thought about this and how I’ve received feedback in previous classes, and now I completely agree with what the text was saying.  For assignments (especially essays!), I always went straight to the mark first (and I still do this, sadly).  If I am satisfied with the mark that I received, I wouldn’t look at the descriptive feedback; if I was unsatisfied with it, then I would actually go back and read through the comments and take them seriously.  So, I do strongly agree with this statement and it definitely made me more aware of the type of feedback I should be giving to my students.

After reading this, I still am left with a few questions.  The first question I have is about grading:  Should we grade on the individual quality of work and how much a student has grown or should we mark based off of certain standards already set out by the teacher/school?  I just have this question because I do believe that students who put in quite a bit of effort and have grown should deserve a good grade, even if they aren’t quite getting the content versus a student who doesn’t try very hard and hasn’t grown much.  My second question is: If students improve more when we only give descriptive feedback, should we be doing more descriptive feedback type of assessment or should be grading them?  One thing that I have talked about in this class and others is that we need a variety of assessment for students because not all students excel at certain tasks, so it wouldn’t be fair to only grade exams and tests or just homework because not all students can properly show their understandings and knowledge that they have gained through certain tasks.  So, what type of feedback should we be mostly giving them?  Could it be the combination of the grading and the descriptive feedback but only give them the descriptive feedback?  Or could we do both as well but give the grade some time after we have given the descriptive feedback and they’ve had a chance to look over the comments?  I’m thinking that it should be the last, but that one itself does pose problems, such as students could catch on to the fact that they will just receive their grade later so then they won’t even bother to look at the feedback.  So I am curious… what are your thoughts?

Statement of commitment: I really wish that I could create a statement of commitment for finding the answers to either of my questions but I feel that they are almost dependent on what the teacher believes and so then there really is no right or wrong answer.  So, I will not commit to finding an absolute answer to either of these questions, but what I can commit to is trying to find what I feel is the answer that reflects both who I am and what I believe as a teacher.