The grading system is designed to be standards-based, i.e. your grade should reflect your current understanding, not an average of all attempts. However, I cannot test everything on the last day, so over the course of semester you will demonstrate mastery of all the topics.

## 35% Content Badges

You will be quizzed frequently, and each question will belong to one of the following badges. Grades will be 0, 0.5 or 1, representing no, partial and full mastery. When you get a badge, you have earned that badge from that point on. There will be many attempts. Your grade will depend on how many badges you have earned.

- Sets I: basic definitions (set, element, equality, empty, cardinality)
- Sets II: operations (union, intersection, difference, universe, complement, Venn diagram)
- Sets III: Set-builder notation
- Sets IV: ordered pairs, Cartesian products and powers, subset and powersets, including cardinality
- Counting I: basic (subsets, independent choices)
- Counting II: advanced (possible overcounting)
- Logic I: boolean expressions and truth tables
- Logic II: converse and contrapositive
- Logic III: quantifiers (for all, there exists)
- Logic IV: negating statements
- Logic V: logical equivalence, logical laws and algebraic manipulations of boolean expressions
- Relations I: basic definitions, ordered pairs and arrow diagrams
- Relations II: properties of relations (transitive, symmetric, reflexive, equivalence)
- Modular Arithmetic (computation, inverse by verification)
- Functions I: definitions (domain, codomain, image and preimage)
- Functions II: definitions (injective, surjective and bijective)
- Function III: composition of functions, and inverse functions
- Proofs I: setting up a proof by contradiction
- Proofs II: setting up a proof by contrapositive
- Proofs III: setting up an inductive proof
- Synthesis I: questions involving synthesis of the topics
- Synthesis II: questions involving synthesis and more creativity
- Complete study: questions based on thorough textbook reading

There are 23 badges. Each one has an attainment score of 0, 0.5 or 1. Your grade will be (sum of scores) / 23.

## 40% Proof Writing (20% Reasoning, 20% Writing)

Click here for my grading rubric. You will be quizzed frequently (about once weekly), and your scores (one for reasoning, one for writing) over the semester will be adaptive. Your first grade will come from your first quiz. After that, each time you do better, it moves up a little, each time you do worse or miss a quiz, it moves down a little. You will have two dropped quiz grades (if you miss more than that, the missed quizzes are zero; no makeups).

The formula for moving up or down is

new grade = (2*current grade + most recent 3-quiz running avg)/3

This should mean your current grade will always reflect your ability heavily weighted to take into account the recent time frame.

## 5% Groupwork

You will meet with your study groups weekly. As a group you will do homework to hand in; one scribe will be elected. Every person must scribe at least twice during the whole semester. On Fridays you will share your groupwork with the class. Every person must present at least twice during the whole semester (scribe must not present). Groupwork will be graded, and the grade will count for the whole group.

Group homework will be graded on a simple 0, 0.5, 1 system (nothing, partial, complete). Presentations will be graded similarly. Learning gains (effort, demonstration of effective thought process) count much more than final correctness in this situation. Homework and presentations will be averaged to give your groupwork grade. If you do not scribe or present the required number of times, your groupwork grade will be multiplied by (n/4) where n depends on the number of times you did. Therefore if you do not scribe or present, it will be 0.

Whether you are doing your homework will also count toward this grade. The reason is that groupwork will not progress well unless everyone has done their preparation. I will periodically check daily homework for completeness as I circulate groups in class, and keep a record. I will multiply your grade by the percentage of time you do homework. So:

groupwork grade = (handed-in-work + presentations)*(scribing/presenting factor)*(homework diligence factor).

In other words, provided you are doing your daily work and groupwork diligently, and you are helping your groupmates to scribe and present to the best of their ability, you will get a full 5% or nearly so. If you are not doing some part of this, your grade will suffer.

## 20% Traditional Final Exam

This is what we’re all working toward. The final will look like the in-class quizzes and be graded similarly, but is traditional in the sense that you only get one chance at the test. It will be designed to take 2 hours to write, and you will be given 2.5 hours to do so.