Item Text | Actively tested |
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a. Calculate percentages like e.g. calculating the value added tax.Item Text:Recommendations:
The variance in response behavior is largely due to the use of technical aids. Therefore, it should be specified whether only mental arithmetic or also the use of tools such as paper or calculators is allowed.
Findings:14 test persons stated that they could calculate percentages without any problems, four test persons could do so with certain difficulties and two test persons stated that they could do so only with great difficulties.
Two test persons asked the cognitive interviewer whether the calculation should be done in the head or with the help of a pocket calculator, whereby test person 06 (answer: with great difficulty) assumes mental arithmetic when answering and test person 20 (answer: I can do it without any problems) decides to use a pocket calculator as an aid when classifying their everyday mathematical competence. With the help of the questionnaire it becomes clear that 14 test persons (TP 01, 04, 06, 07, 08, 09, 10, 11, 13, 15, 16, 17, 18, 19) thought of mental arithmetic when assessing their abilities, two test persons (TP 03, 20) thought of using a calculator or cell phone and four thought of both (TP 02, 05, 12, 14). When asked whether they would have answered differently if they had thought about using a calculator, five of the 14 test persons who thought about mental arithmetic said that they could do this without any problems.
Question Topic:
Job and career/ Job situation & professional activity
Construct:Self-assessment of everyday mathematical competence
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Yes |
b. Calculate simple areas such as the area of a wall to buy tiles.Item Text:Recommendations:
No changes recommended.
Findings:In terms of simple area calculation, e.g. the area of a wall to buy tiles, 15 test persons state that they can do this without any problems, four test persons are of the opinion that they can do this task with certain difficulties and one test person with great difficulties.
All test persons have a more or less comprehensive idea of what is meant by the term "simple surface". Apart from test person 12, who thinks of calculating the area of a circle, all test persons think of a rectangle when using this term or name the example wall. Furthermore, seven persons (TP 01, 04, 08, 10, 13, 15, 16) state that the term "simple surface" is used to connect a square and two test persons (TP 01, 04) triangles. 13 of the 15 test persons who state that they can easily calculate a simple area think of calculating a wall, i.e. a rectangle:
Again, the variance of the scale is largely due to the presumed complexity of the computational operations to be performed and not exclusively to the assessment of the underlying computational competence. Question Topic:
Job and career/ Job situation & professional activity
Construct:Self-assessment of everyday mathematical competence
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Yes |
c. Convert units such as milliliters to liters or miles to kilometers.Item Text:Recommendations:
Only two test persons consider both examples when answering. If the conversion between metric and American systems is of central importance, this should be recorded explicitly and above all individually:
"Convert units of different measurement systems, e.g. miles to kilometers." [„Einheiten unterschiedlicher Messsysteme umrechnen, z. B. Meilen in Kilometer.“] If this is not desired or irrelevant in terms of the construct, only examples within a system should be used: "Convert units such as milliliters into liters or meters into kilometers" [„Einheiten umrechnen wie z.B. Milliliter in Liter oder Meter in Kilometer.“] Findings:Twelve test persons state that they manage to convert units without any problems, five test persons find this task somewhat difficult and three test persons even find it very difficult.
None of the 20 test persons express any difficulties in understanding the term "mile". However, eight test persons (TP 03, 08, 09, 10, 13, 15, 16, 17) do not think of the conversion of miles into kilometers when answering, but of something else:
Except for test persons 02 and 04 (conversion of miles to kilometers) and 05 (conversion of "cups" to grams), the majority of respondents only consider the conversion of units within the metric system when answering. When asked how easy or difficult it was for them to answer this statement about the conversion of units, only four test persons (TP 06, 07, 08, 14) classified this as "rather difficult", mainly because they did not know the conversion factor from miles to kilometers. Question Topic:
Job and career/ Job situation & professional activity
Construct:Self-assessment of everyday mathematical competence
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Yes |
d. Perform calculations that require several steps or arithmetic operations, such as calculating the cheapest cell phone contract for specific needs.Item Text:Recommendations:
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.“] Findings: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:
Question Topic:
Job and career/ Job situation & professional activity
Construct:Self-assessment of everyday mathematical competence
|
Yes |
e. Understanding and interpreting statistical information or data, such as a graph showing the development of housing prices in different districts.Item Text:Recommendations:
No changes recommended
Findings:This is the first item to use the full scale width. While eight test persons state that they can easily understand and interpret statistics and data using the example of housing price developments in different parts of the city, six test persons believe they can do so with some difficulty and one person with great difficulty. Three test persons state that they are not able to do so.
There are indications that two test persons (TP 03, 11) do not understand the statement in the intended sense:
In contrast, the following test persons, for example, refer to concrete statistical information that may contain images. Here it becomes clear that persons have very different associations.
Question Topic:
Job and career/ Job situation & professional activity
Construct:Self-assessment of everyday mathematical competence
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Yes |
f. Summarize or display information and data from different sources in tables or graphics.Item Text:Recommendations:
The item contains several stimuli and is complexly formulated. Many test persons have no concrete idea what it is all about. Therefore the formulation should be simplified, e.g. like this:
"Create your own tables or graphics to summarize or illustrate information from different sources" [„Eigene Tabellen oder Grafiken erstellen, um Informationen aus unterschiedlichen Quellen zusammenzufassen oder zu veranschaulichen“] Findings:The full scale width is also used for this item. A total of eight test persons state that they can summarize or display information and data in tables and graphics, six persons can do so with certain difficulties, three with great difficulties and three test persons state that they cannot do so.
When asked, twelve test persons (TP 01, 05, 06, 07, 08, 09, 14, 15, 16, 17, 19, 20) stated that they had thought of creating tables or graphics themselves when answering:
In general, it is noticeable that the test subjects rarely refer to concrete information or data that are to be summarized or presented, but rather mostly make generalized statements. A total of nine persons (TP 01, 02, 03, 10, 11, 12, 13, 14, 16) state that they have great or certain difficulties with it or are unable to do so because they are not concerned with it or are simply afraid of it:
The use of the term "or" in the phrase "tables or graphs" is not perceived as problematic here, rather it appears as a non-exclusive disjunction, i.e. an inclusive "or". This enables the test persons to refer to one of the two aspects or both together. No test person indicates to answer differently for the creation of tables than for graphics. Question Topic:
Job and career/ Job situation & professional activity
Construct:Self-assessment of everyday mathematical competence
|
Yes |