"Real learning requires stepping into the
unknown, which initiates a rupture in knowing..." 
It has been a concern to many University teachers why certain students
"get stuck" at particular point of their education whilst others
grasp knowledge with comparative ease. What might account for this variation in
student performance and what could teachers do in order to help students
overcome such barriers to their learning? As students from a wide range of
educational backgrounds enter the University, the problem of threshold is
becoming of increasing importance across all disciplines .
Students are challenged within a discipline when they
don't see the relevance of subject to other areas of engineering and life
sciences . As it was previously reported by Cousin : "First student:
I understood it in class, it was when we went away and I just seemed to have
completely forgotten everything that we did on it, and I think that was when I
struggled because when we were sat in here, we would obviously got help if we
had questions but... when it came to applying it...I understood the lectures
and everything that we did on it but couldn't actually apply it, I think that
was the difficulty." Therefore, students are lacking the motivation to
gain insight course assignments, and later, are not able to translate their
knowledge to other disciplines due to the previous surface learning. The
essence of deep learning is understanding - true knowledge . The term
threshold concept denotes concepts that are essential to knowledge and
understanding within the educational program or particular disciplines .
Threshold concepts act like doorways that enable students to comprehend a topic
or an entire subject that they have not understood previously. The
transformative nature of the threshold concept can create challenges to both
students and teachers. Students may experience a threshold as a transformative
process that is able to change student views on educational program or subject,
integrative process that connects non-integrated ideas, irreversible process
where the knowledge will remain for a long time and bounded process that refers
to a subset of disciplines [6,7].
My personal teaching experience showed that every year
students struggle with the obligatory master level courses. Certain students
have difficulties with the programming using MatLab because they are unfamiliar
with this software. Other students cannot remember basics of mathematics. The
master program administration considered both student groups eligible for the
course participation. We know that there are always students which are
exceptions e.g. lacking motivation, without clear educational goals, with
different mental problems, etc. But, in general, I believe that it is possible
to structure the whole master program in the way that students with their
weaknesses and strengths will be on a similar level.
The application of concept mapping to university
teaching has revealed the significance of knowledge structures in the process
of student learning. Kinchin  reported two learning models, as shown in
Figure 1: Learning models (a) Chain model and (b) Network model .
Figure 2: Kinchin’s learning model .
The chain model shows a learning process as a single
possible route from beginning to end, in which dialogue plays a minor role .
The chain model is understandable with the clear boundaries and defined
responsibilities for students and teachers. In contrast to the network model,
the chain model structure does not permit the further program development .
The network model includes more sources of uncertainty e.g. the nature of
students' prior knowledge that requires teacher-student dialogue. The network
model includes various routes without a clear start and end points.In order to find a way to manage students
with the different levels of knowledge and bringing them to the same start
point and the same learning velocity, both models should be combined in one
model, as shown in Figure 2.
The combination of chain and net models
supports Norman's contention that "expertise lies in the availability of
multiple representations of knowledge . During the high-school and
undergraduate studies, students establish a chain of understanding, whereas
during graduate and post-graduate education, students develop and integrate
nets of understanding that suits to particular contexts . The chains might
be also considered as competing. Net structures, which are focused on the
integration of understanding, need to be explicitly connected to chains of
practice. The understanding developed through the memorizing of information is
integrated into a more holistic subject understanding, according to the
development of knowledge structures from chains to nets. The combined model
plays a key role in the learning process when we try to adjust a student
The threshold of knowledge refers to the boundary
between "We know for sure" and "we don't know". If we want
to come to the next step of our education, we have to go through the obstacles
of threshold. In the master's program students obtain different levels of
knowledge in dependency on the learning and teaching methodology of the
bachelor studies. Certain students have learned only to memorize or to do a lot
of routine practical work following the chain model, but other students used to
learn through the discussion-based teaching and have already formed the
interdisciplinary thinking. When students come to the master program, all of
them have weak and strong knowledge in different spheres. Therefore, it is
important to combine the practical and theoretical knowledge of their program
in the course assignments. Students should have an equal opportunity to apply
their strengths and weaknesses. At master level there is also a chance that
students move from a core area of knowledge to pursue and specialize in
particular spheres within a module. The explicit use of a threshold concept
allows this process to occur within a coherent, wider "field" of
study, whilst individuals may begin to investigate different subject areas and
contexts the concepts ensure a level of coherence and allow a common point of
contact for discussion and engagement with the work of others. In addition,
both new insights and new knowledge can emerge.
What can we do about student threshold as
The information about prior student knowledge can be
obtained from colleges or experience from previous years. The pre-test of
student knowledge at the beginning of the course is an additional option to
estimate how the teaching methodology, learning activities and assessment
should be structured for the class. The first two-three weeks could be used for
the repetition of the material which will be used in the main course.
Repetition is vital to secure long-term memories. Spaced practice, mastery
learning, repetition and homework (not at primary level) all give opportunities
for repetition. Once new knowledge is understood, it can be safely learnt by
heart as it will secure the links to prior knowledge. The spin model in the
engineering is another option where 1-2 courses will be added to the master
program, as shown in Figure 3.
Figure 3: Threshold concept in engineering using a spin model.
These courses will include assignments which are
relevant to other courses in the master program. Spin is a well-known term
given to rotation of a body. It has an influence across many branches of
engineering, in fact almost anywhere where there is motion. Spin is a threshold
concept because it explains and describes a lot of different types of motion
and the understanding of spin is unlikely to be forgotten becoming a
transformative and integrative knowledge. Once you understood "spin",
you will use it in other subjects e.g. thermodynamics, chemistry, etc. Another
option is to establish an introductory course at the beginning of master
program where less simple assignments with narrower questions than in the
mandatory course will be used. Such introductory courses will help students to
repeat the information which they studied previously, and step up into the requirements
of the mandatory course. The faculties will avoid situations when students
cannot follow the course program and are not able to work on assignments and
thus, the course level has to be lowed. These three options to adjust the
student threshold will give an additional opportunity for both students and
teachers to exchange the feedback, and create a "deep knowledge"
platform for the participation in mandatory courses of the master program. When
we talk about blended learning, we have all opportunities to use the digital
tools for short quizzes, feedbacks and mi-term exams to influence the student
threshold during the course time.
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