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University of Bayreuth
Center for Mobile Learning with Digital Technology
ISSN 2942-1373
Digitalization at School –
but in a Well-Balanced Way
publications
8
Peter Baptist
Publisher University of Bayreuth
Center for Mobile Learning with Digital Technology (CMLDT)
Universitätsstraße 30
95447 Bayreuth
Germany
+49 921 55 3266
Series CMLDT publications
ISSN 2942-1373
Editor Carsten Miller, carsten.miller@uni-bayreuth.de
Alfred Wasserman, alfred.wassermann@uni-bayreuth.de
License CMLDT publications © 2023 by University of Bayreuth – Center
for Mobile Learning with Digital Technology is licensed under
CC BY-ND 4.0. To view a copy of this license, visit
http://creativecommons.org/licenses/by-nd/4.0/
Layout Carsten Miller, carsten.miller@uni-bayreuth.de
Internet https://mobile-learning.uni-bayreuth.de/CMLDTpublications
Issue 8 Year of publication 2025
Title Digitalization at School – but in a Well-Balanced Way
Autor Peter Baptist
– 3 –
Digitalization at School –
but in a Well-Balanced Way
Peter Baptist
Center for Mobile Learning with Digital Technology
University of Bayreuth
peter.baptist@uni-bayreuth.de
Digitalization is necessary and important, especially at school. However, there
are now complaints that digitalization has often been exaggerated, leading
to negative effects on learners, such as poor concentration and weak writing
skills. So, is the digital school a mistake? Should we abandon digitalization and
ban laptops, tablets, and smartphones from the classroom in the future?
This question is the subject of controversial public debate. The end of the
digitalization euphoria in some Scandinavian countries is often cited as an
argument for a return to purely analog teaching and learning. However, the
cause of the decline in school performance in these countries is not con￾sidered in a differentiated manner. For education researchers at the Karolinska
Institute in Stockholm, one reason for the failure is that, during digitalization,
students have used the internet as a broad knowledge resource rather than
developing their own digital learning tools. Especially younger schoolchildren
do not yet have the cognitive abilities to acquire knowledge independently.
However, a return to purely analog schooling cannot be the solution. Digi￾tal technologies permeate and shape both our personal lives and the world
of work. Schools, as places that prepare us for life, cannot ignore these
media. However, digital support does not necessarily lead to better education.
Teaching and learning can only be improved if these media are integrated into
the classroom in a well-designed way.
– 4 –
In geometry lessons suitable digital support can be used to promote interest
in and understanding of mathematics in the long term, starting as early as
5th grade. (Paper) worksheets contain tasks and instructions. Smartphones or
tablets with the appropriate software are suitable for discovery and experi￾mentation, and the results are recorded by hand. Analog and digital “learning
worlds” are meaningfully linked with each other.
The success of digital teaching and learning in schools also depends largely on
teachers‘ competence in using digital media and the available teaching con￾cepts. To ensure that this approach becomes widespread, it must be possible
to use mobile devices and software without extensive training. Students learn
how to use these tools in class, not theoretically, but in relation to subject￾specific content. Modern teaching takes advantage of both analog and digital
learning environments. The key is to find the right balance.
Going your own way in learning – added value through digital tools
The following section uses mathematics as an example to illustrate how in￾dependent learning can be promoted with appropriate digital support.
Students work with tablets or smartphones and use the gesture-based soft￾ware sketchometry, which is available online directly in the browser or as an
app for various operating systems (http://sketchometry.org). The software
can be used for free both at school and at home. A major advantage is that
learners can work with their own devices, meaning that they are not dependent
on special equipment at school.
Tablets and smartphones – electronic sketchpads
Like calculators, tablets and smartphones can be valuable learning tools in
math class when used appropriately. Students use these devices with sketcho￾metry as an electronic sketchpad. They draw figures with their fingers, which
are automatically converted into accurate drawings. The innovative feature of
– 5 –
sketchometry is its intuitive gestures, which replace the usual tools of conven￾tional dynamic software.
For example, if a circle is to be drawn through three given points, the circle is
indicated with a corresponding gesture through the three points. The students
consciously make a circular movement with their index finger. As an “extra,” the
program generates the corresponding center point of the circle at the same
time as the circle line.
 
The sketchometry gestures replace the usual tools of dynamic geometry soft￾ware. These gestures are visually close to the object to be created (e. g., angle,
perpendicular, tangent to a curve, parallel to a straight line, reflection on a
straight line, etc.) and are therefore easy for students to remember.
The fine motor movements of the finger when sketching gestures involve re￾gions of the brain in the learning process that are not activated when clicking
on an icon or an item in a menu list. This is because clicking is always the same
process, regardless of the geometric activity it initiates. Gestures, on the other
hand, differ from one another, depending on the desired construction.
– 6 –
Learning with your finger
Maria Montessori (1870 – 1952) promoted “learning with the finger” at the
beginning of the 20th century. She used letters made of sandpaper to teach the
alphabet. The children listen to the letters spoken by the teacher, look at their
appearance, and trace them with their index finger.
The finger technique offers further advantages. Several years ago, Australian
scientists conducted several studies that demonstrated that tracing shapes
with the index finger can assist in solving mathematical problems. The resear￾chers assume that pointing or tracing with the finger increases attention and
thus gives this information priority in the brain‘s processing. Tracing with the
finger can also reduce the load on working memory and improve the ability to
retain more complex information, as other regions of the brain are activated in
addition to visual perception.
Therefore, the results from Australia and also from researchers at the Max￾Planck-Institute in Leipzig suggest that the positive learning effects of networ￾king with motor areas of the brain also apply to mathematics when students
work with sketchometry. This is because they use their index finger to create
their constructions and apply the intuitive sketchometry gestures. The dynamic
possibilities of the software are exploited when the configurations created are
modified by dragging with the index finger to discover certain properties or
relationships.
Teaching and learning with sketchometry teaching modules
The concept of sketchometry teaching modules enables the transition from
passive, receptive teaching to active, inquiry-based learning. The content is not
presented as a “finished system.” In a construction phase, learners first receive
instructions on paper worksheets for constructing objects and configurations
with sketchometry. In the subsequent exploration phase, work assignments
are given that encourage learners to experiment and observe independently.
– 7 –
They use their tablet or smartphone as an electronic sketchpad. The results are
documented by hand (self-formulated texts, freehand sketches) on a struc￾tured result sheet or in a study journal. These records are then compared and
discussed in pairs. Finally, a discussion takes place in class, moderated by the
teacher.
Analog and digital “learning worlds” are linked together. However, this is by
no means about bringing technology into schools for technology‘s sake. Digi￾tal learning tools such as tablets, smartphones, and software should only be
used if they add value to existing teaching methods. Such added value results,
among other things, from
ा greater and sustained motivation,
ा increased clarity through the possibility of dynamic modifications,
ा understandable presentation of complex issues,
ा individualized learning processes,
ा learning independent of time and location.
– 8 –
Structure of a sketchometry teaching module
Each teaching module is dedicated to a specific topic and consists of five com￾ponents:
1. Information sheet for teachers
ा Prerequisites and objectives for the student worksheet.
ा Notes on sketchometry: Indication of the gestures needed for the
worksheet.
2. Student worksheet
ा Instructions for constructing.
ा Instructions for exploring, experimenting and documenting.
3. Result sheet
ा Predefined structure to facilitate clearly documentation of the results of
the exploration and experimentation instructions.
ा Possibility for individual notes.
4. Exercise sheet
ा Tasks for practicing or deepening the topic of the student worksheet.
ा Further tasks or additional topical suggestions.
5. Video for the student worksheet
– 9 –
What are the advantages of using sketchometry teaching modules?
The content is not presented as a “prefabricated system”.
ा Independent construction familiarizes students with the task at hand.
ा A self-created construction provides a sense of success.
ा “Slowing down” the process.
ा Intensive engagement with the respective topic.
ा Being active.
ा Working independently.
ा Taking your own notes forces you to think and structure your thoughts.
ा Determining your own learning pace.
ा No prior technical knowledge is required.
For organizational reasons alone, it is not possible for teachers to completely
change their teaching methods overnight. A prerequisite for a change in
approach is the seamless integration of new elements into the existing teaching
script. This is possible with the sketchometry teaching modules. This concept
allows a gradual and low-threshold transition to independent learning with the
use of digital media. Individual teaching modules initially replace conventional
teaching units. With increasing experience, this happens more often. Gradu￾ally, a collection of teaching modules can be created and then combined into
a textbook. Tablets and smartphones prove to be learning tools that students
can use for sketching and discovery.
sketchometry teaching modules and the “think-pair-share method“
The sketchometry teaching modules are also ideal for teaching according to
the proven “think-pair-share method“ tested in the nationwide pilot projects
SINUS and SINUS Transfer in Germany. This method combines active, indepen￾dent work phases for students (guided by tasks involving construction, explo-
– 10 –
ration, documentation, and discussion) with a presentation and results secu￾ring phase moderated by the teacher.
Think phase
Students first work independently on the worksheet. They work on the
construction tasks and then carry out the exploration tasks. At the same time,
they write down their observations, assumptions, and findings on the result
sheet. The teacher will provide help for self-help if necessary or on request.
Pair phase
Students compare their results with those of their seatmates or within their
learning group. They add to their notes if necessary. The teacher observes each
group and is again available to give advice (help for self-help). In this way, the
teacher will find out what assumptions or solutions are being made and thus
gain an overview of the results achieved.
Share phase
The results are discussed with the whole class. This can be done based on a
completed result sheet from a learning group. In this more teacher-centered
phase, the teacher guides the discussion and, if necessary, corrects and adds
to the results presented. New terms can also be introduced at this stage.
Confirming the results
Together with the students, a model result sheet can be produced and made
available to the whole class, either electronically or as a hard copy. This col￾laborative work is recommended rather than a result sheet prepared by the
teacher. Otherwise, there is a risk that the students will not contribute enough
because they know that they will get a sample sheet from the teacher.
– 11 –
Do we need new content in the curricula?
Are we learning for school or for life?
The meaning and usefulness of the knowledge acquired at school is often the
subject of controversial discussions. The question “Why do we need this?”
reveals an overemphasis on immediate practical application. There are repea￾ted calls to “declutter” curricula! But do curricula really contain clutter?
Of course, it makes sense to review curriculum content at regular intervals and
modify it if necessary. But even with the existing curricula, it is possible to
deliver contemporary teaching. The mandate of a school providing general
education is far more comprehensive than simply imparting directly applicable
everyday knowledge. Of course, such knowledge should and must also be con￾sidered in education, but teaching must not be limited to this. Who can predict
what specialist knowledge current students will need in their future studies or
careers?
We usually acquire knowledge within a specific context. This makes it difficult
to transfer it to other situations and contexts. If knowledge is not immediately
available, it is referred to as inert knowledge. To be able to apply it, we must
adapt it to the respective situation, modify it, and possibly expand it. The more
intensively the knowledge acquired at school has already been applied and
used in different contexts in class, the easier and better this is achieved. Both
situational and systematic learning are necessary and should complement each
other. Despite the limitations of immediate applicability, knowledge acquired
in school in this way is never useless, as it facilitates learning outside of school.
“School” is an abstract concept: the concrete factors are “students“ and “tea￾chers” (...). It doesn‘t really matter what is taught, but how it is taught. It seems
to me that classical schooling can also prepare students quite well for modern
life: the lessons just need to be designed accordingly!
This demand by Heinrich Mann (1871 – 1950) remains relevant today. In the
pilot projects SINUS and SINUS Transfer, we provided inspiration for new
learning methods and developed and successfully tested corresponding
– 12 –
teaching concepts together with teachers. As soon as teachers and learners
engage in “experiencing mathematics,” the world of mathematics, which is
initially unfamiliar to many students, transforms into a familiar world—a world
that is as much about the importance of mathematics for technical, medical,
informational, and economic progress as it is about the development of inno￾vative, creative, and critical thinking.
References
[1] Baptist, Peter (2023): Maths with the Index Finger – sketchometry.
CMLDT publications, issue 1,
https://mobile-learning.uni-bayreuth.de/CMLDTpublications
[2] Baptist, Peter (2025): Active Learning with sketchometry Teaching
Modules. CMLDT publications, issue 7,
https://mobile-learning.uni-bayreuth.de/CMLDTpublications
[3] Fang-Tzu Hu, Paul Ginns, Janette Bobis (2015): Getting the point:
Tracing worked examples enhances learning. Learning and Instruction,
vol. 35, pp. 85 – 93.
[4] Ginns Paul, Fang-Tzu Hu, Erin Byrne, and Janette Bobis (2016): Learning
by Tracing Worked Examples. Applied Cognitive Psychology, vol. 30,
pp. 160 - 169
[5] Lucy Macken, Paul Ginns (2014): Pointing and tracing gestures may
enhance anatomy and physiology learning. Medical Teacher, vol. 36,
issue 7, pp. 596 – 601
[6] Brian Mathias, Andrea Waibel, Gesa Hartwigsen, Leona Sureth,
Manuela Macedonia, Katja M. Mayer, and Katharina von Kriegstein (2021):
Motor Cortex Causally Contributes to Vocabulary Translation following
Sensorimotor-Enriched Training. Journal of Neuroscience 13,
41 (41) 8618-8631;
DOI: https://doi.org/10.1523/JNEUROSCI.2249-20.2021
– 13 –
Author
Prof. Dr. Peter Baptist
Center for Mobile Learning with Digital Technology
University of Bayreuth
95440 Bayreuth
Germany
peter.baptist@uni-bayreuth.de

Digitalization at School – but in a Well-Balanced Way

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