## STACKドキュメント

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## How are my answers assessed?

A STACK question may have one or more parts. Each part may have one or more inputs, such as typing in a mathematical expression as your answer. An individual mathematical expression you type might be used in more than one part. This sounds complicated, but since there are many possibilities it is difficult to make general statements. The question should be clear. If not, please ask your teacher.

If you need to answer a part but have not then you will be told to do so. You should normally answer all the parts!

2. Once all answers relevant to a part are valid the mathematical properties will be established. What properties are required depends on the question being asked!

Sometimes these processes are done in one step, sometimes you will need to submit a page twice. Therefore you should answer parts of a question and press check to validate your answer. If all parts are valid, then you should press check again to ask for your answer to be assessed.

You may change your answer. Just press check to validate and then check again to assess. The system keeps track of any changes you make.

You will never loose marks for making a syntax error, e.g. missing a closing bracket. However, you may type in a valid expression which is not what you meant and which is wrong. You need to learn how to express yourself using an unambiguous syntax. This is simple and comes to most students easily with practice. If you make a mathematical mistake you should try to do the question again!

If you have asked for a worked solution then you may not change any of your answers.

Mathematical expressions are often either input as a typed linear syntax or built up with an equation editor such as dragmath.

## Repeated attempts

STACK encourages repeated attempts if you do not get the correct answer first time. Normally, a small percentage (e.g. 10%) of the marks available for the question are deducted for each valid but incorrect attempt. However, your final mark will be the maximum mark you achieve over all attempts. You are never worse off trying a partially correct question again.

## Why is my answer invalid?

Only when all the interaction elements for a question part are valid do we consider assessing your answer to the question. The validation process is designed to help you express your mathematics in the correct form and in an unambiguous way. On paper we might "know what you meant" but with the computer you have to "say what you mean". You do not lose marks if one of your interaction elements is invalid so do not be afraid of typing in your answer. Feedback is always provided.

There are a number of reasons why your answer could be considered to be invalid.

• You may have a syntax error in your answer, such as mismatched brackets.
• The range of Maxima functions you are permitted to type in is limited to mathematical ones, not programming, plotting, and so on.
• Sometimes the teacher may insist your answer is of the correct type. There are lots of types of mathematical objects, such as

• equations: 3*x=x^2-1. These need an equals sign!
• inequalities: x<=1.
• sets: {1,2,3}. Sets must be in curly brackets.
• lists: [1,1,2,3]. List must be in square brackets.
• matrices. matrix([1,2],[3,3]).

• Sometimes the teacher may not let you type in certain strings for educational reasons.
• Sometimes the teacher may not permit you to use floating point numbers, e.g. $$0.33$$. In this case you should give an exact answer as, e.g. a fraction: 1/2 or a surd: sqrt(2).
• Some expressions make no mathematical sense at all, e.g. one divided by zero. These are also invalid.

## What are mathematical properties?

When your answers are all valid you submit them again. This time they are assessed. The outcomes are a mark, and sometimes some written feedback. If you did not obtain full marks then you should try the question again.

Assessing your answer is not often a simple case of correct or incorrect. Often we might want your answer to satisfy a number of different mathematical properties. For example:

• If your expression algebraically equivalent to the correct expression?
• Is your expression fully simplified (e.g. have you gathered all like terms or factored your expression)?
• does your expression satisfy the equation?
• Is every element of your set a solution? Does your set of solutions contain them all?