A.
Introduction to Teaching Numbers
Numbers or Complex Numbers is the set of
all Real numbers and Imaginary numbers, but in teaching numbers in high school
we only teach about Real Numbers. Real numbers consists of Rational and
Irrational numbers. Rational numbers is the set of all numbers that can be
expressed as a/b,
and b ≠ 0, whereas
irrational numbers is like π,
e, √2, and soon. The main point of learning numbers understands
of numbers, the system, properties, and its application in our daily life. We
have to make our students to understand numbers, not just remembering it
because according to Kamii and Dominick 1998, if the students only memorize
without understanding, they will get confuse of methods or forget the steps, so
they will get hard to apply the numbers in their life.
B.
Content Standards of Numbers in Secondary Mathematics
in Indonesia
Indonesian standard in teaching numbers in
high school is less than NCTM standard. In 7th grade, Competency
Standard of numbers is only “Understand the characteristics of number operation
and its use in problem solving,” and for the 9th grade is
“Understand the characteristics of exponential numbers and radical numbers, and
its use in solving problems,” also “Understand sequence and progression and its
use in problem solving.” Whereas, for NCTM standard for 7th and 9th
grades are more than that, we can check it in www.nctm.org/standards/content.aspx?id=7564#numbers.
C.
NCTM Standards for Teaching Number and
Operation for Grades 9-12
As I said before, the NCTM standard is more
than Indonesian standard, and we can check it in the website above. The standards
are deeper, clearer, and more specific. It makes the students more easily to
apply it in their life.
D.
Students’ Problem and Students’
Difficulties in Learning Numbers: Researched based
Generally, some problems that faced by the
students are:
a. Incomplete in mastery of number facts.
Ex:
operation of two negative numbers: -3+4=… ; 5-(-6)… ; -4(-2)=… ; -9/(-3)=…
b. Misread or misunderstand signs “>” ,
“<” , “≤” , and “≥”
Ex: solving inequalities: 3x-2y ≤ 24 ; -7x+2y
> 6, and soon.
c. Difficult to
link the connection between numbers and their experiences.
d. Difficult to solve the problems dealing
with numbers and real life.
e. Teaching ability of teachers which causes unclear
and not understanding in students.
f. Understanding about fraction.
g. Representing very large number and very
small number.
Ex: 0.00000009895623 = 9.895623 x 10-8
E.
Teachers’ Problem in Teaching Numbers
Some problems which exist on the teachers
are:
a. Teacher’s ability in presenting the
material in appropriate topic and understandable.
b. Difficult to identify the concept which is
needed to move to next chapter or concept and linking it to the previous
concept.
c. Difficult to explain mathematical ideas and
ability to engage the students.
d. Sequencing the topics. Most of them follow
the suggested flow of the text book which sometimes is not really good to be
followed.
F.
Pedagogical Content Knowledge of Teaching
Numbers
They have to focus on:
a. Improving teachers’ ability in connecting
mathematical ideas, the learning process can be meaningful and connected.
b. Classroom instruction to organize the class
and employing the technology around us.
c. Making the transition from one activity to
the next activities.
G.
Teaching Number System
a. Why learn number system?
We have to learn numbers because it is a
part of solving problems in our daily life. Without learning it, we cannot
calculate anything, so it’s really important to be learned.
b. Number System
Students in high
school should develop their understanding of:
- Real numbers and its system.
- Distinguishing the rational and irrational
numbers.
- Exploring the new systems, such as matrices
and vectors.
- Using matrices and connect it to another
concept of math, for example using matrices to solve linear equations.
c. Computation and Estimation
- The students must be able estimate,
appropriate approximation in answering the problems.
- Selecting suitable steps for computing,
ability to use calculators and computers.
