Title: Default for Reasoning
Course: Demonstrating STACK (v4.4.7)

Line by line reasoning is a very important part of elementary algebra, leading on to more advanced mathematics.

This quiz is part of a project which aims to improve understanding of how to design online tools to help students solve equations. This work contributes to an ongoing study undertaken by the University of Edinburgh. In this study you will be asked to answer mathematics questions, working line by line. You will also be asked to explain your reasoning where appropriate.

 All responses will be handled by the project researcher Prof Chris Sangwin. Once collected, all data will be anonymised and securely stored on the University of Edinburgh computers. You have the right to withdraw from the study at any time and may request that your data be destroyed and excluded from any further analysis.

Please note, this quiz is a working prototype.  One reason for asking you to test it is to identify and help eliminate any problems. Please report any difficulties you have.

Thank you very much indeed for participating in this study.

If you would like further information please contact Prof. Chris Sangwin, C.J.Sangwin@ed.ac.uk

You can "submit all and finish" to see further feedback.

If you would like to find out more about the STACK project you can enrole on the existing "demonstration" course.

In this quiz you will be asked

1. to type in your answers to mathematical questions exactly as you would imagine an "ideal" system would accept them. These answers will not be assessed automatically.
2. interact with a prototype system and respond to the automatic feedback
3. reflect on how the interface worked.

Your answers to this quiz will inform the development of the system, and will influence how students learn line by line reasoning online.

This is an actual A-level question, set in 2015, and it has been completed.  The feedback will be generated when you click "check".  You need to press "check" twice, once to validate this answer and once to assess it.

How important is it that a student should follow a method specified by the teacher?

Please comment on your overall experience of working line by line.

How can this be further developed into a useful tool to help students learn algebraic manipulation, and mathematics in general?

Solve \(x^2-6\,x+9=0\), working line by line.  Leave your answer in fully simplified form.

[Note: there is no automatic feedback.  This is a survey only.]

Please comment on your experience of solving the quadratic \(x^2-6\,x+9=0\), working line by line.

How would you expect to indicate a root is "repeated"?

In the previous question immediate feedback was available in the form of arrows such as \(\color{green}{\Leftrightarrow}\). To what extent is immediate feedback helpful to students learning algebraic manipulation?

How much should students be expected to type in?

1. Should students be expected to express equivalence and implication symbols with each line?
2. Should students be expected to explain *what* they are doing as well as actually doing it?

Please comment on your experience of solving \(\frac{x+5}{x-7}-5=\frac{4\,x-40}{13-x}\), working line by line.

Please comment on your experience of solving the quadratic \(\sqrt{3\,x+4}=2+\sqrt{x+2}\), working line by line.

In particular, how would you expect students to indicate that one solution has been "rejected" in context?

Solve [value], working line by line.  Leave your answer in fully simplified form.
Feedback: \[ [value] \]

Make [value] the subject of the formula [value], where \(r>0\).

Solve [value], working line by line.  Leave your answer in fully simplified form.

[This question gives immediate feedback.]
Feedback: \[ [value] \]

Solve [value], by factoring and working line by line.  Leave your answer in the form \([value]=\cdots \mbox{ or } [value]=\cdots\) in fully simplified form.
Feedback: \[ [value] \]

Solve [value], working line by line.  Leave your answer in the form \(x=\cdots\) in fully simplified form.
Feedback: \[ [value] \]

Q: I have read the information above and consent to participating in this study.

(Ignore any marks associated with this question.  It is simply used as a "choice")
- True (Thank you.)
- False (Thank you for your time. Your responses will be deleted from the study.)
A: True

Q: Do you think the system has any concept of "step size"?
- True (Actually, there is no "step size" in the system. The student simply has to stay within an equivalence class of algebraic statements, starting and ending in the right place.)
- False (There is no "step size" in the system.)
A: False

Solve \(\sqrt{3\,x+4}=2+\sqrt{x+2}\), working line by line.  Leave your answer in fully simplified form.

[Note: there is no automatic feedback.  This is a survey only.]

Working Line by Line

In some situations you can work line by line. STACK gives immediate feedback on whether lines are equivalent, allowing students to enter their complete answer.