1) A remedial math course was offered to incoming engineering students to address high dropout rates.
2) Students who took the course (the studio group) had significantly higher average marks and success rates compared to students who did not take the course (the control group).
3) A statistical analysis found the studio group outperformed the control group across compulsory subjects, demonstrating the effectiveness of the remedial course.
Preparing Junior High School Students in Science, Technology, Engineering and...IJAEMSJORNAL
The authors applied a one group pretest-posttest quasi-experimental research design to one section of GVAHS with 45 students to look into the effectiveness of journal writing in mathematics performance consequently preparing the students to technical subjects in the STEM track of the K to 12 curricula. The findings of the study revealed that journals in mathematics produce better and improved scores for students in problem solving tasks. Likewise, journal writing helped the students communicate with their Math Teacher. It can improve their abilities on how to use mathematical tools, symbols and numbers, use math models, analyze, understand and solve problems preparing them for higher mathematics and other related sciences. Also, journal writing helped students to learn how to transfer ideas clearly and convey their feelings and thoughts effectively. Likewise, it enhanced different characteristics that they can use in pursuing the STEM track andin living in the globally competitive world of work.
`
Dr. M.THIRUNAVUKKARASU
Research Associate
Department of Education
Bharathidasan University,
Tiruchirappalli - 620 024, Tamil Nadu, India
E-mail: edutechthiru@gmail.com
Dr. S. SENTHILNATHAN
Director (FAC),
UGC - Human Resource Development Centre
(HRDC)
Bharathidasan University
Khajamalai Campus
Tiruchirappalli - 620 023
E-mail: edutechsenthil@gmail.com
Metacognitive Strategies: Instructional Approaches in Teaching and Learning o...IJAEMSJORNAL
The purpose of the study is to determine the effectiveness of the metacognitive strategies as instructional approaches in teaching and learning of Basic Calculus. A number of 48 students consisting of 24 boys and 24 girls were purposively sampled in this study. Pretest-posttest quasi experimental research design was used which applied t-test and descriptive statistics. Both groups were subject to two instruments that were comprised of problem-solving test (pretest and posttest) and observation guide. Experimental group was taught Basic Calculus using metacognitive strategies while the control group was taught Basic Calculus using traditional teaching strategies. Both groups were subject to a pretest. Class observation was done while the two teaching strategies were applied. In the end, the posttest was administered to both groups to identify the effectiveness of the two teaching strategies. The data gathered were treated using paired sample t-test and independent sample t-test. The results of the study showed that the experimental group had significantly higher posttest scores as compared to control group which proved that metacognitive teaching strategies were more effective in improving the performance and problem-solving skills of the students than the traditional teaching strategies. It was also observed that students who taught using metacognitive strategies helped the students to be extremely engaged in Basic Calculus lessons cognitively, behaviorally, and affectively. The study reveals that the significant increase of the students’ learning engagement in Basic Calculus lessons led the students to a corresponding increase in their posttest scores.
Preparing Junior High School Students in Science, Technology, Engineering and...IJAEMSJORNAL
The authors applied a one group pretest-posttest quasi-experimental research design to one section of GVAHS with 45 students to look into the effectiveness of journal writing in mathematics performance consequently preparing the students to technical subjects in the STEM track of the K to 12 curricula. The findings of the study revealed that journals in mathematics produce better and improved scores for students in problem solving tasks. Likewise, journal writing helped the students communicate with their Math Teacher. It can improve their abilities on how to use mathematical tools, symbols and numbers, use math models, analyze, understand and solve problems preparing them for higher mathematics and other related sciences. Also, journal writing helped students to learn how to transfer ideas clearly and convey their feelings and thoughts effectively. Likewise, it enhanced different characteristics that they can use in pursuing the STEM track andin living in the globally competitive world of work.
`
Dr. M.THIRUNAVUKKARASU
Research Associate
Department of Education
Bharathidasan University,
Tiruchirappalli - 620 024, Tamil Nadu, India
E-mail: edutechthiru@gmail.com
Dr. S. SENTHILNATHAN
Director (FAC),
UGC - Human Resource Development Centre
(HRDC)
Bharathidasan University
Khajamalai Campus
Tiruchirappalli - 620 023
E-mail: edutechsenthil@gmail.com
Metacognitive Strategies: Instructional Approaches in Teaching and Learning o...IJAEMSJORNAL
The purpose of the study is to determine the effectiveness of the metacognitive strategies as instructional approaches in teaching and learning of Basic Calculus. A number of 48 students consisting of 24 boys and 24 girls were purposively sampled in this study. Pretest-posttest quasi experimental research design was used which applied t-test and descriptive statistics. Both groups were subject to two instruments that were comprised of problem-solving test (pretest and posttest) and observation guide. Experimental group was taught Basic Calculus using metacognitive strategies while the control group was taught Basic Calculus using traditional teaching strategies. Both groups were subject to a pretest. Class observation was done while the two teaching strategies were applied. In the end, the posttest was administered to both groups to identify the effectiveness of the two teaching strategies. The data gathered were treated using paired sample t-test and independent sample t-test. The results of the study showed that the experimental group had significantly higher posttest scores as compared to control group which proved that metacognitive teaching strategies were more effective in improving the performance and problem-solving skills of the students than the traditional teaching strategies. It was also observed that students who taught using metacognitive strategies helped the students to be extremely engaged in Basic Calculus lessons cognitively, behaviorally, and affectively. The study reveals that the significant increase of the students’ learning engagement in Basic Calculus lessons led the students to a corresponding increase in their posttest scores.
KEYWORD APPROACH AND SOLVING WORD PROBLEMS INVOLVING ADDITION OF WHOLE NUMBER WayneRavi
This study was conducted to determine the effect of keywords approach on solving word problems involving addition of whole numbers with sums up to 99,999 including money following the steps in problem solving. Results revealed that the pre test score was low; the post test score was high. There was a significant difference on the pre test and post test scores of keywords approach. Further, the keywords approach has large effect on the solving word problems involving addition of whole number.
Santiago Moll-Lopez, Jose Antonio Moraño, M.-Dolores Roselló, Luis Manuel Sánchez Ruiz and Francisco Mínguez Aroca.
Polytechnic University of Valencia (UPV)
Redesign of remedial math instruction from traditional classroom to emporium model where students work independently on computers and complete modules to prepare for college algebra.
The Effectiveness of Problem based learning Model to improve the understandin...AI Publications
The aim of the study is to find out the ability to understand mathematical concepts of teachers prospective in Mathematics Education Program FKIP University Nommensen in the fractional count operations material. This research is a descriptive study with the aim of the study describing the effectiveness of the Problem Based Learning Model. The results of the second trial described that the effectiveness of the Problem Based Learning Model was concluded: (i) the percentage of the students who understood the concept at least 85.29% or 29 students out of 34 students who took the test. (ii) the achievement of the ideal percentage of time for each category of student activity, (iii) the average of the lecturer ability to manage learning is 3.54, including the good category, (iv) student responses to the components and learning activities are positive is 90%.
The purpose of this research is to develop test questions of problem solving ability on work-energy material for high school students class X. This type of research is research and development. The model used in this study is ADDIE with the stages of analyzing, planning, developing, implementing, and evaluating, but this study only up to the implementation stage. The test developed in this research consists of three items of problem solving ability description that is multi context. Validation of item was done by content validation and empirical validation. The results of content validation indicate that the average score of test items is 3,125 with good category. The results of empirical validation indicate that there are two valid questions and one invalid question. Two valid questions have a Cronbach Alpha coefficient of 0.807. The results of the implementation of the test showed that the average student problem solving abilities in Question 1 is 17.41 of a maximum score of 25, the lowest score is 10 and the highest is 23. The results of students in the question number 2 by 16.60 of a maximum score of 25, with the lowest score is 10 and the highest is 22. These results indicate that the test instrument is feasible to use to assess students' problem solving abilities.
The study explores the effect of Smart class on the Academic Achievement of students. The sample consisted of 60 students (15 boys & 15 girls in each group) from two higher secondary schools of Bhilai city, Durg (C.G.). The samples were taken from class VIII students having academic achievement of 60% to 65% of scores in the formative assessments and first Summative assessment. An academic achievement test developed by both the subject teachers was used as data collection tool. The thirty students, fifteen boys and fifteen girls, from the first school formed the experimental group and same number of boys and girls from the second school was treated as control group. The experimental group was taught a topic from Science subject through smart class and the control group was taught the same topic through the traditional method of teaching. An achievement test was administered to both the groups after the completion of topic. Scores were analysed to find out which group fared better.
This includes the process how you can construct a test for academic achievement of the students. Characteristics, principles, types, steps all are discussed here. Calculation of weightage and difficulty level and also making of blue print is also included.
EVALUATION OF STUDENT PERCEPTIONS ON “MUDDIEST POINT” CLASSROOM ASSESSMENT TE...John1Lorcan
The purpose of this study is to use “Muddiest point” classroom assessment technique as a type of formative
assessment in Software Development Practices (ICT) course at University of Vocational Technology and to
assess student perceptions on the technique. The study employed “Muddiest point” classroom assessment
technique in the class and conducted a perception survey with regard to use of muddiest point assignments
at the end of the course. As per the survey A majority of students 30 numbers agreed that Muddiest Point
CAT is beneficial to the course (Mean =4.24 n=45) and 28 agreed Muddiest point CAT to be continued in
the course.(Mean=4.22) 24 students agreed that The Muddiest Point CAT should be applied to other
courses as well (Mean=4.18. 53% of students satisfied with the use of Muddiest point CAT for Classroom
learning and 31% were extremely satisfied . The perception survey showed positive overall student
perception on CAT used. And the technique can be used as a simple, but effective formative assessment
method for Software Development Practices (ICT) course.
The Implementation Of Concept Main Map In Basic Calculation Of Engineering Su...IJERD Editor
This research began from problem in spacious about teaching and learning by doing where is the method learning is not effective because used descriptive subject mater with writing on black board or descriptive by essay. In order that is not efficient and effective in used teaching and the student can not comprenship understand? With this method will hope can handle it. The used method in this research is classroom action and focus at pump and compressor subject mater in Basic Calculation of Engineering subject. This research was doing in Makassar State University with subject 15 students at machine department. The instrument is used test, interview, observation, and spacious writed. In this learning method is development 5 concept, they are congcrete concept, abstract concept with example kongret concept, abstract concept, concept that process basic and concept with principle. The result of this research showing with mapping concept method in pump and compressor subject, that have improvement competition students at the last siklus II is 7,0 – 10 or 86,67% is mean the students can said that they are competent in learning.
Confidence is key: a successful approach to teaching statisticsLearningandTeaching
Teaching statistics has increasingly been regarded as a complex mission to accomplish as it consists of many different mathematical components with many variables. Despite extensive research work in developing education in statistics, this discipline still requires significant improvement in how it is taught. Most students at university have a lack of interest in undertaking statistics courses due different factors - some of them are related to teaching techniques and others are related to method of assessment.
In these slides, Saad Odeh presents an effective teaching technique in statistics developed by SIBT teachers. Rather than enabling the cohort by providing them with extra help to progress in statistics, the idea was to improve their confidence when they do the major assessment, 'the final exam'.
TEACHING STRATEGIES TO ENHANCE MATHEMATICAL THINKING FROM ENVIRONMENTAL SITUA...Eugenio Theran Palacio
In this work we report research results that reference the title. The project was developed in freshmen, Basic Education, through sociocultural problem situations and science under a qualitative design in three phases: design and implementation of a diagnostic test for recognition of potential difficulties of students, classroom intervention, to overcome the difficulties encountered, and contrast test to assess the achievement of the strategies applied and obtain information for improving student learning.
KEYWORD APPROACH AND SOLVING WORD PROBLEMS INVOLVING ADDITION OF WHOLE NUMBER WayneRavi
This study was conducted to determine the effect of keywords approach on solving word problems involving addition of whole numbers with sums up to 99,999 including money following the steps in problem solving. Results revealed that the pre test score was low; the post test score was high. There was a significant difference on the pre test and post test scores of keywords approach. Further, the keywords approach has large effect on the solving word problems involving addition of whole number.
Santiago Moll-Lopez, Jose Antonio Moraño, M.-Dolores Roselló, Luis Manuel Sánchez Ruiz and Francisco Mínguez Aroca.
Polytechnic University of Valencia (UPV)
Redesign of remedial math instruction from traditional classroom to emporium model where students work independently on computers and complete modules to prepare for college algebra.
The Effectiveness of Problem based learning Model to improve the understandin...AI Publications
The aim of the study is to find out the ability to understand mathematical concepts of teachers prospective in Mathematics Education Program FKIP University Nommensen in the fractional count operations material. This research is a descriptive study with the aim of the study describing the effectiveness of the Problem Based Learning Model. The results of the second trial described that the effectiveness of the Problem Based Learning Model was concluded: (i) the percentage of the students who understood the concept at least 85.29% or 29 students out of 34 students who took the test. (ii) the achievement of the ideal percentage of time for each category of student activity, (iii) the average of the lecturer ability to manage learning is 3.54, including the good category, (iv) student responses to the components and learning activities are positive is 90%.
The purpose of this research is to develop test questions of problem solving ability on work-energy material for high school students class X. This type of research is research and development. The model used in this study is ADDIE with the stages of analyzing, planning, developing, implementing, and evaluating, but this study only up to the implementation stage. The test developed in this research consists of three items of problem solving ability description that is multi context. Validation of item was done by content validation and empirical validation. The results of content validation indicate that the average score of test items is 3,125 with good category. The results of empirical validation indicate that there are two valid questions and one invalid question. Two valid questions have a Cronbach Alpha coefficient of 0.807. The results of the implementation of the test showed that the average student problem solving abilities in Question 1 is 17.41 of a maximum score of 25, the lowest score is 10 and the highest is 23. The results of students in the question number 2 by 16.60 of a maximum score of 25, with the lowest score is 10 and the highest is 22. These results indicate that the test instrument is feasible to use to assess students' problem solving abilities.
The study explores the effect of Smart class on the Academic Achievement of students. The sample consisted of 60 students (15 boys & 15 girls in each group) from two higher secondary schools of Bhilai city, Durg (C.G.). The samples were taken from class VIII students having academic achievement of 60% to 65% of scores in the formative assessments and first Summative assessment. An academic achievement test developed by both the subject teachers was used as data collection tool. The thirty students, fifteen boys and fifteen girls, from the first school formed the experimental group and same number of boys and girls from the second school was treated as control group. The experimental group was taught a topic from Science subject through smart class and the control group was taught the same topic through the traditional method of teaching. An achievement test was administered to both the groups after the completion of topic. Scores were analysed to find out which group fared better.
This includes the process how you can construct a test for academic achievement of the students. Characteristics, principles, types, steps all are discussed here. Calculation of weightage and difficulty level and also making of blue print is also included.
EVALUATION OF STUDENT PERCEPTIONS ON “MUDDIEST POINT” CLASSROOM ASSESSMENT TE...John1Lorcan
The purpose of this study is to use “Muddiest point” classroom assessment technique as a type of formative
assessment in Software Development Practices (ICT) course at University of Vocational Technology and to
assess student perceptions on the technique. The study employed “Muddiest point” classroom assessment
technique in the class and conducted a perception survey with regard to use of muddiest point assignments
at the end of the course. As per the survey A majority of students 30 numbers agreed that Muddiest Point
CAT is beneficial to the course (Mean =4.24 n=45) and 28 agreed Muddiest point CAT to be continued in
the course.(Mean=4.22) 24 students agreed that The Muddiest Point CAT should be applied to other
courses as well (Mean=4.18. 53% of students satisfied with the use of Muddiest point CAT for Classroom
learning and 31% were extremely satisfied . The perception survey showed positive overall student
perception on CAT used. And the technique can be used as a simple, but effective formative assessment
method for Software Development Practices (ICT) course.
The Implementation Of Concept Main Map In Basic Calculation Of Engineering Su...IJERD Editor
This research began from problem in spacious about teaching and learning by doing where is the method learning is not effective because used descriptive subject mater with writing on black board or descriptive by essay. In order that is not efficient and effective in used teaching and the student can not comprenship understand? With this method will hope can handle it. The used method in this research is classroom action and focus at pump and compressor subject mater in Basic Calculation of Engineering subject. This research was doing in Makassar State University with subject 15 students at machine department. The instrument is used test, interview, observation, and spacious writed. In this learning method is development 5 concept, they are congcrete concept, abstract concept with example kongret concept, abstract concept, concept that process basic and concept with principle. The result of this research showing with mapping concept method in pump and compressor subject, that have improvement competition students at the last siklus II is 7,0 – 10 or 86,67% is mean the students can said that they are competent in learning.
Confidence is key: a successful approach to teaching statisticsLearningandTeaching
Teaching statistics has increasingly been regarded as a complex mission to accomplish as it consists of many different mathematical components with many variables. Despite extensive research work in developing education in statistics, this discipline still requires significant improvement in how it is taught. Most students at university have a lack of interest in undertaking statistics courses due different factors - some of them are related to teaching techniques and others are related to method of assessment.
In these slides, Saad Odeh presents an effective teaching technique in statistics developed by SIBT teachers. Rather than enabling the cohort by providing them with extra help to progress in statistics, the idea was to improve their confidence when they do the major assessment, 'the final exam'.
TEACHING STRATEGIES TO ENHANCE MATHEMATICAL THINKING FROM ENVIRONMENTAL SITUA...Eugenio Theran Palacio
In this work we report research results that reference the title. The project was developed in freshmen, Basic Education, through sociocultural problem situations and science under a qualitative design in three phases: design and implementation of a diagnostic test for recognition of potential difficulties of students, classroom intervention, to overcome the difficulties encountered, and contrast test to assess the achievement of the strategies applied and obtain information for improving student learning.
This research aimed to determine the effectiveness of the issue, discussion,
establishment, and application (IDEA) learning model in embedding
mathematical concepts understanding. It is a quantitative study with a quasiexperimental
approach. This research was conducted at Malang Islamic
University with students majoring Mathematics education study program
and in their first academic year as the subjects. Subjects were divided into
two group, experimental and control and measured their result using posttest
only control group design. There are six instruments consisting six items
used to measure mathematical concepts understanding. The results
confirmed that H0 is rejected, while Ha is accepted proved by t count
(3.132)>ttable (1.674). It means there is a significant difference between the
of both groups (experimental and control). In addition, the results indicated
that the IDEA learning models is effective to assist students in understanding
mathematical concepts showed by the higher score of experimental groups
than control group. Three factors are involved in order to implement the
IDEA learning model effectively; namely: individual problem-solving
opportunities, active student involvement, and guidance and assistance (from
lecturer) on the IDEA learning model. This research is only limited to
preservice teacher, further research is required in order to implement this
model for mathematics learning at junior and senior high schools’ level.
Effectiveness of Division Wheel in Basic Mathematics Operation Case Study: Pr...iosrjce
Mathematics is important in everyday life. Mathematics involve with the concept of addition,
subtraction, multiplication, and division. Advance topic in mathematics may cause students to experience
difficulty catching up with the syllabus, especially as a majority primary students are not able to understand
basic concept of division. Therefore, this research study has been conducted to determine the effectiveness of
‘division wheel’ in mathematics division operations. The target for sample size is 400 respondents involving
only standard five in between excellent, moderate and poor classes. This research study involves a
questionnaire using the Likert scale, while the analysis used is descriptive analysis. A test will be carry out
before (pre-test) and after (post-test) teaching method using ‘division wheel’. Pre-test analysis shows majority
male respondents have poor achievement, while female respondents have moderate achievement. After applied
the ‘division wheel’, there are increasing numbers for excellent and moderate achievement for male respondents
and excellent for female respondents after taking post-test. Questionnaire results shows that the majority of
students prefer to use ‘division wheel’ as concrete material in learning process. ‘Division wheel’ had helps
students understand the concept of basic division operation and confident to answer question properly without
teacher’s help. Students start to love doing mathematics especially divide questions. In conclusion, the ‘division
wheel’has become a new method in mastering the concept of division.
CONCEPTUAL APPROACH AND SOLVING WORD PROBLEM INVOLVING MULTIPLICATION OF WHOL...WayneRavi
This study was conducted to determine the effect of conceptual approach on solving word problems involving multiplication of whole numbers as well as addition and subtraction. The study was carried out in Tambongon Elementary School to Fourty-one Grade Two students. Descriptive statistics (mean & SD), paired-sample T-test and ETA2 were used as tools in the analysis of data. Results revealed that there was a significant difference on the pretest and post test scores of conceptual approach. Further, conceptual approach has large effect.
REALITY – BASED INSTRUCTION AND SOLVING WORD PROBLEMS INVOLVING SUBTRACTIONWayneRavi
This study was conducted to determine the effect of reality based on the solving word problems involving subtraction. Descriptive-Comparative research design using paired sample T-test was used to utilized in the study. The study was carried out in Tibungol Elementary School to Fifty student of Grade Three section 1. Results revealed that there was a significant difference on the pretest and post test scores of pupils in reality based approach. Further, the reality based approach is effective in improving the performance of student.
Investigating learning strategies in a dispositional learning analytics conte...Bart Rienties
This study aims to contribute to recent developments in empirical studies on students’ learning strategies, whereby the use of trace data is combined with self-report data to distinguish profiles of learning strategy use [3, 4, 5]. We do so in the context of an application of dispositional learning analytics in a large introductory course mathematics and statistics, based on blended learning. Building on our previous work which showed marked differences in how students used worked examples as a learning strategy [7, 11], this study compares different profiles of learning strategies with learning approaches, learning outcomes, and learning dispositions. One of our key findings is that deep learners were less dependent on worked examples as a resource for learning, and that students who only sporadically used worked examples achieved higher test scores.
Are Remedial courses Effective for Engineering Incoming Students?
1. Are Remedial courses Effective for Engineering Incoming Students?∗∗∗∗
M. G. SÁNCHEZ-TORRUBIA, R. MARTÍNEZ-LÓPEZ, E. E. CASTIÑEIRA-HOLGADO
Applied Mathematics Department (DMA)
Universidad Politécnica of Madrid (UPM)
Campus de Montegancedo s.n. Boadilla del Monte (Madrid)
SPAIN
gsanchez@fi.upm.es, rmlopez01@gmail.com, ecastineira@fi.upm.es,
Abstract: - A Remedial+Reinforcement course in Mathematics was offered to Informatics Engineering
incoming students trying to reduce their high dropping and failure ratios. This paper presents several statistical
analyses of their results comparing the marks obtained by those joining the course (studio group) versus those
who did not participate (control group). The results clearly demonstrate that there are significant differences
between both groups, with the studio group consistently outperforming the control group, which proves the
effectiveness of the experience.
Key-Words: - Remedial courses, educational research, mathematics learning, informatics curricula
∗
This work has been partially supported by UPM under projects No. IE06 1010-092 and IE07 1010-029
1 Introduction
As a matter of fact, engineering incoming students
are facing great difficulties to overcome first course
subjects, thus, dropping and failure ratio grow to be
very high among freshmen.
Among the causes of these problems, we should
consider the difference in didactical methodologies
between University and Secondary School: groups
are bigger and students have to become responsible
of managing their own duties, while they are not
conscious enough of the tremendous change they
would have to attain concerning their studying
schemes. Besides, as students are not trained to face
effort and responsibility, they do not have daily
study habits and do not worry if they do not end
their careers in a reasonable time. Anyway, most of
the mentioned difficulties come from the poor level
in math knowledge and logical reasoning acquired
during their secondary education.
Unfortunately, the expounded problem is in fact
rather extended to other engineering studies. Most
technical careers show also rising drop and failure
rates, which makes mandatory to find an effective
way to manage the crisis.
To tackle that situation and increase the students’
success, most universities are trying diverse
solutions, usually remedial or reinforcement
courses, just before or during the first semester ([3],
[5], [10]).
In the fall of 2005, the Department of Applied
Mathematics at Informatics Engineering of
Universidad Politécnica of Madrid, implemented a
remedial + reinforcement course in mathematics,
which was offered to incoming students.
Previous studies, analyzing this course’s impact
on June’s exams marks, provided pretty
encouraging records (see [6], [7], [8]), so we
continued investigating its impact on the final marks
of first year compulsory subjects, including not only
those who passed in June’s exams but those who
succeeded in September’s second opportunity as
well. Data obtained are quite relevant: the means of
the marks obtained by the students show a
statistically significant difference between the
students who joined the course matched up to those
who did not participate, averaging the first ones
higher than their matched counterparts. As a main
effect, it is important to mention a remarkable raise
of passed versus a decrease of drop out for every
first course’s compulsory subject.
2 Scenario
Many incoming students on Informatics
Engineering at Universidad Politécnica of Madrid
are overwhelmed by first course subjects and,
among them, dropping and failure ratio are getting
higher every year.
As stated above, these difficulties are mainly due
to the poor level in math knowledge acquired during
their secondary education (pre university level). In
Sept. 2005, an initial competence test, consisting of
6th WSEAS International Conference on EDUCATION and EDUCATIONAL TECHNOLOGY, Italy, November 21-23, 2007 74
2. 20 questions of secondary school math contents,
four options each, was taken by a 94 students group
joining Informatics Engineering at our University.
In this test [9], as shown in Figure 1, 65.96% failed
more than 10 questions while only 12.77% failed six
or less. Furthermore, most of them had never used
symbolic language as sets, quantifiers or
propositional logics. With this lack of background,
together with a significant deficiency in abstract and
logical reasoning, first course subjects become an
insurmountable obstacle for incoming students.
21,3%
20,2%
24,5%
21,3%
8,5%
2,1% 2,1%
0%
10%
20%
30%
ν<6 6≤ν<8 8≤ν<10 10≤ν<14 14≤ν<18 18≤ν<20 ν=20
Fig. 1: Number of correct answers in the 2005 initial
competence test
An optional curricular complement was proposed
in order to increase the students’ success: a
Remedial+Reinforcement course in mathematics
called "Introduction to Mathematical Methodology"
taught to 24 freshmen from September 2005 to
January 2006.
2.1 Course’s structure
The proposed course combined remedial with
reinforcement training in two differentiated blocks:
First part consisting on 45 hours during September
(before the regular course started). Within that
period, an overall review of the main concepts
extracted from secondary curricula was presented
(with special emphasis on precalculus and basic
algebra), highlighting intuition, logical reasoning
and self-developed methods. A basic overview of
set theory, relations and quantifiers notation was
also included, since those concepts set up the basis
for math language development. The course did not
contain specific Formal Logics topics, as this
subject starts from scratch.
The second part, which ran along with the
regular first semester, was a reinforcement course.
During it, they were asked to solve some exercises
using Maple software in order to strengthen the
concepts imparted in the following math subjects:
Discrete Mathematics, Linear Algebra and Calculus.
The applied methodology consisted in working
with small groups (20 to 30 people who joined the
course voluntarily) and developing together an
intuitional and practical vision of mathematics. The
teacher promoted direct communication within the
group, trying to guide the students in such a way
that they could reach the proposed problems’
solutions by themselves, encouraging them to use
self-developed methods, better than learned ones. In
this way, the students were provided with new
approaches to catch the concepts as well as
intuitional approximations to the learned methods.
2.2 Students’ opinion
To get a measure of the students’ perception, they
fulfilled a questionnaire at the end of the first part,
rating up to 4 over 5 both contents and methodology
of the course.
During one-to-one interviews, after the first
semester’s examinations, the students valued the
experience very positively. They considered
especially beneficial the following facts: it was a
small group, the work was customized to their
needs, it meant a more rational and less memory
based approach to mathematics and finally, they
appreciated very much the possibility of using
Maple software. They ended remarking an increase
on self-confidence and the revision of topics facing
the beginning of the course, as positive
achievements.
2.3 Data description
We have performed a comparison between two
groups of students: the studio group, which consists
of 24 incoming students who joined the remedial
course, and the control group, which comprises the
remaining 99 students who enrolled in Informatics
Engineering on June 2005. The total number of
incoming students that year was 198; the remaining
75 have been excluded because they enrolled in
September and did not have the opportunity to join
the course.
The comparison includes compulsory subjects’
marks, and dropping and success’ percentages. The
students joining the remedial course were mixed up
with the remaining students and distributed in
groups for compulsory subjects. Thus the professors
teaching those subjects and the evaluation process
have no influence on the marks obtained by both
groups.
6th WSEAS International Conference on EDUCATION and EDUCATIONAL TECHNOLOGY, Italy, November 21-23, 2007 75
3. In first course, there are seven compulsory
subjects, four within math fields (Calculus, Linear
Algebra, Formal Logics and Discrete Mathematics),
plus Programming Methodology, Foundations of
Hardware and Physics Foundations of Informatics.
The marks a student can get are: P (when the
students did not take the exams), S (if they took but
did not pass the exam) and a numeric value from 5
to 10 according to their learning level. Since
numeric values are required in order to calculate
means, we have defined P=0 and S=2.5 as an
average approximation.
3 Analysis
The impact of the remedial course has been
analyzed by studying three types of comparisons:
• For each student the arithmetic mean of the
obtained marks has been calculated and the two
groups’ data have been compared.
• For each compulsory subject the dropping and
success percentages of both groups have been
compared.
• A multifactor analysis of variance for marks has
been performed to determine which factors have
a statistically significant effect on marks. Apart
from this, it also allows to examine for significant
interactions amongst the factors.
3.1 Comparison of arithmetic means
Data compared here are, for each student, the
arithmetic mean of the marks obtained in
compulsory subjects.
Control G. Studio G.
Count 99 24
Average 2.902 3.69333
Variance 4.93926 4.89898
Standard deviation 2.22245 2.21336
Range 8.22857 7.57286
Stnd. skewness 2.57047 0.120151
Stnd. kurtosis -0.965559 -0.925003
Table 1: Summary Statistics for arithmetic means
According to 2.3 we are studying the whole
population enrolled in Informatics Engineering on
June 2005. The standardized skewness value outside
the normal range in Control Group is due to the
huge dropping and failure ratios.
Fig2 compares the means obtained by the
components of both groups.
Means Control G.
Means Studio G.
percentage
-1 1 3 5 7 9 11
30
20
10
0
10
20
30
Fig. 2: Histogram of means
3.1.1 Comparison of means for students’
arithmetic means
95% confidence interval for mean of Control G.:
2.902 +/- 0.44326 [2.45874, 3.34526]
95% confidence interval for mean of Studio G.:
3.69333 +/- 0.934623 [2.75871, 4.62796]
95.0% confidence interval for the difference
between the means assuming equal variances:
-0.791337 +/- 1.00032 [-1.79165, 0.20898]
T-test to compare means
Null hypothesis: mean Control G = mean Studio G
Alt. hypothesis: mean Control G < mean Studio G
Assuming equal variances: t = -1.67077 and
P-Value = 0.0486756
The T-test has been constructed to determine
whether the difference between the two means
equals 0 versus the alternative hypothesis that the
difference is below 0. Since the computed P-value is
less than 0.05, we can reject the null hypothesis in
favor of the alternative, what means that there is a
statistically significant difference between the
means of the two groups, with the mean of the
control group lower than the mean of the studio
group at the 95.0% confidence level.
These results assume that the variances of the
two samples are equal. In this case, that assumption
appears to be reasonable based on the results of an
F-test to compare the standard deviations that gives
a P-value of 0.808785.
Box-and-Whisker Plot
Means
0
2
4
6
8
10
Control G. Studio G.
Fig. 3: Arithmetic means comparison
6th WSEAS International Conference on EDUCATION and EDUCATIONAL TECHNOLOGY, Italy, November 21-23, 2007 76
4. 3.2 Drop out and success
Tables 2 – 3 and figures 4 – 5 represent the
comparison between the dropping rates of incoming
students who did not join the course matched up
with those who joined the course in the compulsory
subjects taught in the first year: Linear Algebra
(LAlg) Discrete Mathematics (Disc), Calculus
(Calc), Programming Methodology (Prog), Formal
Logics (Log), Foundations of Hardware (FHw) and
Foundations of Physics (FPh). Data are expressed in
percentage on the group totals.
17%
38%
27%
34%
8%
29%
17% 13%
8%
21%
51%
53%
33%
9%
0%
10%
20%
30%
40%
50%
60%
LAlg Disc Calc Prog Log FHw FPh
Studio G. Control G.
Fig. 4: Dropping rates
LAlg Disc Calc Prog Log FHw FPh
Studio
G
16.7 8.3 37.5 29.2 16.7 12.5 8.3
Control
G
26.8 9.3 53.1 50.5 33.0 33.7 21.2
Table 2: Dropping rates
63%
50%
38%
42%
50%
42%
46%
51%
52%
26%
28%
40%
36%
30%
0%
10%
20%
30%
40%
50%
60%
70%
LAlg Disc Calc Prog Log FHw FPh
Studio G. Control G.
Fig. 5: Success rates
LAlg Disc Calc Prog Log FHw FPh
Studio
G
62.5 50.0 37.5 41.7 50.0 41.7 45.8
Control
G
50.5 51.5 25.5 28.3 40.4 35.7 30.3
Table 3: Success rates
From these data it is clear that:
• Studio group’s success ratio is higher in every
compulsory subject, with the exception of
Discrete Mathematics, reaching the difference of
nearly 16% in Foundations of Physics.
• Drop out percentages diminish in every subject.
• Dropping ratios difference rises to more than
21% in Programming Methodology and
Foundations of Hardware.
• The Studio group clearly outperforms the Control
group
3.3 Multifactor analysis
A multifactor analysis of variance (ANOVA) was
selected to investigate the effects of different factors
(in this case, the subject and the belonging group)
and their interactions on the students’ marks. Table
4 summarizes the results. Though the subject is
introduced as a factor, it is not relevant to our
analysis, since is well-know that students behave
differently in front of diverse subjects.
Source
Sum of
Squares
Df
Mean
Square
F-Ratio P-Value
MAIN EFFECTS
A: Subject 236.488 5 39.4147 5.65 0.0000
B: Belonging
group
100.546 1 100.546 14.42 0.0001
INTERACTIONS
AB 12.6554 6 2.10923 0.30 0.9357
RESIDUAL 5907.09 847 6.97414
TOTAL
(CORRECTED)
6403.6 860
Table 4: Analysis of Variance for Marks -
Type III Sums of Squares
The ANOVA table decomposes the variability of
the marks into contributions due to each of the
factors. Since P-value for belonging group is less
than 0.001, this factor has a statistically significant
effect on marks at 99% confidence level.
Interactions & 90,0 % LSD intervals
Subject
Marks
Control Group
Studio Group
1,5
2,5
3,5
4,5
5,5
Calc Disc FHw FPh LAlg Log Prog
Fig. 6: Comparison by subject
Figure 6 shows the differences on marks’
averages by subjects and the Least Significant
Differences intervals at 90% confidence level. It is
6th WSEAS International Conference on EDUCATION and EDUCATIONAL TECHNOLOGY, Italy, November 21-23, 2007 77
5. clear that considering the subjects separately, in
most cases there is a statistically significant
difference among both groups, with the studio group
surpassing the control group.
Method: 99 percent LSD
Belonging
group
Count LS Mean LS Sigma
Homogeneous
Groups
Control
Group
693 2.87388 0.100318 X
Studio Group 168 3.73619 0.203747 X
Contrast Difference +/- Limits
Control Group - Studio Group *-0.862309 0.373554
* denotes a statistically significant difference.
Table 5: Multiple Range Tests for Marks by Belonging
group
Table 5 and Figure 7 show the least squares
mean of each group marks. It also shows the
standard error of each mean, which is a measure of
its sampling variability.
Fig. 7: Comparison of belonging group factor
They evidence a statistically significant
difference between both groups at 99% confidence
level and prove the impact of the presented course
on students’ results.
4 Conclusions
From the above exposed, the following conclusions
may be obtained:
• There is a statistically significant difference
between the means of the two groups, with the
mean of the control group lower than the mean of
the studio group at the 95.0% confidence level.
• Studio group’s success ratios are higher, except
for Discrete Mathematics, reaching a difference
of nearly 16%, while drop out ratios are, except
for one case, visibly lower with a difference
rising up to more than 21%.
• Considering the subjects separately, in most
cases, there is a statistically significant difference
among both groups.
• Once having removed the effect of other factors,
the fact of belonging to the studio group has a
statistically significant effect on the marks at the
99% confidence level.
• The lack of mathematical basis and reasoning
ability results in high dropping and failure ratios.
• Both enhanced reasoning and analyzing ability
must get the credit for outstanding results in math
as well as non math subjects.
The results clearly demonstrate that there are
significant differences between both groups, with
the studio group consistently outperforming the
control group, which proves the effectiveness of the
experience. Consequently, the convenience of
complementing Engineering Curricula by means of
a Remedial/Reinforcement course like the presented
one is inferred. Thus, incoming students’ negative
results might be amended.
Additionally, the development of mathematical
reasoning entails an enhancement in logical and
abstract reasoning, needed in other first course
subjects. Therefore, as we had suspected ([6], [7],
[8]), the course’s positive impact has spread to
every subject’s outcomes.
After this analysis, the requirement of improving
the alumni’s mathematical basis is clear. Math
constitutes a foundation for every science or
engineering topic, as it is an essential tool for
modeling, as well as a main language. Apart from
this fact, but not less important, there is an increase
in logical reasoning capacity as well as scientific
method provided by math.
References:
[1] American Diploma Project report. Ready or
not: Creating a high school diploma that
counts. The American Diploma Project 2004.
[2] Grubb, W.N. From Black Box to Pandora's
Box: Evaluating Remedial/Developmental
Education. CCRC Brief No. 11. New York:
Columbia University, Teachers College,
Community College Research Center. 2001.
[3] Gutierrez Labory, E.M. Cursos de
armonización de conocimientos, una
experiencia docente. IX Congreso
Internacional de Expresión Gráfica
Arquitectónica. 287-289. 2002. (in Spanish)
[4] Martel Escobar, M.C., et al. Estrategias para el
Aprendizaje Electrónico en las Matemáticas
para las ciencias Económicas y Empresariales
en el marco del EEES.
http://www.webs.ulpgc.es/eaematee/. (2005).
(in Spanish)
Means and 99,0 Percent LSD Intervals
Belonging group
Marks
Control Group Studio Group
2,6
3
3,4
3,8
4,2
6th WSEAS International Conference on EDUCATION and EDUCATIONAL TECHNOLOGY, Italy, November 21-23, 2007 78
6. [5] Reyes, P.J., et al. Estrategias docentes dirigidas
a incrementar la eficacia del proceso
enseñanza-aprendizaje en alumnos de primer
curso de ingeniería. Proc. 3er
Congreso
Internacional Docencia Universitaria e
Innovación, (vol 1), no. 281, 2004. (in Spanish)
[6] Sánchez-Torrubia M.G., Castiñeira-Holgado
E.E., Giménez-Martínez, V. Analysis of a
Remedial+Reinforcement Course’s impact on
Informatics Engineering first course rates.
WSEAS Transactions on Advances in
Engineering Education Issue 11 Vol. 3,
November 2006 pp. 984-990.,
[7] Sánchez-Torrubia M.G., Castiñeira-Holgado
E.E., Giménez-Martínez, V. The Convenience
of Remedial and/or Reinforcement Courses in
Engineering Curricula. Proc. 5th
WSEAS
International Conference on Education and
Educational Technology (EDU'06), 2006.
[8] Sánchez-Torrubia M.G., Giménez-Martínez, V.
Remedial course in mathematics for Computer
Science new income students: experience and
impact. Proc. 3rd
International Conference on
the Teaching of Mathematics, 2006.
[9] Universidad Politécnica de Madrid. Results of
the 2005 initial competence test.
[10] Universität Dortmund. Vorkurs in Mathematik
2006. http://www.mathematik.uni-dortmund.de/
vorkurs/vorkurs.nhtml (in German)
6th WSEAS International Conference on EDUCATION and EDUCATIONAL TECHNOLOGY, Italy, November 21-23, 2007 79