Nothing speaks stronger about my students’ progress in mathematics and personal growth than their own words. Over the course of a few years, students reflected deeply on their experiences in my Honors Precalculus, Intermediate Algebra, and Math Topics classes. The reflections were a requirement of the portfolio assessment.
They explained briefly in the table of contents what an entry represented and why it was chosen, or placed detailed explanations with an actual entry. In the summary, they talked about their accomplishments and the challenges of the class. The quality of their self-analysis allowed me to assess them in a more complex way. The following excerpts come from the reflections of the portfolios collected in my junior Honors Precalculus classes in 1999, 2001, 2002, and 2003.
“I have already grown a lot in Precalculus. I no longer fear this class as I did before school started last August. So far I have become more comfortable with the concepts previously learned and have learned new concepts as well. […] Explaining solutions to the class has helped me to overcome my shyness. Now I even enjoy presenting board problems. I also feel I learn a lot from my classmates’ presentations.”
“I believe that my personal overall progress could be a lot better. However, I am learning and I sincerely admit that my logic in going about math has developed as a result of this class. The reason why I am doing so poorly is that I don’t think I put enough effort into studying the section every night.”
“Overall I feel I am progressing well in Precalculus. I have noticed that the one constant in all of the assignments I included in my portfolio is the fact that I put a lot of effort into each of them. […] in order to be successful in this class I have to put forth a good deal of effort. I suppose I am not used to having to put forth such effort in math class before. Although it has taken me two and a half months to figure this out, I now realize it is crucial to my success in the class.”
“I feel that over the last few months, my feelings about math have undergone a huge shift. All my life I have thought of myself as a reader or writer – never as a mathematician. I have always laughed and made fun of my math abilities I think because it has been a subject I feel intimidated by. Both of my parents always say they were not great in math and have pushed me more towards reading and writing. Adding to this, for the past few years I have always had male math teachers which has enhanced the belief in my mind somehow that, “girls must just not be good at math”. (This sounds incredibly stupid even to me, yet I think that I must have felt this because it has given me more confidence these last few months to have a women teacher.) I think these things combined have all contributed to my feelings of inadequacy and inability in math. These past months, with a woman as my math teacher and topics I find interesting, math has actually been fun and interesting and understandable for me. This is a huge leap for me. In the past, I have found math interesting at times, fun at times, understandable at times. However, this is really the first time that math has been all three.”
“I have learned the importance of organization, the significance of working ahead and staying on the top of my work, and the benefit of asking other people to help me with my math homework. […] I believe that I have learned much more than math skills this year, though. I have learned the power of reflective assignments such as this one…. I would guess that most math classes do not provide students with the opportunity to write reflections about their progress. I am glad that I have been given this opportunity to learn more about myself through analysis of my math work.”
“I have noticed a consistent improvement in my math grades, especially on tests and quizzes, and I attribute this to my hard work and dedication. […] I have come to enjoy math so much during this year; it is one of my favorite subjects, if not the favorite. I think part of this positive attitude originates in my good grade, which in turn originates in a positive attitude and hard work, so in a way it is a cycle dependent upon portions of itself for success. […] I also need to remember Sophocles’ ‘One learns by doing the thing; for, though you think you know it, you have no certainty until you try.’ Ensuring my understanding is ultimately more important than ensuring my grade, though the former tends to obviate the concern for the latter, and I need to keep sight of my goal. This year has also enabled me to gain confidence to succeed in my mathematical studies.” – Diana T
“The work ethic that I have learned in this class has carried over in to my other classes improving my overall academic performance drastically.” – Griffin D
“This year was a huge challenge for me, but also very rewarding. I struggled very often to fully grasp the concepts and apply them in homework and tests, however with hard work and help from you and my friends I was able to get past the difficulties. Although I know I probably could have put more work into my math homework and studying, in general I feel that I worked hard to succeed in Pre-Cal. And even though I may not have received perfect scores this year, I think that what you learn is more important than the grade itself and I definitely learned a lot over the course of the year.” – Sydney F
“This will always be one of my most memorable years in math class. Everyone in my math class brought such a unique personality – from the teacher to the students. […] My progress as a math student has soared beyond anything I could have expected. […] I know I will need everything I have gained this year – fundamental math skills, a stronger work ethic, appreciation for math, and a new found confidence.” – Lauren C
“It is one thing to work hard and it is another to enjoy working hard and I for one enjoy working hard in your class due to the excellent learning environment it presents.” – Ryan L
“I am at a loss of things to say about this class. It has been exciting at times, it has been challenging at times, and it has even been very funny at times.” – Chris H
“I think it can easily be seen through this portfolio that I have been trying to work through long periods of not understanding. I think that so far this year I have really improved in math in many ways. The big one I think is all the effort that I have put into this math class. […] Also, at times I get very frustrated with myself and my performance in the class because I am used to doing very well and this class has showed me that I now need to WORK for my grades and improve on things and, most importantly, learn the material. […] And, while it may seem like I am just really complaining about how hard math is and how I am trying, I am not saying it just to whine. I actually REALLY enjoy this class. It is my favorite class and I look forward to coming into it every day and knowing that I am going to be challenged. Knowing that it is my choice if I am willing to meet that challenge.” – Aislinn W
“This class taught me the importance of being careful and being focused. […] This class has made me believe that I can learn anything. […] This class has taught me believe in myself, and to never give up. I have been challenged to think in ways I never thought possible. Above all, this class taught me that learning can be fun. In fact, it is probably the most fun I have had learning since coming to Seattle Prep.” – Connor D
“I am proud of myself for not losing motivation and trying my hardest. Although my grade in this class was not my best grade, I think I learned the most in this course, not only concerning pre-calculus but lessons in life to never give up even when you are discouraged.” – Erin M
“I have really enjoyed being in this Precalculus this entire year. I feel that I have truly grown as a student who can absorb information and apply it to problems well. […] I learned best and developed my thinking the most when I was challenged. I discovered how to avoid careless mistakes and how to grow from past errors.” – Ayaka I
“One of the numerous things I learned during this year is the importance of daily practice.”
– Ellen M
“For me, this year in Precalculus has really changed the way I think about math. This was the first year that math was actually one of my top priority classes. It was the first math class that was extremely challenging. […] This year I have come to the realization that teachers are key in a student’s learning not only in math but also in every other subject.” – Ariana E
“I consider myself a very hard working math student and I don’t always feel that tests reflect my hard work or knowledge. But I realize that tests help teachers to see how much students understand, so I have made improving my tests a top priority. This has helped me be motivated and excited about math class, because I want to understand everything. In the past, I always used to work on assignments by myself, and if I got stuck, I would get frustrated and think and think until I got it. This isn’t always possible in this class because the problems can be very difficult. So to help myself I started working with other people to get help. I find then when working with others, you learn much more and everyone else learns more.” – Jeremiah G
“The pop-quizzes forced me to stay on my toes, and the surplus of bright students in the class forced me to “compete” in the class. For me, a feeling of competition is usually a good thing, and it was in math this year. In other classes I could “coast,” yet in math I could either sink or swim. My personal assessment is that I swam (for the most part). I am proud of my homework, as I worked hard on it most of the time. I would have liked my quiz and test scores to have been higher, but my diligence in other aspects of the class made up for some of my poor showings on tests.” – Andrew P
“My perspective on school in general has also matured as a result of my experiences in Honors Pre-Calculus. […] I came to view the assessments not as a method of accumulating grades and a reason to be stressed, but rather as a learning experience. […] The shift from focusing on grades to focusing on knowledge reflects my increased confidence in my abilities as a mathematician.” – Pilar O
“Pre-Calculus was overwhelmingly difficult because it forced me to step outside my comfort zone. […] I soon realized that frustration and unanswered questions are a necessary component of learning. I am still adjusting to frequent bouts of temporary but complete confusion and missing problems on all of my quizzes. Nevertheless, I am glad to still be in Pre-Calculus because it has accelerated my growth as a student. Being in another math class might have been better for my self-esteem. But it would not have presented the challenges that make me excited for math.” – Pilar O
Learn next what my students’ parents had to say about the math portfolios.
