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BEGIN:VEVENT
SUMMARY:A qualitative study on the levels of mathematical explanation in J
apanese elementary textbook
DTSTART;VALUE=DATE-TIME:20190916T163000Z
DTEND;VALUE=DATE-TIME:20190916T183000Z
DTSTAMP;VALUE=DATE-TIME:20211021T050827Z
UID:indico-contribution-1-76@tagung.math.uni-paderborn.de
DESCRIPTION:Speakers: Takahiro Okubo ()\nIn Japan (maybe\, also around oth
er countries)\, one has pointed out that elementary students’ ability an
d skill for explanation in mathematics lacked. For this reason\, we should
analyze our own mathematics textbooks because it works as curriculum. (No
tes: In Japan\, all textbooks are authorized by the Ministry of Education)
.\nOur theoretical framework is framework for mathematical explanation in
elementary school that is proposed by Miyazaki (1995). The purpose of Miya
zaki(1995) is to improve teaching and learning proof and proving in junior
high school students\; for this purpose\, he also construct the framework
because explanation in elementary school will connect with proof. Miyazak
i(1995) identify and distinguish 4 levels of explanation in elementary sch
ool mathematics\; level 1 is lowest\, and 4 is highest. Our methodology is
qualitative analysis by the framework. Our object is “formula for the a
rea of a parallelogram” in the fifth grade (Shimizu\, Funakoshi\, Negami
\, Teragaito et al.\, 2015\, pp.124-125)\, because there are 4 explanation
s for one problem\; since the number of explanations for one problem is mo
st\, it is expected that the intention of the textbook appears.\nAs a resu
lt\, we can pointed out there are explanation of level 2\, 3\, and 4 are w
ritten in it (there are two level 2)\; however\, its order is not from 2 t
o 4\, but from 4 to 2. Thus\, we can say the textbook has not paid attenti
on to level (or quality) of explanation.\nOn the other hand\, actual stude
nts may explain as it\, level 2 or 3. Miyazaki’s (1995) framework does n
ot refer how to improve it or reveal conception of students who explain as
level 1\, 2 or 3. Thus\, we found necessity of another types of theoretic
al frameworks for it.\n\nhttps://tagung.math.uni-paderborn.de/event/1/cont
ributions/76/
LOCATION: O1 258
URL:https://tagung.math.uni-paderborn.de/event/1/contributions/76/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Exploratory Research on Understanding Proof by Coincidence: Buildi
ng an Analytical Framework by Comparing Japanese Textbooks
DTSTART;VALUE=DATE-TIME:20190916T163000Z
DTEND;VALUE=DATE-TIME:20190916T183000Z
DTSTAMP;VALUE=DATE-TIME:20211021T050827Z
UID:indico-contribution-1-56@tagung.math.uni-paderborn.de
DESCRIPTION:Speakers: Toru Hayata ()\nThis paper aims to create an analyti
cal framework for empirical studies seeking to understand “proof by coin
cidence\,” a type of indirect proof. Although little is known about teac
hing and learning proof by coincidence\, all junior high school mathematic
s textbooks in Japan include this method of proof. To hypothesize the pote
ntial problems of teaching proof by coincidence\, we investigated the vari
ety of ways in which Japanese junior high school textbooks present the Con
verse of the Pythagorean Theorem (CPT)\, which is usually proven by coinci
dence. We found that the figures and emphatic points used to present the P
ythagorean Theorem (PT) and its converse are often identical. It is notewo
rthy that we are not sure whether the differences in the ways textbooks pr
esent the PT and the CPT necessarily contributes to the resolution of stud
ents’ confusion\, while we can conduct empirical research on students’
process of understanding of proof by coincidence from this point of view.
Further research is therefore required to determine what influence this e
diting policy may have on students learning the proof by coincidence metho
d.\n\nhttps://tagung.math.uni-paderborn.de/event/1/contributions/56/
LOCATION: O1 258
URL:https://tagung.math.uni-paderborn.de/event/1/contributions/56/
END:VEVENT
BEGIN:VEVENT
SUMMARY:The use of a digital textbook with integrated digital tools
DTSTART;VALUE=DATE-TIME:20190916T163000Z
DTEND;VALUE=DATE-TIME:20190916T183000Z
DTSTAMP;VALUE=DATE-TIME:20211021T050827Z
UID:indico-contribution-1-73@tagung.math.uni-paderborn.de
DESCRIPTION:Speakers: Maxim Brnic (University of Münster)\nThe use of mat
hematics textbooks makes an impact on teaching and learning in the classro
om. Because of the important role of textbooks\, it can be presumed that d
igital mathematics textbook also have an effect on didactic aspects of the
organisation of lessons and teaching. Since 2019\, the project KomNetMath
surveys the influence of a digital mathematic textbook regularly used by
teachers and students in grade 10 and 11 at German schools. The goal is to
examine the actual use of the digital textbook and the impact on teachers
’ and students‘ attitude towards the use of digital textbooks as well
as its influence on the progress of mathematical competencies. In this con
tribution\, we present the concept of the digital textbook\, the theoretic
al background\, the research questions and the research design.\n\nhttps:/
/tagung.math.uni-paderborn.de/event/1/contributions/73/
LOCATION: O1 258
URL:https://tagung.math.uni-paderborn.de/event/1/contributions/73/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Geometrical properties as assumptions in proofs in Japanese junior
high school mathematics textbooks
DTSTART;VALUE=DATE-TIME:20190916T163000Z
DTEND;VALUE=DATE-TIME:20190916T183000Z
DTSTAMP;VALUE=DATE-TIME:20211021T050827Z
UID:indico-contribution-1-49@tagung.math.uni-paderborn.de
DESCRIPTION:Speakers: Mikio Miyazaki (Shinshu University)\nGiven the inter
national evidence that students have trouble in understanding proof in mat
hematics (e.g. Hanna & de Villiers\, 2012)\, the appropriateness of the co
ntent of textbooks is one crucial factor (Fan et al.\, 2018). Here\, we fo
cus on the introduction of proof in Japanese mathematics textbooks at the
junior high school level. In one of these textbooks\, authorized by the Mi
nistry of Education in Japan\, a proof is defined as ‘an explanation of
a statement based on properties that we already know to be true’. If the
se ‘already known to be true statements’ are treated ambiguously or un
clearly in the textbooks\, this might underlie some of the difficulties in
the teaching and learning of proofs. Hence our research question is: in J
apanese junior high school mathematics textbooks\, what is the relationshi
p between the set of geometrical properties as assumptions in the definiti
on of a proof\, and the geometrical properties that appear in the proofs?
For our analytic framework\, we define ‘correspondence’ as the consist
ency between facts for students and geometrical properties\, and ‘cohere
nce’ as the deductive consistency between geometrical properties. We fin
d that there is a ‘gap’ of adopting ‘correspondence’ and the ‘co
herence’. One way to overcome this gap is to design textbooks for geomet
ry that provide the sections for the proof structure\, ‘justification’
and ‘systematization’ as the functions of proofs.\n\nhttps://tagung.m
ath.uni-paderborn.de/event/1/contributions/49/
LOCATION: O1 258
URL:https://tagung.math.uni-paderborn.de/event/1/contributions/49/
END:VEVENT
BEGIN:VEVENT
SUMMARY:THE PRESENCE OF GEOMETRY IN FRACTION TASKS: AN ANALYSIS OF TEXTBOO
KS
DTSTART;VALUE=DATE-TIME:20190916T163000Z
DTEND;VALUE=DATE-TIME:20190916T183000Z
DTSTAMP;VALUE=DATE-TIME:20211021T050827Z
UID:indico-contribution-1-92@tagung.math.uni-paderborn.de
DESCRIPTION:Speakers: Liara Alves Gentil ()\, Rúbia Barcelos Amaral-Schi
o ()\nThis work presents results of a research\, in development\, which ai
ms to investigate how Geometry is present in the other branches of Mathema
tics in some textbooks. We make a cut here\, focusing on fraction tasks in
textbooks destined to the Final Years of Elementary Education. We are loo
king at two books in the sixth year (because they contain most of the frac
tion content) of two different collections. First\, we selected the chapte
rs dealing with the fractions notions\, and then separated the tasks in wh
ich Geometry appears. We analysed the tasks based on Arcavi (2003). The re
sults show that Geometry appears in tasks that work the correspondence bet
ween fractional numbers and points of the numerical line and in the fracti
on representation through the decomposition of figures or geometric solids
. Thus\, the visual representations of Geometry can aid in the process of
teaching and learning by making visible purely algebraic properties.\n\nht
tps://tagung.math.uni-paderborn.de/event/1/contributions/92/
LOCATION: O1 258
URL:https://tagung.math.uni-paderborn.de/event/1/contributions/92/
END:VEVENT
BEGIN:VEVENT
SUMMARY:A mathematics college textbook: design intentions and reading prac
tice
DTSTART;VALUE=DATE-TIME:20190916T163000Z
DTEND;VALUE=DATE-TIME:20190916T183000Z
DTSTAMP;VALUE=DATE-TIME:20211021T050827Z
UID:indico-contribution-1-63@tagung.math.uni-paderborn.de
DESCRIPTION:Speakers: Bethany Woollacott (Loughborough University)\nReadin
g mathematics is difficult for many reasons such as dense text explaining
abstract concepts. Many undergraduate mathematicians still struggle to rea
d mathematics proficiently suggesting that not enough is being done at sch
ool or college to support learning this important skill. Although research
in this area is increasing\, research into the most widely used reading m
aterial in the mathematics classroom – the textbook – is relatively sc
arce. This project aimed to explore whether mathematics textbooks are fulf
illing their potential by conducting two investigations into the design an
d use of a specific college-level textbook. Firstly\, we interviewed autho
rs of the textbook to investigate intentions behind design decisions and t
hen we recorded students’ eye-movements as they read the textbook. We th
ematically analysed the interviews and the resultant themes helped to gene
rate specific research questions for the eye-tracking investigation. Conse
quently\, we found that authors tended to correctly predict how the textbo
ok would be read even when the reading strategies were not representative
of best practice. This poster recognises how better communication between
educators\, researchers\, authors and publishers could improve a textbook
’s potential as a facilitator of mathematical reading. Additionally\, we
explore differences between how students read and processed specific elem
ents of the textbook’s design and discuss how better design might inspir
e more efficient reading.\n\nhttps://tagung.math.uni-paderborn.de/event/1/
contributions/63/
LOCATION: O1 258
URL:https://tagung.math.uni-paderborn.de/event/1/contributions/63/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Registration / Coffee
DTSTART;VALUE=DATE-TIME:20190916T063000Z
DTEND;VALUE=DATE-TIME:20190916T080000Z
DTSTAMP;VALUE=DATE-TIME:20211021T050827Z
UID:indico-contribution-1-134@tagung.math.uni-paderborn.de
DESCRIPTION:https://tagung.math.uni-paderborn.de/event/1/contributions/134
/
LOCATION:Paderborn University\, Germany
URL:https://tagung.math.uni-paderborn.de/event/1/contributions/134/
END:VEVENT
BEGIN:VEVENT
SUMMARY:A study on the senior high school students’ algebraic activities
and the digital tools in Japanese digital mathematics textbook
DTSTART;VALUE=DATE-TIME:20190916T163000Z
DTEND;VALUE=DATE-TIME:20190916T183000Z
DTSTAMP;VALUE=DATE-TIME:20211021T050827Z
UID:indico-contribution-1-75@tagung.math.uni-paderborn.de
DESCRIPTION:Speakers: Kazumichi Tanaka ()\nIn this study\, we analyse Japa
nese digital mathematics textbook in senior high school with focusing on s
tudents’ algebraic skills or notions. For learning algebra\, generalizat
ion plays essential role\; especially\, Dörfler (1991) pointed out that
to use algebraic letters relates with students’ activities. For insta
nce\, according to Fujii (2000)\, when students can not consider about rel
ationships between mathematical objects\, they can not use algebraic lette
rs well\; Dörfler (1991) said students abstract these relationships th
rough their own activities.Thus\, our theoretical framework is Dörfler (
1991)\, and methodology is qualitative analyses of the digital textboo
k\; we focus on unit of quadratic function because it is compulsory and
core unit of learning algebra in senior high school. \nAs a result\, we c
an point out the layout of digital textbook is same as paper textbooks\; h
owever\, each problem has an icon to access the digital tools. From our th
eoretical view\, almost of all these tools are for validating (and/or ju
stifying) explanation by sentences. In other words\, we found that these
tools do not allow students’ activities (in sense of Dörfler (1991))
. Based on this result\, we discuss nature of digital tools and propose c
oncrete tools and theoretical perspective for digital tool which realize
Dörfler's (1991) activities.\n\nhttps://tagung.math.uni-paderborn.de/even
t/1/contributions/75/
LOCATION: O1 258
URL:https://tagung.math.uni-paderborn.de/event/1/contributions/75/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Opening Ceremony
DTSTART;VALUE=DATE-TIME:20190916T080000Z
DTEND;VALUE=DATE-TIME:20190916T090000Z
DTSTAMP;VALUE=DATE-TIME:20211021T050827Z
UID:indico-contribution-1-135@tagung.math.uni-paderborn.de
DESCRIPTION:https://tagung.math.uni-paderborn.de/event/1/contributions/135
/
LOCATION: O1
URL:https://tagung.math.uni-paderborn.de/event/1/contributions/135/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Closing Ceremony
DTSTART;VALUE=DATE-TIME:20190919T103000Z
DTEND;VALUE=DATE-TIME:20190919T113000Z
DTSTAMP;VALUE=DATE-TIME:20211021T050827Z
UID:indico-contribution-1-136@tagung.math.uni-paderborn.de
DESCRIPTION:https://tagung.math.uni-paderborn.de/event/1/contributions/136
/
LOCATION:Paderborn University\, Germany
URL:https://tagung.math.uni-paderborn.de/event/1/contributions/136/
END:VEVENT
BEGIN:VEVENT
SUMMARY:LIMIT OF TEXTBOOK IN CONCEPTUAL UNDERSTANDING
DTSTART;VALUE=DATE-TIME:20190916T163000Z
DTEND;VALUE=DATE-TIME:20190916T183000Z
DTSTAMP;VALUE=DATE-TIME:20211021T050827Z
UID:indico-contribution-1-95@tagung.math.uni-paderborn.de
DESCRIPTION:Speakers: Tsutomu Ishii (Bunkyo University)\nIn this paper\, w
e consider the solution based on the universal mathematical idea in Japane
se mathematics textbooks. We consider the conceptual understanding in the
multiplication of the fraction. Teachers teach it in the fifth graders of
elementary school. The conclusion is applying to numerators and denominato
rs each other. It is the mere procedural understanding. In order to make t
his conceptual understanding\, the area of the square is shown in the text
book. For example\, the right figure illustrates 1/2×3/4. The Japanese fo
urth grader in elementary schools learn decimal × decimal. The teachers u
rge conceptual understanding based on the number line. However\, that teac
hers do not use that number line in this scene. Because it is not used in
textbooks. It can be expected that conceptual understanding is urged to ex
amining the area of the square on the other hand. The relation of such Tex
tbook and Student\, Teacher\, and Mathematical knowledge is as being shown
in Rezat's model. So\, in the multiplication of the decimal and fraction\
, it is concluded that the method of urging conceptual understanding is no
t related.\n\nhttps://tagung.math.uni-paderborn.de/event/1/contributions/9
5/
LOCATION: O1 258
URL:https://tagung.math.uni-paderborn.de/event/1/contributions/95/
END:VEVENT
BEGIN:VEVENT
SUMMARY:CURRENT STATUS AND ISSUES OF DIGITAL TEACHING MATERIALS IN JAPAN
DTSTART;VALUE=DATE-TIME:20190916T163000Z
DTEND;VALUE=DATE-TIME:20190916T183000Z
DTSTAMP;VALUE=DATE-TIME:20211021T050827Z
UID:indico-contribution-1-104@tagung.math.uni-paderborn.de
DESCRIPTION:Speakers: MANABU GOTO (Sagami Women's University)\nA considera
ble amount of time has elapsed since ICT was introduced into the class in
Japan and it is recognized that it is comprehensively effective\, but it i
s in progress in mathematics department. In this article\, research trends
related to mathematics education and technology are described as follows:
(1) timing and scene of utilization in the class\, (2) what kind of abili
ty of the child to improve\, (3) how to use commercial software\, self-mad
e software\, (4) class design\, The four points were organized. In classes
\, methods of using PCs in accordance with conventional learning processes
are being studied\, but research on the evaluation method is in short sup
ply. It is not enough to clarify what kind of ability a child is able to d
evelop\, and it is necessary to combine the functions and properties of PC
with self-made software after clarifying the aim and purpose of the lesso
n. As a future topic\, I showed that desktop PC study from arithmetic educ
ation is desirable for PC to contribute to mathematics education.\n\nhttps
://tagung.math.uni-paderborn.de/event/1/contributions/104/
LOCATION: O1 258
URL:https://tagung.math.uni-paderborn.de/event/1/contributions/104/
END:VEVENT
BEGIN:VEVENT
SUMMARY:A study on the educational ideology of modernization in the case o
f Japanese textbook
DTSTART;VALUE=DATE-TIME:20190916T163000Z
DTEND;VALUE=DATE-TIME:20190916T183000Z
DTSTAMP;VALUE=DATE-TIME:20211021T050827Z
UID:indico-contribution-1-77@tagung.math.uni-paderborn.de
DESCRIPTION:Speakers: Takahiro Mabuchi ()\nPurpose of this study is to des
cribe an ideology of era of modernization in mathematics education by our
theoretical framework. According to Chevallard (2015)\, our current ideolo
gy is ‘paradigm of visiting monuments’\, on the other hand ‘paradigm
of questioning the world’ should replace it. Here\, we focus on the ter
m ‘paradigm’ which is proposed by Kuhn (1970) because it was critiqued
by Lakatos’s (1978) notion of ‘research program’. Base on it\, we c
onstructed our hypothetical framework which consists unseparatable three l
evels of ‘hard core’ and ‘protective belt’: ‘rational level’\,
‘belief level’\, and ‘society level’\; ‘rational level’ is id
entical with Lakatos’s (1978) research program.\nOur methodology is phil
osophical consideration for mathematics textbook because it reflects socia
l and ideological conditions and constraints in era of modernization. The
reason for paying attention to modernization is that\, it is one of most i
mportant educational movements and\, in Japan\, the curriculum clearly sta
ted that the purpose is to foster students’ attitude for first time.\nAs
a result of consideration\, we can describe that modernization attacked o
nly protective belt in ‘belief level’ and ‘society level’\; for ex
ample\, it changed the contents and arrangement of mathematical knowledge
in curriculum. Thus\, modernization can not change hard core so it becomes
new protective belt for monumentalism.\n\nhttps://tagung.math.uni-paderbo
rn.de/event/1/contributions/77/
LOCATION: O1 258
URL:https://tagung.math.uni-paderborn.de/event/1/contributions/77/
END:VEVENT
BEGIN:VEVENT
SUMMARY:The Analysis of the Diagrams in the textbook of Arithmetic
DTSTART;VALUE=DATE-TIME:20190916T163000Z
DTEND;VALUE=DATE-TIME:20190916T183000Z
DTSTAMP;VALUE=DATE-TIME:20211021T050827Z
UID:indico-contribution-1-52@tagung.math.uni-paderborn.de
DESCRIPTION:Speakers: Haruka Kitabori (Faculty of Psychology Meiji Gakuin
University)\nIt is useful and meaningful to used diagrams for making sense
of calculation and solving word problems. But it is difficult for pupils
to interpret and use the diagrams (NIER\, 2014). In response to this situa
tion in Japan\, we need to reconsider using diagrams in teaching/leaning o
f calculations from the cross-sectional perspectives for the development o
f number concepts and meaning of calculation. So\, the purpose of this stu
dy is to examine and consider the features and classification of diagrams
in textbooks used in teaching/leaning of calculations in elementary school
. As a method on this study\, based on the theory of mathematical expressi
ons by Nakahara (1995) and a process of solving word problems by Mayer (19
92) as a theoretical framework\, we are analysed and considered the diagra
ms used in textbooks. In this paper\, we will cover teaching/leaning of ad
dition and subtraction of integers of Japanese textbooks used from grade 1
to grade 3. As conclusions of this study\, we have two points as below: (
1) to suppose the new classification of the diagrams and (2) the differenc
e of the quality of diagrams according to pupils’ development.\n\nhttps:
//tagung.math.uni-paderborn.de/event/1/contributions/52/
LOCATION: O1 258
URL:https://tagung.math.uni-paderborn.de/event/1/contributions/52/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Analyzing Math Textbook in Elementary School Mathematics in Japan:
Focusing on the explanations of multiplication of decimal numbers
DTSTART;VALUE=DATE-TIME:20190916T163000Z
DTEND;VALUE=DATE-TIME:20190916T183000Z
DTSTAMP;VALUE=DATE-TIME:20211021T050827Z
UID:indico-contribution-1-55@tagung.math.uni-paderborn.de
DESCRIPTION:Speakers: Shigetaro Sato (Matsumoto university)\nThe purpose o
f this paper is to analyze mathematics textbooks used in elementary school
math classes in Japan. In Japan\, textbooks are prepared based on the Cou
rse of Study prepared by the Ministry of Education (including guidelines).
This study indents to analyze explanations of how to multiply decimals in
the fifth grade of elementary school. In the Japanese calculation guidanc
e\, two explanations are recommended: one for writing expressions\, and th
e other for calculating them. For these two kinds of explanations\, two di
fferent publishers were compared and analyzed. The analysis was conducted
using a modified and reinforced version of the TIMSS framework (Valverde e
t al. 2002). The results revealed that\, while the subject being explained
remained unchanged\, there were differences in the following areas. First
\, in terms of the explanation of the grounds on which the formula was set
up\, Publisher T had an explicit activity explaining the process using a
proportional relationship\, while Publisher K did not use the proportional
relationship. In addition\, in the explanation regarding how to calculate
\, Publisher T used a number line\, along with a verbal explanation of how
to perform the calculation. Meanwhile\, Publisher K used only a verbal ex
planation. Based on the above\, it became clear that in the teaching of ho
w expressions are written and calculated\, the type of formula\, and the c
ontent of the explanation differ\, depending on the publisher.\n\nhttps://
tagung.math.uni-paderborn.de/event/1/contributions/55/
LOCATION: O1 258
URL:https://tagung.math.uni-paderborn.de/event/1/contributions/55/
END:VEVENT
BEGIN:VEVENT
SUMMARY:A Study of the Characteristic of Japanese Textbooks towards the Gr
owth of Children's Mathematical Representation
DTSTART;VALUE=DATE-TIME:20190916T163000Z
DTEND;VALUE=DATE-TIME:20190916T183000Z
DTSTAMP;VALUE=DATE-TIME:20211021T050827Z
UID:indico-contribution-1-94@tagung.math.uni-paderborn.de
DESCRIPTION:Speakers: kunihiko shimizu ()\nThe purpose of this research is
to clarify the measures being used in Japanese elementary and junior high
school’s textbooks to foster children’s understanding and usage of ma
thematical representations.\nFirst\, a discussion were conducted on the ki
nds of representations required as well as the process of its development
based on the national curriculum and achievement test. Both of them posses
s an explicit process of the continuity between elementary school and juni
or high school. As grade level increases\, subject matter changes from ari
thmetic to mathematics as representations become more formal and mathemati
cal\, as well as more logical and systematic. \nNext\, measures used by th
e textbooks were considered. As students progress through grade levels\, t
heir understanding and usage of representations\, in the same manner as th
eir textbooks\, becoming more formal\, for instance\, from Manipulative Re
presentation and Illustrative Representation to more Linguistic Representa
tion\, as well as the usage of more Symbolic Representation. Additionally
\, measures of representations are conducted not only through a textbook
’s speech bubbles or comments\, but also by preparation and usage of mat
hematical notes and reports that guide students in the development of thei
r understanding and usage of representations. Certain textbook companies d
evelop students’ representations by including content focused on knowled
ge and usage of vocabulary necessary for students to represent themselves
logically.\n\nhttps://tagung.math.uni-paderborn.de/event/1/contributions/9
4/
LOCATION: O1 258
URL:https://tagung.math.uni-paderborn.de/event/1/contributions/94/
END:VEVENT
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