By **Sherry Schulz** of Montclair State University

### Description #

Mistakes in mathematics are inevitable. Let’s turn those mistakes into valuable and positive learning opportunities. While it is important to prepare for an exam, processing the final results of an exam is just as important. Annotating a graded exam will allow us to identify the key weakness areas, reinforce correct techniques for problem solving, and avoid common pitfalls. This assignment re-imagines math test grading utilizing hypothes.is.

### Purpose #

Mistakes in mathematics are inevitable. Let’s turn those mistakes into valuable and positive learning opportunities. While it is important to prepare for an exam, processing the final results of an exam is just as important. Annotating a graded exam allows the student to identify the key weakness areas, reinforce correct techniques for problem solving, and avoid common pitfalls.

### Instructions #

The professor will compile all of the work from each problem submitted on an exam. Then select one student’s answer from a problem of the graded exam (no more than 2 annotations per student answer) and respond to the following questions in your annotations:

**Assess the Problem:**What is/are the objective(s) of this problem? What to solve and what methods are required based on what’s given in the problem?**Assess the Situation:**What steps are done correctly? What steps are done incorrectly and why?**Assess the Solution:**What steps should be taken to fix the mistakes?**Assess the Procedure:**What should one watch out for when solving this type of problem? Or, how can this exercise help you solve a similar problem?**Assess the Response:**Respond to another student’s annotation (no more than 2 annotations per each annotated answer). Reply to your peer’s annotation and address whether the assessments of the problem, situation, solution, and procedure done correctly.

### Important Notes about Annotating #

- Make sure you hit “post” after you complete your annotation, or else your annotation will not be saved.
- Make sure it says “post to [this class]” and not “post to only me,” or else I won’t be able to review your annotations.
- If someone replies to your annotation, you will not receive a notification. Check back periodically to continue the conversation!

### Grading Criteria #

Excellent (4-5 pts) All parts of the questions are answered. The student gives a complete response with clear, coherent, unambiguous, and elegant explanations. | Good (2-3 pts) The student’s responses are unclear, inconsistent or not complete. | Needs Improvement (0-1 pts) The student’s responses are not understandable or not present. | Pts | |

Assess the Problem | ||||

Assess the Situation | ||||

Assess the Solution | ||||

Assess the Procedure | ||||

Assess the Response | ||||

Total | /25 |

**Sample Graded Exam:** #

- Solve x – 3x + 4 = 7x + 1

#### Student 1’s answer: #

x – 3 (x + 4) = 7x + 1

x – 3x + 4 = 7x + 1

-2x + 4 = 7x + 1

-9x + 4 = 1

-9x = -3

x = -3/-9 = 1/3

#### Student 2’s answer: #

x – (3x+4) = 7x + 1

x – 3x + 12 = 7x + 1

-2x+12=7x+1

-9x=-11

x=-11-9=119

- Find the point of intersection of the lines with equations y=2x-5 and 8x-y=10 using an algebraic method.

#### Student 1’s answer: #

8x – 2x – 5 = 10

6x – 5 = 10

6x = 15

x = 15/6 = 5/2

y = 2 (5/2) – 5 = 0

(5/2 , 0)

#### Student 2’s answer: #

2x – y = – 5

8x – y = 10

10x = 5

x = 5/10 = 1/2

y = 2 (1/2) – 5 = -4

(1/2, -4)