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Online exams with calculations and graphics

On the following website, you will find recommendations for the administration of online written exams containing calculations and graphical sketches.

Please remember that it must be possible for students to acquire the competences necessary for an examination prior to the exam. This is especially relevant if students are required for an examination prior to the exam. This is especially relevant if students are required to work with formular editors or external calculation and drawing software, or to download materials and save them in a new format before uploading. To avoid problems, it is therefore advisable to offer appropriate sample tests in advance.

How do I check calculation results and/or calculation paths?

[A] Automated correction of the arithmetic result

For an automated correction of arithmetic results, create a cloze question with text field(s) or a single or multiple choice question for every arithmetical task.

When using a cloze question, enter the correct result of the calculation in a text field.

In a single or multiple choice question, the correct result is given as an alternative answer.

Students receive points for a correctly entered or correctly selected calculation result. The points are calculated automatically according to the pre-set grading system.

In case of an assignment consisting of several arithmetic problems, you can use a composite question. This allows you to combine up to five single, multiple choice and cloze questions. Using the composite question, the results of the individual questions are weighted and share a common score, or within a sample exam, one overall weighting.

[B] Automated correction of the calculation result - manual correction of the calculation path.

For each calculation task, create a learning module strict sequencing, consisting of

  • either an assignment with file upload
  • .or an assignment with text field for the examination instruction and the upload/entry of the calculation path
  • and a cloze question with text field for entering the calculation result.

The calculation path is assessed manually. The assessment of the cloze question is calculated automatically.

For entering the calculation path in the simple text field, students can enter formulas in text format in the text field of the assignment (e.g. WURZEL(4) + 4^2) and do not need to familiarise themselves with a formula editor. However, the text notation must be practised in advance.

When entering the calculation result, it is advisable to state the required spelling and number of decimal places of the result precisely by using the hint field of the gap in order to minimise errors during automatic correction.

(see setting: Rechnung und Rechenweg.PNG in German only)
(see students' perspective: Rechenweg.mp4 in German only)

It is recommended to provide students with cloze gap tasks to practise prior to the exam. That way, they can try out for themselves which spelling will be counted as "correct" in the examination. You can then indicate that only correctly written results can be graded as positive in the examination.


In the grade book, the two parts of the task (calculation path and / or calculation result) can be weighted differently or assigned to different categories (e.g. bonus points for secondary calculations and regular points for the result).

[C] Manual correction of calculation path and result

Create an assignment with text field or an assignment with file upoad.

In case of the text field, students enter the entire calculation including the result into the text field. The answers from text fields can be exported and checked e.g. in Excel.

In case of file upload, you can attach the assignment as a download file to the assignment (see "Designing assignments"). Students can then download the assignment and answer the examination question either analogue or digitally.

  • [C1 analogue] Students print out the assignment and then work on it by hand. The examination sheet is then scanned / photographed with the help of a scanner or a smartphone and handed in as a PDF in the task (see "Documentation of calculation path in PDF format").
  • [C2 digital] Students work on a digital version of the assignment in an external programme and then hand it in as a PDF in the task (see "Converting photos to PDFs on the PC"). Drawings and calculations can be made digitally and copied into the assignment (siehe "Options").

[D] The questions for checking the calculation results are created as explained in point [A].

In order to inquire about the calculation path, you additionally create an Open Work Order with a file upload, which students use to hand in the photographed secondary calculations.

The deadline for this file upload can be shortly after the end of the processing time for the examination, so that, for example, additional 20-30 minute are allotted for editing the pictures  (see "Documentation of the calculation pathway in PDF format").

It is recommended to encourage students to keep the original notes that have been photographed. These can be provided if needed, e.g. to check authenticity.


  • To avoid cheating, you can use random questions. This means that students are randomly assigned a qustion from a question pool during the examination, so that each student has to work on different questions. You can include these questions in a sample exam, for example.
  • To further prevent cheating, different sample exams can be created and assigned to selected students. Students only see the sample exam assigned to them. In the grade book, the results can be combined again in a manually created partial performance.
  • If you want to work with single or multiple choice questions in a large course, you can create individual single and multiple choice questions automatically, e.g. with the following R-Package. This allows you to create larger numbers of questions and then assign them, for example, to question pools. It is advisable to work with at least four distractors per answer for SC questions, which should all be very similar. For MC questions, 3-5 independent answer options are recommended.
  • In a cloze question, you can create several gaps in the question to make it even more difficult. You can, for example, ask for intermediate results. To make it more difficult to guess the answers, it is advisable to define a uniform character length per gap, e.g. 10 characters. Students can nonetheless enter content that is much shorter or longer. Information on the required format of the solution, such as the spelling of the decimal point (full stop or comma) and the number of decimal places, can be entered in the hint for the gap.
  • NOTE: It is advisable to state the required spelling and number of decimal places of the result precisely in the hint field of the gap in order to minimise errors during the automatic correction. It is recommended to provide students with cloze text tasks as "practice" before the examination. They can then try out for themselves which spelling will be counted as "correct" in the examination. You can then indicate that only correctly written results can be graded as positive in the examination.
  • It is also advisable to conduct the examination in a separate online examination environment with online proctoring.
How to have the calculation path documented in PDF format?

You can instruct your students to convert their calculation path into a PDF and then upload it to LEARN. Students have different options for converting their calculation path to PDF format.


If the upload to LEARN is not possible, students can send the PDF directly to the teacher(s) by e-mail. In this case, point out to the students that the date of sending must be within the submission deadline.

An image-PDF-page usually has a size of 1.5 MB. In order to keep the load on the bandwidth and thus the time for an upload to LEARN as low as possible, the recommended file size of the entire PDF is a maximum of 10 MB.

  • Advise students to set the photo camera in a way that the resoluation of the resulting picture is reduced. This will also help to minimise the file size when converting to PDF format.
  • If you allow uploads using "flexitime", then specify in the assignment by when the submission is due, but deliberately set the official end of the processing time, e.g. 30 minutes later. You can see the time at which the submission was received and can then decide how you want to handle it. It is advisable to activate the "Submission comment for course instructors" for this purpose. Students can then enter a reason for a possibly delayed upload.

NOTE for teachers who work with large datasets: If the upload takes too long due to the file size, students can be asked to submit a file hash and upload the file later. Files can be uniquely identitfied with the help of hash values. A changed hash value of a file is proof that the file was changed subsequently by the student. Windows: Freehash, Mac: Android: Hash Droid, iOS: Hash Calculator.

Students have the possibility to convert handwritten notes into a PDF format using their smartphone. You can recommend the following helpful apps for this:

  • With the help of the free app Adobe Scan, notes can be scanned or PDF documents can be created from previously taken pictures. Scans can be edited and annotated. The app is available for iOS and Android.
  • With the Microsoft Office Lens PDF Scanner, handwritten notes can be scanned in very good quality, visually edited and merged into a PDF. The app is available for Android and iOS devices.
  • iOS: In PDF Expert, files can be imported from the Pictures or Files app as well as from the computer and from the cloud.
  • Android: In the Image to PDF Converter, images from selected folder can be converted into a PDF.

NOTE: If you have activated online proctoring during the exam, students must transfer the images to the computer before uploading them in LEARN. A smartphone cannot access the proctored task (cf. Automated Online Proctoring).

If the students do not have a smartphone, the following options are available on a computer / laptop:

Windows 10: You can send the following instructions to the students:

  1. Open the picture in the default programme or in Paint 3D.
  2. Click on "Menu" at the very top left.
  3. Select "Print" and "2D Print".
  4. Then select "Microsoft Print to PDF" in the printer selection at the top.
  5. You will find the PDF in the specified storage location.

Mac: You can send the following instructions to the students:

  1. In the finder, open the folder with the required images and select them.
  2. Right-click on one of the selected files.
  3. In the context menu, click on "open with > preview (default)".
  4. In the sidebar of the preview app, you can see all the images. You can now change the order by moving the images and thus change the later display order within the PDF.
  5. After you have made all the necessary adjustments, click on "file > print" in the menu bar at the top of the screen.
  6. Then click on the drop-down menu at the bottom left and select "save as PDF".

Browser-based: You can send the following instructions to the students:

  1. Open your browser and go to the Online2PDF website.
  2. Click on the "select files" button
  3. Now navigate to the photos you want to convert. You can select more than one by holding down Shift while clicking on each file.
  4. Click on "open" to upload the files.
  5. Select "image to PDF" underneath.
  6. Click on "convert" to start the process. The converted files will be downloaded automatically and can be found in your download folder. As files have to be uploaded twice here, this browser-based converesion may take longer.

How to design and provide information on examinations?

You can decide whether students receive the examination specifications in a document in which they can enter their answers directly or if you provide a document that cannot be edited. In this case, students have to enter their answers in a separate document.

  • If the examination information is only to be an instruction, then save it in a format that makes it difficult for students to write in, e.g. PDF. In such a case, it is advisable to inform students exactly in which format the assignments are to be worked on and uploaded again (analogue vs. digital processing, extent of text answers, how to refer to the questions, necessary personal information such as name and student ID number, page numbering, file format of the upload)
  • If students should refer directly to the exam information in their answers, then you can also ask them to comment on the downloaded specification. Each comment is displayed with name / time stamp. For commenting, we recommend installing the free programme Adobe Acrobat Reader DC.
  • If you want students to enter their answers directly, you can add the above-mentioned content and formatting already in the document, e.g. by including information about the student at the beginning and by using formatted spaces or text boxes after each sub-question [Beispiel Prüfungsangabe DE.docx] (German only)
  • Exam specifications in PDF, Word and Excel can be designed as a form. This allows teachers to precisely indicate in which areas students can enter content and protects sections that may not be changed or deleted by students, for example.


The vast majority of documents can be protected with a password.

These protected documents can be made available to students, e.g. as a file upload, prior to the examination. Students can download the examination specifications in advance of the exams and save them to their local files. In this way, problems that may arise during the download can be sorted out in advance of the examination.

At the beginning of the examination, the password is provided, e.g. in the work order of an assignment order, and students can then open and edit the information that has already been saved locally.

Please inform yourself in advance about the current level of security of the respective password protection.

Excel is particularly suitable for mathematical tasks and the use of macros. Macros can be used to fill variables with different numbers and to carry out automated assessment, e.g. on a page that can only be viewed by teachers.

PowerPoint (or Keynote) is particularly suitable for integrating videos, pictures, self-designed graphics and audio annotations. You can create assignments as slides and specify, for example, the maximum number of slides that students can add in response to each question, or you can prepare the answer slides yourself.

  • Students work out a calculation with an external programme and document their calculation path with a dubbed screen recording, which they embed in the presentation.
  • Students take a picture of their handwritten calculations and embed the picture in the presentations. They then add an audio commentary where they briefly explain their procedure.
  • Students design graphics with PowerPoint and include them.

Here, too, it is important that students know which format to use for the presentation. It is recommended not to choose a video format, but rather the simple presentation format (pptx or ppts).

With the integrated formula editor in Word, students can enter symbols and expressions. If you prepare a Word document as a form, you can also create mathematical formulas using field instructions and make them available to students as quick modules ([Formel_Editor.pdf] in German only).

Inform students in advance which version of Windows is required or whether they need to install certain add-ins, such as Microsoft Math-Add. Since macros can contain viruses, running macros on local computers is often prevented. In the security and privacy settings of e.g. Word, the execution of macros can be activated.

Note that content controls and Active-X controls often cannot be displayed by Mac / iOS devices.

Which digital calculation and drawing options are available?

Microsoft Paint is a graphics software integrated into Microsoft Windows that allows for easy creation and editing of raster graphics. Paint has existed as a component of Windows since the first version. It can be used to draw charts and graphs. Mac users can draw with Pages and Linux users can use GIMP.

Microsoft and Apple offer formulas that you and your students can insert directly into documents (e.g. Word/Pages, PowerPoint/Keynote or Excel/Numbers). If the built-in formulas do not meet your needs, you can edit them, modify an existing formula or create your own formulas from scratch.

Formula Editor: Windows. Formula Editor: Mac. The open-source variant LibreOffice also contains a formula editor.

The cost-free programme GeoGebra can be used to both calculate and draw. Students can access GeoGebra in the browser, e.g. to draw graphs (graphing calculator) and then export the drawing as an image. If you use GeoGebra in exam mode (informationen here), the programme opens in kiosk mode and saving files is not possible. The version of GeoGebra is therefore only available as a tool during the exam. Source:

This open source programme can be used to create dynamic geometric drawings on Windows computers, i.e. drawings in which points can be moved with the mouse without losing the relationships between geometric objects that were previously defined. The programme does not work on Mac / iOS or Linux devices. Source:

With this simple, browser-based drawing programme, function graphs can be drawn digitally. Since there is no export function, students have to take a screenshot of their drawing (instructions for all operation systems in german and english) and save it as an image. Source:

With the cost-free visualisation programme, diagrams can be created and shared in a web browser. Students can also edit diagrams offline and save them locally using the desktop application of for MacOS, Windows and Linux. A variety of diagrams can be created, including flowcharts, process diagrams, ER diagrams, network diagrams, organisational charts, UML and more. Quick start guide (in German only):Draw_IO_Kurzanleitung.pdf