Appendiix 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