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Geometry Teaching in Transition: An Investigation 
on the Importance of School Geometry in Primary 
Education 
Ana Kuzle
1
• Mathematics instruction in primary school has been influenced by 
many policy changes and empirical findings in the previous two dec -
ades. Geometry lessons, in particular, were re-evaluated due to a para -
digm change and, consequently, were attributed a new meaning within 
the mathematics curriculum worldwide. The present paper focuses on 
this paradigm shift in the sense of the evaluation to what extent both the 
didactical potential and the practical value of geometry instruction in 
elementary education are currently recognised and utilised by primary 
grade teachers. In total, 120 primary grade teachers participated in the 
study. The results showed that there had been positive recognition of the 
didactical potential of school geometry by the teachers over the previous 
two decades; however, it lacked actual implementation in school prac -
tice for different reasons. The results are discussed not only with regard 
to the latter of these but also with regard to their theoretical and practi -
cal implications.
 Keywords: geometry, geometry instruction, primary education,  
in-service teachers 
1 Faculty of Human Sciences, University of Potsdam, Germany; kuzle@uni-potsdam.de.
Doi: 10.26529/cepsj.1267

98 geometry teaching in transition
Poučevanje geometrije v tranziciji: poizvedba 
pomembnosti šolske geometrije v osnovni šoli
Ana Kuzle
• Poučevanje matematike v osnovni šoli je bilo v zadnjih dveh desetle- Poučevanje matematike v osnovni šoli je bilo v zadnjih dveh desetle -
tjih pod vplivom številnih preoblikovanj politik pa tudi empiričnih 
ugotovitev. Pouk geometrije je bil ponovno ovrednoten skladno s pa -
radigmatsko spremembo, čemur je sledilo pripisovanje novega pomena 
geometriji znotraj učnih načrtov za matematiko po svetu. Prispevek se 
osredinja na ta paradigmatski premik v smislu evalvacije, do katere mere 
sta didaktični potencial in praktična vrednost poučevanja geometrije v 
osnovni šoli trenutno priznana in izkoriščena pri učiteljih. Skupno je v 
raziskavi sodelovalo 120 učiteljev razrednega pouka. Rezultati kažejo, da 
lahko zaznavamo pozitivno prepoznavo didaktičnega potenciala šolske 
geometrije pri učiteljih v zadnjih dveh desetletjih, vendar pa do dejan -
ske izvedbe v šolsko prakso zaradi različnih razlogov ni prišlo. Rezultati 
niso pojasnjeni samo z upoštevajočim primanjkljajem, ampak sklicujoči 
se na teoretične in praktične posledice.
 Ključne besede: geometrija, poučevanje geometrije, osnovnošolsko 
izobraževanje, učitelji

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Introduction
When Winter published an article titled ‘What’s the purpose of geom -
etry in primary education?’ in 1976, the debate about the relevance of geometry 
for students in the early grades was already in full swing. Even though there 
is a clear consensus that geometry instruction is indispensable even at the el -
ementary school level (Franke & Reinhold, 2016; Sinclair & Bruce, 2015; Sitter, 
2019), the fundamental debate has not been completely settled (Eichler, 2005). 
Arguably, there is little reason to do so, as the status of elementary school ge -
ometry instruction is still considered unsatisfactory in many cases, especially 
compared to that of arithmetic (Backe-Neuwald, 2000; Sinclair & Bruce, 2015). 
Furthermore, ‘study after study shows that students perform quite poorly on a 
wide range of geometry tasks’ (Sinclair & Bruce, 2015, p. 319) independent of the 
country, which calls for emergent attention to primary school geometry (e.g., 
Glasnović Gracin & Kuzle, 2018).
Backe-Neuwald’s (2000) holistic study ‘Meaningful geometry in pri -
mary school’ provided the first impressions of various aspects of geometry 
teaching in German elementary schools two decades ago. However, the picture 
emerging from the study was full of contradictions. Despite manifold advantag -
es that lift it in a positive way from the rest of mathematics, geometry teaching 
appeared as the stepchild of mathematics in the eyes of the respondents (Backe-
Neuwald, 2000). The main reason for this was the uncertainty of the teachers, 
both regarding the selection of central geometry contents and the criteria that 
determined their significance.
In the previous two decades, geometry lessons were re-evaluated due to a 
paradigm change and were assigned new meaning within school mathematics in 
primary and secondary education (Franke & Reinhold, 2016; Kultusministerkon -
ferenz [KMK], 2005; Mammana & Villani, 1998). Only a few studies (e.g., Sitter, 
2019; Wiese, 2016) have been based on recent data following the paradigm shift. 
This paper focuses on recent developments and discussions, with a particular in -
terest in teachers and their attitudes toward teaching geometry, with the aim of 
providing additional empirical evidence based on current data on the state of 
elementary school geometry. Concretely, the focus of the investigation was the 
extent to which both the didactical potential and the practical value of geometry 
instruction in elementary education are recognised and utilised by primary grade 
teachers nowadays. Understanding the status quo of current geometry teaching is 
the basis for different policy decisions, such as the further development of math -
ematics curricula and teacher training, and, therefore, highly relevant for the im -
provement of geometry teaching in primary education.

100 geometry teaching in transition
Theoretical Background
In this section, I first present the reasons for teaching geometry from 
early grades onward, which is followed by empirical research on the topic. The 
section ends with the two research questions that guided the study.
Reasons for Teaching Geometry in Primary Education
The goals and aspects of the modern didactics of geometry have changed 
and evolved (see Franke & Reinhold, 2016; Radatz & Rickmeyer, 1991; Winter, 
1976; Wittmann, 1999). This didactic potential of geometry can be combined 
with other mathematical topics and has great potential to complement them 
and make them comprehensible through other approaches (Franke & Reinhold, 
2016). In the following, the topics and contents relevant to modern geometry 
didactics are outlined. The detailed descriptions of the goals and contents of 
good geometry teaching are intended to illustrate their relevance for mathe -
matics teaching as a whole and highlight the versatile didactical potential of 
geometry for primary education.
The proponents of an early introduction of geometric content in school 
assert various reasons. First, geometry promotes knowledge and skills that 
have relevance and overlap with a wide range of school content, not only in 
mathematics. For mathematics, a discipline in which, more than in many other 
subjects, the contents build on each other (van den Heuvel-Panhuizen, 2008), 
this connection seems to be obvious, and in that manner provides not only 
a foundation for further geometry instruction (Franke & Reinhold, 2016) but 
also for other mathematical topics (Hattermann et al., 2015). Furthermore, Bau -
ersfeld (1992) argued that geometry is the basis of arithmetic, both in terms of 
content and teaching-learning processes in general; he called this the ‘genetic 
connection’ (p. 7) between geometry and arithmetic whose argumentation was 
based on a constructivist view, namely by putting thought processes over the 
correctness of the final results or imparting competencies instead of poorly 
contextualised subject knowledge. Consequently, geometry can contribute to 
absorbing the strong heterogeneity of learning preconditions and socialisations 
present in elementary school and to creating sustainable learning foundations 
from it (Krauthausen, 2018; Wollring, 2007). These specific features of geom -
etry lessons (e.g., possibilities for activity-based teaching, discovery learning, 
action-oriented instruction) relate more strongly to the students (Radatz & 
Rickemeyer, 1991) and, in that manner, may influence students’ motivation 
and help them develop a positive attitude towards mathematics (Krauthausen, 

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2018). In addition to content areas of mathematics, geometry instruction also 
facilitates access to process-related competencies, such as problem solving and 
argumentation (KMK, 2005; NCTM, 2000). Researchers (Kuzle & Bruder, 
2016; Wittmann, 1999) emphasised that geometry instruction can contribute to 
the development of problem-solving abilities due to the richness of geometric 
content, which opens possibilities for the heuristic approach in the sense of a 
discovering, trying out, and composing and decomposing procedures.
Geometry is viewed in a special way as a tool for acquiring skills, not 
only, as mentioned above, in the area of school competencies, but much more 
generally, such as the acquisition of intellectual, cognitive and practical life 
competencies (Franke & Reinhold, 2016; Graumann, 1994; van den Heuvel-
Panhuizen, 2008; Wittmann, 1999). For example, language is permeated by 
mathematics concepts in the sense of knowledge of the mathematical necessity 
of a particular mathematical relationship (Simon, 2017). In everyday speech, 
we use geometric concepts, such as positional relations (Franke & Reinhold, 
2016; van den Heuvel-Panhuizen, 2008). Three-dimensional space in particu -
lar is difficult for young students to access in planar representations (Eichler, 
2005). Geometry can bridge this gap by helping students to gently navigate this 
process of abstraction with constant recourse to their familiar environment, 
and in that manner may support the development of the orientation ability 
and the ability to operate with objects mentally (Franke & Reinhold, 2016; van 
den Heuvel-Panhuizen, 2008). The process is complete when children learn to 
comprehend their environment and to see it in a different light through geom -
etry instruction (Eichler, 2005; Franke & Reinhold, 2016). Winter speaks of the 
‘spatial reality of the child being carefully disciplined’ (Winter, 1976, p. 14) when 
natural experiences are reflected on, analysed, and structured in the classroom. 
Nowadays, this list certainly needs to be supplemented by digital technologies, 
which can further support the teaching and learning of geometry (Jones, 2000; 
Sinclair & Bruce, 2015).
Empirical Studies on the Role of Geometry Teaching
The much-cited work of Backe-Neuwald (2000) still represents a mile -
stone in the contemporary empirical examination of primary school geometry 
and its role in the school structure. It reflected the importance of geometry 
in the teaching practice at the end of the 1990s from the perspective of 108 
in-service and 22 trainee teachers using a comprehensive questionnaire. The 
results of Backe-Neuwald’s work have since been followed up twice in the form 
of a replication (Sitter, 2019) or extension study (Wiese, 2016).

102 geometry teaching in transition
The teachers’ image of geometry lessons was rather ambivalent (Backe-
Neuwald, 2000). When the teachers were asked about associations with el -
ementary school geometry lessons, some described it as ‘a welcome change’ 
or ‘an exciting thing’ , while others considered it ‘secondary’ or ‘not important’ 
(Backe-Neuwald, 2000, pp. 16–18). Furthermore, many teachers suggested that 
the short teaching time should be filled with more important mathematical 
content, especially arithmetic. Nevertheless, Backe-Neuwald (2000) reported 
that geometry instruction was described in a positive manner compared to 
arithmetic instruction, with the teachers emphasising teaching principles more 
typical for geometry instruction, such as action-orientation, discovery-based 
learning, problem-oriented teaching, orientation to the children’s real lives, 
and working with hands-on materials and manipulatives. Regarding the lat -
ter, Backe-Neuwald (2000), however, reported that many teachers shied away 
from the preparatory intensity of geometry lessons as was also reported in a 
later study by Sitter (2019). Furthermore, the teachers stated that geometry les -
sons were increasingly characterised by partner and group work, allowed free 
work and open lessons, and could be taught across subjects. The majority of the 
teachers surveyed felt that geometry instruction had a motivating effect on the 
students.
When it came to the advantages of teaching geometry, the three benefits 
that were by far most often chosen by the teachers were ‘offers children many 
opportunities to make independent discoveries’ , ‘promotes and supports spa -
tial visualisation ability’ , and ‘makes an important contribution to the develop -
ment of reality’ , which are aligned with the literature in geometry didactics (e.g., 
Franke & Reinhold, 2016; Sinclair & Bruce, 2015; Winter, 1976). Furthermore, 
the statement ‘lays the foundation for later systematic geometry teaching in 
secondary school’ was also recognised by the teachers. This may indicate a cor -
responding long-term perspective of the teachers or be the reason for the ne -
glect in elementary school, since teachers may classify geometry instruction as 
a topic of secondary school (Backe-Neuwald, 2000). Despite the teachers gen -
erally showing positive attitudes toward geometry instruction, they also pro -
vided several reasons for neglecting it (Backe-Neuwald, 2000). Geometry was 
predominantly taught in Grades 1–2 and less so in Grades 3–4. Backe-Neuwald 
(2000) assumed different reasons for this result. Firstly, it may be that the teach -
ers felt pressured to cover all arithmetic topics which prevented them from 
teaching geometry in Grades 3–4. Secondly, it may be that the teachers did not 
feel competent in teaching the subject (Backe-Neuwald, 2000). The latter was 
also supported by Hofbauer (2018) who reported that geometry had a low pri -
ority for many secondary in-service teachers in their educational studies and, 

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therefore, felt inadequately trained in this regard. Wiese’s (2016) comparative 
study with 16 primary grade in-service teachers confirmed the earlier results 
of Backe-Neuwald (2000). On average, geometry instruction took up about 
8% of all mathematics lessons in the school year, however, the values fluctu -
ated between 2% and 19% among the individual teachers (Wiese, 2016). Wiese 
(2016) put this in relation to the roughly calculated weight of the geometry in 
the curriculum, which she specified as 20% to 30% (Wiese, 2016). Accordingly, 
she concluded that geometry lessons were still not given the weight that the 
curriculum assigned them.
Overall, Backe-Neuwald (2000) found that many of the respondents 
dealt extensively with geometry instruction on a theoretical level, and some 
showed a very reflective and self-critical attitude toward their own geometry 
instruction. However, the teachers’ answers reflected the disparity between the 
importance they attached to the subject and the significance that the subject 
had in their teaching practice. In total, 80% of the teachers surveyed agreed 
with the thesis that geometry instruction was neglected in elementary school, 
despite the stated advantages. Thus, there was a clear gap between the aspira -
tions and the reality of geometry instruction in elementary education. Conse -
quently, Backe-Neuwald (2000) concluded that the mathematics curriculum 
should be reconsidered, namely geometric and arithmetic content should be 
more closely interlinked and prepared in the sense of modern mathematics di -
dactics. Since Backe-Neuwald’ s findings, however, the mathematics curriculum, 
and with it also geometry instruction, have been subject to significant external 
changes (Mammana & Villani, 1998). The impulses are due to, on the one hand, 
the results of the large-scale studies (i.e., PISA, TIMSS), and the revaluation of 
geometry in the context of the revised (inter-)national standards, on the other; 
this makes a reassessment of existing empirical findings necessary.
Research Questions
Based on the above theoretical considerations and empirical results, the 
following research questions were investigated:
1. What didactical potential do in-service teachers assign to elementary 
school geometry? 
 – To what extent does the didactical potential of different geometry 
teaching goals and aspects discussed in the modern geometry didac -
tics correspond to current teaching practices? 
 – Considering the didactical potential of geometry teaching, which 
goals and aspects are relevant to in-service teachers?

104 geometry teaching in transition
2. What practical value do in-service teachers assign to elementary school 
geometry? 
Method
Participants
For this study, a mixed-methods research design was chosen using a 
convenience sample. Here, elementary schools were selected through existing 
contacts with the researcher’s university. Of the 159 schools contacted, only 45 
participated in the study; of the 176 questionnaires distributed, 120 of them were 
returned anonymously. The sample of 120 in-service primary teachers (Grades 
1–6) consisted of 22 male (18.3%) and 97 female teachers (80.8%). One person 
did not provide gender information. A total of 90 teachers taught mathematics 
as subject specialists (75%) and 29 of them as non-subject specialists (24.2%). The 
data of one person was not provided. In terms of professional experience, the fol -
lowing picture emerged: 16 teachers (13.3%) have been teaching mathematics for 
less than or up to two years, 18 (15%) for up to 5 years, 19 (15.8%) for up to 10 years, 
16 (13.3%) for up to 20 years, and 51 (42.5%) for more than 20 years.
Data Collection Instrument
The main source of data was a questionnaire on the state of the art of 
school geometry in primary grades that was based on an adaptation of the in -
strument from the work of Backe-Neuwald (2000). Additionally, new items or 
statements for a specific item were developed on the basis of literature published 
in the previous 20 years that (amongst other factors) reflected the paradigm 
shift, curriculum developments, and factors influencing geometry instruction 
(Franke & Reinhold, 2016; Krauthausen, 2018; Senatsverwaltung für Bildung, 
Jugend und Wissenschaft Berlin, Ministerium für Bildung, Jugend und Sport 
des Landes Brandenburg [RLP], 2015). T o cover a wide field of research and dif -
ferent research questions, the items about geometry teaching were very broad. 
The questionnaire consisted of six sections: (1) personal information (e.g., gen -
der, teaching experience, professional background), (2) characteristics of teach -
ing geometry (i.e., associations regarding teaching geometry, number of les -
sons dealing with geometric topics per grade level, instruction form, teaching 
principles, topics covered, use of digital tools, teaching sources), (3) material 
(i.e., importance of material in geometry teaching, goals of using material for 
teaching purposes, concrete material being used regarding teaching a specific 

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geometry topic), (4) goals and aspects of teaching geometry (i.e., importance 
of teaching of geometry for its application in everyday life, characterisation of 
students in geometry classes in comparison with other mathematics areas (e.g., 
motivation, interest, concentration), advantages of teaching geometry), (5) ne -
glect of teaching geometry (i.e., teachers’ opinion on whether geometry is ne -
glected in school mathematics, evaluation of the reasons leading to the neglect 
of geometry instruction), and (6) personal attitude toward teaching geometry 
(i.e., emotions associated with teaching geometry). 
Each section consisted of items with both open and closed questions. 
Thus, the questionnaire was self-contained and formed a coherent instrument 
in its structure and design, which should have always been filled out completely, 
even if (as in the present work) a selection of the given answers was made af -
terwards along with the own main points of investigation. The former enabled 
comparability between the groups studied, whereas the latter allowed the par -
ticipants the opportunity to write down their own opinions without imposing 
the researcher’s view. In this paper, I focus on sections (2) and (4) of the ques -
tionnaire, namely ‘characteristics of teaching geometry’ , and ‘goals and aspects 
of teaching geometry’ , respectively. With respect to the former, three items were 
analysed and with respect to the latter one item was analysed.
Data Analysis
The questionnaire was for the most part distributed on the site after 
agreement with the school management; in isolated cases, it was also sent by 
email and returned to the author within one week. The questionnaires were 
analysed after all the data had been collected. 
To determine what didactical potential in-service teachers assign to el -
ementary school geometry two items were analysed: an open-ended item from 
section (2) ‘characteristics of teaching geometry’ and a standardised item from 
section (4) ‘goals and aspects of teaching geometry’ . The open-ended item was 
as follows: ‘Geometry teaching in elementary school is for me…’ which al -
lowed an insight into teachers’ goals and aspects of their geometry teaching. 
The analysis of the item was based on qualitative content analysis according to 
Mayring (2000). Here, the theory-based deductive category system was used, 
which resulted from the literature review presented earlier in the paper and was 
applied to the teachers’ answers. In the qualitative analysis step, the deductively 
derived categories were methodically assigned to text passages. The core ele -
ment here is the precise definition of the given categories (Mayring, 2000). In 
this study, the categories emerged from the literature research and the current 

106 geometry teaching in transition
state of the modern geometry didactics, providing the foundation for a coding 
manual for the evaluation of the qualitative item. Accordingly, the material was 
coded based on the following eight categories:
•	 Motivation: geometry instruction has a motivating effect on students 
through alternative instructional concepts and a sense of achievement 
by experiencing success (Krauthausen, 2018).
•	 Sustainable learning environments: in geometry instruction, coopera -
tive, differentiable, and action-oriented learning environments have a 
high didactical potential (Wollring, 2007).
•	 Problem solving: geometry lessons offer many opportunities to support 
the development of problem-solving abilities (Kuzle & Bruder, 2016).
•	 Opening up reality: geometry aids in understanding reality, and trains 
learners in everyday practical competencies (Graumann, 2009; van den 
Heuvel-Panhuizen, 2008).
•	 Spatial visualisation ability: geometry instruction supports the deve -
lopment of the ability to orientate oneself in three-dimensional space, 
and to operate mentally (Franke & Reinhold, 2016; Sinclair & Bruce, 
2015; van den Heuvel-Panhuizen, 2008).
•	 Acquisition of arithmetic concepts: geometry supports and comple -
ments the acquisition of arithmetic concepts (Bauersfeld, 1992; Franke 
& Reinhold, 2016; van den Heuvel-Panhuizen, 2008).
•	 Geometric concept formation: the knowledge of geometric concepts 
provides a foundation for further geometry instruction and supports the 
development of knowledge to systematise geometric concepts (Franke & 
Reinhold, 2016).
•	 Basic knowledge: geometry (content) is part of general knowledge and 
provides a foundation for understanding other mathematical and histo -
rical topics (Hattermann et al., 2015).
Concretely, the text material was examined to determine to what extent 
the categories can be applied and whether there are problems of demarcation 
between the categories. In the case of the present work, the category system could 
be tested as suitable for all texts. However, there were statements that could not 
be categorised in the presented category system as they contained no content 
pertaining to the didactical potential of geometry teaching. With respect to the 
former, after the first pass with the help of the interpretation rules, which are 
based on Mayring’s work (2000) regarding the applied techniques of ‘paraphras -
ing’ and ‘generalisation’, eight categories were formed. All collected statements 
of the teachers were shortened in paraphrasing to the essential content of the 

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statement and then by generalisation, the main statement was extracted. These 
main statements were assigned to each category. The resulting category system 
now contained those aspects that could be filtered out and summarised from 
the available text material in a theory-based manner on the basis of the defined 
characteristics for ‘goals and aspects of geometry instruction’ . With respect to the 
statements that did not fit the developed category system, an additional category 
system needed to be developed as they contained no content mathematics-relat -
ed statements but more affect-related statements revealing values (i.e., personal 
truths of individuals) and beliefs (i.e., cognitive statements to which the holder 
attributes truth or applicability) (Hannula, 2012) of the participating teachers re -
garding teaching geometry. The nature of these was (independent of the level) 
classified into three categories: positive (e.g., positive values such as ‘important’ , 
‘indispensable’ or positive beliefs such as ‘Geometry is an essential part of math -
ematics teaching. ’), negative (e.g., negative values such as ‘secondary’ or negative 
beliefs such as ‘difficult’ , ‘stressful’) and neutral (Laine et al., 2015). By using two 
different coding systems (i.e., one reflecting the didactical potential of teaching 
geometry and the other reflecting the mathematics-related affect), it was possible 
to assign each statement to one of the developed categories. 
In contrast to the open-ended question, the standardised item included 
22 statements on the advantages of teaching geometry that have been taken 
from the work of Backe-Neuwald (2000) but also supplemented with state -
ments from the more recent literature outlined earlier in the present paper with 
an option of writing an additional statement. Through these statements, all 
eight categories of the didactical potential of geometry were covered (i.e., mo -
tivation, sustainable learning environments, problem solving, opening up real -
ity, spatial visualisation ability, acquisition of arithmetic concepts, geometric 
concept formation, and basic knowledge). The participants were asked to mark 
aspects of school geometry that were most relevant to them, and to hierarchise 
five answers accordingly (e.g., 1-most relevant). The item was evaluated accord -
ing to the frequencies of all answer options and assigned rankings. Regarding 
the latter, a simple score was generated, which valued the most important rea -
son with five points, the second most important with four points, and so on. 
The score, as opposed to merely looking at the absolute frequencies, allowed 
for a better assessment of the importance of the reasons, even though both 
metrics showed an almost equal ordering of the reasons. Both items comple -
mented each other; by evaluating the open-ended item, teachers were given the 
opportunity to express themselves freely without being steered in one direc -
tion by predetermined answer choices. Through the additional evaluation of 
the standardised item, the spectrum of answers was expanded. It was therefore 

108 geometry teaching in transition
of particular interest whether the answers to the open-ended question cor -
responded to those of the standardised item, and to what extent new aspects 
emerged through the standardised item.
To determine the practical value of teaching geometry from the teach -
ers’ perspective, two items were analysed. Two items from section (2) ‘charac -
teristics of teaching geometry’ focused on a quantitative aspect of teaching ge -
ometry, namely the number of lessons dealing with geometric topics per grade 
level, and on the form in which geometry instruction was anchored in math -
ematics instruction (i.e., parts of lessons, individual lessons, integrated into the 
weekly or daily schedule, integrated into interdisciplinary projects or series of 
lessons). In addition, when evaluating this item, the ranking undertaken by the 
teachers (e.g., 1-most often) was considered, which allowed individual items a 
higher weighting than others. Thus, it was assumed that teachers who checked 
the item ‘series of lessons’ and ‘integration into the weekly or daily schedule’ 
gave more space to geometry instruction than teachers who checked ‘parts of 
lessons’ or ‘individual lessons’ . The item ‘integrated into interdisciplinary pro -
jects’ indicated that geometry lessons were not considered as a part of regular 
mathematics lessons but were only treated in so-called project weeks. All stand -
ardised items were analysed using descriptive statistics. 
Results
In this section, the results pertaining to the two research questions are 
presented. Concretely, I present the results regarding the didactical potential of 
teaching geometry recognised by the in-service teachers and the practical value 
they assign to teaching geometry.
Didactical Potential of Elementary School Geometry:  
Goals and Aspects
Here I present the results regarding teachers’ associations with teaching 
geometry, and the benefits of teaching geometry that cover (2) ‘aspects per -
taining to characteristics of teaching geometry’, and (4) ‘goals and aspects of 
teaching geometry’, respectively from the questionnaire. The results reflect a 
clear tendency regarding the teachers’ responses to the open-ended item (see 
Table 1). Statements
2
 regarding several categories are presented below along the 
2 A subjective selection of content statements by the author is unavoidable; this has been handled in 
a comparable manner in the previous research (Backe-Neuwald, 2000), and does not necessarily 
diminish the validity of the conclusions.

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variables of teaching experience, and professional background. The motivation 
category made up the largest part of the content-related statements with a total 
of 34 teachers (29.1%) stating that geometry lessons were highly motivating for 
the students. Their answers included statements such as:
•	 ‘a way to get children interested in mathematics who otherwise do not like 
the subject. ’ (up to 2 yrs., specialist)
•	 ‘nice, because the students are motivated to do it.’ (up to 2 yrs., 
non-specialist) 
•	 ‘motivates the students, also those who don’t like arithmetic so much. ’ (up 
to 20 yrs., specialist) 
In the second place of content-related statements, 12 teachers (10.3%) in -
dicated sustainable learning environments, with a particular emphasis being as -
signed to the action-oriented aspect. Their answers included statements such as:
•	 ‘very interesting, because it is so versatile and exciting, and a lot can be 
practically discovered, tinkered with and developed with the children. ’ (up 
to 2 yrs., specialist)
•	 ‘above all action-oriented work. ’ (over 20 yrs., specialist)
•	 ‘laying, folding, drawing, constructing, comparing, etc. practical, visuali -
sed, active learning. ’ (over 20 yrs., specialist)
Even though in the third place of content-related statements, only 8.5% 
of the teachers’ answers ( n = 10) associated geometry teaching with the de -
velopment of spatial visualisation ability. Their responses included statements 
such as:
•	 ‘a lot of mental geometry, i.e., work on spatial visualisation ability ... ’ (up 
to 10 yrs., specialist)
•	 ‘a branch of mathematics, important for the development of spatial visua -
lisation … ’ (over 20 yrs., specialist)
All other content categories were coded to a limited extent, namely 
opening up reality, problem solving, acquisition of arithmetic concepts, geo -
metric concept formation, and basic knowledge. Seven teachers did not fill out 
the item (5.8%). 
Lastly, worth reporting are affect-related statements, which made up al -
most one-third of all statements. A total of 23.3% of the teachers ( n = 28) had 
positive affect-related values and beliefs about teaching geometry. Occasion -
ally, positive statements were associated with too little weight being given to 

110 geometry teaching in transition
geometry. The positive responses included statements such as: 
•	 ‘one of the most exciting and interesting subject areas, but nevertheless 
often underrepresented. ’ (up to 10 yrs., specialist, belief)
•	 ‘extremely important and a significant part of mathematics. ’ (over 20 yrs., 
specialist, value)
Furthermore, eight affect-related statements (6.7%) reflected strong 
negative affect-related values and beliefs about teaching geometry. Negative re -
sponses included statements such as:
•	 ‘secondary’ (up to 2 yrs., non-specialist, value)
•	 ‘difficult because motor skills (holding pencil, drawing lines) are underde -
veloped. ’ (up to 2 yrs., non-specialist, belief)
•	 ‘always a challenge. ’ (up to 20 yrs., specialist, belief)
•	 ‘stressful because I would have to have 20 hands to help everyone. ’ (over 20 
yrs., specialist, belief)
Table 1
Distribution of In-service Teachers’ Free Associations Regarding Geometry 
Teaching
Type of category Category Absolute and relative frequencies
Content-related 
statement
Motivation 34 (28.3%)
Sustainable learning environments 12 (10%)
Problem solving 4 (3.3%)
Opening up reality 7 (5.8%)
Spatial visualisation ability 10 (8.3%)
Acquisition of arithmetic concepts 4 (3.3%)
Geometric concept formation 2 (1.7%)
Basic knowledge 2 (1.7%)
Affect-related 
statement
Positive affect-related values and beliefs 28 (23.3%)
Neutral affect-related values and beliefs 2 (1.7%)
Negative affect-related values and beliefs 8 (6.7%)
No statement 7 (5.8%)
The results from the standardised item pertaining to the benefits of 
teaching geometry in primary school are shown in Table 2. Of 120 surveys, 
119 teachers filled out this item. Additionally, not all participants ranked their 
answers ( n = 24), so these data were not considered for the Top 5 Score. The 
teachers’ answers predominantly confirmed the findings of the aforementioned 

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open-ended item. Motivational aspects were included in several statements, 
such as ‘is fun for students’ (item 4.3.1), ‘can promote a positive attitude towards 
the subject of mathematics’ (item 4.3.17), and similarly was the most frequently 
coded content-related aspect. Likewise, the benefit of teaching geometry to 
support the acquisition of arithmetic concepts (item 4.3.19) was recognised by 
11 teachers only. Here, in contrast, the relevance of spatial visualisation (item 
4.3.13) predominated with 79.2% of teachers ( n = 95) attributing this geometric 
goal the greatest relevance in primary school geometry. A total of 32 teachers 
attributed this statement one of the five possible rankings, with 18 of them giv -
ing it rank 1. Also, opening up reality (item 4.3.10), and problem solving (item 
4.3.18) were attributed greater importance than was reflected on the open-end -
ed item, with 39 and 41 instances, respectively.
Table 2
Benefits of Teaching Geometry in School Mathematics
Item Statement Geometry in primary school ...
Absolute frequencies 
(max.119)
Top 5 Score
4.3.13 promotes and supports spatial visualisation ability. 95 258
4.3.14
gives children who are otherwise weak in math-
ematics a sense of achievement.
73 126
4.3.6
offers children many opportunities to make inde-
pendent discoveries.
69 127
4.3.1 is fun for students. 68 122
4.3.21
trains motor skills (e.g., sheathing, folding, stretch-
ing, drawing).
67 94
4.3.16
is an indispensable part of mathematics educa-
tion.
59 84
4.3.2 promotes children’s creativity. 53 59
4.3.3
promotes elementary mental abilities like ordering 
and classifying.
51
71
4.3.12 sharpens perception. 48 77
4.3.22
enables them to grasp content using concrete 
material.
47 50
4.3.18
makes an important contribution to the develop-
ment of reality.
41 58
4.3.17
can promote a positive attitude towards the 
subject of mathematics.
39 50
4.3.10
enables a contribution to the formation of general 
mathematical competencies (e.g., reasoning, 
problem solving).
39 49
4.3.7 offers opportunities for open forms of teaching. 38 24

112
Item Statement Geometry in primary school ...
Absolute frequencies 
(max.119)
Top 5 Score
4.3.9 promotes and challenges language competence. 35 31
4.3.20
lays the foundation for later systematic geometry 
teaching.
33 27
4.3.8 offers opportunities for interdisciplinary work. 33 26
4.3.4 enables individual differentiation. 25 25
4.3.15 promotes describing and uncovering structures. 24 15
4.3.11 promotes aesthetic sensibility. 22 10
4.3.5 promotes social skills. 20 10
4.3.19 supports the acquisition of arithmetic concepts. 11 7
4.3.23 Other:__________ 0 0
Practical Value of Elementary School Geometry 
Here I present the results pertaining to the practical value of elemen -
tary school geometry, specifically the form of instruction and teaching hours in 
geometry. Regarding the implementation form in which geometry lessons are 
taught, the results showed that they were mainly taught in the form of a series 
of lessons (65%), and individual lessons (64.2%) (see Figure 1). About one-third 
of participants indicated that parts of lessons, projects or daily/weekly sched -
ules were filled with geometric content. In total, six participants did not fill out 
this item. Furthermore, only half of the teachers ranked the marked answers 
by frequency ( n = 54) so that only a tendency could be depicted. Accordingly, 
42.6% of teachers ( n = 23) most often conducted a series of lessons, followed 
by 33.3% of teachers ( n = 18) who conducted individual lessons. Here, the Top 
5 Score was higher for individual lessons with a score of 186 than for a series of 
lessons with a score of 149 since more teachers gave ranks 1 and 2 to the former. 

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Figure 1
Different Implementation Forms of Geometry Lessons
Table 3 illustrates results regarding the teaching hours per grade level 
within geometry instruction. It must be taken into account that there were 
missing data since the participating teachers did not necessarily teach math -
ematics in all grades. Furthermore, each federal state prescribes a contingent of 
hours in each subject within own elementary school policy regulations. Gener -
ally, these vary between 160 and 200 hours for mathematics. There are no con -
crete specifications as to how many hours and which areas should be covered. 
In the school’s internal curriculum, this is mostly determined from school to 
school. Thus, the information on how many mathematics lessons and specifi -
cally geometry lessons were taught in total varies in every school. As an exam -
ple, one participating school provided information on the number of geometry 
lessons per grade level: Grades 1–2 50 hours, Grade 3 50 hours, and Grades 
4–6 70 hours. Lastly, some answers were given in percentages, and for that rea -
son, could not be used and were unfortunately not included in the evaluation. 
Since these pieces of information were not available, only a tendency could be 
depicted; the number of geometry lessons in mathematics increases with the 
increasing grade level. However, similarities can be seen with respect to its ex -
treme minimum value independent of the grade level.

114 geometry teaching in transition
Table 3
Distribution of Teaching Hours per Grade Level
Grade
1 2 3 4 5 6
Average 15.77 18.83 20.74 25.76 28.29 34.23
Median 15 20 20 20 30 35
Standard deviation 9.416 9.903 11.710 16.239 15.332 18.390
Minimum 1 1 0 1 1 1
Maximum 35 40 60 55 60 80
Discussion 
This study investigated the importance of school geometry in primary 
education by providing an insight into the extent to which both the didactical 
potential and the practical value of geometry instruction in elementary schools 
nowadays are recognised and utilised by primary grade teachers. Even though 
the importance of geometry instruction within elementary school mathemat -
ics increased significantly, as reported in the Backe-Neuwald’s (2000) study as 
well as in newer replication and extension studies (Sitter, 2019; Wiese, 2016), 
the question about the current importance of geometry teaching cannot be an -
swered unambiguously. 
The results revealed that teachers employ teaching practices conducive 
to geometry learning but also revealed their insecurity regarding other impor -
tant aspects as reported in the literature (Bauersfeld, 1992; Franke & Reinhold, 
2016; Radatz & Rickmeyer, 1991; van den Heuvel-Panhuizen, 2008; Winter, 
1997; Wollring, 2007). The evaluation of the open-ended item ‘Geometry teach -
ing in elementary school is for me … ’ showed an explicit subject didactic con -
ception, especially for the topics of spatial visualisation, development of reality 
as well as problem solving. A total of 8.5% of the respondents associated spatial 
visualisation ability as a central aspect of teaching geometry in primary school. 
In the evaluation of the standardised items, item 4.3.13 ‘promotes and supports 
spatial visualisation ability’ was ranked most significant with 95 respondents 
marking this statement. This result can be seen to be consistent with the study 
of Backe-Neuwald (2000) which was the third most common item chosen by 
teachers. Franke and Reinhold (2016), and Sinclair and Bruce (2015) also assign 
to this content one of the most important didactical potentials of geometry 
teaching in primary education; spatial visualisation is often listed as one of the 
main goals of primary grade geometry (Franke & Reinhold, 2016). On the one 

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hand, spatial visualisation is found in many geometric topics, and, on the other, 
the topic of ‘Space and Shape’ is extensively anchored in the framework cur -
riculum (RLP , 2015). 
Other findings from this research suggest that geometry instruction 
is poorly linked to the rest of mathematics instruction. Although Graumann 
(2009), and Kuzle and Bruder (2016) make it clear that geometry instruction is 
particularly suited for training problem-solving abilities, few teachers reported 
this aspect. In the open-ended item, only 3.4% of the teachers commented on 
problem solving; in the standardised item, statement 4.3.10 on general math -
ematical competencies such as problem solving and reasoning, is ranked 13 
out of 23 ( n = 39). Similarly, this aspect had the least relevance in the study of 
Backe-Neuwald (2000). This is rather problematic, since problem-solving abili -
ties are highly relevant for the whole mathematics education and can be learned 
and extended especially through geometry problems (Kuzle & Bruder, 2016). 
However, on a positive note, discovery learning, which is related to problem-
solving skills in the broadest sense, was rated as a highly relevant aspect of 
geometry instruction. The fact that geometry ‘offers children many opportuni -
ties to make independent discoveries’ (item 4.3.6) was ranked 3 out of 23 ( n = 
69). This is aligned with Backe-Neuwald’s (2000) study where this aspect was 
recognised as the most important aspect of teaching geometry by about 60% of 
respondents.
In Backe-Neuwald’s (2000) study, discovery learning and opening up 
reality were ranked first and second as the most important aspects of geometry 
instruction, respectively. These can be seen as part of a successful geometry 
learning environment. The teachers surveyed referred to geometry learning en -
vironments in 10.3% of their responses ( n = 12). According to Franke and Rein -
hold (2016), and Wollring (2007), geometry instruction is particularly suitable 
for creating sustainable learning environments. Concretely, teachers recognised 
differentiating instruction, and action orientation as important aspects of ge -
ometry instruction. These answers indicated that they dealt with individual as -
pects of successful learning environments. However, action orientation and dif -
ferentiation were mentioned rarely on the open-ended item; ‘enables individual 
differentiation’ (item 4.3.4) and ‘enables them to grasp content using concrete 
material’ (item 4.3.22 ) appeared in 47 and 25 instances, respectively. Since the 
evaluation of the standardised item 4.3.6 showed that the statement ‘offers chil -
dren many opportunities to make independent discoveries’ was highly ranked 
by the teachers, it can therefore be assumed that geometric learning environ -
ments are designed by teachers in the sense of discovery learning. However, 
it remains questionable to what extent these make a connection to the lived 

116 geometry teaching in transition
experiences of the students since (other than in the study of Backe-Neuwald 
(2000)) only about one-third of participants ( n = 41) attributed importance to 
‘makes an important contribution to the development of reality’ (item 4.3.18). 
Since it is through the connection to reality that children understand the rele -
vance and the meaning of the content being learnt (Winter, 1976) it is worrying 
that this aspect has declined in relevance in the previous two decades. 
The study results indicated that the teachers had a concrete idea of what 
geometry teaching was about and which aspects were considered to be particu -
larly important (see Table 1). Nevertheless, the subject-specific responses only 
partially reflected the geometry discourse in the community since the answers 
on the open-ended item reflected the motivational aspect more (29.1%) rather 
than geometrical topics. Such association with geometry teaching can be fur -
ther differentiated. One main argument for motivation was that children who 
are weak in arithmetic lessons can achieve a sense of achievement in geometry 
lessons and are therefore motivated. Also, in the evaluation of the standardised 
item, the statement ‘enables children who are otherwise weak in mathematics to 
experience success’ (item 4.3.14) was the second most frequently marked ( n = 
73; 61.3%). Thus, the teachers agreed with the statement of Krauthausen (2018, 
p. 105) that children can achieve a positive self-concept regarding mathematics 
through geometry instruction, creating an opportunity to compensate for weak -
nesses in arithmetic instruction. Even though this aspect was ranked fourth in 
the study of Backe-Neuwald (2000), it was more dominant since only about 30% 
of teachers ( n = 32) agreed with this statement. Furthermore, teachers indicated 
that both they and the children enjoy geometry lessons. For instance, Graumann 
(1994) assumed that geometry instruction offered great potential for learning in 
an action-oriented, playful, and fun way. This view was also reflected in the teach -
ers’ statements as well as in the standardised item, with the statement, ‘is fun for 
students, ’ (item 4.3.1) being marked fourth most often.
Furthermore, the survey supported the results of Backe-Neuwald 
(2000) that geometry is still barely connected to other areas of mathematics, 
such as arithmetic and algebra, which was revealed by both the open-ended 
item and the standardised item. The statement ‘supports the acquisition of 
arithmetic concepts’ (item 4.3.19) was hardly seen as relevant by the teachers 
(n = 11) or mentioned by the teachers on the open-ended item ( n = 4). Fur -
thermore, the statement ‘promotes describing and uncovering structures’ (item 
4.3.15) was also recognised by 24 teachers only. These responses indicate that 
teachers treat geometry as an autonomous part of mathematics and make few 
references to arithmetic or algebra. These results clearly show that the two ar -
eas are still strongly separated. Additionally, the statement ‘lays the foundation 

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for later systematic geometry teaching’ was selected least frequently by teach -
ers ( n = 33). This result indicates that geometry is still not being taught in the 
sense of a spiral curriculum, as Wittmann had called for it in 1999 but in a 
canonical way and not integrated into the network of different contextualised 
areas of competence. Wittmann (1999) spoke of the fact that ‘geometry has no 
tradition in elementary school’ (p. 208). Geometry can and must be the basis 
of arithmetic, both in terms of content and in the formation of mathemati -
cal teaching-learning processes (Bauersfeld, 1992; van den Heuvel-Panhuizen, 
2008; Wittmann, 1999). Geometry is also useful in the subject area ‘Patterns 
and structures’ to understand and deepen arithmetic concepts, and to initiate 
algebraic structures (van den Heuvel-Panhuizen, 2008). If the often-lamented 
weak institutional, and also practical anchoring of geometry lessons in the cur -
riculum is to be overcome, better integration with other mathematical sub-
areas and competencies must be ensured. This is unfortunately not reflected in 
the current framework curriculum (RLP , 2015). A similar picture was reported 
by Glasnović Gracin and Kuzle (2018) regarding the designated curriculum in 
Croatia and students’ performance. In order to link different mathematical ar -
eas, references between arithmetic, algebra and geometry should also be made 
within the framework curriculum. Also, in teacher training, greater emphasis 
on the subject and didactic interdependencies between geometry, arithmetic, 
and algebra instruction should be given (Franke & Reinhold, 2016). 
The question of the practical value that in-service teachers assign to 
geometry instruction in elementary schools provided a much clearer picture. 
Geometry teaching offers a great potential to train and extend a wide variety 
of mathematical skills and abilities. The fact that 65% of the respondents con -
duct entire lesson series on geometric content and less than one-third teach 
geometry lessons in projects (30.8%) or as part of a lesson (32.5%) shows that 
geometry lessons have become highly valued. Thus, it seems that the teach -
ers give geometric topics a high priority both in terms of content and time 
and that they have taken up a fixed place in mathematics lessons and are not 
outsourced in the form of a project but are an integral part of mathematics in -
struction. This is somewhat contradictory to results pertaining to the amount 
of time spent per grade level teaching geometry (see Table 3), but this item of -
fers only a reliable result to a limited extent. However, there is a tendency that 
the number of teaching hours increases continuously from Grade 1 to Grade 
6. Backe-Neuwald (2000) came to a similar conclusion, suggesting that more 
instructional time was needed for arithmetic basics in the lower grades and 
that geometry instruction was neglected for this reason. This result could be 
explained by the paradigm shift that started at the end of the 1990s. National 

118 geometry teaching in transition
and international movements within mathematics have led to a new emphasis 
on the subject, which has had a great influence on school life in general, but also 
on the teaching of geometry in elementary schools (Mammana & Villani, 1998) 
as well as on new educational standards (KMK, 2005). It remains problematic 
that Germany’s educational system is famously decentralised, which means 
that Germany effectively has 16 different school systems, one for each federal 
state. Thus, the number of prescribed hours for each subject, and hence also 
mathematics differs. Also, each federal state’s curriculum does not prescribe 
the number of hours for each mathematical topic which makes it difficult to 
understand the trend describing the teachers’ choices.
Conclusions
The geometry didactic community attributes a high didactic potential to 
geometry instruction and a didactic and content-related dovetailing with the rest 
of mathematics instruction is demanded (Bauerfeld, 1993; Franke & Reinhold, 
2016; Radatz & Rickmeyer, 1991; Winter, 1971; Wittmann, 1999). In recent dec -
ades, many goals and aspects of good geometry teaching have been elaborated, 
which were only partially implemented by the teachers surveyed. The study 
showed that the participating teachers had generally a positive attitude toward 
the teaching of geometry and a professional knowledge of basic topics of geom -
etry didactics. However, it also became clear that the potential of geometry teach -
ing was not being fully exploited by the teachers at the present time. Many of the 
geometry-relevant topics, goals and aspects were mentioned to a limited extent or 
were attributed minimal relevance. The positive attitudes and the willingness to 
deal with the topic field are optimal prerequisites for granting geometry didactics 
more attention. Many teachers stated that both they and their students are par -
ticularly motivated to deal with geometric content in the classroom. Essentially, 
some of the goals and aspects of good geometry teaching have already found their 
way into mathematics lessons. However, the results pertaining to the number of 
hours spent on geometry topics showed that the subject is still not treated equally 
compared to other areas of school mathematics. 
This study was a mixed-methods study using convenience sampling. 
Thus, the participating teachers only represented the country to a limited ex -
tent. One should not forget that Germany’s educational system is decentralised. 
Hence, the results of the study are limited to the curricula of the federal states of 
Berlin and Brandenburg. As such, the results may be limited to specific cultural 
and contextual characteristics. Also, due to voluntary participation, one may 
assume that the teachers were more motivated and that the results reflect the 

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practices of motivated teachers. However, this is questionable since the data did 
not reveal a unanimous picture nor conclusive results in all cases. For the gen -
eralisability of the results in a wider setting, it is essential to recruit a larger sam -
ple from a variety of settings (e.g., federal states or countries) using alternative 
sampling strategies (e.g., maximum variation sampling, probability sampling), 
so that a researcher could create a less-biased and more thorough description 
of the current state of geometry teaching on both national and international 
levels, which can then be generalisable to a population.
The results have also provided evidence of possible theoretical as well as 
methodological biases. With respect to the former, an extensive literature re -
view concerning modern geometry didactics was undertaken. However, surely 
not all aspects of its didactical potential have been covered but rather the main 
ones. With respect to the latter, some items were not entirely or fully answered 
by all participants (e.g., item 2.2), and some answers were not free of contradic -
tions; for example, a majority of the respondents considered geometry teaching 
to be neglected and its topics to be unimportant in large parts, but neverthe -
less taught geometry with a positive attitude. Eliminating these problems with 
such an extensive and aspect-rich questionnaire is not likely to be trivial and 
would include the use of complementary instruments that are not based on 
self-assessment, such as student achievement tests, classroom documentation, 
or protocols as suggested by Wiese (2016). In that manner, one would obtain 
a more objective ‘truth’ by taking two perspectives in focus: the perspective 
of a teacher himself, and the perspective of the researcher. Furthermore, since 
this study showed that teachers were fundamentally positive about geometry 
instruction, and partially recognised its didactic potential, it would be inter -
esting to further explore how teachers could be supported in conducting a 
high-quality geometry instruction that has an adequate place in mathematics 
education. Also, with the results of the questionnaire, it was difficult to make 
a statement about the number of hours geometry was taught in the individual 
grades. In this context, it would be interesting to investigate which concrete 
goals and contents are implemented and to what extent geometry is actually 
taught. By using the above-mentioned methods, it would be possible to make 
precise statements about the scope, goals, and content of geometry instruction, 
and to identify and analyse gaps. 
By relating the study results to educational practice, some implications 
can be drawn as well as possible research of practical nature. Historically, edu -
cational policy, educational standards, and framework curricula have a strong 
influence on the status, goals, and content of school geometry (Franke & Rein -
hold, 2016). The strong influence of educational policy regulations on everyday 

120 geometry teaching in transition
teaching practice suggests that particularly relevant goals and content need to 
be more strongly anchored in framework curricula and standards. In the case 
of Germany with its decentralised system, it is questionable to what extent it 
is possible to set this as a goal as well as to prescribe hours for geometry top -
ics. The existing curriculum models (e.g., Remillard & Heck, 2014) present the 
starting point for providing students’ well-established opportunities to learn 
geometry. The designated curriculum (i.e., instructional plans specified by an 
authorised, governing body) here plays a vital role since it influences all compo -
nents of the operational curriculum (i.e., teacher-intended curriculum, enacted 
curriculum, attained curriculum). Likewise, this may also affect countries with 
highly centralised educational systems when policymakers attribute geometry 
little attention within the designated curriculum. Also, at this point, it would 
be interesting to further research the extent to which teachers design their ge -
ometry instruction according to current framework curricula. It also remains 
to be critically questioned how well the paradigm shift in teacher education 
can be distinguished from the paradigm shift in schools over the previous two 
decades. To what extent has the paradigm shift been introduced in higher ed -
ucation institutions? Here, the questionnaire would need to be expanded by 
items focusing on the respective teacher training program which would involve 
a very extensive and time-consuming study.
The study showed that the teachers were basically positive about the 
geometry instruction and also partially recognised its didactic potential. That 
said, it would be interesting to further investigate how teachers can be sup -
ported in order to carry out optimal geometry teaching, which takes an ad -
equate place in mathematics education. Adequate and solid teacher training 
focusing on both content and pedagogical content knowledge is essential as 
well as supplementary training in order to dissolve uncertainties when teaching 
geometry (Jones & Mooney, 2003). Thus, solid teacher training needs to better 
prepare future mathematics teachers to play the roles and to reflect the teach -
ing practices conducive to geometry learning that have been emphasised in the 
literature. Thus, we need to understand how teachers may be better prepared 
to play the roles that have been emphasised in the literature as well as ongoing 
developments (Sinclair & Bruce, 2015). More generally, regular empirical stud -
ies on the status of elementary school geometry on different levels (e.g., school, 
university) should be conducted to obtain up-to-date developments. Only in 
this way can general statements be substantiated, and reality be depicted.

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Biographical note
Ana Kuzle, PhD, is an associate professor in primary education in 
mathematics at the Faculty of Human Sciences, University of Potsdam. Her 
main fields of interest are: development of teaching quality in primary math -
ematics teaching and long-term competence development of learners (focus: 
problem solving, argumentation, metacognition, geometry), teacher beliefs 
(focus: geometry, problem solving), and children’s fundamental ideas and so -
cio-emotional atmosphere in geometry lessons using drawings.