There
are a lot of factors which make people do not enjoy doing or learning
mathematics. One of them is the mathematics teachers’ skill in presenting
mathematics to the students. Generally, there are many teachers who still use
“direct instruction” or “lecturing” method only in teaching mathematics. Based
on Apriyanto (2012) experience and his interview to some teachers when he was
doing School Experience Program (SEP), the teachers stated that using lecturing
is the best way to teach mathematics. If we use another method, it’s just
wasting the time, while in another side there is too much material to teach, so
lecturing is the best.
Ellington
(1999) stated in her book about some weaknesses of lecturing method. She
explained that one aspect of lecturing method which causes some concern is that
its effectiveness is inevitably very dependent on the teacher's skill. The
ability to organize and explain a topic does not come naturally. It needs a
long process to be successive teacher who teach using lecturing method only, or
others are fortunate person. Another disadvantage of this method is that the students
are mostly passive in the learning process, spending most of their time either
listening or writing down notes; this method is usually non-interactive.
However,
lecturing method is not mostly bad. It is better to combine the lecturing
method with another teaching method. The teacher should use multiple methods in
presenting mathematics to the students, so that the students will not get bored
and feel enjoy in learning. Still based on Apriyanto (2012) experience, he saw
that the teacher gave a piece of paper to the students, and the teacher called
it as a worksheet. According to Apriyanto’s thought, it’s not a good worksheet
because the paper only consists of routine questions, so he calls it as
exercise instead of worksheet. Apriyanto states that a good worksheet should
contain the explanation and the exemplification, so that the worksheet can
guide the students into our learning objectives.
There
are many studies which show the use of worksheet can increase students'
comprehension in mathematics. One of the researches has been held by Putri
(2008). She was a student of Mathematics Education in Universitas Negeri
Yogyakarta. He did the research of the use of worksheet to the 7th grade
students of Rintisan Sekolah Bertaraf Internasional (RSBI) SMP Negeri 1 Bantul.
According
to her study, the improvement of students' comprehension in mathematics was
indicated by three indicators; the increase of the mean score of the class, the
increase of the percentage of students' comprehension of mathematical concept,
and the successive of passing the minimum standard-score. Also, the data of the
observation shows that there was an improvement of analyzing and students'
creativity during the learning process.
Talking
about the worksheet cannot be separated from the use of examples. Liz et.all
(2006) stated that examples are the main role in the development of mathematics
as a discipline and also in the teaching and learning context. Still in the
same literature, “Examples in the
form of worked solutions to problems are key features in virtually
any instructional explanation, Leinhardt (2001).”
Moreover, “Examples of all kinds are one of the principle devices used to illustrate and
communicate concepts between teachers and learners, Bruner et al. (1956), Tall & Vinner (1981),
Peled & Zaslavsky (1997)”. So, the existence of examples is very crucial in
mathematics classroom.
Leinhardt
(2001) in Liz et. all (2006) defines that examples are as tools for
communication and explanation. Examples are a communication device that is
fundamental to explanation and mathematical discourse. As the illustration,
Zaslavsky & Lavie (2005) in Liz et. all (2006) give example in the chapter
of function. there are three expressions of quadratic functions;
Those are three different
representation of the same function. Each of them has strength and weakness;
such as the roots, the position of the vertex and minimum value, or the
y-intercept. However, they are not likely to be obvious to the students without
some guidance on how to read or interpret each of the expression.
Moreover, it is
also not even clear that students will consider all three as acceptable example
of a quadratic function, since for example the power of two (the second example)
is less obvious in the factored form, and a quadratic like the third
expression. The teacher may choose to deal with only one of the above
representations, or s/he may use the three different representations in order
to exemplify how algebraic manipulations lead from one to another, or in order
to deal with the notion of equivalent expressions.
Teaching and
learning in the classroom can be assessed as effective or not by many aspects.
One of the aspects is when we are success in using worksheet in our teaching in
the classroom. National Centre
for Excellence in the Teaching of Mathematics (NCETM) states that there are
some aspects when our teaching is more effective.
First,
builds on the knowledge learners already have. This means developing formative
assessment techniques and adapting our teaching to accommodate individual
learning needs. So, by using the worksheet it is really hope can meet the
learning objective and can accommodate the students in learning.
Second,
exposes and discusses common misconceptions. The learning activities should
expose current thinking, create ‘tensions’ to the students by confronting them
with inconsistencies, and allow opportunities for the solutions through
discussion. By utilizing the worksheet, we can use it as the media.
Third,
uses higher-order questions. Questioning is more effective when it promotes
explanation, application and synthesis rather than mere recall. However, before
doing that we can do the exemplification on that worksheet as for the big
picture for the students' thinking.
The
last, creates connections between topics. Many students often find it is
difficult to generalise and transfer their learning to other topics and
contexts. Related concepts (such as division, fraction and ratio) remain
unconnected. Effective teachers build bridges between ideas in the worksheet.
Again, the power of exemplifying is needed.
I
have given a worksheet by my lecturer. I think the worksheet was very good in
guiding the students building their concept of the topic. The worksheet was
about linear equation by comparing two kinds of taxi. Let’s see on the
attachment. Honestly, I don’t know who the creator of the worksheet was, but my
lecturer said that s/he was her friend. Let’s we analyse the worksheet by some
aspect mentioned above.
In
building the knowledge of the students already have, this worksheet has started
since the beginning of the information. This worksheet gives general problem
that should be solved. Next, is exposing and discussing common misconceptions.
There are some a question given to the students that can be discussed to
overcome the misconception, which is “taksi
mana yang lebih murah? Kenapa?” This worksheet compares the same thing but
different case. By giving that question, it can be the problem to be discussed.
Moreover,
this worksheet uses higher-order questions. The questions provided are getting
high-order and getting high. It hopes can stimulate and build the concept of
linear equation to the students and can guide them to the learning objectives.
Next is creating connection between topics. This worksheet really provides it,
since the object of the problem is about the transportation that is really
familiar with the students like taxi, bus, and many others.
Actually,
there are no absolute aspects to assess that our teaching and learning are
effective or not. However, those some tips are good to be tried and to be done
in our teaching and learning mathematics. We can reduce the peoples’ paradigm
that mathematics is hard by presenting the mathematics in an enjoyable way. It
can be done by using a method of using worksheet in learning process; not only
a lecturing method, so that the students will not get bored of listening the
teacher’s explanation. In using the worksheet, there are some tips to make it
worthwhile as stated by the NCTEM by utilize the power of explaining and
exemplifying in the worksheet. All in all, I hope mathematics can be seen as an
enjoyable subject in people’s sight because mathematics exists in every single
part of our life.
References
Ellington, H. (1999). Facilitating Student Learning. Malaysia:
Universiti Teknologi Malaysia.
Putri, R. S. M.
(2008). Upaya Peningkatan Pemahaman
Konsep Matematika Siswa Kelas VII RSBI di SMP Negeri 1 Bantul melalui Penerapan Metode
Penemuan Terbimbing dengan Menggunakan Student
Worksheet. Yogyakarta: Universitas
Negeri Yogyakarta.
Liz et. All.
(2006). Exemplification in Mathematics Education. In J. Novotna (Ed.), Proceedings
of the 30th Conference of the International Group for the Psychology of
Mathematics Education. Prague, Czech Republic: PME.
National Centre for Excellence in the Teaching of Mathematics. Mathematics Matters: Final Report.
Nottingham, United Kingdom: University of Nottingham. Retrieved from www.ncetm.org.uk
