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BEGIN:VEVENT
SUMMARY:TEXTBOOK RESEARCH VIA THE ANTHROPOLOGICAL THEORY OF DIDACTICS (ATD
): THE CASE OF REPRESENTATION OF FUNCTIONS
DTSTART;VALUE=DATE-TIME:20190916T130000Z
DTEND;VALUE=DATE-TIME:20190916T133000Z
DTSTAMP;VALUE=DATE-TIME:20211021T061059Z
UID:indico-contribution-4-37@tagung.math.uni-paderborn.de
DESCRIPTION:Speakers: Solomon A. Tesfamicael (Department of Teacher Educat
ion at The Norwegian University of Science and Technology (NTNU))\nWe pres
ent a work in progress of a new method for textbook research based on the
Anthropological Theory of Didactics (ATD). Representation of the concept
of function is chosen as a particular example to validate how the praxeolo
gy and levels of didactic co-determination of ATD can be used for textbook
research. Two different Norwegian textbooks published at different times
are selected. The analyses of the data via relevant theories contributes t
o the ongoing discussion and addresses recommendations of recent research
focusing on mathematics textbooks.\n\nhttps://tagung.math.uni-paderborn.de
/event/1/contributions/37/
LOCATION: O1 258
URL:https://tagung.math.uni-paderborn.de/event/1/contributions/37/
END:VEVENT
BEGIN:VEVENT
SUMMARY:MATERIALS FOR INCLUSIVE MATHEMATICS EDUCATION – DESIGN PRINCIPLE
S AND PRACTICES
DTSTART;VALUE=DATE-TIME:20190916T133000Z
DTEND;VALUE=DATE-TIME:20190916T140000Z
DTSTAMP;VALUE=DATE-TIME:20211021T061059Z
UID:indico-contribution-4-61@tagung.math.uni-paderborn.de
DESCRIPTION:Speakers: Uta Häsel-Weide ()\, Marcus Nührenbörger (TU Dort
mund)\nIn this paper\, we aim at identifying inclusive practises in inclus
ive maths lessons. Based on the textbook “Das Zahlenbuch” and the acco
mpanying artefacts\, the lessons should offer occasions for all children t
o participate in and benefit from the learning situation. In our study\, w
e analyse videographed lessons\, considering the ideas of sensitivity of d
ifferences\, language and materials and connections of content-related and
social learning. In this paper\, the results of the qualitative analysis
of an introductory phase with all children in the field of simple subtract
ion tasks are discussed.\n\nhttps://tagung.math.uni-paderborn.de/event/1/c
ontributions/61/
LOCATION: O2
URL:https://tagung.math.uni-paderborn.de/event/1/contributions/61/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Why the textbook matters - a two-domain impact analysis
DTSTART;VALUE=DATE-TIME:20190916T120000Z
DTEND;VALUE=DATE-TIME:20190916T123000Z
DTSTAMP;VALUE=DATE-TIME:20211021T061059Z
UID:indico-contribution-4-35@tagung.math.uni-paderborn.de
DESCRIPTION:Speakers: Henning Sievert (IPN Kiel)\nIn primary schools aroun
d the world\, mathematics textbooks are the most relevant medium for lesso
n preparation for the vast majority of teachers. Though the field of textb
ook research is constantly growing\, our knowledge about textbook effects
on students learning is still rather constrained. In this contribution\, t
hree studies are presented\, which address that research gap for the field
of primary school arithmetic by using a large-scale longitudinal sample o
f 1664 students from Grade 1 to 3. The first study shows general effects o
f the textbooks on the students’ mathematical achievement in arithmetic
over the first three years of schooling. Studies 2 and 3 deepen this analy
sis by focusing on the domains of adaptive strategy choice and the use of
arithmetic principles\, and explain the effects by the quality of learning
opportunities presented in the textbooks.\n\nhttps://tagung.math.uni-pade
rborn.de/event/1/contributions/35/
LOCATION: O1 258
URL:https://tagung.math.uni-paderborn.de/event/1/contributions/35/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mathematical and linguistic features of word problems in grade 4 a
nd 5 German textbooks - A comparative corpuslinguistic approach
DTSTART;VALUE=DATE-TIME:20190919T090000Z
DTEND;VALUE=DATE-TIME:20190919T093000Z
DTSTAMP;VALUE=DATE-TIME:20211021T061059Z
UID:indico-contribution-4-38@tagung.math.uni-paderborn.de
DESCRIPTION:Speakers: Jennifer Dröse (TU Dortmund University - IEEM)\nMat
hematical and linguistic features of word problems have been investigated
with respect to their potential difficulties in various studies. In the cu
rrent study\, the transition of grade 4 (primary school) to grade 5 (secon
dary school) is studied for identifying changing demands in these features
. For this\, the study focuses word problems using the basic rules of arit
hmetic in different German grade 4 and grade 5 textbooks. By a corpus ling
uistic approach\, similarities among the features can be revealed as well
as differences depending on the grade and the type of rule of arithmetic.
The results of the study concerning these features and changing demands ar
e relevant in order to design word problems for teaching-learning arrangem
ents\, which prepare students to cope with the word problems in German gra
de 5 textbooks.\n\nhttps://tagung.math.uni-paderborn.de/event/1/contributi
ons/38/
LOCATION: O2
URL:https://tagung.math.uni-paderborn.de/event/1/contributions/38/
END:VEVENT
BEGIN:VEVENT
SUMMARY:A COMPARISON OF PAGE SAMPLING METHODS FOR MATHEMATICS TEXTBOOK CON
TENT ANALYSIS
DTSTART;VALUE=DATE-TIME:20190916T123000Z
DTEND;VALUE=DATE-TIME:20190916T130000Z
DTSTAMP;VALUE=DATE-TIME:20211021T061059Z
UID:indico-contribution-4-36@tagung.math.uni-paderborn.de
DESCRIPTION:Speakers: Dustin Jones (Sam Houston State University)\nWe util
ize four sampling methods (simple random sampling\, systematic sampling\,
stratified random sampling\, and cluster sampling) to select pages from te
n textbooks\, resulting in forty samples of pages. For each sample\, we es
timate the proportion of pages containing statistics tasks and the number
of statistics tasks within each textbook. These estimates are compared wit
h the actual values obtained by examining every page of each textbook. Wit
hin these data\, stratified sampling produces the least error in the numbe
r of statistics tasks\, and all confidence intervals for the proportion of
pages containing statistics tasks based on stratified sampling contain th
e actual proportion. We discuss the strengths and limitations of each samp
ling method\, and suggest reasons to use various sampling methods.\n\nhttp
s://tagung.math.uni-paderborn.de/event/1/contributions/36/
LOCATION: O1 258
URL:https://tagung.math.uni-paderborn.de/event/1/contributions/36/
END:VEVENT
BEGIN:VEVENT
SUMMARY:THE NARRATIVE OF SETS OF Learning RESOURCES AS DESCRIBED BY TEACHE
RS
DTSTART;VALUE=DATE-TIME:20190916T123000Z
DTEND;VALUE=DATE-TIME:20190916T130000Z
DTSTAMP;VALUE=DATE-TIME:20211021T061059Z
UID:indico-contribution-4-39@tagung.math.uni-paderborn.de
DESCRIPTION:Speakers: Shai Olsher (University of Haifa)\nTeachers are cent
ral actors in the interpretation and implementation processes of curricula
r resources. Holding this central position in the teaching and learning pr
ocess of mathematics\, teacher's interactions with curriculum resources ar
e often studied in different stages and forms of interactions. In this stu
dy we focus on means of communication that teachers use to describe the na
rrative\, underlying main characteristics\, of a set of curricular resourc
es. This study explores which characteristics do teachers use when they ch
aracterize through tagging a set of curricular resources\, and how do thei
r description of the curricular resources' narrative make use of these cha
racteristics. The study analyses the tagging and descriptions of 4 individ
ual teaches as part of a professional development program during a MA cour
se. The course focused on analysis of textbooks and curricular materials\,
and included experimenting in tagging and representing different sets of
curricular materials. The tagging included selecting the characteristics t
o be tagged\, and then the use of these characteristics to describe the na
rrative of the set of curricular resources\, composed of 50 different reso
urces (tasks).\n\nhttps://tagung.math.uni-paderborn.de/event/1/contributio
ns/39/
LOCATION: O1 224
URL:https://tagung.math.uni-paderborn.de/event/1/contributions/39/
END:VEVENT
BEGIN:VEVENT
SUMMARY:THE CONVERSION ACTIVITIES BETWEEN REPRESENTATION REGISTERS AS AN I
NSTRUMENT FOR THE ANALYSIS OF MATHEMATICS TEXTBOOKS
DTSTART;VALUE=DATE-TIME:20190917T093000Z
DTEND;VALUE=DATE-TIME:20190917T100000Z
DTSTAMP;VALUE=DATE-TIME:20211021T061059Z
UID:indico-contribution-4-68@tagung.math.uni-paderborn.de
DESCRIPTION:Speakers: Oihana Moreno (University of Basque Country)\nSemiot
ics raises an increasing interest in Mathematical \nEducation since Semiot
ics provides an array of methods and concepts to understand \nthe nature o
f mathematical discourse. Signs are carriers of cultural conventions and \
nSemiotics helps to understand the way in which individuals think and comm
unicate \nwith signs in a cultural context. Duval's theory of semiotic rep
resentations \ncharacterizes Mathematical learning in terms of the ability
of students to handle \nseveral representation registers of mathematical
concepts. Using as an example a\nconcept of higher mathematics\, in this w
ork we propose as criteria for the analysis of \ntextbooks the existence o
f activities that aim at students making conversions between \nrepresentat
ions of the concept among the diverse representation registers.\n\nhttps:/
/tagung.math.uni-paderborn.de/event/1/contributions/68/
LOCATION: O1 258
URL:https://tagung.math.uni-paderborn.de/event/1/contributions/68/
END:VEVENT
BEGIN:VEVENT
SUMMARY:REPORT ON THE DESIGN AND REALISATIONS OF THE WORKSHOP ‘WRITING M
ATHS TEXTBOOKS’
DTSTART;VALUE=DATE-TIME:20190919T090000Z
DTEND;VALUE=DATE-TIME:20190919T093000Z
DTSTAMP;VALUE=DATE-TIME:20211021T061059Z
UID:indico-contribution-4-43@tagung.math.uni-paderborn.de
DESCRIPTION:Speakers: Thomas Jahnke (University of Potsdam)\nReport on the
main ideas\, the design\, the practical and theoretical components and th
e realisations of the workshop ‘Writing Maths Textbooks’ which the aut
hor developed on behalf of the GIZ (Deutsche Gesellschaft für Internation
ale Zusammenarbeit) for the Republic of Yemen to teach future textbook wri
ters how to write Maths Textbooks. Because of acts of war the workshop was
delivered in 2016 per skype. A second face to face realisation of the wor
kshop took place 2018 at the Hanoi National University of Education (HNUE)
in Vietnam.\n\nhttps://tagung.math.uni-paderborn.de/event/1/contributions
/43/
LOCATION: O1 258
URL:https://tagung.math.uni-paderborn.de/event/1/contributions/43/
END:VEVENT
BEGIN:VEVENT
SUMMARY:The learning of double integral concept using a textbook
DTSTART;VALUE=DATE-TIME:20190916T130000Z
DTEND;VALUE=DATE-TIME:20190916T133000Z
DTSTAMP;VALUE=DATE-TIME:20211021T061059Z
UID:indico-contribution-4-44@tagung.math.uni-paderborn.de
DESCRIPTION:Speakers: Karina Silva (Universidade Tecnológica Federal do P
araná)\, LOURDES MARIA WERLE DE ALMEIDA ()\nA challenging task when doing
research about the use of mathematics textbooks is the comprehensible des
cription of activity shown by students and their construction of knowledge
when using the textbook. As argues Kadunz (2016)\, the semiotics of Charl
es S. Peirce seems to be a promising tool for fulfilling this task.\nIn th
is paper\, we turn our attention to student’s inscriptions (e.g.\, their
drawings\, their written signs) when they using a differential and integr
al calculus textbook to learn the concept of double integral. It will be s
hown that certain kind of inscriptions are diagrams\, in Peirce’s sense\
, which are valuable means to learn the double integral concept. We analyz
ed the diagrams of students of an integral and differential calculus lectu
re of an engineering course in a Brazilian university. \nThe methodologica
l perspective of the study is the flipped classroom learning environment (
Bhagat et al.2016). The students began the study of the double integral co
ncept using the textbook Calculus vol 2 of James Stewart. Findings indicat
ed that the way the textbook introduces the double integral concept favors
the students learning process. The invented and transformed diagrams by t
he students when they used the textbook influenced their learning activity
.\n\nhttps://tagung.math.uni-paderborn.de/event/1/contributions/44/
LOCATION: O1 224
URL:https://tagung.math.uni-paderborn.de/event/1/contributions/44/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Meaning making schoolbook materials for promoting subtraction with
regrouping skills
DTSTART;VALUE=DATE-TIME:20190916T133000Z
DTEND;VALUE=DATE-TIME:20190916T140000Z
DTSTAMP;VALUE=DATE-TIME:20211021T061059Z
UID:indico-contribution-4-47@tagung.math.uni-paderborn.de
DESCRIPTION:Speakers: Daniela Götze (TU Dortmund)\nIn Germany\, primary s
chool children should learn to not only execute the subtraction algorithm.
They should also understand why the algorithm works. But this understandi
ng is hard to achieve because the description of these processes is domina
ted by many technical terms and phrases like: “Unbundle one ten to ten o
nes. Reduce the number of tens…” – in this case for the subtraction
algorithm with regrouping. Therefore\, the German textbook “Das Zahlenbu
ch” (“The Number Book”\, Nührenbörger et al.\, 2018) has designed
language sensitive support material based on a meaning-related vocabulary
for understanding the subtraction algorithm. Meaning-related in this conte
xt means that we do not focus on fostering technical terms in the first pl
ace. Instead we foster phrases and sentences combined with iconic represen
tations for describing how the algorithm works and what “regrouping” m
eans.\nTherefore\, this paper gives a short insight into the support mater
ial and in the individual learning trajectory of the fourth grader Osman w
ho has been fostered with this support material. Osman has already learnt
the subtraction algorithm at school. But at the beginning of the support h
e can hardly explain how the algorithm works. The analyses demonstrate tha
t the language sensitive support seems to be a very promising approach for
promoting subtraction with regrouping skills.\n\nhttps://tagung.math.uni-
paderborn.de/event/1/contributions/47/
LOCATION: O1 224
URL:https://tagung.math.uni-paderborn.de/event/1/contributions/47/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Transitioning from Print to Digital Curriculum Materials: Promotin
g Mathematical Engagement and Learning
DTSTART;VALUE=DATE-TIME:20190916T133000Z
DTEND;VALUE=DATE-TIME:20190916T140000Z
DTSTAMP;VALUE=DATE-TIME:20211021T061059Z
UID:indico-contribution-4-42@tagung.math.uni-paderborn.de
DESCRIPTION:Speakers: Alden Edson (Michigan State University)\, Elizabeth
Phillips (Michigan State University)\, Kristen Bieda (Michigan State Unive
rsity)\nCurrently\, too few students\, including those in underrepresented
groups\, are engaged in making sense of mathematics. Our curriculum and d
evelopment research goals are to enhance student productive disciplinary e
ngagement and learning through four design principles: problematizing\, au
thority\, accountability\, and resources (Engle\, 2011). Examining student
behaviors\, participations\, and interactions in classroom environments a
re essential for understanding the extent to which students are engaged in
personal thought and the thinking of their peers.\n\nThe context for the
work is transitioning the problem-based curriculum\, Connected Mathematics
\, to a digital environment. Through design research\, we are connecting t
he (re)design efforts to the learners’ enacted experiences and associate
d outcomes. These efforts have resulted in a new problem format: (1) the I
nitial Challenge to problematize the situation\, (2) What If...? scenarios
to surface the embedded mathematics\, and (3) Now What Do You Know? to co
nnect learning to prior and future knowledge.\n\nInitial analysis has focu
sed on small group interactions. We have developed a framework for charact
erizing problematizing as students work on problems in a highly digital co
llaborative environment. The findings reveal that while tasks promote a hi
gh degree of problematizing in students’ work\, a high degree of authori
ty and accountability in students’ small group interactions is associate
d with mathematically productive problematizing.\n\nhttps://tagung.math.un
i-paderborn.de/event/1/contributions/42/
LOCATION: O1 258
URL:https://tagung.math.uni-paderborn.de/event/1/contributions/42/
END:VEVENT
BEGIN:VEVENT
SUMMARY:50 YEARS OF REALISTIC MATHEMATICS EDUCATION IDEAS AND THEIR IMPLEM
ENTATION IN TEXTBOOKS – LEARNING FACILITATORS FOR ADDITION AND SUBTRACTI
ON
DTSTART;VALUE=DATE-TIME:20190917T133000Z
DTEND;VALUE=DATE-TIME:20190917T140000Z
DTSTAMP;VALUE=DATE-TIME:20211021T061059Z
UID:indico-contribution-4-69@tagung.math.uni-paderborn.de
DESCRIPTION:Speakers: Marc van Zanten (Netherlands institute for curriculu
m development & Utrecht University)\nThe Dutch reform movement towards Rea
listic Mathematics Education (RME) started at the end of the 1960s. As an
alternative for the then prevailing mechanistic approach\, tasks\, lessons
and longitudinal teaching sequences were developed together with suggesti
ons for helpful contexts and didactical models. Over the years\, RME ideas
were laid down in many studies\, covering both general ideas on the teach
ing of mathematics\, and elaborations in specific subdomains. Simultaneous
ly\, these ideas were implemented in succeeding generations of mathematic
textbooks. A systematic analysis of RME documents and textbooks with the f
ocus on addition and subtraction revealed that Dutch textbooks to a certai
n degree have evolved along the lines of RME\, but also deviated from RME
ideas.\n\nhttps://tagung.math.uni-paderborn.de/event/1/contributions/69/
LOCATION: O1 224
URL:https://tagung.math.uni-paderborn.de/event/1/contributions/69/
END:VEVENT
BEGIN:VEVENT
SUMMARY:UNDERSTANDING MATHEMATICS TEACHERS’ PEDAGOGICAL DESIGN CAPACITY
IN A CONTEXT OF HIGH PRESCRIPTION
DTSTART;VALUE=DATE-TIME:20190919T090000Z
DTEND;VALUE=DATE-TIME:20190919T093000Z
DTSTAMP;VALUE=DATE-TIME:20211021T061059Z
UID:indico-contribution-4-86@tagung.math.uni-paderborn.de
DESCRIPTION:Speakers: Moneoang Leshota (University of the Witwatersrand)\n
Results from earlier research found that textbook use by teachers of mathe
matics was largely tacit and not deliberate\, making for un-intimate teach
er-textbook relationships\, and therefore low levels of teacher capacity f
or pedagogic design. The change from textbooks as primary curricular resou
rces for teaching to daily scripted lesson plans begs a question about the
kinds of relationships teachers forge with the scripted lesson plans. The
present article explores the affordances and constraints of the scripted
lesson plan\, and how one teacher mobilises the scripted lesson plan in he
r lesson. The analysis\, from a socio-cultural perspective\, illuminates t
he teacher’s PDC-in-action\, and sheds light on how context helps us to
understand and reflect on the notion of PDC.\n\nhttps://tagung.math.uni-pa
derborn.de/event/1/contributions/86/
LOCATION: O1 224
URL:https://tagung.math.uni-paderborn.de/event/1/contributions/86/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Comparing mathematics textbooks – an instrument for quantitative
analysis
DTSTART;VALUE=DATE-TIME:20190917T083000Z
DTEND;VALUE=DATE-TIME:20190917T090000Z
DTSTAMP;VALUE=DATE-TIME:20211021T061059Z
UID:indico-contribution-4-48@tagung.math.uni-paderborn.de
DESCRIPTION:Speakers: Jennifer Postupa ()\nTextbooks are different in many
ways. Not only the mathematical content differs even more the presentatio
n and handling of mathematics show great varieties.\nTo explore the field
and to identify the differences with statistical methods\, an instrument f
or analysing textbooks was developed. This instrument focuses on the three
main structural elements of textbooks: tasks\, pictures and explanations.
Typical aspects for analysing textbooks\, such as number and type of task
s\, are supplemented by results from research about the three structural e
lements. These are aspects like mathematical modeling or open-ended tasks.
Overall\, the instrument can give information about 140 characteristics o
f these three structural elements. It can be used for frequency analysis\,
such as the number or amount of tasks that require mathematical argumenta
tion. Additionally the correlation of two characteristics can be shown\, f
or example the relationship between the type of explanations and the mathe
matical content. The instrument makes it possible to analyse and compare t
extbooks from different countries\, decades\, publishers\, school types an
d so on. In addition\, the effect of pedagogical\, didactical or mathemati
cal influences on textbooks\, like the New Math in the 1960th\, can be ana
lysed.\nFirst assumptions (based on 30.000 records) can be made as a resul
t of the analysis of 14 different 7th grade textbooks from Germany publish
ed between 1940 and 2011.\n\nhttps://tagung.math.uni-paderborn.de/event/1/
contributions/48/
LOCATION: O1 258
URL:https://tagung.math.uni-paderborn.de/event/1/contributions/48/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Resources for teaching graph theory for engineers - issue of conne
ctivity
DTSTART;VALUE=DATE-TIME:20190917T123000Z
DTEND;VALUE=DATE-TIME:20190917T130000Z
DTSTAMP;VALUE=DATE-TIME:20211021T061059Z
UID:indico-contribution-4-45@tagung.math.uni-paderborn.de
DESCRIPTION:Speakers: Theresia Tabchi (Cérep EA 4692 – University of Re
ims Champagne Ardenne / Lebanese University)\nOur work is part of a thesis
that deals with university teachers’ practices\, particularly the relat
ion between research and teaching practices of university professors. We s
tudy this issue from the lens of interactions with resources (including te
xtbooks). We choose graph theory as an object of study. Graph theory is a
contemporary mathematical field\, taught in several academic paths (comput
er sciences\, mathematics\, engineering education\, etc.) and no consensus
has been made on the choice of concepts and notions to be included in a u
niversity course (West\, 2001). We seek to characterize the impact of the
epistemological specificities of graph theory along with the institutional
context on the resources designed in the tertiary level. \nWe considered
seven graph theory textbooks\, in particular contents related to eulerian
and hamiltonian paths. We identified that the teaching of graph theory all
owed different kinds of connections: connecting different concepts\, diffe
rent registers of representation (Duval 2006)\, and different topic areas.
Based on these results\, we use here the concept of connectivity (Gueudet
\, Pepin\, Restrepo\, Sabra\, & Touche\, 2018) to analyze a chapter of a g
raph theory course for future engineers in France. Finally\, we present a
discussion of findings and their implications. \n\nDuval\, R. (2006). A co
gnitive analysis of problems of comprehension in a learning of mathematics
. Educational Studies in Mathematics\, 61(1 - 2)\, 103-131.\nGueudet\, G.\
, Pepin\, B.\, Sabra\, H.\, Restrepo\, A.\, & Trouche\, L. (2018). E-textb
ooks and connectivity: proposing an analytical framework. International Jo
urnal for Science and Mathematics Education\, 16(3)\, 539-558.\nWest\, D.
B. (2001). Introduction to graph theory ( second edition ed.). Pearson edu
cation.\n\nhttps://tagung.math.uni-paderborn.de/event/1/contributions/45/
LOCATION: O2
URL:https://tagung.math.uni-paderborn.de/event/1/contributions/45/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Same Textbook\, Different Points of View: Students and Teachers as
Textbook Users
DTSTART;VALUE=DATE-TIME:20190917T100000Z
DTEND;VALUE=DATE-TIME:20190917T103000Z
DTSTAMP;VALUE=DATE-TIME:20211021T061059Z
UID:indico-contribution-4-71@tagung.math.uni-paderborn.de
DESCRIPTION:Speakers: Dubravka Glasnovic Gracin (University of Zagreb\, Fa
culty of Teacher Education)\nThe utilization of textbooks by mathematics t
eachers has been the subject of many recent studies\; students’ opinions
\, however\, have not received such attention. The study presented in this
paper aims to investigate both students’ and their teacher’s ways of
and reasons for using the textbook\, with an emphasis on the vertices of t
he Socio-Didactical Tetrahedron. The findings indicate that the beliefs ab
out being a teacher and about being a student strongly influence textbook
utilization. Also\, the students’ use of the textbook is influenced by t
he teacher’s intentions. Here the extension of the didactical tetrahedro
n to a socio-didactical tetrahedron proved to be very valuable due to the
social factors involved in textbook use.\n\nhttps://tagung.math.uni-paderb
orn.de/event/1/contributions/71/
LOCATION: O1 224
URL:https://tagung.math.uni-paderborn.de/event/1/contributions/71/
END:VEVENT
BEGIN:VEVENT
SUMMARY:HOW JAPANESE TEACHERS USE MATHEMATICS TEXTBOOKS FOR “KYOZAI-KENK
YU”: CHARACTERIZING THEIR DIFFERENT USES BY PARADIDACTIC PRAXEOLOGIES
DTSTART;VALUE=DATE-TIME:20190916T120000Z
DTEND;VALUE=DATE-TIME:20190916T123000Z
DTSTAMP;VALUE=DATE-TIME:20211021T061059Z
UID:indico-contribution-4-33@tagung.math.uni-paderborn.de
DESCRIPTION:Speakers: Tatsuya Mizoguchi (Tottori University)\, Yusuke Shin
no (Osaka Kyoiku University)\n“Kyozai-Kenkyu” is an essential part of
Japanese lesson study and involves task design for classroom lessons. Most
of Japanese teachers often refer to textbooks as a main resource in doing
“Kyozai-Kenkyu”. However\, there are different kinds of use with rega
rd to different approaches to knowledge at stake. In this study\, we aim t
o examine teachers’ paradidactic activities related to “Kyozai-Kenkyu
” using mathematics textbooks. For this purpose\, some notions of Anthro
pological Theory of the Didactic (ATD) are adopted for characterizing teac
hers’ paradidactic praxeologies by analyzing “Kyozai-Kenkyu” about t
he knowledge of fractional numbers in primary schools. As a result\, we id
entified three types of paradidactic praxeologies (PDP-a\, PDP-b\, & PDP-c
) which are related to different aspects of didactic transposition process
es. PDP-a characterizes a straightforward “Kyozai-Kenkyu” which is tot
ally relied on both mathematical and didactic organizations of the textboo
k. PDP-b characterizes a “Kyozai-Kenkyu” which is partly based on the
textbook but some modifications are made on the didactic organization. PDP
-c characterizes a “Kyozai-Kenkyu” which slightly refers to the textbo
ok but alternative approaches are adopted on the mathematical and didactic
organizations. Accordingly\, we discuss teachers’ different attitudes t
owards mathematics textbooks as a resource.\n\nhttps://tagung.math.uni-pad
erborn.de/event/1/contributions/33/
LOCATION: O1 224
URL:https://tagung.math.uni-paderborn.de/event/1/contributions/33/
END:VEVENT
BEGIN:VEVENT
SUMMARY:ANALYZING DYNAMIC TEXTBOOKS’ USER DATA: METHODOLOGICAL CONSIDERA
TIONS
DTSTART;VALUE=DATE-TIME:20190917T120000Z
DTEND;VALUE=DATE-TIME:20190917T123000Z
DTSTAMP;VALUE=DATE-TIME:20211021T061059Z
UID:indico-contribution-4-87@tagung.math.uni-paderborn.de
DESCRIPTION:Speakers: Vilma Mesa (University of Michigan)\nIn the Undergra
duate Teaching and Learning in Mathematics with Open Software and Textbook
s (UTMOST\, Beezer et al.\, 2018) project we study the use of open source
computational resources in the teaching and learning of mathematics at und
ergraduate level. The project gathers (a) real-time\, individualized viewi
ng data from three dynamic undergraduate textbooks authored in textbooks a
uthored in PreTeXt (Calculus\, Linear Algebra\, and Abstract Algebra)\; (b
) ongoing surveys of users’ descriptions of the textbook use\; (c) users
’ questionnaires (beliefs and attitudes towards mathematics\, technology
\, teaching\, and learning)\; and student performance (tests of knowledge
and grades). The textbooks have been enhanced with additional features suc
h as WeBWorK\, Javascript\, Geogebra\, and include interactive sections in
which students can submit answers to Reading Questions\, and instructors
can see the responses in real time.\nViewing data indicate which sections
are being accessed by users\, but are insufficient for knowing what users
are actually doing when they view the textbook. For this reason\, every tw
o weeks we ask users for descriptions of what they do during their own vie
wing of the textbook via a survey that is sent to 6 to 9 courses every sem
ester (each with an average of 20 students). Each survey generates between
120 and 300 responses that are synchronized with the viewing data and ana
lysed for patterns. We have turned into natural language processing progra
ms that facilitate the identification of patterns in the responses. In the
presentation we will address issues of identification\, classification\,
and integration\, that we have faced and how we have managed them in the c
urrent project.\n\nhttps://tagung.math.uni-paderborn.de/event/1/contributi
ons/87/
LOCATION: O1 258
URL:https://tagung.math.uni-paderborn.de/event/1/contributions/87/
END:VEVENT
BEGIN:VEVENT
SUMMARY:THE FUNCTIONS OF A HIERARCHICAL CLASSIFICATION OF QUADRILATERALS I
N JAPANESE TEXTBOOK: ITS PRESENTATION AND LIMITATION
DTSTART;VALUE=DATE-TIME:20190917T120000Z
DTEND;VALUE=DATE-TIME:20190917T123000Z
DTSTAMP;VALUE=DATE-TIME:20211021T061059Z
UID:indico-contribution-4-54@tagung.math.uni-paderborn.de
DESCRIPTION:Speakers: Shogo Murata (University of Tsukuba)\nIn mathematics
teaching and learning\, it is important for students to learn not only ma
thematical contents but also roles and functions of the contents. Function
s of a hierarchical classifications are particularly related to mathematic
al definition and defining. The purpose of this paper is to clarify functi
ons of a hierarchical classification of quadrilaterals in Japanese textboo
k. From the perspective of the five functions of a hierarchical classifica
tion of quadrilaterals (de Villiers\, 1994)\, geometry in the latest Japan
ese elementary and middle school textbooks were analysed. Three functions:
simplification of deductive structure\, a useful conceptual schema during
problem solving\, a useful global perspective\, were identified related t
o contexts of problem solving. On the other hand\, the rest two functions:
economical definitions and formulations of theorems\, alternative definit
ions and new propositions\, were not identified in textbooks\, because Jap
anese textbooks don't explicitly deal with exclusive definitions or equiva
lent definitions of quadrilaterals. The results of analysis imply there is
a limitation that contradictory definitions must not be presented in text
books\, and that textbooks can present only a part of defining processes.
This paper suggests teachers should pay attention to the limitation of tex
tbooks and try to teach authentic defining activity beyond textbooks.\n\nh
ttps://tagung.math.uni-paderborn.de/event/1/contributions/54/
LOCATION: O2
URL:https://tagung.math.uni-paderborn.de/event/1/contributions/54/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Representation of vectors in German mathematics and physics textbo
oks
DTSTART;VALUE=DATE-TIME:20190917T083000Z
DTEND;VALUE=DATE-TIME:20190917T090000Z
DTSTAMP;VALUE=DATE-TIME:20211021T061059Z
UID:indico-contribution-4-34@tagung.math.uni-paderborn.de
DESCRIPTION:Speakers: Frederik Dilling (University of Siegen)\nThe concept
of vector is a central part of mathematics and physics at school. Three a
pproaches to the concept of vector can be distinguished: arrow classes\, n
-tuples and vector space axioms. In order to develop adequate conceptions
of vectors\, different facets of the concept should be presented to the st
udents and the representation in the subjects mathematics and physics shou
ld be coordinated. The method of textbook analysis was chosen to investiga
te this relationship with the help of a deductively developed system of ca
tegories. These categories are based on the theoretical framework using qu
alitative content analysis according to Mayring (2000). The following ques
tion was focused: How are vectors represented in German mathematics and ph
ysics textbooks?\n\nhttps://tagung.math.uni-paderborn.de/event/1/contribut
ions/34/
LOCATION: O2
URL:https://tagung.math.uni-paderborn.de/event/1/contributions/34/
END:VEVENT
BEGIN:VEVENT
SUMMARY:THE GENDER TROUBLE IN MATHEMATICS TEXTBOOKS: A COMPARATIVE ANALYSI
S BETWEEN BRAZIL AND THE USA
DTSTART;VALUE=DATE-TIME:20190916T120000Z
DTEND;VALUE=DATE-TIME:20190916T123000Z
DTSTAMP;VALUE=DATE-TIME:20211021T061059Z
UID:indico-contribution-4-70@tagung.math.uni-paderborn.de
DESCRIPTION:Speakers: Vanessa Neto (Federal University of Mato Grosso do
Sul)\nTextbooks\, which still are one of the most used tools in the mathem
atics classroom worldwide have a substantial impact on the production of s
tudents’ subjectivities. In this sense\, despite research showing that t
here is a need in eliminating gender bias in mathematics textbooks\, they
still reproduce the portrayal of what it means to be a girl/woman or a boy
/man in our current society. Therefore\, this study provides a comparison
between one of the most used 6th-grade mathematics textbooks in Brazil and
in the USA in order to unveil the ways gender subjects were presented. We
highlighted the similarities and differences in gender inscriptions. Usin
g Discourse Analyses as a framework\, our methodological approach consiste
d of the reading of each textbook and selecting the appeal for gendered ch
aracters (professions\, occupations\, and performed activities). Thus math
ematics tasks\, exercises/activities as well as images and drawings were t
he content of analysis. In our interpretation\, the systems of images that
surrounded representations weaved a discursive logic that exposed the des
irable gender practices of girls/women and boys/men. This analysis conclud
ed that textbooks are still major tools to reproduce and create stereotype
d gender positions for girls and boys\, influencing in the creation of stu
dents’ subjectivities in both countries.\n\nhttps://tagung.math.uni-pade
rborn.de/event/1/contributions/70/
LOCATION: O2
URL:https://tagung.math.uni-paderborn.de/event/1/contributions/70/
END:VEVENT
BEGIN:VEVENT
SUMMARY:PRESERVICE TEACHERS’ LEARNING TO USE EXISTING RESOURCES
DTSTART;VALUE=DATE-TIME:20190917T093000Z
DTEND;VALUE=DATE-TIME:20190917T100000Z
DTSTAMP;VALUE=DATE-TIME:20211021T061059Z
UID:indico-contribution-4-67@tagung.math.uni-paderborn.de
DESCRIPTION:Speakers: Ok-Kyeong Kim (Western Michigan University)\nThe cap
acity needed for using existing resources was explored and its potential c
omponents were identified previously in the context of elementary teachers
using various curriculum programs in the United States. This study furthe
r explored the capacity needed for productive resource use in a mathematic
s methods course\, focusing on preservice teachers’ learning to use exis
ting resources productively. \nData were gathered from 15 preservice teach
ers in the course\, including videotapes of their teaching\, photos of stu
dent solutions\, surveys with open-ended questions\, and reflection papers
on the teaching experience. The data were examined using Sleep’s (2009)
conceptualization of teachers’ work of steering instruction toward the
mathematical point.\nTeaching toward the mathematical points of the lesson
was a very challenging task for the preservice teachers. They attended to
and managed multiple purposes\, spent instructional time on the intended
mathematics\, and opened up and emphasized key mathematical ideas\, as in
Sleep’s framework. Careful preparations for the lesson did not result i
n productive teaching\; many struggled to probe and develop students’ th
inking to the desired level. Overall\, the result leaves the course instru
ctor in particular and mathematics educators in general a challenging task
of articulating the complexity of preparing preservice teachers to use ex
isting resources productively.\n\nhttps://tagung.math.uni-paderborn.de/eve
nt/1/contributions/67/
LOCATION: O1 224
URL:https://tagung.math.uni-paderborn.de/event/1/contributions/67/
END:VEVENT
BEGIN:VEVENT
SUMMARY:INADEQUATE LEARNING SEQUENCE AND ERRONEOUS FACT-LIKE STATEMENT IN
A MATHEMATICS TEXTBOOK: WHAT CAN STUDENTS TAKE FROM THEM?
DTSTART;VALUE=DATE-TIME:20190917T090000Z
DTEND;VALUE=DATE-TIME:20190917T093000Z
DTSTAMP;VALUE=DATE-TIME:20211021T061059Z
UID:indico-contribution-4-79@tagung.math.uni-paderborn.de
DESCRIPTION:Speakers: Josip Slisko (Facultad de Ciencias Físico Matemáti
cas\, Benemérita Universidad Autónoma de Puebla)\nTo be used in Mexican
public schools\, all mathematics textbooks have to pass an allegedly rigor
ous review process by Ministry of Public Education (Secretaría de Educaci
ón Pública). Nevertheless\, various revisions of approved mathematics te
xtbooks reveal many deficient features\, going from orthographical\, mathe
matical and contextual errors to inadequate learning sequences. The aim of
this initial exploration study was to find out what can secondary-school
students (N = 155) take from an inadequate learning sequence and an errone
ous fact-like statement in the mathematics textbook they use. The inadequa
te learning sequence was related to positive and negative numbers. Its ina
dequacy comes from (a) artificial context\; (b) unclear questions regardin
g concepts and calculations\; and (c) unnecessary complicated drawing task
s. Erroneous fact-like statement\, related to the age of young persons sho
uld have in order to work legally\, contains the affirmation that “four
of ten” is 37 %. The results show that students’ performances are infl
uenced negatively by unclear questions and unnecessary complication of the
drawings tasks. Although many students were able to detect the erroneous
percentage value in the statement\, they differ greatly in their argumenta
tive skills. The students with poor skills only say “something is wrong
with the percentage”\, while those with good skills affirm “the percen
tage is erroneous because “four in ten” is not 37 % but 40 %”.\n\nht
tps://tagung.math.uni-paderborn.de/event/1/contributions/79/
LOCATION: O1 224
URL:https://tagung.math.uni-paderborn.de/event/1/contributions/79/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ratio\, rate and proportional relationships in Japanese curriculum
materials
DTSTART;VALUE=DATE-TIME:20190917T090000Z
DTEND;VALUE=DATE-TIME:20190917T093000Z
DTSTAMP;VALUE=DATE-TIME:20211021T061059Z
UID:indico-contribution-4-41@tagung.math.uni-paderborn.de
DESCRIPTION:Speakers: Tad Watanabe (Kennesaw State University)\nRatio\, ra
te and proportional relationships are arguably the most important topics i
n middle grades mathematics curriculum before algebra. However\, many teac
hers find these topics challenging to teach and students find them difficu
lt to learn.\nWe examined the Japanese national course of study published
by the Ministry of Education and one of the most widely used elementary an
d lower secondary school mathematics textbook series. Both vertical and ho
rizontal analyses (Charalambous et al\, 2010) were conducted\, examining w
hen and what specific topics are discussed and how they are treated in the
Japanese curriculum materials. \nHighlights of the findings are listed be
low.\n• Japanese curriculum discusses comparisons of 2 quantities in Gra
de 5\, both 2 quantities with the same measurement unit and 2 quantities w
ith different measurement units.\n• Ratio is discussed in Grade 6 in the
Japanese curriculum.\n• A proportional relationship is initially define
d as the relationship of 2 co-varying quantities such that when one quanti
ty becomes 2\, 3\, 4\, … times as much\, the other also becomes 2\, 3\,
4\, … times as much. In Grade 6\, the definition is extended: 2 quantit
ies are in a proportional relationship when one quantity becomes m times a
s much\, the other also becomes m times as much\, where m is a positive ra
tional number. Finally\, in Grade 7\, m is extended to the entire rational
numbers.\n\nhttps://tagung.math.uni-paderborn.de/event/1/contributions/41
/
LOCATION: O2
URL:https://tagung.math.uni-paderborn.de/event/1/contributions/41/
END:VEVENT
BEGIN:VEVENT
SUMMARY:How are mathematicians represented in Chinese mathematics textbook
s?
DTSTART;VALUE=DATE-TIME:20190916T123000Z
DTEND;VALUE=DATE-TIME:20190916T130000Z
DTSTAMP;VALUE=DATE-TIME:20211021T061059Z
UID:indico-contribution-4-85@tagung.math.uni-paderborn.de
DESCRIPTION:Speakers: Na Li (East China Normal University)\n*Integrating h
istory of mathematics into mathematics textbooks is a commonly accepted id
ea and practice in modern textbook development in China\, and mathematicia
ns are an integral part of mathematical history. So how do Chinese mathema
tics textbooks fare in this particular aspect? In this study\, we investig
ate how mathematicians are represented in two series of primary and junior
secondary school mathematics textbooks currently used in China\, one used
in Shanghai and the other by People’s Education Press (PEP). We aim to
reveal the similarities and differences in the representation of mathemati
cians in the two series of textbooks\, and explore the implications of the
findings on mathematics textbook research and development. Our findings s
how that each series introduced both Chinese and non-Chinese mathematician
s\, though most of the mathematicians introduced were ancient mathematicia
ns\, and there is a higher level of consistency in the distribution of the
introductions of mathematicians in both series in terms of mathematics co
ntents and the structures of the chapters. However\, the PEP mathematics t
extbooks introduced considerably more mathematicians than the Shanghai mat
hematics textbooks\, and moreover\, the PEP series presented a wider and\,
in our view\, a better distribution of the introductions of mathematician
s in terms of the grade levels\, the ethnic origins\, and the timeline of
history.*\n\nhttps://tagung.math.uni-paderborn.de/event/1/contributions/85
/
LOCATION: O2
URL:https://tagung.math.uni-paderborn.de/event/1/contributions/85/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Theory of geometrical thinking in elementary textbook: case study
of Japan
DTSTART;VALUE=DATE-TIME:20190917T100000Z
DTEND;VALUE=DATE-TIME:20190917T103000Z
DTSTAMP;VALUE=DATE-TIME:20211021T061059Z
UID:indico-contribution-4-40@tagung.math.uni-paderborn.de
DESCRIPTION:Speakers: Toru Hayata (Naruto University of Education)\nAs alr
eady known well\, for learning geometry\, students start from their own ex
perience and concrete shapes\; on the other hand\, students have to leave
from them for developing their geometric thinking (cf. van Hiele\, 1958).
\nWhen we seen textbooks as (implemented) curriculum\, textbook must help
students’ this process.\nFor this background\, our research question is:
Are Japanese elementary school textbooks appropriate for developing stude
nts’ geometric thinking from 1st to 6th grade\, especially leaving from
their own experiences and shapes?\nOur theoretical framework is “praxeol
ogy (Chevallard\, 2015\; Bosch & Gascón\, 2014)” for revealing the char
acter of knowledge in textbook.\nHere\, we focus on theory[Θ] in praxeolo
gy \; because\, Θ is fundamental principle for justifying praxis- (taskty
pe and technique).\n\nOur methodology is quantitative analysis of geometri
cal knowledge in Japanese elementary textbook (1st - 6th grade)\; ratio o
f Θ as following 5 categories.\nΘ of geometric knowledge in the textbook
is classified into four categories: i) empirical (shapes and/or visual)\,
ii)measurement\, iii) definition\, property\, and/or theorem\, iv) mathem
atical operation. In addition\, some knowledge has no “theory” because
students’ activities themselves are purpose (e.g. making animals by usi
ng boxes)\; we identified them as X) which is fifth category of knowledge.
\nAs a result\, the developing process from 1st grade to 5th grade is appr
opriate\; because ratio of i)\, ii)\, and X) gradually decrease\, and iii)
and iv) gradually increase. However\, 6th grade has specific character\;
i) has obviously increased than the 5th grade because they start to learn
properties of solid figures.\n\nhttps://tagung.math.uni-paderborn.de/event
/1/contributions/40/
LOCATION: O2
URL:https://tagung.math.uni-paderborn.de/event/1/contributions/40/
END:VEVENT
BEGIN:VEVENT
SUMMARY:EXAMINING PROPORTIONAL REASONING IN MIDDLE SCHOOL MATHEMATICS TEXT
BOOKS
DTSTART;VALUE=DATE-TIME:20190917T120000Z
DTEND;VALUE=DATE-TIME:20190917T123000Z
DTSTAMP;VALUE=DATE-TIME:20211021T061059Z
UID:indico-contribution-4-65@tagung.math.uni-paderborn.de
DESCRIPTION:Speakers: Yasin MEMİŞ (Anadolu University)\nProportional rea
soning is an important skill that requires a long process of development a
nd is a cornerstone at the middle school level. One of the reasons why stu
dents cannot demonstrate this skill at the desired level is the learning o
pportunities provided by the textbooks. The aim of this study examines the
extent to which selected Turkish\, Singaporean and Canadian middle school
mathematics textbooks provide students opportunities to experience propor
tional reasoning. In the study\, 4 developmental shifts were used. These s
hifts processes have been developed in the form of adept at forming ratios
\, reasoning with proportions\, and understanding rates. The ratio and rat
e units of the textbooks were evaluated as 4 main content structures as na
rratives\, tasks\, examples\, and representations. Shifts were graded as
“none-weak-medium-strong “according to the frequency of taking part in
the content structures. As a result of the study\, it was determined that
the selected Turkish and Canadian textbooks presented one shift strongly\
, and Singaporean textbooks presented two shifts strongly. The results sho
w that the selected textbooks in Singapore provide the strongest opportuni
ty for proportional reasoning.\n\nhttps://tagung.math.uni-paderborn.de/eve
nt/1/contributions/65/
LOCATION: O1 224
URL:https://tagung.math.uni-paderborn.de/event/1/contributions/65/
END:VEVENT
BEGIN:VEVENT
SUMMARY:MATHEMATICAL POWER IN THE MATHEMATICS IN CONTEXT CURRICULUM
DTSTART;VALUE=DATE-TIME:20190917T130000Z
DTEND;VALUE=DATE-TIME:20190917T133000Z
DTSTAMP;VALUE=DATE-TIME:20211021T061059Z
UID:indico-contribution-4-60@tagung.math.uni-paderborn.de
DESCRIPTION:Speakers: Nicholas Witt (Western Michigan University)\nIn the
United States\, teaching mathematics for social justice has the potential
to make studying advanced mathematics more accessible to students coming f
rom low income and historically underrepresented ethnic groups. Gutstein
’s (2005) work on teaching students to “read” and “write” the wo
rld with mathematics laid the foundation for the framework that will be us
ed in this middle school textbook analysis. The purpose of this textbook a
nalysis was to determine the nature of “mathematical power” (Gutstein
2005) within the sections focused on ratios and rates in the “Mathematic
s in Context” (Holt\, Rinehart & Winston\, 2006) curriculum. This was do
ne by searching for evidence of the development of “mathematical power
” (as defined by Gutstein) in conjunction with alignment to the National
Council of Teachers of Mathematics (NCTM) publication Essential Understan
dings of Ratios\, Rates\, and Proportions for Middle School Teachers (Loba
to\, et. al 2010). The analysis of sampled sections focused on evidence of
this author’s operationalization of the five Essential Understandings (
EUs) of ratios and rates along with an operationalization of Gutstein’s
working definition of mathematical power. Results suggest that Gutstein’
s characterization of the mathematical power in Mathematics In Context (Mi
C) is accurate and evidence of EUs suggest that the written curriculum all
ows for the potential to develop an essential understanding of ratios and
rates.\n\nhttps://tagung.math.uni-paderborn.de/event/1/contributions/60/
LOCATION: O2
URL:https://tagung.math.uni-paderborn.de/event/1/contributions/60/
END:VEVENT
BEGIN:VEVENT
SUMMARY:An Analysis of Teaching methods of Division of Fractions in South
Korea Elementary Mathematics textbooks
DTSTART;VALUE=DATE-TIME:20190917T133000Z
DTEND;VALUE=DATE-TIME:20190917T140000Z
DTSTAMP;VALUE=DATE-TIME:20211021T061059Z
UID:indico-contribution-4-106@tagung.math.uni-paderborn.de
DESCRIPTION:Speakers: Hyoungmi Cho (East China Normal University)\nIn this
paper\, the contents of Korean elementary school math textbooks before an
d after the revision were analyzed in order to present the trend of teachi
ng method of ‘division of fractions’ in South Korea. Fraction division
can be easily solved by using 'invert and multiplying' algorithm\, It is
easy for students to perform calculation mechanically without understandin
g. But in fact\, it is very difficult for students to understand why they
should use ‘the invert’ in fraction division. The division of fraction
s should understand the calculation process using complex fraction concept
s. Therefore\, the understanding of students will vary depending on the or
der in which fraction concepts are presented and what math materials are u
sed.\n South Korea is one of the East Asian countries that maintains the
highest ranking in international assessments such as PISA and TIMSS\, usin
g a single state-authored textbook that applies to the national curriculum
. Also\, Korea recently revised its curriculum in 2015. In this study\, I
compared two Korean elementary school math textbooks that were applied wit
h the revised curriculum in 2009 and 2015. To provide framework of the tea
ching method of fraction division\, this study focus on the concept(meanin
g) of fractions and the visual models used in textbooks that were analyzed
with the changes in Korea elementary school math textbooks.\n\nhttps://ta
gung.math.uni-paderborn.de/event/1/contributions/106/
LOCATION: O1 258
URL:https://tagung.math.uni-paderborn.de/event/1/contributions/106/
END:VEVENT
BEGIN:VEVENT
SUMMARY:GENDER DIFFERENCES IN MIDDLE SCHOOL MATHEMATICS LEARNING NEEDS: PR
OMOTING GENDER EQUITY THROUGH TEXTBOOK DESIGN
DTSTART;VALUE=DATE-TIME:20190919T083000Z
DTEND;VALUE=DATE-TIME:20190919T090000Z
DTSTAMP;VALUE=DATE-TIME:20211021T061059Z
UID:indico-contribution-4-28@tagung.math.uni-paderborn.de
DESCRIPTION:Speakers: Yan Zhu (East China Normal University)\, Lyu Ni (Eas
t China Normal University)\nIt is widely recognized that textbooks play an
important role in teaching and learning of mathematics. Therefore\, the w
ay in which textbooks address gender equity is expected to have a signific
ant influence on learning outcomes. However\, when gender stereotyping is
often investigated by textbook researchers\, gender equity is rarely a con
cern when selecting and organizing teaching contents during textbook desig
n. The aim of this study is to identify whether male and female middle sch
ool students have different needs in their actual mathematics learning. It
is believed that the findings of this study would provide insightful info
rmation for the curriculum development and textbook design. \nIn the study
\, a total of 1000 male and 1000 female middle school students were random
ly selected from a mathematics online-question-answering system. Based on
the mathematics topics covered\, the questions posed by the 2000 students
were first coded aligning to the PEP mathematics textbook chapters and sec
tions. Using a multiple regression model\, the differences on learning nee
ds between male and female students were then quantified. It is found that
female students have a larger demand for consultation in terms of number
of chapters as well as sections than their male peers. Female students ten
d to need more help on the topics related to function and plane geometry\,
while male students need more help on statistics. Moreover\, the average
difficulty level of the topics on which female students have significantly
larger demands is much higher than that on which male students have signi
ficantly larger demands (8.13 vs. 7.30). This work closes with discussions
about the potential factors causing these gender differences and educatio
nal implications for teaching and learning of mathematics\, particularly f
or textbook and learning resource developers.\n\nhttps://tagung.math.uni-p
aderborn.de/event/1/contributions/28/
LOCATION:University of Paderborn O1 258
URL:https://tagung.math.uni-paderborn.de/event/1/contributions/28/
END:VEVENT
BEGIN:VEVENT
SUMMARY:ANALYSIS OF TEXTBOOKS IN DISTINCT COUNTRIES: RESOLUTION OF EQUATIO
NS AND INEQUALITIES
DTSTART;VALUE=DATE-TIME:20190919T083000Z
DTEND;VALUE=DATE-TIME:20190919T090000Z
DTSTAMP;VALUE=DATE-TIME:20211021T061059Z
UID:indico-contribution-4-97@tagung.math.uni-paderborn.de
DESCRIPTION:Speakers: Luisa Rodríguez Doering (Federal University of Rio
Grande do Sul)\nIn this article\, we examine and compare how the procedure
s for solving one-variable linear equations and inequalities are presented
in the narrative of Brazilian\, Portuguese and Spanish textbooks. We anal
yze the main resources used\, the relationships between the procedures of
solving equations and inequalities\, and the presence of reasoning-and-pro
ving in the exposition of content. Results include the fact that all autho
rs use the (two-plate) scales as a resource to illustrate some property in
order to solve a specific equation\, however\, this feature is not used a
s a reasoning-and-proving opportunity\, merely as an empirical example. On
ly one author uses scales to solve inequalities. We also verified that the
relationship between solving procedures for equations and for inequalitie
s is little explored in these textbooks. Moreover\, we present suggestions
for the use of (two-plate) scales with two different goals: firstly\, as
a tool to illustrate properties of both equations and inequalities\, thus
as an instrument to compare their solving procedures\, and\, secondly\, as
a generalization tool\, providing\, as proposed by Stylianides (2009)\, a
reasoning-and-proving activity.\n\nhttps://tagung.math.uni-paderborn.de/e
vent/1/contributions/97/
LOCATION: O2
URL:https://tagung.math.uni-paderborn.de/event/1/contributions/97/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Research Actuality and Trend on the Representations of Textbooks
DTSTART;VALUE=DATE-TIME:20190917T130000Z
DTEND;VALUE=DATE-TIME:20190917T133000Z
DTSTAMP;VALUE=DATE-TIME:20211021T061059Z
UID:indico-contribution-4-98@tagung.math.uni-paderborn.de
DESCRIPTION:Speakers: Yang Shen (East China Normal University)\nTo underst
and current state of the research on the representation of textbooks\, 170
articles on mathematical representation are randomly selected to explore
the research objects in recent decades\, with the result of only 10.6% pap
ers focusing on mathematics textbooks. Then\, those papers are analyzed in
terms of research questions\, theoretical frameworks and research methods
. Results show that 1）there are four main research problems\, and most o
f the studies presented or compared the characterization of the mathematic
s textbooks. 2）There are four main theoretical frameworks\, and most of
the studies focus on different types of representation and different types
of problems. 3）59% articles use the document analysis method and 29% ar
ticles use comparative research method. The trend of the representation ab
out textbooks are studied at last.\n\nhttps://tagung.math.uni-paderborn.de
/event/1/contributions/98/
LOCATION: O1 258
URL:https://tagung.math.uni-paderborn.de/event/1/contributions/98/
END:VEVENT
BEGIN:VEVENT
SUMMARY:COMPETENCIES AND TEXTBOOK DEVELOPMENT: A THREE-DIMENSIONAL CONTENT
MODEL ENACTED IN THE DANISH TEXTBOOK SERIES MATEMATRIX FOR GRADES K-9
DTSTART;VALUE=DATE-TIME:20190919T100000Z
DTEND;VALUE=DATE-TIME:20190919T103000Z
DTSTAMP;VALUE=DATE-TIME:20211021T061059Z
UID:indico-contribution-4-100@tagung.math.uni-paderborn.de
DESCRIPTION:Speakers: Tomas Højgaard (Danish School of Education\, Aarhus
University\, Denmark)\nCurricula around the world make more and more use
of goals trying to capture different\nkind of processes for the students t
o master. For mathematics education in Denmark\,\nthese ambitions have bee
n described in terms of a set of mathematical competencies.\nHowever\, bri
nging such competencies into the actual teaching practices has proved\ncha
llenging. Matematrix is a Danish mathematics textbook system for grades k-
9\ndesigned to support the mathematics teachers in facing this challenge.
In this paper\,\nI – as one of the designers and authors of the textbook
s – present one of the key\nelements in this endeavour: A three-dimensio
nal content and objectives model combining\nmathematical competencies\, ma
thematical core concepts and grade level. Following that\,\nI exemplify th
e use of the model at three different levels of textbook design: The\nstru
cturing of the content for the books in general\, the focal points for eac
h chapter\nin the various books and the development of tasks for a specifi
c chapter.\n\nhttps://tagung.math.uni-paderborn.de/event/1/contributions/1
00/
LOCATION: O1 258
URL:https://tagung.math.uni-paderborn.de/event/1/contributions/100/
END:VEVENT
BEGIN:VEVENT
SUMMARY:TEXTBOOK CONTENT IN USE: MANUAL AND MACHINE CODING
DTSTART;VALUE=DATE-TIME:20190917T123000Z
DTEND;VALUE=DATE-TIME:20190917T130000Z
DTSTAMP;VALUE=DATE-TIME:20211021T061059Z
UID:indico-contribution-4-101@tagung.math.uni-paderborn.de
DESCRIPTION:Speakers: Yannis Liakos (University of Michigan)\, Han Zhang (
)\nIn the arena of mathematics teaching and learning at undergraduate leve
l\, we strive to assess and evaluate the use of dynamics textbooks authore
d in PreTeXt. We seek to investigate how mathematical content in a textboo
k is taken up by instructors as they plan and teach their lessons\, and by
students who participate in those lessons. We analyze textbook raw conten
t to identify competencies afforded by it\, and textbook usage reported by
the users via periodic surveys and automatic real-time textbook viewing d
ata (heat maps).\nTo analyze the textbook raw content\, we apply manual an
d automatic coding\, using 25% of the entire textbook as training data. Th
is is followed by automatic coding using natural language processing techn
iques that will derive a set of competencies for the rest of the textbook.
\nUnderlying this investigation are two frameworks: the didactical tetrahe
dron (Rezat & Strasser\, 2012) that models the mediating role of textbooks
in instruction (Cohen\, Raudenbush\, & Ball\, 2003) and competencies (Nis
s\, 2011) which refers to a set of mathematical competencies that are affo
rded by the textbook\, instructors’ actions and resources\, and activate
d by the students.\n\nhttps://tagung.math.uni-paderborn.de/event/1/contrib
utions/101/
LOCATION: O1 258
URL:https://tagung.math.uni-paderborn.de/event/1/contributions/101/
END:VEVENT
BEGIN:VEVENT
SUMMARY:On the Introduction of Vectors in German Textbooks for upper Secon
dary School
DTSTART;VALUE=DATE-TIME:20190916T130000Z
DTEND;VALUE=DATE-TIME:20190916T133000Z
DTSTAMP;VALUE=DATE-TIME:20211021T061059Z
UID:indico-contribution-4-110@tagung.math.uni-paderborn.de
DESCRIPTION:Speakers: Tobias Mai (Paderborn University)\nIn this contribut
ion\, we present a praxeological analysis of (introductory) tasks on vecto
rs in German textbooks for secondary schools in the state North Rhine-West
phalia. We motivate our research concern from our interest in transition r
esearch from school to university and found a lack of research on vectors
in this area. The Anthropological Theory of the Didactic (ATD) has already
proven to be suitable for textbook analysis in other studies and was chos
en as a framework for our research on vectors in textbooks. With the recon
struction of a praxeological model from the textbooks\, an initial analysi
s on the introduction of vectors with a minimal institutional bias was pos
sible. The reconstructed model builds up from a task-oriented (praxis) per
spective by identifying types of tasks at first. Afterwards\, a connection
is drawn to the knowledge (logos) in form of explanations and justificati
ons the textbooks offer and thereby the reconstructed model is extended an
d further structured. Applying the model in an analysis of the textbooks a
llowed us to summarize the textbooks along the model\, identify similariti
es of the textbooks\, and systematically describe differences between them
. In the end\, the results and possible conclusions are discussed.\n\nhttp
s://tagung.math.uni-paderborn.de/event/1/contributions/110/
LOCATION: O2
URL:https://tagung.math.uni-paderborn.de/event/1/contributions/110/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Equivalence of fractions in 6th grade Brazilian textbooks
DTSTART;VALUE=DATE-TIME:20190917T123000Z
DTEND;VALUE=DATE-TIME:20190917T130000Z
DTSTAMP;VALUE=DATE-TIME:20211021T061059Z
UID:indico-contribution-4-111@tagung.math.uni-paderborn.de
DESCRIPTION:Speakers: Cydara Cavedon Ripoll (Universidade Federal do Rio G
rande do Sul)\nThe integer numbers structure and the idea of equivalence a
re elementary in the mathematical construction of the ordered field of the
rational numbers. Hence\, the concept of equivalence should not be absent
in the Elementary School´s classrooms and textbooks\, and it should be w
ell constructed with the students in the sense that they are able to answe
r the question ‘How can one decide if two fractions a/b and c/d are equi
valent?’ and explain their answer. However\, this discussion does not ap
pear in many 6th grade Brazilian textbooks. This paper is motivated by thi
s fact and is based on the belief that proofs should be present in the cla
ssrooms\, which was the focus of the Topic Study Group 18 entitled Reasoni
ng and Proof in Mathematics Education\, in the International Congress on M
athematical Education (ICME 13)\, in 2016. \nWe present a ‘proof that ex
plains’ (Hanna\, 1990) for the characterization for two given fractions
to be equivalent which we consider is adequate for 6th grade students. The
n we compare textbooks up to the 6th grade from six other countries\, focu
sing mainly on the questions: Is a complete characterization for equivalen
t fractions clearly presented to the students? Is equivalence used in the
comparison\, addition and subtraction of fractions? \nOnly partial charact
erizations were found\, and in most of the analyzed books a complete chara
cterization is not even suggested. We conclude that an important opportuni
ty of developing students’ mathematical thinking is lost.\n\nhttps://tag
ung.math.uni-paderborn.de/event/1/contributions/111/
LOCATION: O1 224
URL:https://tagung.math.uni-paderborn.de/event/1/contributions/111/
END:VEVENT
BEGIN:VEVENT
SUMMARY:THE VALUE OF TECHNOLOGY IN CHILEAN SCHOOL MATHEMATICS TEXTBOOKS: A
WAY OF CONDUCTING CONDUCTS
DTSTART;VALUE=DATE-TIME:20190919T093000Z
DTEND;VALUE=DATE-TIME:20190919T100000Z
DTSTAMP;VALUE=DATE-TIME:20211021T061059Z
UID:indico-contribution-4-118@tagung.math.uni-paderborn.de
DESCRIPTION:Speakers: Alex Montecino (Universidad Católica Silva Henríqu
ez)\nThis paper seeks to explore the value given to technology in the Chil
ean school mathematics textbooks. In recent years\, digital media has been
incorporated as an important part of the school mathematics textbook. Thi
s phenomenon has unfolded forms of producing a particular reality\, as wel
l as\, conducting—and sometimes delineating and shaping—students’ an
d teachers’ ways of thinking and acting. That is\, the use of technology
is affecting how students and teachers experience and perceive school mat
hematics. Within the materials provided by the Chilean Ministry of Educati
on\, it is possible to identify a gap between the use and representation o
f technology—its value—and the technology—actual technological devic
es—needed for the proper implementation of the activities suggested in t
hese materials. The identified gap increases in schools with a high level
of vulnerability. We contend the need of problematizing both the use of te
chnology as part of the content of school mathematics tasks (i.e. as conte
xt for and activity) and the use of digital materials as a way of improvin
g students achievement given that\, more often than expected\, digital sch
ool mathematics textbooks do not help—and even obstruct—teacher´s pra
ctices.\n\nhttps://tagung.math.uni-paderborn.de/event/1/contributions/118/
LOCATION: O2
URL:https://tagung.math.uni-paderborn.de/event/1/contributions/118/
END:VEVENT
BEGIN:VEVENT
SUMMARY:ON THE MARKETING AND DISTRIBUTION OF SCHOOL MATHEMATICS TEXTBOOKS
IN A NEOLIBERAL CONTEXT
DTSTART;VALUE=DATE-TIME:20190919T100000Z
DTEND;VALUE=DATE-TIME:20190919T103000Z
DTSTAMP;VALUE=DATE-TIME:20211021T061059Z
UID:indico-contribution-4-117@tagung.math.uni-paderborn.de
DESCRIPTION:Speakers: Melissa Andrade-Molina (Pontificia Universidad Cató
lica de Valparaíso)\nThis paper focuses on troubling the distribution and
market strategies of school mathematics textbooks in a context embedded i
n neoliberal policies and assumptions about education. And so\, it raises
a set of questions about the dynamic of the production\, distribution\, an
d selection of the official mathematics textbooks for Chilean schools and
the market that unfolds simultaneously of non-official mathematics textboo
ks. Some of these non-official textbooks—meaning these are not distribut
ed by the Chilean Ministry of Education—are been sold at highest rates i
n bookstores and\, because of it\, are considered to be of better quality.
The paper grasps how circulating narratives of ‘if you pay more\, you w
ill have a better product—a better textbook—and thus better opportunit
ies in life’ within neoliberal-based market strategies govern the select
ing of some textbooks in schools. This has led to some schools deciding no
t to use the official mathematics textbooks that are distributed for free
by the Chilean Ministry of Education\, and rather asking parents to buy th
e other “better” and expensive textbooks for their children’s educat
ion.\n\nhttps://tagung.math.uni-paderborn.de/event/1/contributions/117/
LOCATION: O1 224
URL:https://tagung.math.uni-paderborn.de/event/1/contributions/117/
END:VEVENT
BEGIN:VEVENT
SUMMARY:A Comparative Analysis on Trigonometry Textbooks from three countr
ies
DTSTART;VALUE=DATE-TIME:20190919T100000Z
DTEND;VALUE=DATE-TIME:20190919T103000Z
DTSTAMP;VALUE=DATE-TIME:20211021T061059Z
UID:indico-contribution-4-116@tagung.math.uni-paderborn.de
DESCRIPTION:Speakers: Xiaoyan He (School of Mathematical Sciences\, East C
hina Normal University)\nThis paper presents an examination about mathemat
ical textbooks for high school students from China\, Japan and the United
States at both macro and micro levels\, paritcularly with respect to gener
al features\, the trigonometric content included\, the sequencing of trigo
nometric content\, the structure of trigonometric content\, presentation f
eatures and the requirement of problems. We have found the following resul
ts: The American textbook is visually attractive and many pictures in full
colour. In contrast\, the other two textbooks are plain. Meanwhile\, both
Chinese and American textbooks are convenient for students to read. These
three countries value the trigonometry highly\, but the Chinese textbook
includes less trigonometric content than the other two countries. American
and Chinese textbooks present trigonometric application after trigonometr
ic function\, while Japanese textbook presents these topics much earlier.
The Chinese and Japanese textbooks have more emphasis on content instructi
on and less emphasis on problems when compared to the American textbook. A
lmost of the textbooks emphasize the development of students’ procedural
skills. Several suggestions are proposed at the end.\n\nhttps://tagung.ma
th.uni-paderborn.de/event/1/contributions/116/
LOCATION: O2
URL:https://tagung.math.uni-paderborn.de/event/1/contributions/116/
END:VEVENT
BEGIN:VEVENT
SUMMARY:DEVELOPING THE CHILD’S OWN MASTERY OF MANY
DTSTART;VALUE=DATE-TIME:20190919T093000Z
DTEND;VALUE=DATE-TIME:20190919T100000Z
DTSTAMP;VALUE=DATE-TIME:20211021T061059Z
UID:indico-contribution-4-115@tagung.math.uni-paderborn.de
DESCRIPTION:Speakers: Allan Tarp (MATHeCADEMY.net)\nPresent setcentric and
pre-setcentric math are challenged by\npost-setcentric math seeing math\,
not as a goal\, but as a means to develop\nthe mastery of Many children b
ring to school.\nAsked “How old next time?”\, a 3year old says “Four
” showing 4 fingers\; but\nprotests if held together 2 by 2: “That is
not four\, that is two 2s”\, thus\ndescribing what exists\, and with uni
ts: the total is bundles of 2s\, and 2\nof them. Children thus develop bot
h word- and number-sentences with a\nsubject\, a verb and a predicate. The
outside total exists as a natural\nfact\, but the inside predication it c
hosen and can be changed: T = 4 1s = 2\n2s = 1Bundle 1 3s = 0Bundle less 1
5s\, etc.\nPost-setcentric textbooks allow children to develop further th
eir mastery\nof Many by counting and recounting totals before adding them\
; and to number\ninstead of being taught about numbers. A textbook thus ca
n be based upon\nthe following ‘research’ questions.\n• The digit 5
is an icon with five sticks. Does this apply to all digits?\n• How to co
unt fingers in different sequences and bundles?\n• How can a calculator
predict a recounting result?\n• What to do with the unbundled singles?\n
• How to recount in the same or in another unit?\n• How to recount bet
ween tens and icons?\n• How to recount the sides in a block halved by it
s diagonal?\n• How to perform and reverse next-to and on-top addition?\n
\nhttps://tagung.math.uni-paderborn.de/event/1/contributions/115/
LOCATION: O1 258
URL:https://tagung.math.uni-paderborn.de/event/1/contributions/115/
END:VEVENT
BEGIN:VEVENT
SUMMARY:HistoS - Teachers connotations about historical snippets in textbo
oks
DTSTART;VALUE=DATE-TIME:20190919T083000Z
DTEND;VALUE=DATE-TIME:20190919T090000Z
DTSTAMP;VALUE=DATE-TIME:20211021T061059Z
UID:indico-contribution-4-122@tagung.math.uni-paderborn.de
DESCRIPTION:Speakers: Sebastian Schorcht (Justus-Liebig-University Giessen
)\nInteractions between teachers and textbooks are an active process and h
ave an impact on mathematical lessons. International studies show that his
torical snippets are one way to including the history of mathematics in te
xtbooks. Teachers must handle these tasks\, but in which way they use thes
e historical snippets? The aim of this explorative survey is to identify t
eachers’ language about tasks concerning the history of mathematics. Whi
ch connotations do teachers have about these textbook tasks? Do teachers i
dentify the same benefits of the history of mathematics in education as re
searchers do? This paper proposal will give an insightful view of a pilot
study on prospective teachers’ language about historical snippets. The s
urvey uses an online instrument\, presents teachers three tasks concerning
history of mathematics\, and records teachers’ connotations about these
tasks. The results indicate different views on historical snippets and\,
on more than one occasion\, that the benefits of history of mathematics ar
e missing. Therefore\, teachers need an introduction to handle these tasks
occurring in every-day mathematical textbooks.\n\nhttps://tagung.math.uni
-paderborn.de/event/1/contributions/122/
LOCATION: O1 224
URL:https://tagung.math.uni-paderborn.de/event/1/contributions/122/
END:VEVENT
BEGIN:VEVENT
SUMMARY:A LESSON STUDY INTERVENTION TO DEVELOP PRIMARY SCHOOL STUDENTS’
ABILITY TO PERFORM MENTAL FOLDING OPERATIONS’
DTSTART;VALUE=DATE-TIME:20190917T083000Z
DTEND;VALUE=DATE-TIME:20190917T090000Z
DTSTAMP;VALUE=DATE-TIME:20211021T061059Z
UID:indico-contribution-4-50@tagung.math.uni-paderborn.de
DESCRIPTION:Speakers: satoshi watanabe (jissen women's university)\nThe ai
m of this research is to design age-appropriate curriculum to nurture chil
dren’s mental operations ability and to clarify these effects through co
ncrete classroom-based lessons.\nI designed two lesson plans for grade4 st
udents that nurtured children’s mental operations\, and taught these in
two classes. Two of the lesson plans were as follows.\n1. The group 1 less
on was the same order in the textbook. The first lesson was looking for tw
o sides of the frat rectangular pattern\, which would overlap with each ot
her when assembled. The next lesson was to look for the missing one face o
f position that flat cube pattern could be assembled correctly.\n2. The gr
oup 2 lesson was the reverse order of group 1. \nI observed what type of m
ental strategies were used by children in these two courses of lessons. \n
Results\nGroup 1 \nThe first lesson\, the children searched for overlappin
g edges to join sides of the same length. The next lesson\, I observed chi
ldren who used a mental operation strategy. Finally\, children found the f
our locations of the one remaining face. However\, they did not apply the
strategy of joining sides that they used for rectangles.\nGroup 2\nThe fir
st lesson\, I observed that children used mental strategy of mind operatio
n and manipulation to do this. The strategy children used was to establish
one bottom face to start and then to manipulate the remaining four sides
to find the upper face. In the next lesson\, children applied a strategy t
hat involved setting out a starting bottom face and manipulating the remai
ning four sides to ensure that the sides would overlap with each other whe
n it was assembled as a rectangle. \nConclusion\nThe results of the study
found that the strategy of mental operation\, which was used to assemble c
ubes could be applied to imaginarily construct the more difficult rectangu
lar flat pattern. In addition\, the children who had the experience of usi
ng this mental strategy for other problems and recognizing its usefulness\
, began to aggressively use it for other similar problems and showed that
they had acquired the skill of spatial ability.\n\nhttps://tagung.math.uni
-paderborn.de/event/1/contributions/50/
LOCATION: O1 224
URL:https://tagung.math.uni-paderborn.de/event/1/contributions/50/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Research on Difficulty of Mathematics Curriculum and Textbook in C
hina:A review of literature
DTSTART;VALUE=DATE-TIME:20190917T090000Z
DTEND;VALUE=DATE-TIME:20190917T093000Z
DTSTAMP;VALUE=DATE-TIME:20211021T061059Z
UID:indico-contribution-4-62@tagung.math.uni-paderborn.de
DESCRIPTION:Speakers: Zhuo Li (East China Normal University)\nThis paper s
ummarized domestic main models of degree of difficulty of curriculum and t
extbook from two aspects：the quantification of the component factors and
the proportion of the component factors. Based on this\, we propose five
points the future research on models of degree of difficulty of curriculum
and textbook needs to focus on: the concept definition in the study of mo
dels of degree of difficulty of curriculum and textbook\, clarifying influ
ence factors of the degree of difficulty of curriculum and textbook\, the
scientificity of quantification of the component factors and the proporti
on of the component factors\, the reliability and validity of the research
on degree of difficulty of curriculum and textbook\, constructing more sc
ientific and complex model of degree of difficulty of curriculum and textb
ook.\n\nhttps://tagung.math.uni-paderborn.de/event/1/contributions/62/
LOCATION: O1 258
URL:https://tagung.math.uni-paderborn.de/event/1/contributions/62/
END:VEVENT
END:VCALENDAR