$$ \newcommand{\RR}{\mathbb{R}} \newcommand{\QQ}{\mathbb{Q}} \newcommand{\CC}{\mathbb{C}} \newcommand{\NN}{\mathbb{N}} \newcommand{\ZZ}{\mathbb{Z}} \newcommand{\EE}{\mathbb{E}} \newcommand{\HH}{\mathbb{H}} \newcommand{\SO}{\operatorname{SO}} \newcommand{\dist}{\operatorname{dist}} \newcommand{\length}{\operatorname{length}} \newcommand{\uppersum}[1]{{\textstyle\sum^+_{#1}}} \newcommand{\lowersum}[1]{{\textstyle\sum^-_{#1}}} \newcommand{\upperint}[1]{{\textstyle\smallint^+_{#1}}} \newcommand{\lowerint}[1]{{\textstyle\smallint^-_{#1}}} \newcommand{\rsum}[1]{{\textstyle\sum_{#1}}} \newcommand{\partitions}[1]{\mathcal{P}_{#1}} \newcommand{\erf}{\operatorname{erf}} \newcommand{\ihat}{\hat{\imath}} \newcommand{\jhat}{\hat{\jmath}} \newcommand{\khat}{\hat{k}} \newcommand{\pmat}[1]{\begin{pmatrix}#1\end{pmatrix}} \newcommand{\smat}[1]{\left(\begin{smallmatrix}#1\end{smallmatrix}\right)} $$

Reflection & Correction

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 full amount of points missed on one problem of your choice. That is - if you got a 2/10 on one problem you can earn back 8 points if you do a correction on that problem.
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 100% 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 RECIEVED

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 recieve 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).

What were your study strategies? How did you go about preparing for this exam? Did you redo homework problems? Re-read lecture notes? Go back through the chapters in the book? 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)?

How did you learn outside of class? Do you do practice problems beyond the homework? And if so, how do you decide what topics you need more problems for?
If not, how can you begin to use the homework to your advantage, as a means of helping you identify what the most difficult points in a given week are? When reviewing a new concept, do you spend time reading the book chapters that accompany lecture, or watching internet videos on these topics (or both, or neither)? Does the amount of time you spend on this class match its relative difficulty? (ie are you spending alot of time because its one of your hardest classes, or little time because its easy? This would mean it does match. If you are spending not much time but its one of your harder classes, this would not match.) This is a four credit course - the university expects students to spend eight hours outside of classtime studying for the course.
Reflect on what you can do each week going forward to ensure that you are using the homework to your advantage: are you not finishing problems and so wish you could find a bigger study group to work with? Are you relying too much on friends and coming away from problems with an incomplete understanding (even though you get them correct)?

What are some recommendations for your future self? If you could help your past self set up a strategy to leverage your own strengths (and efficiently identify your points of struggle) for the first third of this class, what would you do? What parts of your current strategy will you keep, and what would you have changed? Be realistic (ie don’t just say “I would study X hours more” if adding X hours to your current plan leaves you with an unsustainable work balance across your classes), and take what you have learned about yourself in the above questions to build a reasonable plan.