A.
What
is Mathematics?
B. Misconception about Mathematics
The word mathematics
comes from mathematikos from the
Greek that has meaning of “inclined to learn.” At present, mathematics is looked
in three different ways:
1.
Mathematics as the sum of its branches.
In example, we have learned about
Arithmetic, Algebra, Combinatory, and Geometry through our schools. Since we
learned it, it means that we learn mathematics.
Mathematics is a queen of science, so
every science is based on mathematics. Physics, Chemistry, Biology, Geography,
Economy, Accounting, and soon are based on mathematics. Without mathematics, we
cannot learn them.
3.
Mathematics as a language.
Mathematics has a various vocabularies
and grammar that sometimes have different meaning with Bahasa Indonesia, or
English. Mathematics is used to make something unclear to be clear, make
something abstract to be understandable easily. By using mathematics as a
language in our daily live, we can solve so many problems in the real world.
B. Misconception about Mathematics
Benneth and Briggs
(2002) consider that there are six misconception about mathematics:
1.
Mathematics requires special brain
2.
The Mathematics in modern issues is too
complex
3.
Mathematics makes you less sensitive
4.
Mathematics makes no allowance for
creativity
5.
Mathematics provides exact answer
6.
Mathematics is irrelevant to my life
That’s
why so many people feel fear of mathematics or it is often called “Math
Phobia”.
C.
Problem
and Learning Difficulties in Mathematics
Many
people face the problems and difficulties when they learned mathematics because
of some reasons:
1.
Incomplete
Mastery of Number Facts
The
students are required to remember the computation. Ex: 9x8 = 72
2.
Computational
Weakness
The students are
inconsistent when they were computing, they misread the plus or minus sign,
wrong typed the numbers, wrong put the correct columns, etc.
3.
Difficulty
Transferring Knowledge
Because of the wrong
strategy that is used by the teacher, it makes the students feel difficult to
transform the abstract conceptual of mathematics into the real world.
4.
Making
Connection
The students difficult
to connect the mathematical concepts to their experience. They feel hard to
recall and apply their previous knowledge to the new situation.
5.
Incomplete
Understanding of the Language of Mathematics
The students don’t
understand mathematics because of their ability in reading, writing, and
speaking. They have difficulty in verbal and written instruction.
6.
Difficulty
Comprehending the Visual, Spatial and Perceptual Difficulties
The students have difficulty on visualizing
mathematical concept. In example is 3-D shape.
In general, so many mathematics difficulties that
exist, there are:
1.
Output
Difficulties
The
students feel hard to recall their previous knowledge.
2.
Organizational
Difficulties
The
students answer the problem not in order.
3.
Language
Difficulties
The
students don’t understand the vocabularies, or the language in the problems.
4.
Attention
Difficulties
The
students easily loss of their concentration.
5.
Visual
Spatial or Ordering Difficulties
The
students have difficulties on interpreting and manipulating geometrical shape.
6.
Difficulties
with Multiple Tasks
The
students have a bad ability in managing the tasks.
D.
The
Content Standards for Secondary Mathematics (Background)
Mathematics
has been given since elementary, even kindergarten to build and develop our
brain to be more analytically, logically, critically, systematically,
creatively, and work collaboratively. It has been set on Standard Competencies
(SC) and Basic Competencies (BC). The implementation of SC and BC are:
1. The
knowledge proficiencies and problem-solving
2. Thinking
skills
3. Creative
thinking
4. Independent
learning
5. Knowledge
application and content creation
6. Use
new well-researched and proven teaching
methodologies
7. Learning
approaches and assessment modes that are suitable for the new generation.
Teacher’s task is
making the best methods to make the students easily understand the material
appropriately.
E.
The
Goal of Learning Mathematics at Secondary School
The
students are expected to have the following capabilities:
1. Conceptual
Understanding (Understanding, explaining, and applying in appropriate way)
2. Mathematical
Reasoning (Use the pattern, reasoning, manipulating and explaining mathematical
ideas)
3. Mathematical
Problem Solving (Solving the real-life problem)
4. Mathematical
Communication (Understanding the symbol, diagrams, charts, etc)
5. Appreciate
mathematics in daily life.
F.
The
Structure of High School mathematics Curriculum in Indonesia
It
consists of SC and BC for three years. For grade X – XII, it is allocated in 4
hours in semester 1 and 2. Each hour means 45 minutes.
G.
Mathematics
Curriculum Framework (NCTM)
The
main concept of NCTM Mathematics Framework, the students must be developed in
mathematical power by problem solving, reasoning, communication, and
connection.
H.
Teaching
Mathematics and Its Standards
Teaching
Mathematics is not only merely mastering the content of mathematics, there are
four knowledge that should we have.
1. Knowledge
of content. (for this case is mathematics)
2. General
Pedagogical Knowledge. (having a good instructional strategies, classroom
management)
3. Pedagogical
Content of Knowledge. (how to present the topics in ways that are
understandable)
4. Knowledge
of Learner and Learning. (recognition how students learn, motivation, and
needs)
Standards for teaching mathematics
Based
on NCTM standards, those are”
1. Determining
the goal, then choosing or making mathematical task to help our students.
2. Stimulating
the classroom.
3. Creating
a classroom environment.
4. Analyzing
student learning.
I.
Principles
for School Mathematics (NCTM, 2000)
1. Equity.
High expectation and strong support for all students.
2. Curriculum.
It must be coherent, focused on important mathematics.
3. Teaching.
Requiring understanding what students know and need to learn.
4. Learning.
Learning mathematics by prior knowledge.
5. Assessment.
It should support the learning of importance mathematics.
6. Technology.
By technology, it helps us in so many ways.
Also,
here are some principles for school mathematics:
-
The Teaching Principles
As
a teacher, it’s no fair for our students if we don’t keep learning because they
will not get any new thought of mathematics.
-
The Use of Technology in Teaching
Mathematics
Technology
helps us to make our tasks easier.
-
The Technology Principles
Technology
cannot replace teacher’s role, nor can be used or operated by itself, so the
teacher decides when the class use technology or not.
J.
Sample
of Activities Using Technology with Mathematics Project
1. Example
of Mathematical Connection
Teacher asked the
students to investigate the connection or the relationship between disaster and mathematics.
2. Writing
in Mathematics Class
Writing
about specific issues, reflections, biography of mathematicians, etc.
3. Sample
of Group Exercises in Writing Research in Mathematics
It’s
about research, find a lot of information in Internet, and make the
presentation.
Conclusion
Teaching is not easy,
especially mathematics which is well-known as an abstract subject, but as a new
generation of teacher we must be very creative in teaching mathematics.
Sometimes conventional teaching is needed to teach the conceptual of
mathematics, after that we have to be very creative in presenting the material
in appropriate way for their understanding.
Resource: Module of Teaching and
Learning Numbers, Logic, Algebra, and Geometry 2011.
