The Illusion of Linearity - Sample Assignment

Running head: How teachers can use their TPACK knowledge to help young
students overcome the obstacle of “illusion of linearity”
Education Mathematics
Institution Name
Student Name

2
How teachers can use their TPACK knowledge to help young students overcome
the obstacle of “illusion of linearity”
Introduction
The project objective is to create an understanding of teachers in relation to the
“illusion of linearity” phenomenon. In addition, the study will analyze ways in which
teachers TPACK (Technological Pedagogical Content Knowledge) can be applied to assist
students in overcoming the phenomenon. The description of Van (Wim Van Dooren, 2009)
(Dooren, 2003) (Dooren, 2003) in their article originally written in 2003 indicates that by
applying proper use of the TPACK framework teachers can change mathematics education
whenever the linear thinking process is not applicable.
Contextual Background
The previous research has indicated that extensive attention spent by students in their
proportional reasoning have given them a strong tendency to apply linear or proportional
models in all situations. With this the students sometimes try to apply the models in situations
where they are not applicable. This is what the phenomena referred to as “illusion of
linearity”. For example, several students undertaking Geometry tend to believe that should
the sides of a figure be doubled then the area will also double. In this study the empirical
evidence for the phenomenon is expanded to reflect the probabilistic reasoning domain.
The first step will be to highlight the notion of chance and give some justifications for
expecting the overgeneralization in the probability domain. Thereafter, we will describe
several well-known as well as less popular probabilistic misconceptions. This will prove that
they all have a single remarkable common feature. That is, they all can be interpreted in
terms. A teacher can apply the use of visual representation of the given geometric figure as a
technique to overcome the challenge of “illusion of linearity”. To do this the teacher needs to
have a prominent level of TRACK prior to the lesson.
This concept indicates that the teachers’ integration skills result from mastering the
pedagogical, content as well as technological knowledge. The above three elements normally
do integrate to give several types of ICT integration: technological content knowledge,
TPACK, pedagogical content knowledge and finally technological content knowledge. The
teacher’s educators have enthusiastically accepted the notion of teachers’ ICT knowledge.
This is because it possesses the ability to generate theoretical underpinning needed to define
the competency of teachers in ICT integration. TPACK knowledge can be applied in two