d. Perform calculations that require several steps or arithmetic operations, such as calculating the cheapest cell phone contract for specific needs. [Berechnungen durchführen, die mehrere Schritte oder Rechenoperationen erfordern, wie z.B. den günstigsten Handyvertrag für bestimmte Bedürfnisse ausrechnen.]

Nein

Also in this everyday mathematical activity almost three quarters of the test persons (n=14) state that they can do this without any problems, two test persons can do this with certain difficulties and three with great difficulties. One test person does not make any statement because he says of himself that he never calculates cell phone contracts for certain needs.

There are two questions of particular interest in this item. One is to find out if the test persons think of several arithmetical operations when answering the question and the other is to find out if the mentioned example of calculating the most favourable cell phone contract for certain needs is useful for answering the question. When asked which arithmetical operations the test persons thought of, the answers vary from basic arithmetical operations such as addition and multiplication to equations or trisentence calculation up to the calculation of functions e.g. a straight line. With a total of 14 test persons (TP 01, 02, 03, 04, 05, 06, 07, 09, 12, 13, 14, 16, 18, 19) it becomes clear that they thought of several arithmetical operations when answering, regardless of whether they were referring to cell phone contracts or not:

• "Calculate three-sentence calculation in the same way as for fuel consumption. I do that occasionally in my head and it's easy for me.” (TP 04)
• "I think that's something you do more often. The contract has this and the other has that. I might not use one of them. Or I have free SMS. [...] For a short time I thought of a formula where different things are used one after the other, but you can't calculate that directly with the contract. You have different steps." (TP 06)
• "I do also always make that, if I must decide between two offers, that does not have to be al-ways a cell phone contract, then one goes also there and computes only times. For example also electricity providers. That I compare the fixed costs and also the variable costs and look at me, what I need and/or use. That can also be a multi-level comparison calculation." (TP 09)
• "I was thinking about some text tasks where you have to do several steps. First like this, then plus, minus and then a three-part sentence in the back." (TP 16)

The remaining six test persons (TP 08, 10, 11, 15, 17, 20) refer to the example "cell phone contract", but in their explanations they only refer to comparing the costs of different flat rates:

• "It is not a multiple bill. You compare who offers the cheapest Allnet flat rate and has a good net and all that. Well, I'll manage that, I'll have to find the right cell phone contract.” (TP 10)
• "To the calculation from the telephone provider for me. 25€ and 9,95€ are a big difference for me.” (TP 11)
• "I was thinking about the cell phone contract. Per month, with Internet flat rate without Internet flat rate, i.e. the services per month." (TP 17)
• "You read it through. So and so much Flatrate for so much euro etc. and compare that." (TP 20)

There is no assessment of their everyday mathematical competence with regard to their ability to use a multi-stage calculation method. These six test persons all decide on the answer category "I can without problems". This means that six of the 14 persons who claim to be able to do this without any problems, may be misplaced due to an incorrect understanding. Furthermore, it means that the example of calculating the cheapest cell phone contract no longer works today, since the costs for the widespread smart phones are based on flat rates and there is no longer any need for a multi-stage calculation method with basic arithmetic operations. In addition, there are also comparison computers on the Internet that can perform the actual computing power when the user enters the individual usage data.

It is not clear, what is meant by the abstract notion "arithmetic operations". To make clear, what shall be considered at this item, either the formulation "arithmetic operations like plus, minus, multiply or divided" or the term "basic arithmetic operations" could be used.
In addition, the example with the cheapest cell phone contract does not work, since mainly a comparison of monthly costs for flat rates is considered. In contrast to this probably rather a multi-level computation procedure (basic and consumption costs, possible bonus payments, etc.) might find consideration with the determination of the most favorable current offerer:
"Perform calculations that require multiple steps or arithmetic operations such as addition, substraction, multiplication or division, such as calculating the cheapest electricity provider for specific needs".
[„Berechnungen durchführen, die mehrere Schritte oder Rechenoperationen wie Plus, Minus, Mal oder Geteilt erfordern, wie z.B. den günstigsten Stromanbieter für bestimmte Bedürfnisse ausrechnen.“]

true