# Appendiix I

Appendix I

 Overview of labeled remarks about goal statements of mathematics education Lable Understanding Teacher Mathematical concepts use contexts to stimulate imaginableness and understand math concepts (for arts and humanities students) D abstraction as a developmental process of generalization D use contexts to understand and to solve problems (e.g. use a bridge to understand the Riemann-sum) E insight in math concepts makes possibilities to applications F insight is essential, see and see through patterns H think about what you are doing instead of how you are doing I mathematical concepts are essential (for science students) O useful in other professions because of an abstract level P mathematics consists of abstractions and its relationships Q Structure order and structure circumstances in contexts A read analyze texts in assignments (for arts and humanities students) C understand problems in situated contexts D search for relations in a framework of math concepts F recognize patterns and understand its features H consideration about procedures is essential I search for structure and restrict to main points, accentuate the show difference between central and side issues J structure is mathematics in itself (for science students) L patterns are essential to learn mathematics M insight in problem situations is essential N mathematical concepts to develop a cognitive structure R Logical use arguments correctly and take well defined decisions B arguments justify all used manipulations D reasoning with math concepts is a scientific challenge F argue logically without exceptions, be precise and exactly G argue logically, calculate automatically and use algorithms H try to attain an abstract level of thinking by correct arguments I rather think logically then solve problems as an automatism K conclusions should not be too easy (for arts and humanities students) L conceptual thinking is required to understand mathematics S
 Overview of labeled remarks about goal statements of mathematics education Lable Procedures to solve problems Teacher Problem correct deliberations and decisions at problems A solving problem solving actions by valid arguments (for science students) D skills mathematics does support to solve problems in difficult domains E be an expert in problem solving skills with insight F procedures and strategies to solve problems should make sense (for arts and humanities students) I procedures to solve problems step-by-step will help to understand mathematical concepts J problem solving skills are dependent of understanding K problem solving skills are dependent of understanding M get knowledge, tricks are not desired O get knowledge how to solve problems, not only a trick P Mathematical be trusted with math techniques, algorithms and calculations B techniques discover and puzzle to solve problems (for science students) C use algorithms and make calculations (for science students) C use the calculator to solve problems (for arts and humanities students) C actions with symbols, calculate accurately as a basis for thinking (for science students) D be an expert in mathematical technical skills to solve problems E math concepts but also practical skills to apply mathematics H calculate and prove, be conscious of the results of actions J calculations and proves are essential (for science students) L mathematics is attractive: puzzle, prove, calculate, draw M exercises with numbers and figures P technical math skills should be mastered to solve problems in difficult domains S apply formulas to solve practical problems is necessary R Real life mathematics is applicable and relevant in society E situations mathematics is important in real life situations G manipulations with numbers to solve real life problems (for arts and humanities students) L think about what can be happen in real life is important for everyone N practical problems are essential, be familiar with applications (for arts and humanities students) O mathematical concepts are useful to act in real life situations Q

Note. Only those teachers who make a statement are included. Some teachers indicate their statements into different groups like arts and humanities students versus science students or. These statements are marked by special group indications into brackets behind the statements.