Becoming a teacher doesn’t mean just teach the
material to the students, but also the ways to teach, the strategy in class,
and many more. It means we do not only learn about the content itself, but also
the strategies.
For if-then problems:
The first, the teachers should learn about “knowledge of content”. It is the
main knowledge for us to teach the content of the subject to our students, and
then they will learn and get the right information or concept from us to be
applied in their life. If we do not master the content, we can give them wrong
information or concept unconsciously, and then it will make them confuse and
misconception. If our students misconception about the concept, it will bring
them to the wrong way and they will get hard to learn the
continuance of another concept in the next chapter or topic.
For example, we will teach them about logic. If we
don’t master the concept of logic, so we just give them the patterns of
conjunction, disjunction, and soon without don’t know the reasons how to get
those patterns. We will tend to direct them to use this pattern for this kind
of problem, those patterns for that kind of problem, this one for this, etc.
However, when they face another problem, they will get confuse to solve because
they don’t know the main concept of the logic, and finally they only can solve
the problems based on patterns which have given.
The second, we have to master “pedagogical content knowledge” is the knowledge
for presenting our content or topic in the appropriate ways which
understandable. So many teachers present their material in conventional way.
They only use lecturing to teach their students. We know that sometimes
lecturing is really needed to do when we have to deliver the difficult concept.
However, do not always use the same methods in our classroom, the students will
interested to learn if we use the various methods. We can use students’
presentation, group discussions, etc. So it requires the teachers to be very
creative to present their material or topic. Also, we can start by giving them the problem, then they have to solve
it and finally they will get something or making inference by the experience
(the problem given)
The third, we also have to learn about “general pedagogical knowledge” such as
instructional strategies, how to manage our classroom, how to deal about the
rules or agreement with our students, etc. Many teachers feel difficult to
manage their class because they don’t master this knowledge, most of them are
the teachers that have non-education background, so they did not learn how to
be a teacher but they are becoming a teacher. For example is elementary
teachers in Indonesia, most of them are non-educational or non-PGSD graduate,
but they tech so many subjects. It’s related with “knowledge of content”, they
don’t master the content and also the general pedagogical about being a
teacher.
The last
is “knowledge of learners and learning.” It’s about how to understand our
students’ learn, their needs, their motivations, etc. It requires our
metacognitive ability, as a teachers we know that our students have different
characteristics in learning; visual learner, audio learner, and kinaesthetic
learner. We have to know how to teach the material with the methods that cover
all students. It requires our higher order thinking to present our material to
them, so it’s really related to the “pedagogical content knowledge”.
In
short, as an effective teacher we have to learn four kinds of knowledge. We
cannot only master some of them because all of them are interdependent. If we
only master the knowledge of content only, we will get difficulty to manage our
class, present our topics appropriately and understandable, etc. If we only
master the general pedagogical knowledge without knowledge of content, we can
give a wrong concept unconsciously to them.
There
are two big fallacies that student do:
a) Affirming the consequent
For example if we give some promises to
our students.
Premise 1: If the weather is hot, then
Kiran eats an ice cream.
Premise 2: Kiran is not eating an ice
cream.
Conclusion: The weather is not hot.
We have to clarify to the students why
they answer like that, just give them the counterexample, it’s like how if the
weather is hot, but she has a stomachache, so she doesn’t eat an ice cream? Or
maybe she has not money then she can’t buy it.
b) Denying the Antecedent
For example if we give some promises to
our students
Premise 1: If Erin is in pregnant, then
she may to furlough.
Premise
2: Erin is not in pregnant.
Conclusion:
Kiran may not to fourlough.
Again, we have to check to them about
their conclusion. It’s like how if she has to go to another city for a long
time, why she may not to furlough? To overcome those two problems, we can use
our content knowledge and pedagogical content knowledge by delivering the right
concept and using the right methods.
By presenting the right concept and
using the right methods for teaching logic, it means that we are implementing
the “high order thinking” on our students because when they learn about logic,
it requires their thought in drawing the conclusion, reasoning and analyzing
the statements, proofing the step by step of mathematical problem solving, so
it needs the sequence of steps then it challenge students’ thought to be high
order in thinking. Also, in problem solving about logic, students are required
to connect the problem with their experience, so we have to choose the best way
in delivering the chapter of logic, so that the students can reach the high order
thinking.
In the activity for teaching logic, we
can ask the students to work in group so that they can investigate, explore,
discuss and share it together. The problem given could be either formal logic
or informal logic. The problems themselves could be quantifiers, if-then, and
many more. For example, determine if the statement true or false, then give the
example or the counterexample of these statements, then find the negation of
each!
For quantifier problems:
-
Some
perfect squares are odd numbers:
Answer: It’s TRUE, let say x = 3, then
x2 = 9
The negation: No perfect squares are
odd numbers. Then it’s being false since the counterexample is let say x = 5,
then x2 = 25
For if-then problems:
Evan
is a tourist, he concludes that if the median cost of his five trips in a month
$700, then the total cost of all his five trips is $3.500.
Answer: This statement could be FALSE
if each cost trip is $450, $580, $600, $870, and $1.200. It shows that $600 is
a median cost, but the total cost is $3.700 which is more than $3.500.
The negation: The median cost of his five trips in a
month is $700 and the total cost of all his five trips is not $3.500.
