METHODS AND TECHNIQUES OF TEACHING MATHEMATCS
IN COLLEGES OF ENGINEERING IN IRAQ
Muhammad Fadhel Jaf
Tula State University, Tula
Learning mathematics is a key fundamental in every education system that aims to
prepare its citizens for a productive life in the 21st century[1]. Mathematics is important to an
individual and for national and international development [2].Many countries are paying
attention to the quality of their mathematics education. At the individual level, mathematics
underpins many aspects of our everydayactivities, from making sense of information in the
newspaper to making informed decisions about personal finances. It supports learning in
many fields of study, whether it is in the sciences or in business. A good understanding of
basic mathematics is essential wherever calculations, measurements, graphical interpretations
and statistical analysis are necessary. The learning of mathematics also provides an excellent
vehicle to train the mind, and to develop the capacityto think logically, abstractly, critically
and creatively. We must imbue these important 21-century competencies in our students, so
that they can lead a productive life and be life-long learners.
Students have different starting points. Not all will have the same interests and natural
abilities to learn mathematics. Some will find it enjoyable; others will find it challenging.
Some will find the theorems and results intriguing; others will find the formulae and rules
bewildering. It is therefore important for the mathematics curriculum to provide differentiated
pathways and choices to support every learner in order to maximize their potential. The
curriculum must engage the 21-century learners, who are digital natives comfortable with the
use of technologies and who work and think differently. The learning of mathematics must
take into cognizance the new generation of learners. It is the goal of the national mathematics
curriculum to ensure that all students will achieve a level of mastery of mathematics that will
serve them well in their lives, and for those who have the interest and ability, to pursue
mathematics at the highest possible level. Students begin to learn mathematics from the day
they start formal schooling, and minimally up to the end of secondary education. This gives
every child at least 10 years of meaningful mathematics education[1].
A classroom teaching experiment intended to elicit a high frequency of creative
mathematical thinking is reported [4]. To indicate that the skill and the professional
knowledge of the teacher who mediates the interaction, and facilitates the development of
pupils’ creative responses at the interface of technology, which is critical to the enhancement
of the whole-class teaching and learning processes [5].
For the gifted mathematics student, Traditional teaching methods involving
demonstration and practice using closed problems with predetermined answers insufficiently
prepare students in mathematics and discuss the issues and implications for the teaching of
mathematics [6]. Teaching experiment’ as “a series of teaching episodes and individual
interviews that covers an extended period of time”. The teaching experiment is part of a
broader study of the role of optimism in collaborative problem solving. To gain insights into
group ‘collaboration’ in class, access to collaborative activity was required. ‘Collaboration’,
for the purposes of this study involves groups working together beyond their present
conceptual level to explore questions they spontaneously set themselves because of
identifying unfamiliar complexities and deciding to unravel them [4].
Creativity" is a highly complex phenomenon, and for some people it seems to be
somehow incompatible with mathematics teaching. The traditional style of working in the
mathematics classroom seems not to allow many creative ideas. To develop and further
creativity in mathematics education teachers and students need more than a correct and solid
mathematical knowledge [7].
All students can learn math through acting out math problems; for instance, go on
Internet fieldtrips with a typically able peer and manipulate tangible objects that help them to
concretize abstract concepts. By using the strategies and approaches in this article, teachers
can help support the teaching of language acquisition while teaching the content area. In
reality, these strategies really are just best practice for the teaching of mathematics in general
[8]. The first thing to understand is that mathematics is an art.
Part of the problem is that nobody has the faintest idea what it is that mathematicians
do. The common perception seems to be that mathematicians are somehow connected with.
Science perhaps they help the scientists with their formulas, or feed big numbers into
computers for some reason or other. There is no question that if the world had to be divided
into the “poetic dreamers” and the “rational thinkers” most people would place
mathematicians in the latter category. Nevertheless, the fact is that there is nothing as dreamy
and poetic, nothing as radical, subversive, and psychedelic, as mathematics. It is every bit as
mind blowing as cosmology or physics (mathematicians conceived of black holes long before
astronomers actually found any), and allows more freedom of expression than poetry, art, or
music (which depend heavily on properties of the physical universe). Mathematics is the
purest of the arts, as well as the most misunderstood [9].
Many students dislike classes in mathematics. They give a wide variety of reasons for
this and among the most, mentioned ones are that mathematics is hard, mathematics is boring
and mostly irrelevant. Part of this problem stems from misconceptions about mathematics. It
is described as inflexible and formulaic as opposed to fun and creative [10]. The early years
are especially important for math development. Given that early math learning Predicts later
math and reading achievement, math appears to be a core component of learning and thinking
[11].
Creativity enters mathematics in three important ways different ways, are: abstraction,
connection, and research.
 The creativity of abstraction concerns the creation of models that reflect the real world
and can be solved with mathematical tools known to the individual.
 The creativity of connection is the realization that known mathematical tools can be
applied to new problems, allowing problems to be viewed in a new way. Connections are also
made when mathematical and other knowledge come together to understand and solve
problems from a variety of areas.
 The creativity of researching is the discovery of new mathematical tools that fit
unsolved problems and add to the available tools for other users of mathematics [10].
Mathematics can be used to understand important issues and to solve meaningful
problems, not just in school and colleges but also in life. By extension, the physical
environment for mathematics learning should include:
• spaces where students can use manipulative to solve problems and record their
solutions;
• board and/or wall space to display student solutions for Math Congress;
• space to post co created reference charts such as glossary terms and past and current
summaries of learning that specifically support the development of the big ideas currently
under study;
• instructional materials organized in such a way as to provide easy selection and access
for all students; may include mathematics manipulative, calculators and other mathematical
tools, mathematical texts, handheld technology [12].
Those compare the students’ success in mathematics between boys and girls in college
of engineering in Kirkuk. Fig 3 classified Alignment chart boys/girls bass/fail in mathematics
These suggest different, but not
incompatible, ways to think about
teaching mathematics in general and
teaching mathematics to teachers in
particular. Each of these perspectives
brings a particular aspect of
mathematics into sharp focus [13].
In
this
study
belief
questionnaire
included
four
statements concerning students’
beliefs
conceptions
about
mathematics, learning mathematics,
teaching
mathematics,
and
mathematics pass exams. For the
Fig 3 Classification for the alignment chart boys/girls pass/fail
classification, the statements of the
in mathematics
students by gender. To make
comparisons, the students’ answers (beliefs) were classified in Alignment chart.
The questionnaire based on their contents to the following five levels:
1.
Makecomparisons, thestudents’ answers (beliefs) were classified by gender as
showninfig 4.
2.
Make comparisons, the students’ answers (beliefs) were classified by gender in oil
department shown in fig 5.
3.
Make comparisons, the students’ answers were classified by gender in mechanical
department shown in fig 6.Make comparisons, the students’ answers were classified by
gender in electrical department as shown in fig 7.
4.
Make comparisons, the students’ answerswere classified by gender in all engineering
department’s scheme as shown in fig 8.
Develop creative mathematical thinking and problem solving or processes. By helping
they build strong foundations for learning mathematics. At the same time, understanding of
their development will grow [14].
Excellent teachers of mathematics have a strong knowledge base to draw on in all
aspect of their professional work, including their decision making, planning and interactions.
Their knowledge base includes knowledge of students, how mathematics is learned, and what
effects student’s opportunities to learn mathematics and how the learning of mathematics can
be enhanced. It also include sound knowledge and appreciation of mathematics appropriate to
the grade level and/or mathematics subject they teach [15].
1. Attitude toward Success in Mathematics
The degree to which students anticipate positive or negative consequences as a result of
success in mathematics.
2. Teacher Scale
The student’s perception of his/her teacher’s attitudes toward them as learners of
mathematics.
3. Mathematics as a Male Domain
The degree to which students see mathematics as a male, female or neutral domain [16].
Modern math teaching methodology offers various possibilities for solving the
problem of involving students in independent and research work; it develops their problem
solving skills and develops their creative thinking processes and skills. One of those
possibilities is in the area of scientific framework. The foundation of a scientific framework is
the principle of science and scientific research methods [17].
The findings of this study however show that gender differences in marks in
mathematics were not conclusive. The results also indicated that both male and female
students. In college of engineering ‘special attention was paid to the emotional memories of
the students’ math teachers, the percentage successes for boy is 57.72 % from 246 student
and the percentage for the girls are 67.94 % from 234 student. The percentage results for girls
more than percentage success for boys.
Fig 4scheme for the pass/fail boys/girls in mathematics in civil
department.
Fig 5Scheme for the pass/fail boys/girls in mathematics in oil department.
Fig 6 Scheme for the pass/fail boys/girls
mechanical department.
in mathematics in
Fig 7 Scheme for the pass/fail boys/girls in mathematics in electrical
department.
Fig 8 Scheme for the pass/fail boys/girls in mathematics in the four
departments.
To achieve this more complete knowledge, this paper aim to provide college students
opportunities:
• to connect the mathematics they are currently learning to their previous mathematical
knowledge, to applications within and outside the discipline, and to the history of the subject;
• to communicate mathematics, not just in exam settings, but also in both informal and
formal written assignments and oral presentations.
• to explore mathematics, not just in homework problems, but also in non-standard
examples, projects, and guided discovery, both inside and outside of the classroom.
The influence of the curriculum, the practices of assessment and the dominating views
and values of learning are connected. Those factors mentioned above have an effect on
teacher’s instruction. Because of the uncertainty with mathematics, teachers mainly followed
the order and the instructions of the mathematics books. The right answers were more
important than solution procedures. They were both dependent on mathematics textbooks and
they felt uncertainty with mathematics.In the end, some drawbacks in alignment chart
students are mentioned which occur due to the inappropriate treatment of science in the
teaching process.
The results were inconclusive on whether there is or no statistically significant gender
difference in the learning of mathematics among college of engineering students.Mathematics
teachers need to incorporate in their teaching. The results of the present study give strong
evidence that while girls surpass boys in flexibility dimension of mathematical creativity, in
general there is no gender difference in mathematical creativity. Where found out that while
girls surpass boys in some dimensions of mathematical creativity, boys surpass girls in other
dimensions.
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