The document describes the Iceberg Model for mathematics learning. It uses the metaphor of an iceberg to represent different levels of mathematical knowledge, with the tip of the iceberg being formal, explicit teaching and the larger submerged part representing the foundational, implicit knowledge. The three stages of mathematics learning according to this model are informal experiential learning, pre-formal use of representations and models, and formal explicit procedures. An example is given of converting fractions to percentages to illustrate how students can progress from an informal survey activity to a pre-formal representation using fraction models to the formal procedure.

1. Iceberg Model
for Mathematics Learning
By: Laurado Rindira Sabatini
Reviewed by: Prof. Dr. Zulkardi, M.Sc, M.Komp
Jurusan Pendidikan Matematika
Fakultas Kependidikan dan Ilmu Pendidikan
Universitas Sriwijaya

2. Overview of Iceberg on Mathematics Learning
Tip of
the iceberg
Floating
Capacity
It is an area where
much formal teaching
is directed
Essential stability
and foundation of
mathematical
knowledge

3. Iceberg as a reflective tool
Consider gaps which
may exist in current
stipulation
Reflect upon what
is being taught
Reflect upon the
importance of a
foundation
Reflective
Tool
Recognize the
importance of a clear
outline to facilitate the
development of
previous knowlegde
Consider carefully
the best use of
resources

4. Three distinct stages on
Mathematics Learning
Experiential learning by
the use of
representations, models
and concepts which are
more efficient and
abbreviated
Formal
Pre-formal
Informal
It contains activities which afford opportunities that are
experiential, practical and often pictorial.
It represents
the targeted
formal procedure

5. Example
FORMAL
Students find the procedure to
convert fraction into percent
Students represent the two model into
fraction “a twentieth” and “a hundredth”.
They will find that the two fractions
equivalent with percent that they will get.
PRE-FORMAL
=
INFORMAL
Students represent their
analysis by using percent
grids10×2 which
appropriate with percent
grids 10×10.
Students were given a
task about survey
activity

6. THANKS FOR YOUR ATTENTION
For further information, visit: lauradorindira.wordpress.com