# Mathematical modelling and problem solving

## Reflection and self-assessment

The reflection is done in a second submission of each module, after the follow-up lecture. Please follow the I, II, III structure in your answer!

I. (WEEKLY MEETING AND FOLLOW-UP LECTURE)

a) Did you have your compulsory weekly meeting with a supervisor?

c) If you were asked to talk to a supervisor about the main submission, who did you talk to?

II. (WHAT DID YOU EXPERIENCE AND LEARN?)

Reflect on your experiences from working with the module and try to make the most out of them. If you reflect around individual problems (which is good), try to also draw general conclusions that may be helpful for you going forward (in this course and/or long-term). You are now encouraged to discuss the module with other groups!

Note that time spent in the reflection is time well spent, as it will help you to maximize the learning from the effort you already made when working with the problems.

III. (HOW WELL DID YOU SOLVE THE PROBLEMS?)

Give a single assessment for the whole module and motivate with a sentence or two. This is for your own practice.

Use the scale "insufficient/sufficient/good/very good", or a combination such as "between good and very good" or "good or very good". Use the criteria I have suggested as a guideline, or motivate your own.

(We as teachers will then set the grade for this module. We think it is better if you are able to make a fair assessment rather than an inflated one.)

(SELF-CHECK) Do the self-check also for the reflection! (a self-check is always good practice)

To submit the reflection, please append it to the end of your main submission and submit! Update the total hours spent to also include the reflection.

## Reflecting on what you learned

In the principle of "learning by doing", reflection is an essential part.

In particular, it is not possible to perform a complex skill just by reading and following some instructions. Nobody would even be able to write such instructions in a complete way. Instead, it becomes essential to engage in a task to make experiences, and then to learn by reflecting on these experiences. This enables you to make observations and generalizations, and become more aware of your own thought processes.

Then, when you develop processes such as thinking and problem solving, it makes little sense to only consider the end result. You will learn when you struggle, independently of how experienced you are or how close you come to a solution. And if you are able to improve over and over again, you can in the long run reach any reasonable level.

## Self-assessment

However, it is also good to be aware of your absolute level of performance. For this purpose we suggest to to qualitatively use the levels "insufficient", "sufficient", "good" and "very good".

In a school setting, the most common way to do this is to simply consider the ratio of correct answers. However this simple way to assess doesn't work in more complicated situations like the quality of a report or a project, or deal with tasks that have no correct answers, such as in design.

### Sufficient to do your best

Another way to think is that it is sufficient to do your best given your current abilities and the time available. This notion of acceptance is inevitably more relative, but makes sense while learning a complex skill or process, especially in the beginning.

So I have made a sufficient effort if:

• I have seriously tried to understand and solve the problems.
• basic facts and arguments are correct.
• I have given reasonable attention to quality and detail.
• I have followed given recommendations (like participating in the supervision).
• a generally careful approach to the work.

I then find it less important if:

• I did not reach all the way to a solution.
• I have not understood that something is wrong or inadequate or how.
• I have tried to devise a complicated argument but did not fully succeed.

Examples of when the approach is not careful include:

• obviously wrong or inaccurate statements
• no serious attempt
• not asked supervisor in obvious cases
• misunderstandings that easily could have been resolved with a question
• sloppy presentation
• no clear line of argument in the explanations. Note that even if I have not managed to solve a problem, it is possible to clearly state and discuss this situation.
• an inefficient learning process generally.

### What is very good?

Then what would characterize a "very good" performance? We must here inevitably focus on the quality of the solutions in an absolute sense, including subjective judgement as necessary. Additionally, we should expect that everything around the solution should also be of high quality.

A very good performance would then include:

• Very good solutions.
• Clarity and depth in explanations. For example short and clear explanations, with relevant own observations and reflections. Creativity and originality if possible.
• Some additional energy. A high quality presentation. Additional own investigations. (Solving the optional exercises can be a part of this but I do not see this as a requirement, but rather as an opportunity to learn more.)

I find it reasonable to think that for a "very good" performance, these qualities should be present to the highest level that can reasonably be expected. Note that there is a very large variation in how this can be achieved. For a "good" performance, these qualities should be clearly demonstrated to some extent.

Finally, be aware that it is not possible to write about this in a perfect or complete way - an interpretation is required, and you may even disagree. So it is ultimately about developing your own sense of judgement.