ACTIMATH: A REMEDIAL COURSE IN MATHEMATICS ADAPTED TO
THE NEEDS OF THE STUDENT AND THEIR CHOSEN FIELD OF
STUDY
T. Neijens1, A.Vermeyen1, K. D’haeseleer1,
T. Stevens1, D. Coppens1, B. D’haenens1, L. Van Loon2, G. De Samblanx2,
G. Clarebout3, C. Biront4, E. Van Hoof5, L. Gielen6
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KAHO Sint-Lieven (BELGIUM)
Lessius Mechelen (BELGIUM)
3
K.U.Leuven (BELGIUM)
4
HUBrussel (BELGIUM)
5
KHLim (BELGIUM)
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KHLeuven (BELGIUM)
tim.neijens@kahosl.be, annemie.vermeyen@kahosl.be, katrien.dhaeseleer@kahosl.be,
tony.stevens@kahosl.be, dimitri.coppens@kahosl.be, bart.dhaenens@kahosl.be,
leon.vanloon@mechelen.lessius.eu, gorik.desamblanx@mechelen.lessius.be,
geraldine.clarebout@ped.kuleuven.be, christian.biront@hubrussel.be,
etienne.vanhoof@khlim.be, lut.gielen@khleuven.be
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Abstract
The project ActiMath (University College KAHO Sint-Lieven, University K.U.Leuven) wants to close the
gap between secondary education and higher education concerning mathematics. Many starting
college students fail their mathematics courses because their foundation in mathematics is (too) weak.
ActiMath’s goal is to make an interactive and adaptable remedial course for the student, usable for
different teachers and bachelor/master courses.
Keywords: Maths, remedial, VLE, education, adaptive.
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INTRODUCTION
Many courses in colleges and universities have a need for mathematical concepts in one form or
another. Whether or not mathematics is in a supporting role, all studies expect some basic
foundations. In order to ensure that starting level, many colleges and universities organize remedial
math courses.
For Belgium, most of these courses are organized in a classical way: theory lectures followed by
exercise session. This leaves little to no room for differentiation. Some students don’t need the extra
lessons, while others have trouble keeping up with the speed of the lectures. Summer courses tend to
differ from college to college in content and level, even if the field of study is the same. There is little to
no cooperation between lecturers.
While lecturers have the impression that these summer courses actually help the students to solidify
their mathematical knowledge, no research has been done to check this assumption.
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OBJECTIVES
The main goal is to develop a remedial course for all participating colleges and universities
(Association K.U.Leuven). This remedial course needs to be adaptive. The contents and level have to
be catered to the needs of an individual student, taking into account the chosen field of study and their
personal knowledge of mathematics.
A second objective is to stimulate cooperation and sharing of knowledge, material and experiences
between the lecturers of different colleges/universities, in order to heighten the effectiveness of
teaching in all participating institutions.
Ultimately, we want to improve the foundation of mathematics and to close the gap between
secondary education and higher education. As a result, the failure rate in mathematically oriented
courses should be reduced in the starting semester/year.
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3.1
APPROACH
Preparation
We first studied the way the summer courses were given and the general opinion of the lecturers.
Summer courses for math are almost always taught from the same principle: theory first, then
exercises. Differentiation is minimal and only possible during the exercises.
As a second step we collected the current course materials and tried to find common principles and
content, grouped by the chosen field of study. Discussing these stimulates cooperation and
consultation between the different lecturers.
3.2
Implementation
3.2.1 Platform
ActiMath should be able to be used throughout the whole Association K.U.Leuven; one of the
requirements of the project is the use of a VLE (Virtual Learning Environment) (Toledo, based on
BlackBoard).
From an entrance quiz and questionnaire about their school past we can determine the entrance level
and the subjects that have to be taken. This can be done through the adaptive learning paths provided
by BlackBoard, or through a database system on an external site.
Exercises can be monitored through BlackBoard. Preferably we will use a mathematics assessment
package (for example Maple T.A. or STACK) to give differentiated feedback. The choice will depend
on financial and technological (compatibility) constraints.
3.2.2 Scenarios
To determine the best mix and learning scenarios (self-study, contact education, cooperative
learning), we base ourselves on the previous remedial courses given by lecturers in the association
K.U.Leuven and their experiences.
ActiMath should be usable in all scenarios, depending on the wishes of the student or lecturer. This is
important. Different lecturers have different teaching styles, each with its own merits. A lecturer should
use the teaching style with which he or she is most comfortable in order to improve effectiveness
(Ernest(1989)). As has been pointed out in numerous studies, students have their own learning style
(Kolb (1984)).
Where possible, group exercises should be constructed to stimulate cooperative learning. This is the
most effective way of learning, although it is less efficient (more time, more organizing), see also
Slavin et al. (2009).
3.2.3 Technology use
Construction of the content on the site reflects the differentiation goal by giving the student the choice
of what he wants to do first (learning theory, doing exercises, trying examples, watching a web
lecture). An exercise system will be implemented that gives differentiated feedback. Computer usage
(whether it is in self-study or more traditional learning) should be stimulated, as suggested by Lou et
al. (2001) and Sangwin and Pointon (2004). Mathematics, especially as a supporting subject, is mostly
done by computers or calculators. Easing the student into this technology should be part of their
mathematical education.
3.2.4 Differentiation
Differentiation is partly achieved when giving the student the choice of learning scenario and speed.
We can also differentiate in the contents the students have to learn (depending on choice of study and
starting level in mathematics, measured by an entrance test).
The course materials, and exercises in particular, will be grouped in a few difficulty levels, inspired by
Taxonomy of Bloom (1956), which was later updated for mathematics by Sangwin and Pointon (2004).
First, we will focus on basic math competences (basic calculation), since many lecturers experience
difficulties concerning even the simplest of calculations. The difficulty levels for content are:
3.3

Basic knowledge: reproduction of formulas, definitions, algorithms, and use of those
algorithms (Horner’s Algorithm, solving a quadratic equation).

Comprehension: the meaning of certain symbols in certain formulas, why do formulas work?

Application: using the appropriate method for simple questions and problems.
First test run
The first test run will start in September 2011 (year 2011-2012). The test group will consist of the
students of the professional bachelor studies (construction, real estate, electro mechanics), preferably
across all participating institutions. We will determine through questionnaires how the students and
lecturers experienced ActiMath. We will follow the students in their first year to determine their results,
comparing them to the results of the students of year 2010-2011.
This test run will be held on the VLE Blackboard, using the adaptive learning paths implemented.
Evaluation (entrance test, exercises and final test) will be done using multiple choice questions.
Where needed, the course materials and method can be adapted to suggestions and results.
3.4
Second test run
The second test run will start in September 2012 (year 2012-2013). This test group will consist of the
students of the professional bachelor studies, those of industrial and trade engineering and those of
trade sciences across all participating institutions. Again through questionnaires and studying
students’ results, the effectiveness of ActiMath can be determined.
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FURTHER RESEARCH
Through questionnaires we can determine the preferred or most effective method of studying
(exercises or theory first, lots of examples or not, …) and adjust this course (and maybe others)
accordingly.
Cooperation between lecturers can (and should) lead to uniformization in content and desired starting
level. Further research can determine which materials are absolutely necessary to ensure a good
starting level in mathematics.
Determining a good entrance and final test is no easy task and warrants further research of each field
of study and their demands on entrance level. After a first test run in September 2011, experiences will
be collected through questionnaires and test results in order to improve ActiMath. Comparing these
results to the actual exam results hopefully yields a positive and relevant correlation.
REFERENCES
Bloom, B.S.(ed.), 1956, Taxonomy of Educational Objectives, McKay New York.
Ernest, P., 1989, The Impact of Beliefs on the Teaching of Mathematics, Mathematics Teaching: The
state of the Art, Falmer Press London, p. 249-254.
Kolb, D.A. (1984), Experiential Learning: experience as the source of learning and development,
Prentice-Hall New Jersey.
Slavin, R.E., Groff, C., and Lake, C., 2009, Effective Programs in Middle and High School
Mathematics: A Best-Evidence Synthesis, Review of Educational Research, v. 79(2), p. 839-911.
Sangwin, C.J., and Pointon A., 2004, Assessing Mathematics Automatically Using Computer Algebra
and the Internet, Teaching Mathematics Applications, v. 23(1), p. 1-14.
Lou, Y., Abrami, P.C., and D’Appollonia, S., Small Group and Individual Learning with Technology: A
Meta-Analysis, Review of Educational Research, v. 71(3), p. 449-521.