Your final reflective project is the same as the two formative self-assessments you have done, but covers the whole scope of the semester. You should create a concise (no longer than 6 pages, single-spaced) self-assessment document using word processing software that addresses your learning in the course. Be sure to go back and re-read your initial experiences, essay, and goals so that you can compare where you are now to where you were at the beginning of the semester.
Evidence of your learning may include new writing as well as cutting and pasting entries from your journal or your posts in the discussion forums. You should feel free to include both negative and positive reflections on the course and on your own participation. I am looking for a thoughtful and honest reflection that shows an understanding of your own learning process and your own growth, not a “puff piece.” In your document specifically, self-assess.
Your understanding of the topics and themes of the course and how individual topics connect to each other and to the major themes of the course — think of this piece as telling the story of the course in broad terms and trying to connect different pieces. You might even want to consider drawing a mind map of the topics of the course and showing connections visually instead of writing about the topics. Growth in your mathematical thinking. Give the highlights of what you learned (and didn’t learn!) this semester. New perspectives you have on teaching and learning mathematics. Ways in which you have supported your colleagues in their learning. Questions and comments that you have about the class overall.
Understanding of the topics and themes of the course and how individual topics connect to each other and to the major themes of the course Linear equations, graphs, polynomials, and radical expressions, quadratic equations, functions, exponential and logarithmic expressions, cyclic functions and trigonometry. I feel this course was designed to help to build on algebraic and geometric concepts.
We worked with advanced algebra skills such as imaginary and complex numbers, quadratics, and the study of trigonometric functions. I learned to continue to expand and hone my abilities to model situations and to solve equations, including solving quadratic equations over the set of complex numbers and solving exponential equations using the properties of logarithms.
We connected that arithmetic of rational expressions has the same rules as the arithmetic of rational numbers. We built on our previous work with functions and connected this work to trigonometric ratios and the unit circle. We worked with exponential functions to include solving exponential equations with logarithms. We also explored some transformations of graphs of functions. We looked at and applied knowledge to cyclic functions.
Growth in your mathematical thinking When I discuss growth in mathematical think with my students we talk about learning mathematical knowledge, developing our reasoning abilities, and enabling them to discover something for themselves. The way in which I do this is, given an investigation use what you know to try and reason and solve the problem. Small groups of students work together, and they begin to develop their reasoning abilities. Some draw a picture, some make a table or graph, others will create an easier problem to work out to make sense of the harder problem. Mistakes are a big part of the process. Students present their thinking and will revise their ex[plation after hearing others thoughts. This is when discovering something for themselves shine through. It is after this point in which I “teach” or lecture only 10-20 minutes. Since they are 7th graders, we then have stations of hands-on activities to further our understanding, then they apply their new knowledge in their homework practice sheet. For me, everything in this was was a good review. I made small errors along the way, and was unable to fix those mistakes. However, that is okay, I was able to connect my own practice with my students’ practice. A few things I had forgotten was logarithms, and understanding what Euler’s constant “e” means. This was a good compound interest investigation. We used this formula: (1+r/n)n, r = annual interest rate, n = number of periods within the year, if we use half yearly example for 100% interest: (1+1/2)2 = 2.25, monthly:(1+1/12)12 = 2.613…, 10,000 times a year: (1+1/10,000)10,000 = 2.718…it is heading towards e (and is how Jacob Bernoulli first discovered it).
Give the highlights of what you learned (and didn’t learn!) this semester. We learned to relate arithmetic of rational expressions to arithmetic of rational numbers, we expanded our understandings of functions and graphing to include trigonometric functions, and synthesize and generalize functions and extend our understanding of exponential functions to logarithmic functions. We read a few articles to apply this new learning in the classroom. I learned how to create a webcast. I look forward to applying this lesson in the classroom. A few things we did not review or learn specifically recognized binomials by their patterns. When we multiply the sum and difference of binomials and multiply by squaring and cubing to find some of the cool products in algebra. Sum and difference: (a + b)(a – b) = a^2 – b^2, Binomial squared: (a + b)^2 = a^2 + 2ab + b^2, Binomial cubed: (a + b)^3 = a^3 + 3a^2b + 3ab^2 + b^3. We did not learn about standard equations of conic’s. We did not work with Cramer’s Rule, sums of sequences, permutations & combinations. However, we did play with modular arithmetic, which is my favorite operation!
New perspectives you have on teaching and learning mathematics. I always saw math as something to engage in, to explore like a puzzle. To think… rather than only using rules and procedures. Because of this I see and teach math not as a spectator sport, but as a way to engage my students in constructing knowledge from meaningful experiences.
Ways in which you have supported your colleagues in their learning. On the discussion board, I think for this class, the best way for me to help and support my colleagues, was to post my solution and thoughts as soon as possible. Whether right or wrong, they could then compare their thinking with mine. I think this was helpful to struggling student for them to see someone’s solution. I tried to explain or show my thinking in great detail, as if I was working with one of my own students. If I had a mistake or misunderstanding I figured someone would then question it or ask about it. The other way was through the “Forum: Learner’s Support Forum”. I was more active on this thread in my last class. I tried to answer questions or give my thinking the best way I could. My last professor would usually chime in at a later point to help guide thinking or reassure our own problem-solving technique. However, this was not the case in this class, and I didn’t want to lead anyone down the wrong path. Therefore I found the weekly discussions much more helpful.
Questions and comments that you have about the class overall. In my last online course, we were able to fix mistakes on submitted work. I think this is important in math. I allow all my students to fix mistakes on daily assignments, and quizzes. I see GREAT growth in this process. A summative assessment like a test or project tends to have overall higher results as students have already learned from their mistakes and misconceptions. I felt this was more like a review of high school Algebra 2. My daughter is in Algebra 2 right now, so it was nice to be able to jump right in to help her with her homework without reviewing the concepts. However, other than the webcast, I did not have a lot to apply to my 7th-grade class. I wonder if there is a way to bring this into the middle school classroom?
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