Reflection & Correction II
The goal of a college course is always learning - with homework, exams, and other assignments all just vehicles (and motivation) to help learning occur. Thus, my main goal from this exam is to help you all learn where you currently stand in the course, and to set yourself up for success going forward\(.\)
- The first part of this process was the studying for the exam: where you reviewed all the material on vectors and curves. Here you could earn extra points towards your grade (if you want to use the hold-me-accountable-grading) by writing a study guide for yourself.
- The second part of the process was taking the exam itself.
Here the goal is for both you and me to learn what you know so far in the course, and gauge what needs to be done going forward.
Now, we are at the post-exam-period where we try to use the test to learn from our pasts. To really get set up on the right path requires some work, so there will be a two opportunities to earn points here as motivation.
- First - you can do an extra credit exam correction. You will be able to regain the half the amount of points missed on one problem of your choice. That is - if you got a 1/5 on one problem you missed 4 points, and so you can earn back 2 points by doing a correction. (Note this is half the extra credit compared to the first exam: this fits into a pattern of full EC on exam 1, half the EC on exam 2, and no EC on teh final, as the course is over).
- The second, is to write an exam reflection as part of the hold-me-accountable grading system. Remember this grading system gives weight to other assignments like this, and in the process lowers the amount that exams count towards your final grade.
Extra Credit: Exam Correction
For HALF of the missed points back any problem of your choice: Write a study guide for the problem, addressed to your past self, (or your future self, when you review for the final). MAKE SURE TO INCLUDE BOTH THE PROBLEM STATEMENT, AND THE ORIGINAL SCORE YOU RECEIVED
You are not simply fixing the mistakes in your old solution, but writing a rather involved document teaching the mathematics necessary to succeed at questions like this. Your submission should be neatly hand written or typed and in full paragraphs with complete sentences. It should not be a rough draft, or an outline (bullet-point list of thoughts, etc). Complete submissions will likely be several pages in length. Below is an outline to help you structure such a lesson.
Analysis of your original solution What is the complete statement of the problem you are writing a study guide for? When you were working on the exam, what did you think about or try? If you were stuck at the beginning, or did not write much, what made it difficult to make progress?
Teach the necessary techniques Before you begin writing up your correction, learn how to solve the problem in its entirety. Look at your solution, and identify the main tools you needed: do you need partial derivatives? Parametric curves? Dot and cross products of vectors? Were some of your struggles caused by material prior to our course? (Differentiation rules, or algebraic manipulation rules?). Were your difficulties conceptual (had trouble picturing the difference between a vector and scalar function, unsure how to tell if something is a circle or cylinder) or computational (forgot the formula for cross product, etc)?
For each mathematical technique that is integral to the solution of this problem write a subsection reviewing this technique. Your section should include
- The technique itself (the formula / identity, or set of rules used)
- A discussion of what this technique is : when should your reader (future you) think to use it in a problem?
- An example (or two, or three) of using this technique correctly, in simple problems.
- A discussion of potential pitfalls: what are situations where using this mistake can easily lead to a mistake? (For a calc 2 example; forgetting to convert \(dx\) in \(u\)-sub, or some of the more involved conversions back to \(x\) from \(\theta\) for trigonometric substitution)
A Full Solution of the Problem Now that you have taught your reader all of the mathematics necessary to do this problem, write up a complete, annotated solution. Start by repeating the problem statement, and then talk your reader through (in sentences) what you should be thinking about at each step. I know that I have posted the exam solutions! So I am not asking you to just write symbol for symbol what I wrote. I am asking you to really explain what is going on in the solution. Write this as though you are truly trying to help your future self feel confident about this problem when they are reviewing this material down the road.
A similar problem Now that you have become an `expert’ at this one problem, make up a new example question that is similar (as in, it uses the same techniques to solve). To make sure it is indeed similar - you should solve it after proposing it! But you do not need to include the solution in your writeup. Instead, this problem will be waiting for you to try again next time you study.
Hold-Me-Accountable: Exam Reflection
Reflect on the the first part of the semester, focusing on your studying techniques, your exam performance, and suggestions to your future self. Your submission should be neatly hand written or typed and in full paragraphs with complete sentences. It should not be a rough draft, or an outline (bullet-point list of thoughts, etc). There are no wrong answers, but only submissions showing real work at introspection will receive credit: remember, this is an (optional) opportunity for you to think about what works best for you
How did the exam go? While it is still fresh on your mind, think about the exam itself. How did you do compared to how you expected to do (after studying, but before the exam itself)? After getting feedback, how did the exam go relative to how you felt after taking it? Did you do better or worse than you felt you had (after leaving the exam, but before getting feedback).
If you did well - what were the big contributions to that success for you? If you hoped to have done better, what were some factors that may have affected your performance (these include comfort level with the material, but also things like not sleeping enough the day before, or time pressure etc).
How did you implement your proposed strategy from last time? Last reflection, you wrote yourself a specific list of things that you wanted to try to change up your study strategies. Give yourself an honest evaluation: how well did you follow your past recommendations? Additionally, look at your past recommendations critically - did you suggest things that were reasonable, given your time/energy/bandwidth this semester? Did you suggest things that actually turned out to be helpful?
What were your study strategies? What did you actually do this time in preparation for the exam? Did you study for the exam with friends, or alone? How did you use the practice exam? Of the things you did do, what felt like it had the most payoff? Did any of your studying feel unproductive for you (as in, you put a lot of time into a particular concept or strategy, but in the end still struggled with that)?
Where is this class as a priority for you this term? We all only have so much time in a day, and we have so many obligations in school and in life: its important to try and accurately assess your priorities when making plans for the future - so that they can be realistic and helpful. Take time here to give an honest evaluation of your course load this term: what class are you worried most about? What class do you think will take the most work going forward? What class are you least concerned about? Use your own personal ranking here in the next step, to make a realistic recommendation.
What are some recommendations for your future self? Now that you’ve been through this cycle twice, combine what you have learned to give yourself a concrete plan for how you will work on this class over the last month of the term.