Overcoming Illusion of Linearity through TPACK

The assignment discusses the illusion of linearity, where students tend to treat numerical relationships as linear. It proposes that teachers with advanced knowledge of TPACK can use technology to represent geometrical figures visually, helping students overcome this misconception. The study aims to test this hypothesis through a comparative analysis of two groups: one taught using traditional methods and another using technology-enhanced teaching. The results will be analyzed using t-test correlation and factor analysis to identify factors governing geometric training.

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

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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

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How teachers can use their TPACK knowledge to help young students overcome the obstacle of
“illusion of linearity”
the competency of teachers in ICT integration. TPACK knowledge can be applied in two
aspects. One is for teachers to avoid the creation of the above phenomenon and two to solve
the illusion successfully in case it occurs.
Research questions
Against this backdrop, the thesis is designed to examine children’s misconceptions when
it comes to applications of linear thinking in their daily analysis of situations. Moreover, it
tries to evaluate ways through which the phenomenon can be overcome using TPACK. The
educators’ preparation to assist in the situation will also be highlighted. The questions below
have been formulated to guide the research in attaining the intended objectives.
 How do teachers working with the younger children negotiate this misconception?
 How can young children be taught to enable them to deviate from this misconceptions
in advance?
 What are the avenues for teachers to improve their teaching without relying on the use
of technology?
 What is the impact of introducing the technology on teachers in countering the
misconceptions?
 How does the effect of “illusion of linearity” relate to class and gender?
 Where and in what ways do teachers perform agency?
 Is TPACK knowledge among the practitioners the source of the contributors of the
problem?
 How effective will the test group be when compared to the traditional way of teaching
group?
 What are the aspects of TPACK that teachers need to possess to teach geometrical
figures in ways that can contribute to overcoming the misconceptions?
The project will be conducted within the theoretical framework in a way that the child
social relations cater for the Van Wim’s theory (De Bock, Educational Studies in
Mathematics, 2002). The students who grow applying the proportional linear expertise and
are increasingly familiar with linear models may experience a significant disadvantage. The
linearity illusion is a such a strong urge when it comes to relations in a way that the children
easily yield to the desire to treat numerical relations in a way as if they were linear.

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How teachers can use their TPACK knowledge to help young students overcome the obstacle of
“illusion of linearity”
Therefore, to deal with the illusion of linearity they suggested that practitioners should apply
technology to represent geometrical figures visually.
Teachers need to possess advanced knowledge of TPACK. The notion of using expert
teachers as a source of knowledge was initiated by Shulman in 1986. He termed it
pedagogical content knowledge and further stated that it could be differentiated from the
practitioners pedagogical and content knowledge. The idea was furthered by Koehler and
Mishra by adding technological skills to the already established pedagogical as well as
content knowledge (Koehler, 2009). They suggested that TPACK is applicable in a
comparable manner to represent the unique expertise in technology integration by the
teachers. This resembles how the two made intelligent pedagogical applications of
technology. In (Koehler, 2007) TPACK was originally named TPCK a term later altered to
TPACK to make pronunciation easier. This also clearly emphasized on the integrated
application of technology, pedagogy as well as content knowledge in the efficient technology
integration (Thompson and Mishra,2007).
Analysis
The data analysis will be controlled by the nature of data to an extent. There will be two
groups tested to test the theory. One group will be composed of a group of students tasked
with learning about the volume and area of geometrical figures without applying technology
nor the 3D representation of figures. The two groups will all be administered with a pre-test
prior to classroom’s interventions. Another test will then be taken by the groups after the
intervention. The results will be analyzed using the t-test correlation and factor analysis. The
focus will be to identify factors that govern all the aspects of geometrical training. The
teachers who will be tasked with teaching the test groups will be tested to gauge their
knowledge of the TPACK.
References
De Bock, D. V. (2002). Educational Studies in Mathematics. 50: 311.
De Bock, D. V. (2002). Educational Studies in Mathematics . Retrieved from
https://doi.org/10.1023/A:1021205413749
Dooren, W. D. (2003). Educational Studies in Mathematics . Retrieved from
https://doi.org/10.1023/A:1025516816886

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How teachers can use their TPACK knowledge to help young students overcome the obstacle of
“illusion of linearity”
Koehler, M. J. (2009). What is technological pedagogical content knowledge Contemporary Issues in
Technology and Teacher Education. 60-70.
Leanna M. Archambault, J. H. (n.d.). Revisiting technological pedagogical content knowledge:
Exploring the TPACK Framework .
Wim Van Dooren, D. D. (2009). Students' Overuse of Proportionality on Missing-Value Problems:
How Numbers May Change Solutions. Journal for Research in Mathematics Education, 187-
211.