Volume XII , issue 2 ( 2009 ) | back |

Long term effects in learning mathematics in Finland---curriculum changes and calculators | 51$-$56 |

**Abstract**

Two similar tests to measure the skills of the Finnish school children in mathematics took place in 1981 and 2003. The tests are compared to a test measuring the knowledge of basic concepts in mathematics after the student examination. The results of the tests reflect the changes in the mathematics curriculum and teaching practices in Finland.

**Keywords:** Student's assessment; calculators; PISA; TIMMS.

Understanding algorithms of vertical addition and subtraction | 57$-$72 |

**Abstract**

In this paper, we split into all intermediate steps and illustrate algorithms of vertical addition and subtraction of two-digit and three-digit numbers. We consider the relating of symbolic codes of arithmetic to their iconic representations to be a basic way of supplying them with meaning. Hence, our didactical maxim is: I see, therefore I understand. Writing this paper, our intension is deepening of teachers' understanding of these classical algorithms of arithmetic and, as our analysis shows it clearly, a right understanding is more a matter of good knowledge of didactics of mathematics than of mathematics itself.

**Keywords:** Decimal notation; decimal grouping;
algorithms of vertical addition and subtraction; regrouping and
the Cantor Principle of Invariance of Number.

A contribution to the development of functional thinking of pupils and students | 73$-$81 |

**Abstract**

This contribution provides an idea of a suitable presentation which can contribute to motivation, illustration and deeper understanding in secondary school mathematics of fundamental concepts and ideas of the themes Function, Differential and integral calculus, as well as further development of students' functional thinking.

**Keywords:** Function; graph; differential equation; functional thinking.

Student placement in calculus courses. A case study | 83$-$102 |

**Abstract**

This is a continuation of the author's study on making and using course specific diagnostic tests in college setting. First a predictive power of SAT scores on student performance in calculus classes is discussed and it is shown that SAT scores cannot be used as a useful predictor of students' performance in those classes. Lack of usefulness of SAT scores as a reliable predictor of students' performance has been noted by other authors as well. Reasons for the lack of relevance are given. The necessity of a ``home-made" diagnostic test resulted in creation of such tests and one such test is completely exhibited here. This test proves to be much more useful in gaging students' future performance, to the extent that it would be unrealistic to expect greater explanatory power of students' subsequent performance in class. Uses of the test and the resulting statistics are discussed; comparison with a similar test for statistic classes is given.

**Keywords:** SAT; diagnostic testing; student placement; assessment; predictions of students' performance;
Bloom's taxonomy.