Most technical studies require and assume from the students a certain knowledge of mathematics. In this paper an experiment is described where students, starting with a study of ICT at a bachelor level, are performing a very short test in mathematics to measure their knowledge. The results of this test are compared with the results students are having with the real exams at the end of the rst quarter of the rst year.
At the institute of ICT at the HU Utrecht University of Applied Sciences around 500 students start with a study in ICT with the aim to get a bachelor degree. To start this study, students should have a certain level of education. The students starting at our institute of ICT have a mixed background. Actually two types of students can be distinguished: students with an education that has its focus on working in practice and also has its focus on a certain specialisation and students with a more theoretical background that are supposed to specialise themselves later at a university or higher education. Because of this mixed population of students, the background in mathematics is quite di erent.
For all starting students a small mathematics test has been developed. One of the goals of the mathematics test was to get a feeling of the level of math education of our new students. This would give us a clue what additional courses and help we should o er the students of di erent types.
Apart from that primary goal, it would be interesting to see if the result of the mathematics test predicts the success of the students with their rst exams. This is what this paper is about. The research question that will be the focus of this paper is: is there a correlation with the results of the exams and the math test?
This paper is organised as follows: First related work will be discussed. Next a section will be presented explaining the test setup, followed by a section containing a short description of the courses in the rst quarter. The section "Results" is dedicated to the evaluation of the results of the exams of the rst three courses in regards to the mathematics test. In the section "Discussion" some important remarks will be given about the results found so far. Finally a conclusion and a bibliography will end the paper. 2
Testing students and test design is the subject of many publications and scienti c
research. An example of a publication where the same type of testing has been
used is [
In [
The main goal was to discover the level of math education the students had received. We do not measure the skills, but the knowledge of several mathematical issues. This is done by setting up a list of problems that are easy to solve if the student has had an explanation of the mathematical concept in the past. 3.1
Problems to be Solved In the test a set of problems were presented to the students. Not much work had to be done to solve the problems. There is a certain increase of complexity of the problems. An explanation why this problem was added to the list is given for every problem. This explanation was not presented to the students performing the test. 1. Calculate 2 + 3(5 2) =
2. Solve x in:
3. Solve x in: 7 = 3 (x 2)(x + 3) = 0
that the solutions should be clear without using the solution for the general so-called a b c formula (ax2 + bx + c = 0) 4. Given f (x) = x 7. Calculate:
5. Calculate:
6. Calculate:
case? Even if the student does not know this, the solution can be calculated 7. Simplify:
case? Here there is now escape as in the previous example 8. Calculate: 10log(1000) =
9. Calculate:
Is the student capable to use goniometric functions and radians? 10. Calculate: f (2) = 33 = 22:23 = ab:ac = 2:cos( ) =
3 X n = n=1 Z 3 1 x2dx =
11. What is the rst derivative of f (x) = 2x3 The rst derivative is: ...
12. Calculate:
3.2 Before starting the test, students were told that this test was only meant for information. The results would not in uence a decision to let the students pass or not. The information could be used by the student to discover which eld of mathematics he/she should work on or what supporting courses he/she has to attend to get the presumed level in mathematics.
The test takes only 20 minutes of time and is performed by using the
webbased Socrative environment [
To give the students the possibility to orient on the possibilities in a later phase
of the bachelor program, all three courses in the rst quarter should more or
less be tied to the nal four tracks the student has to select during the rst half
year [
One of the reasons why these three courses are presented in the rst block of
the study is that it is a nice way to demonstrate the layered structure that plays
an important role in many ICT concepts [
To answer our research question, the correlation between the exam results and
the math test results should be calculated. For the correlation the well known
formula for the correlation coe cient r has been used [
r = n P ((xi i=1 s n
P (xi i=1 x)(yi
y)) n x)2 P (yi i=1 y)2 In Table 1 the results for the correlation of the outcomes from the math test and the results of the st examination of the three courses are given. N is the number of students that made the math test. So the answer to the research question presented in the introduction should be: "There is only a small correlation between the results of the exam in programming and the results of the math test. The other two courses have only a very small positive correlation."
The next question that arises is: is there a correlation between the results of the courses given? To investigate this, three correlations were calculated. One for each combination of two courses. In this case the number of students N involved is again 225 as in the previous result. In this case (see table 2) the correlation is much more evident, showing that students who perform good at one exam also had a good result at the other exams and the other way around for students performing not so good. 6
At the start of this research we expected a positive correlation between the level of knowledge of mathematics and the results of the exams for the rst quarter. This was based on the fact that in the course Computer systems and networks the binary system is explained where the use of exponents is inevitable. To our surprise some students did not know anything about use of exponents and the mathematical properties of it. For these students the subject might be hard. The same was true for programming where we expected the notion of a function to be necessary. However, it turned out that the math test cannot be considered as a predictive instrument of how a student will perform. It should be mentioned, as was already done in section 3, that the test does not check the math skills but only the awareness of certain concepts in mathematics has been checked.
The primary goal for which the test has been developed was to see with what level in mathematics the students start at our institute. Though not a subject of this paper it should be mentioned that it turned out to be very helpful to know what extra courses in mathematics were needed during the bachelor phase. As was expected, the diversity in background knowledge with respect to mathematics turned out to be huge. 7
As shown is this paper, the level of knowledge of mathematics does not play an
important role in the rst part of our bachelor program. However, in later part
there are specialisations that rely more heavily on mathematics, so it would be
interesting to see if there is a connection between the mathematical background
of the student and the specialisation he/she will choose. The research presented
in this paper is only a start and later investigations and research should be done
to see if the test is predictive in other aspects. Because we have di erent types
of students entering our bachelor program, it is interesting to see what these
students will actually choose as their specialisation and also how they perform
in other courses that might be more based on mathematical insight. A study on
other types of predictive testing like in [