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Finally, since items referred to contextual stimuli, which were presented in textual formats, reading ability can be regarded as another, shared demand of solving the items.
Sketch (yes, no): This feature includes both sketches contained in the item formulations, which have to be read, interpreted, and/or understood for correctly solving the items or sketches as part of the respondents' answers.
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There is a formula which a typical student would use in solving the item.
The two categories in this dichotomy are (i) the set of items for which knowledge of some mathematical theorem is helpful for solving the item, and (ii) the set of items where it is not.
This paper discusses a framework for analyzing the dependence on mathematical theory in test items, that is, a framework for discussing to what extent knowledge of mathematical theory is helpful for the student in solving the item.
In PISA 2012, only 11.8% of the mathematics items are found to be such that some mathematical theorem which the student can typically be assumed to know about, is helping the student in solving the item.
Figure 5 shows an exemplary item, where the required tractive force for a tackle system shall be computed – for solving the item, it is necessary to understand the distribution of forces on the two rolls.
For these analyses of differences in differences, it is convenient to have the results directly expressed as a difference in p-values, that is, in the percentages of tested students solving the item correctly.
For an item to fall into the T category, one of the following two criteria must be met: Either the item is designed in such a way that some theorem presumably known to the student significantly simplifies the task of solving the item, or the item is such that one would expect use of some theorem from the student.
For an item to fall into the F category, one of the following three criteria must be met: The item contains a formula which the student must use, or The item asks the student to construct a formula, or There is a formula which a typical student would use in solving the item.
Consequently, how a student solved the items of the bMCU test depended solely upon the student's ability.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com