The grading system is designed to be **standards-based**, i.e. your grade should reflect your **current** understanding, not an average of all attempts. That means you can throw away old grades and replace them with new ones. However, I cannot test everything on the last day, so over the course of semester you will demonstrate mastery of all the topics. An **even pace** is key to success.

## 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. There will be many attempts, and **your grade can only go up** with new attempts. Attaining a ‘0.5’ or ‘1’ means you have partially or fully *earned the badge*. 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 creativity
- Synthesis III: questions involving synthesis and more creativity, and/or 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.

Missed quizzes are zero and **there are no makeup quizzes**. You will have many opportunities to test each badge until it is earned.

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

Click here for my grading rubric. You will be quizzed frequently (approximately once weekly), and you will be assigned two scores (one for reasoning, one for writing). If you are unable to provide a useful sample to evaluate writing (that is, I cannot understand well enough to compare what you *wrote* to what you *meant*), you will not obtain a writing score (i.e. you will get zero), or only receive partial credit.

Your score will be made up of the **best half of your quizzes** (strictly speaking, the best of n total quizzes). Missed quizzes are zero, and **there are no makeup quizzes**.

### 5% Participation and Diligence

Whether you are coming prepared to class (having done the Daily Post tasks), and participating helpfully in class will count toward this grade. I will periodically check daily homework for completeness as I circulate groups in class, and keep a record. I will also periodically evaluate your participation in groupwork in class, by a simple system:

0 – not participating, or I see you texting on your phone (even once!), etc.

0.5 – at least listening and writing

1 – demonstrating leadership and helpfulness in a group (this can come in many forms, including asking useful questions, explaining your thoughts, keeping the group on task, etc.)

If you are absent, I will record a grade of absent. Four absences will be excused. Otherwise the final Participation/Diligence grade will be the average of recorded grades.

## 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.