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Calculate confidence interval for the mean, sample variance adaptive marking

A demo of how custom marking algorithms can be used to replace the built-in marking methods.

Two sample t-test to see if there is a difference between scores on questions between two groups when the questions are asked in a different order.

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Example of an explore mode question. Student is given a 2x2 matrix and is asked to find the characteristic polynomial and eigenvalues, and then eigenvectors for each eigenvalue. The part asking for eigenvectors can be repeated as often as the student wants, to be used for different eigenvalues.

Assessed: calculating characteristic polynomial and eigenvectors.

Feature: any correct eigenvector is recognised by the marking algorithm, also multiples of the "obvious" one(s) (given the reduced row echelon form that we use to calculate them).

Randomisation: a random true/false for invertibility is created, and the eigenvalues a and b are randomised (condition: two different evalues, and a=0 iff invertibility is false), and a random invertible 2x2 matrix with determinant 1 or -1 is created (via random elementary row operations) to change base from diag(a,b) to the matrix for the question. Determinant 1 or -1 ensures that we keep integer entries.

The implementation uses linear algebra functions such as "find reduced echelon form" or "find kernel of a reduced echelon form", from the extension "linalg2".

Example of an explore mode question. Student is given a 3x3 matrix and is asked to find the characteristic polynomial and eigenvalues, and then eigenvectors for each eigenvalue. The part asking for eigenvectors can be repeated as often as the student wants, to be used for different eigenvalues.

Assessed: calculating characteristic polynomial and eigenvectors.

Feature: any correct eigenvalue will be recognised by the marking algorithm, even multiples of the obvious one(s) (which can be read off from the reduced row echelon form)

Randomisation: Not randomised, just using particular matrices. I am still working on how to randomise this for 3x3; a randomised 2x2 version exists. I have several different versions for 3x3 (not all published yet), so I could make a random choice between these in a test.

The implementation uses linear algebra functions such as "find reduced echelon form" or "find kernel of a reduced echelon form", from the extension "linalg2".

Student finds a basis for kernel and image of a matrix transformation. Any basis can be entered; there is a custom marking algorithm which checks if it is a correct basis.

There are options to adjust this question fairly easily, for example to get different variants for practice and for a test, by changing the options in the "pivot columns" in the variables. You should be careful to think about and test your pivot options, as some are easier or harder than others, and some don't work very well.

The student is given a number in base 10 and asked to write it in a given base, between 2 and 16. The number has at most 3 digits in the other base.

Until it's possible to derive the expected answer for a part in the marking algorithm (see the issue tracker), this question has "show expected answer" turned off, because it just shows the base 10 number.

This question defines an otherwise-pointless pre-submit task of "wait for a while" before marking the student's answer, in order to demonstrate how to use the pre-submit tasks feature.

Shows how to retrieve the student's answer to another part from a custom marking script.

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A couple of different ways of showing the correct answer to a single part as soon as the student submits an answer. One way allows the student to change their answer, while the other locks the part.

A third part includes a "reveal answers to this part" button, which allows the student to choose to reveal the answer to the part.

Think very carefully before using this: by revealing the answer, you are removing the opportunity for the student to later on realise they've got that step wrong, as a consequence of some further work. It's often possible to use adaptive marking to use the student's answer in place of the correct answer in later parts.

In this demo question, you can see either 2 or 3 gaps depending on the variable \(m\), and the marking algorithm doesn't penalise for the empty third gap in cases when it is not shown.

Reason to use it: for vectors or matrices containing only numbers, one can easily use matrix entry to account for a random size of an answer. But this does not work for mathematical expressions. There we have to give each entry of the vector as a separate gap, which then becomes a problem when the size varies. This solves that problem. For this reason I've included two parts: one very simple one that just shows the phenomenon of variable number of gaps, and one which is more like why I  needed it.

Note that to resolve the fact that when \(m=2\), the point for the third gap cannot be earned, I have made it so that the student only gets 0 or all points, when all shown gaps are correctly filled in.

Note the use of Ax[m-1] in the third gap "correct answer" of part b): if you use Ax[2], then it will throw an error when m=2, as then Ax won't have the correct size. So even though the marking algorithm will ignore it, the question would still not work.

Bonus demo if you look in the variables: A way to automatically generate the correct latex code for \(\var{latexAx}\), since it's a variable size. I would usually  need that in the "Advice", i.e. solutions, rather than the question text.

Marking algorithm that allows NA or any correct counterexample.

In this demo question, you can see either 2 or 3 gaps depending on the variable \(m\), and the marking algorithm doesn't penalise for the empty third gap in cases when it is not shown.

Reason to use it: for vectors or matrices containing only numbers, one can easily use matrix entry to account for a random size of an answer. But this does not work for mathematical expressions. There we have to give each entry of the vector as a separate gap, which then becomes a problem when the size varies. This solves that problem. For this reason I've included two parts: one very simple one that just shows the phenomenon of variable number of gaps, and one which is more like why I  needed it.

Note that to resolve the fact that when \(m=2\), the point for the third gap cannot be earned, I have made it so that the student only gets 0 or all points, when all shown gaps are correctly filled in.

Note the use of Ax[m-1] in the third gap "correct answer" of part b): if you use Ax[2], then it will throw an error when m=2, as then Ax won't have the correct size. So even though the marking algorithm will ignore it, the question would still not work.

Bonus demo if you look in the variables: A way to automatically generate the correct latex code for \(\var{latexAx}\), since it's a variable size. I would usually  need that in the "Advice", i.e. solutions, rather than the question text.

First compute matrix times vector for specific vectors. Then determine domain and codomain and general formula for the matrix transformation defined by the matrix.

Randomising the number of rows in the matrix, m, makes the marking algorithm for part c) slightly complicated: it checks whether it should include the third gap or not depending on the variable m. For the correct distribution of marks, it is then necessary to do "you only get the marks if all gaps are correct". Otherwise the student would only get 2/3 marks when m=2, so the third gap doesn't appear.

First compute matrix times vector for specific vectors. Then determine domain and codomain and general formula for the matrix transformation defined by the matrix.

Randomising the number of rows in the matrix, m, makes the marking algorithm for part c) slightly complicated: it checks whether it should include the third gap or not depending on the variable m. For the correct distribution of marks, it is then necessary to do "you only get the marks if all gaps are correct". Otherwise the student would only get 2/3 marks when m=2, so the third gap doesn't appear.

Simple exam for IGCSE level factorisation and sequences. One of my first projects, probably contains many mistakes (marking is not very dynamic for example).

The student is asked to write a number with a certain property, or tick a box labelled "this is impossible" if it can't be done.

A custom marking algorithm on the gap-fill part first checks if the student ticked the box. If they did, their answer is marked correct if it really is impossible. If they didn't tick it, their number is checked against the required property.

A method of randomly choosing variable names - use the expression() JME function to create a variable name from a randomly chosen string.

(This question also uses a custom marking script to check that the student has simplified the expression)

Do not use this: alternative answers are the best way of accepting multiple correct answers.

Demonstrates that the marking algorithm for "match text pattern" parts doesn't put quotes around substituted strings any more.

Do not use this: JME marking algorithms are the best way to change marking behaviour now, instead of JavaScript.

A very simple example of a custom marking script for a "choose one from a list" part

Two sample t-test to see if there is a difference between scores on questions between two groups when the questions are asked in a different order.

The student is asked to write a matrix with a certain property, or tick a box labelled "this is impossible" if it can't be done.

A custom marking algorithm on the gap-fill part first checks if the student ticked the box. If they did, their answer is marked correct if it really is impossible. If they didn't tick it, their matrix is checked against the required property.

Asks to determine whether or not 6 statements are propositions or not i.e. we can determine a truth value or not.

This question demonstrates defining an 'unknown' function $F(x)$ as a custom function so that it can be used in marking.

The definition of $F$ is arbitrary, so care must be taken to ensure it doesn't have more properties, such as evenness, than necessary.