how to remediate mathematics? demonstration of different possibilities

HOW TO REMEDIATE MATHEMATICS? DEMONSTRATION OF
DIFFERENT POSSIBILITIES
Annemie Vermeyen1, Sophie Ronsse1, Johan Van den Bossche2,
Bart D’Hanenens1, Jan Van Caudenberg1
1
KAHO Sint-Lieven (BELGIUM)
2
LESEC (BELGIUM)
[email protected], [email protected],
[email protected], [email protected],
[email protected]
Abstract
Curricula in secondary education follow the social trend in which encyclopedic knowledge becomes
less important. It is not surprising that math lecturers in higher education feel the consequence of this
shift. A lot of initiatives to remediate mathematics are organized. The project ActiMath[1] is an
interactive course on the Virtual Learning Environment (VLE) Toledo, based on Blackboard usable to
brush up and to improve basic mathematical skills. ActiMath offers several possibilities to remediate
mathematics such as adaptive learning paths, tests, web lectures and interactive exercises and is
usable in different scenarios of teaching and/or study methods.
Keywords: Mathematics, remediate, education, adaptive, interactive.
1
INTRODUCTION
A small survey organized in Flanders, explored lecturers’ perception towards basic mathematical
knowledge and attitudes of new students. The survey revealed that mathematic lecturers at
universities and colleges find that the basic skills (arithmetic and basic algebra) and attitudes such as
punctuality have decreased.
In the project ActiMath, funded by the OOF (Education Development Fund) of Association KULeuven ,
we are developing an interactive course for all participating colleges and universities of the
Association K.U.Leuven to remediate mathematics. During the project we look for an approach which
helps and stimulates students to reach the main goal: to improve their mathematical knowledge, skills
and attitudes so they can make a good start of their study.
The project started in January 2011. ActiMath is developed as a community on the Virtual Learning
Environment (VLE), Toledo, based on Blackboard and uses different types of learning materials to
remediate such as web lectures, interactive exercises, examples, tests, …
Due to unexpected circumstances, the project was stopped form March 2012 until November 2012.
Now, after the restart in December, we can present the situation and the result of the test run in
September 2011. At that moment, ActiMath was tested by students starting their first bachelor year at
KAHO Aalst (Construction, Real Estate, Electromechanics), totaling 120 students. Based on the result
from an entrance test, we gave the students a suggested path to follow in ActiMath, and we instructed
them on how to use the system. Afterwards they could try out ActiMath at home. After two weeks
students were questioned about the use and usefulness of ActiMath. Responses were mostly positive
and gave us a clearer picture of the strengths and weakness of ActiMath which will be useful during
the further development.
2
2.1
SURVEY OF LECTURERS’ PERCEPTION
Survey details
The survey questioned the perception of lecturers concerning mathematical attitudes, skills and
knowledge of incoming students. It was sent by e-mail to all universities and colleges in Flanders. In
total we got an answer from 61 lecturers belonging to 31 of the 39 contacted universities and colleges.
The number of hours mathematics in the last year of secondary school of the incoming students varied
from 2 hours to 7 hours in a week.
For the mathematical skills and attitudes, we gauged mainly the perception of the lecturers towards
the evolution compared with the past 5 to 10 years. Concerning the mathematical knowledge we
asked what the lecturer expected and how students meet these expectations. Lecturers were also
asked if they see an evolution in mathematical knowledge compared with the past 5 to 10 years.
2.2
Survey results
The survey shows that 65% of the participating lecturers think that students preparation concerning
attitudes, skills and knowledge is less compared with 5 to 10 years ago. If we look closer, 75% of the
lecturers especially think that the mathematical knowledge has decreased. None of the respondents
thinks that there is a positive evolution.
The survey also questioned several attitudes. Lecturers only have a positive feeling about the attitude
“teamwork and communication” and in a lesser extent about the attitude “self-confidence and selfdependence”. The majority of the respondents indicates that “the sense of accuracy”, “the sense of
completeness” and “perseverance” have decreased. As to “critical thinking” a few lecturers indicate an
improvement but most of them experience a decline.
Another topic concerns mathematical skills. 44% of the lecturers indicate that “basic mathematical
skills” has strongly declined. “Learning skills”, “problem solving” and “thinking and reasoning skills”
have also reduced but to a lesser extent.
Concerning knowledge, the survey asked for several mathematical topics to which extent students are
adequately prepared. Because of the scattered results, a conclusion was not easily formulated. But
most lecturers have the perception that the knowledge of basic mathematics such as arithmetic and
basic algebra have declined.
2.3
Conclusion
According to the survey, lecturers’ perception is that skills and knowledge of basis mathematics is
declining. There is a positive evolution in teamwork and communication, but accuracy and
completeness is declining the last 5 to 10 years.
2.4
Further developments in Flanders
In the meanwhile this perception of the lecturers has been confirmed in a study commissioned by the
Flemish Minister of Education Pascal Smet [2]. The study was carried out by an interdisciplinary team
of researchers of the university if KULeuven and is based on a calibration test on several
mathematical topics. The study shows that the problem is mainly situated in basic mathematical skills
(arithmetic and algebra).
More information (in Dutch) you can find in:
http://www.ond.vlaanderen.be/curriculum/peilingen/secundaironderwijs/brochures/peiling_wisk_web.pdf
3
3.1
ACTIMATH
Objective
ActiMath is a remedial adaptive course for all participating colleges and universities of the Association
KULeuven. Using ActiMath students can prepare themselves for a better start in higher education
following their own learning path adaptable to their own learning style and at their own pace.
Lecturers can use ActiMath in replacement of or in addition to a traditional lecture.
The main goal is to improve the foundation of mathematics and to reduce the failure rate in
mathematically oriented courses during the starting year. Data are gathered to examine the influence
of the use of ActiMath.
3.2
Approach
Via the VLE students have access to the learning material, gathered in a community.
accommodate to different learning styles, several types of learning material are available:
To
3.2.1 Tests
The tests are made using the possibilities of the VLE, most of them are multiple choice. They are
used to determine whether a student needs to practice more or not for a specific subject. Depending
on the result of the test more material is available for the student.
3.2.2 Web lectures
In short movies skills are demonstrated. To make the web lectures, a simple technique was used: a
webcam was attached to an upright, the lecturer’s hand is filmed, audio is recorded of the lecturer who
is explaining a topic.
3.2.3 Interactive exercises
To practice, students can make interactive exercises. At this moment, the exercises are constructed
using STACK [3] which is open-source software. STACK provides differentiated feedback. Because
of the use of STACK, the exercises are not connected to the gradebook of Toledo, so they cannot be
used for evaluation but only for practising.
3.2.4 Traditional course
ActiMath also has a traditional course in pdf. All topics are explained and provided with examples. So
if a student prefers, it is possible to use ActiMath as an online handbook. This option can be chosen
at the beginning.
3.3
Results of the evaluation of the test run
In September 2011, the first test run was organised.
During a first session students made an entrance test followed by an introduction to ActiMath. Then
they tried out ActiMaht in a PC-classroom.
The day after, a second session was organised in which they got the result of the test. Based on this
result, topics were suggested which they had to practice. The remaining time, students worked on
ActiMath in a PC Classroom. The lecturer helped students personally, no traditional lesson was given.
Student were stimulated by the lecturer to keep using ActiMath during the year.
3.3.1 Survey details
The survey questioned students’ perception about the use and the usefulness of ActiMath.
130 students (40 of Bachelor in Elektromechanics and 90 of Bachelof in Construction) participated at
the survey. 85% of this students followed technical education the year before. 60% of the students
had 3 to 4 hours mathematics, 23% had less than three hours and 17% had more than 4 hours
mathematics. 28% didn’t use ActiMath. They were excluded from the results. So the results are
based on 94 respondents.
3.3.2 Frequency of use
About 55% of the students were using ActiMath regularly, two weeks after the beginning of the
academic year. Unfortunately 25% say they don’t use it anymore. 63% of this 25% say that they
acquired sufficient knowledge by using ActiMah. 5% (=1 student) claims he didn’t acquire sufficient
knowledge.
About 48% of the students intend to use ActiMath regular in the future, 10% say they will not use it
anymore. The remaining students didn’t know yet or had not opinion about it.
3.3.3 Appreciation
The general appreciation of ActiMath is predominantly good. The average is 7,4 ± 1,2 (scale 1 to 10).
Unfortunately nobody motivated his/her score. 73% of the respondents say they find ActiMath fun to
work with.
25% of the students prefer ActiMath instead of a traditional lesson. 33% prefer the traditional lessons.
95% say that ActiMath is a good support for mathematics. In students’ opinion ActiMath must be used
as a supporting tool and not as a learning tool by itself.
About 80% think there is enough material in the package ActiMath to start well prepared his/her study.
Only 57% of the students have the perception that they have sufficient knowledge after using
ActiMath. This is not an objective fact, it is a perception. This impression can be confirmed or denied
during the first weeks or by the first real evaluations. It wasn’t tested at that time.
3.3.4 Learning material
Students were also asked which learning material they used most. Most popular were the exercises
and the examples. The applets were used least.
3.3.5 Informal feedback
During informal talks, students indicated that they find the entrance test important because it gives
them a view of their level at the start of their study.
Students also liked the freedom to choose their own learning path and appreciated that they could
determine their own pace
3.4
Conclusions
Most of the students appreciated ActiMath and liked using it.
Only slightly more than half of the group sayd they use ActiMath on a regular base two weeks after the
start, a little less than half of the group claimed they will use ActiMath after three months.
Students like ActiMath as extra support, but they think it is not a good replacement for the traditional
lessons. Apparently student prefer a mix between self-study and contact education
Students liked most the interactive exercises, followed by the examples and the theory.
The entrance test is important, not only for ActiMath, but also for the student.
3.5
Recommendations
To make sure students use ActiMath to remediate their mathematical knowledge and skills, lecturers
should promote it. This is possible by referring to ActiMath during the lessons at the start of the year,
by organising another test, by promoting ActiMath by means of flyers distributed by enrolment,…
Often students who don’t need the remediation, do practise and use ActiMath, while students who
need most practicing don’t. Lecturers involvement is very important. Also tests at the start of the
semester can motivate students.
3.6
Further developments
At this moment, ActiMath contains tests, weblectures, traditional courses in pdf, interactive exercises
gathered in adaptive learning paths and belonging to the following topics:
•
Basic algebra (combination of operations, fractions, powers, …)
•
Solving equations and systems of equations
•
Trigonometry
In the near future, ActiMath will be extended with calculus topics: Functions, derivatives, integrals…
Lecturers participating in the projected are consulted about the topics that are necessary for their field
of education.
In September 2013 we will organise another test run. Different scenarios will be tested in different
fields of study. Afterwards lecturers as well as students will be surveyed. In that way we can optimize
ActiMath.
Results of entrance tests and exams and other data will be gathered so research can be done to the
link between the use of ActiMath and the final result in the first year/semester.
4
ZOOMING IN ON STACK
STACK (System for Teaching and Assessment using a Computer algebra Kernel) is an open-source
system for computer-aided assessment in Mathematics and related disciplines, with emphasis on
formative assessment. You van find all information on the website http://stack.bham.ac.uk/.
A lot of information and manuals you find after clicking on “Docs”.There you find documentation about
version 3 of STACK, which provides a question type for quizzes in Moodle. Moodle is an open-source
Moodle[2] is a Virtual Learning Environment (VLE). It is a free web application. (More information:
https://moodle.org/)
Since the Association KULeuven uses Toledo (based on Blackboard), ActiMath uses STACK on its
own, which is possible but a server with PHP functionality is needed. The exercises are accessible via
Toledo so students can make interactive excersices and can get feedback. But the exercises are not
linked to the gradebook so they cannot be used as evaluation. For ActMath, all available excersises
and the interface were translated into dutch.
Lecturers who simply want to gather questions in English can find al lot of excercises on
http://stack.bham.ac.uk/worksheets/.
Via “Demo & forums” you find documentation and forums about the installation of STACK on a server
and about building questions.
4.1
Advantages and disadvantaged of STACK
4.1.1 Advantages
STACK is open-source software, so it is free to download and to use. In addition, the package can be
freely adjusted.
STACK uses an open-source mathematical engine Maxima. This enables background calculations,
randomisation of questions,…
There is already a large amount of questions available, free for use, in English. You can find this
questions on http://stack.bham.ac.uk/worksheets/.
The interface of STACK is relatively easy to translate.
STACK v3. can be used in Moodle.
4.1.2 Disadvantages
If STACK is used on its own, you need a server with PHP functionality. To install and implement the
package you need sufficient knowledge. The maintenance of the sever also requires time and specific
knowledge.
Making questions is not simple, you need to learn the specific terminology.
Since STACK questions cannot be linked to the grade book of Blackboard, it can only be used as a
practising tool, not for evaluation.
REFERENCES
[1]
T. NEIJENS et al. (2011), ActiMath: A remedial course in mathematics adapted to the needs of
the student and their chosen field of study. EduLearn 2011, Barcelona, Spain
[2]
J. DEPREZ et al. (2012), Peiling wiskunde in de tweede graad algemeen secundair onderwijs.
[3]
C.J. SANGWIN, S. HAMMOND et al. (2011), STACK, http://stack.bham.ac.uk/