--- tags: mth225 --- # About the MTH 225 Grading Setup This document is intended to give details, explanations, and examples of the grading system used in MTH 225 to supplement the course syllabus. Please make sure to read or re-read the syllabus for the basics, otherwise not much here will make sense. ## The basic idea behind grading in MTH 225 The grading system in MTH 225 is based on two facts about learning and grades: 1. **Learning takes place over time through feedback loops.** Whether you're learning the guitar, how to bake bread, how to program in JavaScript, or anything else, the story is the same: You learn by doing and making mistakes, then getting good feedback from others, then thinking about that feedback and trying again. If you do this right, then *eventually* you will learn. 2. **Grades in a course ought to accurately reflect what you have learned in the course, by the end of the course.** Otherwise what's the point of having grades at all? The grading setup in MTH 225 is entirely based on these two principles. Everything you do in the course[^1] is intended to **get you into a feedback loop where you try something, get feedback, then try again**; and **your grade in the course is based on what you *eventually* learn** through this process, not through one-and-done tests that only look at a single point in time. I started using grading systems like this seven years ago after teaching a Calculus class where I had one student who was extremely bright but, consistently required two weeks longer than the rest of the class to "get" the material. They ended up failing the class because of it, and I swore never to let that happen again. ([Read more about my origin story here](https://gradingforgrowth.substack.com/p/entering-the-feedback-loop-roberts).) ## Why aren't we using points and percentages? Isn't that simpler? Traditional points-based approaches might be simpler, but they *oversimplify* and lose a huge amount of fairness and accuracy in the process. Here's a story to explain. Alice and Bob are two students in a math class. The grade in the class is entirely determined by the average of five 100-point tests. Each test is *cumulative*, so Test 2 contains material from Test 1 plus new stuff, Test 3 contains material from Tests 1 and 2 plus new stuff, and so on. Alice and Bob's test performances over the semester are: | | Test 1 | Test 2 | Test 3 | Test 4 | Test 5 | | :--: | :--: | :--: | :--: | :--: | :--: | | Alice | 0 | 0 | 100 | 100 | 100 | | Bob | 60 | 60 | 60 | 60 | 60 | So Alice struggled initially but eventually not only figured things out but showed strong mastery of the material. Bob, on the other hand, started mediocre and stayed there --- he actually never shows what we'd call "mastery" of the material. What grade do you think is fair for each student? It looks like Alice should earn an "A" in the class because she eventually mastered the material, and Bob should have a "D" because he earned 60% on each test. **But under a points/percentages system they both earn the same grade: 60%, or D.** So points and percentages based on averages might be *simpler*, but they mask over a fundamental unfairness built into the system that you just can't escape. They do a terrible job at surfacing differences between a person who struggles initially but eventually learns and a person who never grows. ## How it works in MTH 225 instead In MTH 225, your grade is based on how much you *eventually* learn, and you have the entire semester to demonstrate what you have learned. When you turn in an assignment other than a Daily Prep --- that is, a Weekly Challenge or some attempt at demonstrating skill on a Learning Target --- here's what happens. * Your work is evaluated by me, using standards for acceptable work that are laid out in detail in the [Specifications for Satisfactory Work in MTH 225](/Cy6P0rGZQzuOM3NwZ3ZuMw) document. Based on my professional judgment as a content expert in mathematics, I'll either determine that your work meets the standards, or that it doesn't. (This information will show up in the Blackboard gradebook in various ways explained in the syllabus.) * If it does meet the standard, you're done, congratulations. Otherwise you will get detailed feedback on what you did well and what needs further work. * Then, using the guidelines in the "Feedback and Revision" section on page 5 of the syllabus, you can reflect on the feedback and then submit a revision of the work. * Then this process starts all over again. So your grade in other words is based on the outcome of a loop. If you'll pardon the terrible pseudocode: ``` while (standard_is_met = FALSE): student.read(feedback) attempt = revision_of_previous_attempt student.submit(attempt) instructor.grade(attempt) if attempt.meets_standards: standard_is_met = TRUE ``` This is the "feedback loop" we keep mentioning. Please note, there are other restrictions that can break this loop, for example Weekly Challenges can only be reattempted twice. The syllabus details all those exceptions. :::success :warning: **There is no penalty for doing work that doesn't meet the standards.** You don't "lose points" because what are points? The only thing that happens, is that you will want to reflect on my feedback and try again. Otherwise **work that does not meet standards has no impact on your grade**. (Seriously!)[^3] ::: ## Cool! But wait, there's no partial credit??! Correct, because there's no "credit" to begin with. It's binary: Your work either meets the standard or it doesn't. This might be terrifying to those who got through school by gaming the system, leveraging partial credit to use competence in one topic to paper over incompetence in another. But at the university level, this is not only unethical but also dangerous. Would you like your heart surgeon or the engineer who built the plane you're riding on to have gotten their degrees this way? **Here in MTH 225, we insist on real competence, consistently and across the board. You can't make up for a lack of growth in one key area by growing twice as much in another**. Again, possibly terrifying. But, never fear, *this is what the revision/reattempt process is for*. Work is never one-and-done; if you don't meet the standard, you'll be told explicitly what to work on and given plenty of chances to try again. The motto is **high standards, with high support**. ## How to track your progress Since we don't really use points, there's no statistics you can use to do any tracking or speculation about your grade. It's actually much simpler than that. On page 5 of the syllabus, you'll find this table that shows exactly what's required for different letter grades: ![](https://i.imgur.com/8Z2AY5S.jpg) Each letter grade is based on **counting accomplishments**, kind of like a video game. Earning more accomplishments will "level you up". The raw data for your accomplishments is on Blackboard, updated at all times. All you have to do, is keep track of how far away you are from the grade level you want. To make this even simpler, I've created a **Grade Tracking Checklist** which [can be found here](https://docs.google.com/document/d/1P5DjDKs2Z5J9SXi4SOf6ibOiUYO0jKjYwi2pYgJI_3M/edit?usp=sharing) or on Blackboard in the *Course Documents* area. ![](https://i.imgur.com/R2A80gR.jpg) This is the exact same table as on page 5 of the syllabus, but in checklist form. Starting at the bottom and moving up, check off accomplishments as you accomplish them. Once you check all the boxes in a row for a grade, you've earned the grade. That's it. Two things to know at this point: 1. **Your grade in the course never goes down.** This is a nice by-product of the fact that your grade is based on counting accomplishments. Once you have done everything you need to do for a "C", for example, you can't "undo" any of those things, so you have a "C" locked in, no matter what else happens. You can only go up from wherever you are.[^2] 2. **You won't be able to "know what grade you have in the course" until later.** You don't "have a grade" in the course until you complete all the accomplishments for that grade. So, if you are wanting to know "what grade do I have in the class" in week 4, there's not enough information to answer that question. Once you earn 25 total points on Daily Prep, earn *Satisfactory* on four Weekly Challenges, and earn fluency on six Learning Targets, you have a D. Then you work your way up from there. Until then, you don't "have a grade" yet. ## Examples of how this works Here are some examples of how this all works. In each of these, we only look at the basic letter grades without plus/minus modifications. ### Alice Alice completes the course having accomplished the following at the end of the semester: - Earned 46 points from Daily Prep - Earned *Satisfactory* on nine (9) Weekly Challenges - Earned fluency (which requires two successful demonstrations of skill) on all eight CORE Learning Targets - Earned fluency on eight (8) non-CORE Learning Targets This is what her checklist would look like: ![](https://i.imgur.com/lDfchYI.png) Alice has checked off all the requirements for a "B", and some but not all of the requirements for an "A". Therefore her grade in the course is a "B" (although this would be a situation where I might consider a B+ due to the partial completion of "A" level requirements). ### Bob Bob's end-of-semester accomplishments look like this: - Earned 39 points from Daily Prep - Earned *Satisfactory* on ten (10) Weekly Challenges - Earned fluency (which requires two successful demonstrations of skill) on all eight CORE Learning Targets - Earned fluency on six (6) non-CORE Learning Targets This is what his checklist would look like: ![](https://i.imgur.com/7FbQFgT.png) He's done well with Weekly Challenges, so yay Bob. But he has not finished *all* the requirements for a B in either Daily Prep or in the non-CORE targets area. He's only satisfied the requirements for a "C". So since the *highest* grade for which he's completed *all* the requirements is a C, that's his grade. (Although again, I'd be up for considering a C+ or even a B- on the strength of his Weekly Challenge accomplishments.) ### Chuck Chuck's end-of-semester accomplishments look like this: - Earned 45 points from Daily Prep - Earned *Satisfactory* on ten (10) Weekly Challenges - Earned fluency (which requires two successful demonstrations of skill) on all eight CORE Learning Targets - Earned fluency on only three (3) non-CORE Learning Targets His checklist: ![](https://i.imgur.com/lgpBi4z.png) You might think that Chuck has an "A" in the bag. But there's a problem: He has only gotten fluent on three Learning Targets outside the core. This means he didn't complete all the requirements for a C, and so his basic grade in the course is a "D". :::info ***Seriously? Chuck did all this great stuff in the class and got a D just because he was fluent on only three non-Core targets instead of six?*** It's jarring, I get it. Three responses to this: 1. **We are insisting on consistent excellence across the board on all types of work.** There is no "averaging" here. Great work in one area does not paper over poor work elsewhere. 2. **Failing to be fluent on more than three non-Core targets is significant.** This lack of growth in "just this one area" is not a small problem, it's a big deal. The Learning Targets cover the signature skills of the course. There are dozens of opportunities to demonstrate skill on them through the semester. Failing to do so on 75% of the non-Core targets is a serious issue and casts doubt on everything else. 3. As with Alice and Bob, this a situation where I'd probably **talk with Chuck about his work with a view toward a C-**. Remember ultimately the grade in this class is the result of a back-and-forth between you and me about your work. The grade system is here to serve us, not the other way around. ::: ### Deanna Deanna is a different situation. She is checking her progress in Week 9 of the semester (that's the week of Fall Break) and wants to know what grade she currently has in the course, and what she needs to do to improve it by the end of the term. **Facts**: By the end of week 9, we will have had eighteen (18) Daily Preps (for a total of 36 points possible), seven (7) Weekly Challenges, and Learning Target quizzes covering fourteen (14) of the Learning Targets. Those targets are CA.1 through C.4; that includes six (6) CORE targets and eight (8) non-Core ones[^4]. Suppose Deanna's checklist looks like this at the end of week 9: ![](https://i.imgur.com/qfecH7B.png) Here's what I would say to Deanna: * You've met all the requirements for a "D" in the class, so there is zero chance that you will earn an "F". So that's good. * You haven't yet earned enough for a "C". For that, you'll need to complete four more points of Daily Prep, *Satisfactory* on two more Weekly Challenges, and fluency on three more CORE Learning Targets. * Earning a C will take effort but it shouldn't be difficult at this point. Each Daily Prep is easy and there are seven more left at two points each. You can revise the one Weekly Challenge you haven't earned *Satisfactory* on, and earn *Satisfactory* on one of the remaining four, so that's not terribly hard either. And you'll just need to really practice on the one CORE target you haven't mastered yet, as well as the two CORE targets that are remaining (RI.4 and RI.6). * If you want a B, you'll need to do more: Earn nine more Daily Prep points, *Satisfactory* on three Weekly Challenges instead of two, and not only finish off the CORE targets but get fluent on one more non-Core one. * If you want an A, it requires more than you need for a B: 14 Daily Prep points, which means completing every single Daily Prep from here on out; four Weekly Challenges, and the three remaining CORE targets and three non-CORE ones. That won't be effortless and there's not a huge margin for missing assignments, but it's doable from where you are. So Deanna does not "have a grade" in week 9. What she has, is *progress toward* a grade and a clear sense of what's possible and the difficulty levels of each potential outcome. She can then make an informed choice about how she'll engage with the class from there on out. Maybe she's OK with a "C", and chooses only to do enough to get that grade. Although I hope she'd push herself, there's nothing wrong with choosing a C, and I will support whatever she chooses. She certainly is under no obligation to make herself miserable getting an A. ## In Conclusion This grading system is designed not only to accurately measure your actual learning in the course, as evidenced by the results of your work and engagement with feedback --- it's also designed to get you focused on **learning, not grades**. The hope is that soon, once we get into the course and get used to the process, you'll stop thinking about grades altogether. **Credits:** I borrowed [the story of Alice and Bob](https://hackmd.io/@rtalbert235/rkTDQjo-K#Why-aren%E2%80%99t-we-using-points-and-percentages-Isn%E2%80%99t-that-simpler) from David Clark. [^1]: With the possible exception of Daily Prep. Daily Preps don't have revision opportunities because (1) they are dead-simple to complete and are only based on completeness and effort, and (2) they're intended to prepare you for a single point in time, the class meeting. So it doesn't make sense to revise them; however you can buy "Pass" marks on them with tokens if you really need to. [^2]: The exception is that you could end up with a "minus" on the basic letter grade depending on how the final exam turns out. [^3]: The exception is if you turn in a Weekly Challenge that earns an "Incomplete" mark as described in the syllabus. Even then, the only "penalty" is that you have to spend a token to revise the work; there's still no impact on your grade. [^4]: Assuming no changes in the syllabus or calendar.