## A breif guide to the reflection quiz

### Most importantly: Writting your answer objectively

To make marks **fair** to everyone, all graders give marks based on **objective claims**. They are trying to verify your claims based on the evidences you have provided.

**Why should we make our claim objective?**

<span style="color:blue">Please forgive us, we are trying hard to distinguish the students who has ability to apply what they have learned to daily life. **Evidences** and **objective statements** are **crutial** to prove your ability. Subjective matters are good and friendly, but since everybody could say that, it **doesn't help us** to know your ability.</span>

## Some example on what is subjective v.s. objective
**Question: Did you do any excercises?**

> *Yes, I did a lot of excercises.*

We can not verify your claim. To make marking scheme fair, this answer worth **No marks**.
> *No, I did not do any excercises.*

We can not verify your claim. To make marking scheme fair, this answer worth **No marks**.
> *Yes I did. There is an excercise about derivatives, asking us to find the derivative of the function $y=x^x$. I find a useful method by thinking $x^x$ as $e^{x\ln x}.$*
>
Confirmed, this excercise is a good excercise. **partial marks given**. (Please continue reading this article to see what is a perfect answer)

## A sample Question and a full-score answer

**Question: How MAT135 helps you in your daily life?**

> *It was a helpful course! It helps me a lot!*

**No marks**. The sentence is completely subjective because everybody could say that. The word *helpful* is undefined and the meaning is not clear. There is no further explaination about *helpful*, no marks.
> *It was a helpful course. Here by helpful I mean it really change my life and protentially promote my understanding of mathematics.*

**No marks**. The sentence is completely subjective because everybody could say that. The phrase "change someone's life" has no explaination and the meaning of "promoting someone's understanding" is unclear.

> *It was a helpful course. Here by helpful I mean it really change my life because I make a lot of money and it also protentially promote my understanding of mathematics because I am able to solve more mathematical questions than I previously do.*

**No marks**.There is no evidence in the sentence for the grader to confirm whether the student has a lot of money, and the relation of the money with MAT135 is not clear. There is no evidence in the answer for the grader to confirm the ability of the student to solve more problems.

**To answer the above question, you should make down-to-earth claims, explain all your sentences until they have been translated to math expressions.**

**Here is a full-score answer**

> MAT135 helpped me on solving a math model established by using the theory in the paper *Marital relationships: A social exchange theory perspective*, where human behaviors are treated by social exchanges. It helps me to understand our behaviors. Here is how the model treat two person in a relationship.
>
> ## List of variables:
>
> $x,y$: subindexes to represent the person.
> $B_x,B_y$:social benifit of $x$ and $y$ from the relationship.
> $C_x,C_y$: social cost of $x$ and $y$ from the relationship.
> $t$: the time elapsed from the begining of their relationship.
>
> **Goal**: **predict** how the quantity $B_x-C_x$ changes over time.
>
> ## Explaination of the model:
>
> In our simplified model, we assume $x$ loves more when he/she feels being loved less, and $y$ loves more when he/she feels being loved more.
>
> Equations of the model:
$$
\left\{\begin{array}{lll}
\frac{d C_x}{dt} &=& -B_x \\
\frac{d C_y}{dt} &=& B_y \\
B_x&=&\alpha_x C_y\\
B_y&=&\alpha_y C_x
\end{array}
\right.
$$
>## Solution of the model:
>**Using knowledge one have learned from MAT135**, we can solve this model to see **general solutions** are given by
$$
C_x= A\sin(t+\phi)\qquad B_x=-A\cos(t+\phi)
$$
$$
C_y=-A\cos(t+\phi)\qquad \qquad B_y=Asin(t+\phi)
$$
>## Results and outcome
>The results of this model could help us **predict** that their future relationship happiness is fluctuating. **To visualize**, the graph of our goal function $B_x-C_x=-A(\cos(t+\phi)+\sin(t+\phi))$ is roughly given by the follwing picture
(The picture indicates the function when $\phi=-\frac{\pi}4$, $A=-\frac{\sqrt2}2$)
**References**: Marital relationships: A social exchange theory perspective, available at https://utsouthwestern.pure.elsevier.com/en/publications/marital-relationships-a-social-exchange-theory-perspective

This answer has included the most important points that **we do care**

- If you an not write clearly in large print, using text is **HIGHLY RECOMMENDED**.
- Using lists to make your answer structure clear is **highly recommended**(see sample answer).
- Describe everything **objectively**. If you wish to write down sentene subjectively, you must explain it objectively afterwards. Your **subjective claims** does not helpful for our grading.
- Explain every concept and subjective words you have introduced( like why fantastic, why good, why bad)
- Explain every variable you have introduced
- Introduce where the concepts comes from
- Clearly list the **title**. And ideally, the **source** of the reference at the end.
- The relationship of the answer and the question must be clear.
- The answer must be explained until the mathematical level. Try use more graphs, tables, variables
- If you are asked to find a connection to daily life, it must be meaningful to daily life.

## Some tips for a high score

- Try to list reasons why you think the sample answer worth full marks and compare your answer with those criteria.
- Math symbols, tables, clear titles are always helpful for graders to understand your answer
- Keep your answer **relatively short** by deleting subjective descriptions.