Manually adding references without bibtex, and How to arrange them in alphabetic order and like APA and Chicago styles etc
Using a siddur to Daven from in a seforim store
Could the E-bike drivetrain wear down till needing replacement after 400 km?
How should I respond when I lied about my education and the company finds out through background check?
My friend sent me a screenshot of a transaction hash, but when I search for it I find divergent data. What happened?
How can "mimic phobia" be cured or prevented?
Diode in opposite direction?
Why has "pence" been used in this sentence, not "pences"?
Can I sign legal documents with a smiley face?
Java - What do constructor type arguments mean when placed *before* the type?
Is XSS in canonical link possible?
Why is Arduino resetting while driving motors?
Could solar power be utilized and substitute coal in the 19th Century
How will losing mobility of one hand affect my career as a programmer?
Divine apple island
Can I Retrieve Email Addresses from BCC?
Bob has never been a M before
Can a significant change in incentives void an employment contract?
Is it possible to have a strip of cold climate in the middle of a planet?
Ridge Regression with Gradient Descent Converges to OLS estimates
Flux received by a negative charge
Why does Async/Await work properly when the loop is inside the async function and not the other way around?
Is camera lens focus an exact point or a range?
Does having a TSA Pre-Check member in your flight reservation increase the chances that everyone gets Pre-Check?
Can I use my Chinese passport to enter China after I acquired another citizenship?
Manually adding references without bibtex, and How to arrange them in alphabetic order and like APA and Chicago styles etc
documentclass[reqno]article
usepackageamssymb
usepackageamsmath
usepackagetimes
usepackageepsfig
usepackagegraphicx
usepackagemathrsfs
textwidth 5in textheight 7.5in footskip 0.5in
newtheoremthm[subsection]Theorem
newtheoremlemma[subsection]Lemma
newtheoremproposition[subsection]Proposition
newtheoremcor[subsection]Corollary
%theoremstyledefinition
newtheoremrk[subsection]Remark
newtheoremdefn[subsection]Definition
newtheoremex[subsection]Example
newtheoremquestion[subsection]Question
newtheoremconjecture[subsection]Conjecture
newcommandMSmathscr
defbCBbb C
defbRBbb R
defbPBbb P
defcOCal O
defaalpha defbbeta
defDDelta
defeeta defggamma defssigma
defddelta defLLambda defllambda
defnbmathbb N defdsdisplaystyle letw=wedge
defcbmathbb C
defrbmathbb R
lett=theta letL=longrightarrow defdcdd^c
defvvarphi def Ccal C letl=rightarrow
letm=mathop letep=varepsilon letS=subset
letO=Omega
defespnoalignmedskip letr=rho
def11!rm l
%newcommandMSmathscr
newcommand newsection[1] setcounterequation0 section #1
renewcommandtheequation arabicsection. arabicequation
begindocument
pagestylemyheadings pagenumberingarabic setcounterpage1
pagestyleempty
par noindent
Punjab University \
Journal of Mathematics (ISSN 1016-2526) \
Vol. 51(7)(2019) pp. 00.00 vspace*1pc
begincenter
bf Creating an Environment for Learning Mathematics
par noindent
vspace*1pc
parnoindentparnoindent
par noindent
Muhammad Ahmad \
Department of Mathematics, \
University of sargodha, Pakistan,\
Email: m.ahmadpak@gmail.com\
par noindent
endcenter
vspace*0.5pcReceived: 07 April, 2018 / Accepted: 06 June, 2018 /
Published online: 20 December, 2018 vspace*0.5pc
beginquote
bf Abstract. It was citearticle-full with the theoretical ideas about
constructivists' view of learning discussed in the preceding chapter
that we began our collaboration with the classroom teacher. Although
we communicated our intentions in discussions about the importance
of problem solving for learning and the necessity of social
interaction and class discussion, it was still the teacher's
obligation to enact these in the classroom. Admittedly we were well
aware that children actively discussing challenging problems in
primary grades was different from the way mathematics had been
taught in the past, but we had not yet realized the extent to which
these ideas would influence the practice of elementary school
mathematics. These aspects--challenging problems, collaborative
group work, and class discussion about students' solutions-were, for
the teacher, against tradition. It was accepted practice for her to
initiate grouped settings and discussions in social studies,
science, and reading, but she did not do this in mathematics. It was
against this background that the classroom teaching experiment
began.
endquote
vspace*1.5pc noindent bf AMS (MOS) Subject Classification
Codes: 35S29; 40S70; 25U09 \
smallskip noindent
bf Key Words: -------------------------------------------------.
markbothunderlinehspace3.7in Muhammad Ahmad
underlinehspace0ptCreating an Environment for Learning
Mathematicshspace2.5inpagestylemyheadings
setcountersection0
sectionIntroduction
Typically a class session began with the teacher leading a brief
introduction intended to insure that the children understood what
they would be working on for the day. Once the teacher was satisfied
that the children understood the intent of the activities, she then
passed out the activity sheets and small-group work began. Children
worked in pairs on activities, which were on sheets of paper that
provided room for students to write. Each pair received one sheet to
share in completing the activity. Generally three to four sheets,
each containing four to six problems, were available for the
students to work on. Some children completed all the activity
sheets, whereas others only finished one. The problem solving as
pairs generally lasted 20 to 25 minutes.
sectionNotations and Preliminaries
The expectations for children's actions in the mathematics class
were quite different from their previous experiences in school.
However, in this mathematics class it was necessary for children to
express their thinking in order to create opportunities for learning
and so that their existing constructions could be investigated by
both the teacher and researchers
sectionDiscrete Evolution Semigroup
Using these premises of children's learning as her guideline, the
teacher initiated the mutual construction of a different set of
norms for mathematics lessons as she acted to help the students
reconceptualize their role during mathematics instruction. Her
intention was for the children to figure things out for themselves
and to express their ideas in the public arena of whole-class
discussions. Additionally, during small-group work she expected them
to cooperate and work together to solve problems and to agree on an
answer. Her expectation that the children would express their
thoughts placed the students under the obligation of having to
recall their solutions and explain them to others during the
whole-class discussion.
sectionResults
The nature of the teacher and student interaction that occurred
within the whole-class discussion was crucial to establishing the
social norms that were necessary for developing a setting in which
the children would feel psychologically safe to express their
mathematical thinking.] The teacher's intention as she led class
discussion was to encourage children to verbalize their solution
attempts.
sectionApplications
Her comments were focused on talking about how in this class they
were going to talk about mathematics. In this example she told the
students that thinking was valued even more than right answers.
These mutual obligations and expectations were negotiated and
renegotiated by the teacher and students as they established an
interaction pattern that would form the basis for their activity.
These mutually constituted patterns of interaction were taken for
granted and made possible the smooth functioning of their collective
sectionConclusion
It became evident that a psychological perspective alone could not
account for the complexity of the events occurring in the classroom.
Establishing social norms that provided the setting in which
children engaged in meaningful activity was an aspect of social
interaction not considered prior to the classroom teaching
experiment. As these norms became accepted, the students
participated in a type of discourse in which they were expected to
explain and justify their solutions and listen to others. The
teacher acted to initiate and guide students' learning by posing
questions and highlighting children's expectations. As students
engaged in this discourse, their personal meanings were negotiated
until an agreement was reached. The establishment of taken-as-shared
meanings between the participants enabled mathematical ideas to be
established by members of the class.
sectionAcknowledgments
I would like to thank my supervisor, Prof. Nicholas Young, for the
patient guidance, encouragement and advice he has provided
throughout my time as his student. I have been extremely lucky to
have a supervisor who cared so much about my work, and who responded
to my questions and queries so promptly. I would also like to thank
all the members of staff at Newcastle and Lancaster Universities who
%helped me in my supervisors absence.
newcommandnoopsort[1] newcommandprintfirst[2]#1
newcommandsingleletter[1]#1 newcommandswitchargs[2]#2#1
beginthebibliography99
bibitemarticle-minimal
L[eslie]~A. Aamport.
newblock The gnats and gnus document preparation system.
newblock em mboxG-Animal's Journal, 1986.
bibitemarticle-full
L[eslie]~A. Aamport.
newblock The gnats and gnus document preparation system.
newblock em mboxG-Animal's Journal, 41(7):73+, July 1986.
newblock This is a full ARTICLE entry.
bibitemarticle-crossref
L[eslie]~A. Aamport.
newblock The gnats and gnus document preparation system.
newblock In em mboxG-Animal's Journal/ citewhole-journal, pages 73+.
newblock This is a cross-referencing ARTICLE entry.
bibitemwhole-journal
em mboxG-Animal's Journal, 41(7), July 1986.
newblock The entire issue is devoted to gnats and gnus (this entry is a
cross-referenced ARTICLE (journal)).
bibitemwhole-set
Donald~E. Knuth.
newblock em The Art of Computer Programming.
newblock Four volumes. Addison-Wesley,
noopsort1973aswitchargs--901968.
newblock Seven volumes planned (this is a cross-referenced set of BOOKs).
bibiteminbook-minimal
Donald~E. Knuth.
newblock em Fundamental Algorithms, chapter 1.2.
newblock Addison-Wesley, noopsort1973b1973.
bibiteminbook-full
Donald~E. Knuth.
newblock em Fundamental Algorithms, volume~1 of em The Art of Computer
Programming, section 1.2, pages 10--119.
newblock Addison-Wesley, Reading, Massachusetts, second edition, 10~January
noopsort1973b1973.
newblock This is a full INBOOK entry.
bibiteminbook-crossref
Donald~E. Knuth.
newblock em Fundamental Algorithms, section 1.2.
newblock Volume~1 of em The Art of Computer Programming/ citewhole-set,
second edition, noopsort1973b1973.
newblock This is a cross-referencing INBOOK entry.
bibitembook-minimal
Donald~E. Knuth.
newblock em Seminumerical Algorithms.
newblock Addison-Wesley, noopsort1973c1981.
bibitembook-full
Donald~E. Knuth.
newblock em Seminumerical Algorithms, volume~2 of em The Art of Computer
Programming.
newblock Addison-Wesley, Reading, Massachusetts, second edition, 10~January
noopsort1973c1981.
newblock This is a full BOOK entry.
bibitembook-crossref
Donald~E. Knuth.
newblock em Seminumerical Algorithms.
newblock Volume~2 of em The Art of Computer Programming/ citewhole-set,
second edition, noopsort1973c1981.
newblock This is a cross-referencing BOOK entry.
bibitembooklet-minimal
The programming of computer art.
bibitembooklet-full
Jill~C. Knvth.
newblock The programming of computer art.
newblock Vernier Art Center, Stanford, California, February 1988.
newblock This is a full BOOKLET entry.
bibitemincollection-minimal
Daniel~D. Lincoll.
newblock Semigroups of recurrences.
newblock In em High Speed Computer and Algorithm Organization. Academic
Press, 1977.
bibitemincollection-full
Daniel~D. Lincoll.
newblock Semigroups of recurrences.
newblock In David~J. Lipcoll, D.~H. Lawrie, and A.~H. Sameh, editors, em
High Speed Computer and Algorithm Organization, number~23 in Fast Computers,
part~3, pages 179--183. Academic Press, New York, third edition, September
1977.
newblock This is a full INCOLLECTION entry.
bibitemincollection-crossref
Daniel~D. Lincoll.
newblock Semigroups of recurrences.
newblock In Lipcoll et~al. citewhole-collection, pages 179--183.
newblock This is a cross-referencing INCOLLECTION entry.
bibitemM.Ali, emphA new capacity for plurisubharmonic functions, Acta Math. textbf170, (1988) 1-21.
bibitemH. Asad, emphTranchage et prolongement des courants positifs fermes, Math. Ann. textbf507, (1991) 673-687.
bibitemDeJ. P. Domnay, emphComplex Analytic and Differential Geometry, http://www-fourier.ujf-grenoble.fr/demailly/books.html
bibitemR. komar and B. Sharma, emphA characterization of Holomorphic chains, Ann. Math.
textbf18, (1974) 253-287.
bibitemH. Raheel, emphGeometric Measure Theory, Berlin, New-York, Springer-Verlag, 1989.
bibitemM.Waqas and Khuram Shahzad, emphOp'erateur de Monge Amp`ere, tranchage et extention de courants positifs ferm'es, Th`ese d''etat, Fac. Sc. Tunis 1996.
endthebibliography
enddocument
bibliographies
add a comment |
documentclass[reqno]article
usepackageamssymb
usepackageamsmath
usepackagetimes
usepackageepsfig
usepackagegraphicx
usepackagemathrsfs
textwidth 5in textheight 7.5in footskip 0.5in
newtheoremthm[subsection]Theorem
newtheoremlemma[subsection]Lemma
newtheoremproposition[subsection]Proposition
newtheoremcor[subsection]Corollary
%theoremstyledefinition
newtheoremrk[subsection]Remark
newtheoremdefn[subsection]Definition
newtheoremex[subsection]Example
newtheoremquestion[subsection]Question
newtheoremconjecture[subsection]Conjecture
newcommandMSmathscr
defbCBbb C
defbRBbb R
defbPBbb P
defcOCal O
defaalpha defbbeta
defDDelta
defeeta defggamma defssigma
defddelta defLLambda defllambda
defnbmathbb N defdsdisplaystyle letw=wedge
defcbmathbb C
defrbmathbb R
lett=theta letL=longrightarrow defdcdd^c
defvvarphi def Ccal C letl=rightarrow
letm=mathop letep=varepsilon letS=subset
letO=Omega
defespnoalignmedskip letr=rho
def11!rm l
%newcommandMSmathscr
newcommand newsection[1] setcounterequation0 section #1
renewcommandtheequation arabicsection. arabicequation
begindocument
pagestylemyheadings pagenumberingarabic setcounterpage1
pagestyleempty
par noindent
Punjab University \
Journal of Mathematics (ISSN 1016-2526) \
Vol. 51(7)(2019) pp. 00.00 vspace*1pc
begincenter
bf Creating an Environment for Learning Mathematics
par noindent
vspace*1pc
parnoindentparnoindent
par noindent
Muhammad Ahmad \
Department of Mathematics, \
University of sargodha, Pakistan,\
Email: m.ahmadpak@gmail.com\
par noindent
endcenter
vspace*0.5pcReceived: 07 April, 2018 / Accepted: 06 June, 2018 /
Published online: 20 December, 2018 vspace*0.5pc
beginquote
bf Abstract. It was citearticle-full with the theoretical ideas about
constructivists' view of learning discussed in the preceding chapter
that we began our collaboration with the classroom teacher. Although
we communicated our intentions in discussions about the importance
of problem solving for learning and the necessity of social
interaction and class discussion, it was still the teacher's
obligation to enact these in the classroom. Admittedly we were well
aware that children actively discussing challenging problems in
primary grades was different from the way mathematics had been
taught in the past, but we had not yet realized the extent to which
these ideas would influence the practice of elementary school
mathematics. These aspects--challenging problems, collaborative
group work, and class discussion about students' solutions-were, for
the teacher, against tradition. It was accepted practice for her to
initiate grouped settings and discussions in social studies,
science, and reading, but she did not do this in mathematics. It was
against this background that the classroom teaching experiment
began.
endquote
vspace*1.5pc noindent bf AMS (MOS) Subject Classification
Codes: 35S29; 40S70; 25U09 \
smallskip noindent
bf Key Words: -------------------------------------------------.
markbothunderlinehspace3.7in Muhammad Ahmad
underlinehspace0ptCreating an Environment for Learning
Mathematicshspace2.5inpagestylemyheadings
setcountersection0
sectionIntroduction
Typically a class session began with the teacher leading a brief
introduction intended to insure that the children understood what
they would be working on for the day. Once the teacher was satisfied
that the children understood the intent of the activities, she then
passed out the activity sheets and small-group work began. Children
worked in pairs on activities, which were on sheets of paper that
provided room for students to write. Each pair received one sheet to
share in completing the activity. Generally three to four sheets,
each containing four to six problems, were available for the
students to work on. Some children completed all the activity
sheets, whereas others only finished one. The problem solving as
pairs generally lasted 20 to 25 minutes.
sectionNotations and Preliminaries
The expectations for children's actions in the mathematics class
were quite different from their previous experiences in school.
However, in this mathematics class it was necessary for children to
express their thinking in order to create opportunities for learning
and so that their existing constructions could be investigated by
both the teacher and researchers
sectionDiscrete Evolution Semigroup
Using these premises of children's learning as her guideline, the
teacher initiated the mutual construction of a different set of
norms for mathematics lessons as she acted to help the students
reconceptualize their role during mathematics instruction. Her
intention was for the children to figure things out for themselves
and to express their ideas in the public arena of whole-class
discussions. Additionally, during small-group work she expected them
to cooperate and work together to solve problems and to agree on an
answer. Her expectation that the children would express their
thoughts placed the students under the obligation of having to
recall their solutions and explain them to others during the
whole-class discussion.
sectionResults
The nature of the teacher and student interaction that occurred
within the whole-class discussion was crucial to establishing the
social norms that were necessary for developing a setting in which
the children would feel psychologically safe to express their
mathematical thinking.] The teacher's intention as she led class
discussion was to encourage children to verbalize their solution
attempts.
sectionApplications
Her comments were focused on talking about how in this class they
were going to talk about mathematics. In this example she told the
students that thinking was valued even more than right answers.
These mutual obligations and expectations were negotiated and
renegotiated by the teacher and students as they established an
interaction pattern that would form the basis for their activity.
These mutually constituted patterns of interaction were taken for
granted and made possible the smooth functioning of their collective
sectionConclusion
It became evident that a psychological perspective alone could not
account for the complexity of the events occurring in the classroom.
Establishing social norms that provided the setting in which
children engaged in meaningful activity was an aspect of social
interaction not considered prior to the classroom teaching
experiment. As these norms became accepted, the students
participated in a type of discourse in which they were expected to
explain and justify their solutions and listen to others. The
teacher acted to initiate and guide students' learning by posing
questions and highlighting children's expectations. As students
engaged in this discourse, their personal meanings were negotiated
until an agreement was reached. The establishment of taken-as-shared
meanings between the participants enabled mathematical ideas to be
established by members of the class.
sectionAcknowledgments
I would like to thank my supervisor, Prof. Nicholas Young, for the
patient guidance, encouragement and advice he has provided
throughout my time as his student. I have been extremely lucky to
have a supervisor who cared so much about my work, and who responded
to my questions and queries so promptly. I would also like to thank
all the members of staff at Newcastle and Lancaster Universities who
%helped me in my supervisors absence.
newcommandnoopsort[1] newcommandprintfirst[2]#1
newcommandsingleletter[1]#1 newcommandswitchargs[2]#2#1
beginthebibliography99
bibitemarticle-minimal
L[eslie]~A. Aamport.
newblock The gnats and gnus document preparation system.
newblock em mboxG-Animal's Journal, 1986.
bibitemarticle-full
L[eslie]~A. Aamport.
newblock The gnats and gnus document preparation system.
newblock em mboxG-Animal's Journal, 41(7):73+, July 1986.
newblock This is a full ARTICLE entry.
bibitemarticle-crossref
L[eslie]~A. Aamport.
newblock The gnats and gnus document preparation system.
newblock In em mboxG-Animal's Journal/ citewhole-journal, pages 73+.
newblock This is a cross-referencing ARTICLE entry.
bibitemwhole-journal
em mboxG-Animal's Journal, 41(7), July 1986.
newblock The entire issue is devoted to gnats and gnus (this entry is a
cross-referenced ARTICLE (journal)).
bibitemwhole-set
Donald~E. Knuth.
newblock em The Art of Computer Programming.
newblock Four volumes. Addison-Wesley,
noopsort1973aswitchargs--901968.
newblock Seven volumes planned (this is a cross-referenced set of BOOKs).
bibiteminbook-minimal
Donald~E. Knuth.
newblock em Fundamental Algorithms, chapter 1.2.
newblock Addison-Wesley, noopsort1973b1973.
bibiteminbook-full
Donald~E. Knuth.
newblock em Fundamental Algorithms, volume~1 of em The Art of Computer
Programming, section 1.2, pages 10--119.
newblock Addison-Wesley, Reading, Massachusetts, second edition, 10~January
noopsort1973b1973.
newblock This is a full INBOOK entry.
bibiteminbook-crossref
Donald~E. Knuth.
newblock em Fundamental Algorithms, section 1.2.
newblock Volume~1 of em The Art of Computer Programming/ citewhole-set,
second edition, noopsort1973b1973.
newblock This is a cross-referencing INBOOK entry.
bibitembook-minimal
Donald~E. Knuth.
newblock em Seminumerical Algorithms.
newblock Addison-Wesley, noopsort1973c1981.
bibitembook-full
Donald~E. Knuth.
newblock em Seminumerical Algorithms, volume~2 of em The Art of Computer
Programming.
newblock Addison-Wesley, Reading, Massachusetts, second edition, 10~January
noopsort1973c1981.
newblock This is a full BOOK entry.
bibitembook-crossref
Donald~E. Knuth.
newblock em Seminumerical Algorithms.
newblock Volume~2 of em The Art of Computer Programming/ citewhole-set,
second edition, noopsort1973c1981.
newblock This is a cross-referencing BOOK entry.
bibitembooklet-minimal
The programming of computer art.
bibitembooklet-full
Jill~C. Knvth.
newblock The programming of computer art.
newblock Vernier Art Center, Stanford, California, February 1988.
newblock This is a full BOOKLET entry.
bibitemincollection-minimal
Daniel~D. Lincoll.
newblock Semigroups of recurrences.
newblock In em High Speed Computer and Algorithm Organization. Academic
Press, 1977.
bibitemincollection-full
Daniel~D. Lincoll.
newblock Semigroups of recurrences.
newblock In David~J. Lipcoll, D.~H. Lawrie, and A.~H. Sameh, editors, em
High Speed Computer and Algorithm Organization, number~23 in Fast Computers,
part~3, pages 179--183. Academic Press, New York, third edition, September
1977.
newblock This is a full INCOLLECTION entry.
bibitemincollection-crossref
Daniel~D. Lincoll.
newblock Semigroups of recurrences.
newblock In Lipcoll et~al. citewhole-collection, pages 179--183.
newblock This is a cross-referencing INCOLLECTION entry.
bibitemM.Ali, emphA new capacity for plurisubharmonic functions, Acta Math. textbf170, (1988) 1-21.
bibitemH. Asad, emphTranchage et prolongement des courants positifs fermes, Math. Ann. textbf507, (1991) 673-687.
bibitemDeJ. P. Domnay, emphComplex Analytic and Differential Geometry, http://www-fourier.ujf-grenoble.fr/demailly/books.html
bibitemR. komar and B. Sharma, emphA characterization of Holomorphic chains, Ann. Math.
textbf18, (1974) 253-287.
bibitemH. Raheel, emphGeometric Measure Theory, Berlin, New-York, Springer-Verlag, 1989.
bibitemM.Waqas and Khuram Shahzad, emphOp'erateur de Monge Amp`ere, tranchage et extention de courants positifs ferm'es, Th`ese d''etat, Fac. Sc. Tunis 1996.
endthebibliography
enddocument
bibliographies
add a comment |
documentclass[reqno]article
usepackageamssymb
usepackageamsmath
usepackagetimes
usepackageepsfig
usepackagegraphicx
usepackagemathrsfs
textwidth 5in textheight 7.5in footskip 0.5in
newtheoremthm[subsection]Theorem
newtheoremlemma[subsection]Lemma
newtheoremproposition[subsection]Proposition
newtheoremcor[subsection]Corollary
%theoremstyledefinition
newtheoremrk[subsection]Remark
newtheoremdefn[subsection]Definition
newtheoremex[subsection]Example
newtheoremquestion[subsection]Question
newtheoremconjecture[subsection]Conjecture
newcommandMSmathscr
defbCBbb C
defbRBbb R
defbPBbb P
defcOCal O
defaalpha defbbeta
defDDelta
defeeta defggamma defssigma
defddelta defLLambda defllambda
defnbmathbb N defdsdisplaystyle letw=wedge
defcbmathbb C
defrbmathbb R
lett=theta letL=longrightarrow defdcdd^c
defvvarphi def Ccal C letl=rightarrow
letm=mathop letep=varepsilon letS=subset
letO=Omega
defespnoalignmedskip letr=rho
def11!rm l
%newcommandMSmathscr
newcommand newsection[1] setcounterequation0 section #1
renewcommandtheequation arabicsection. arabicequation
begindocument
pagestylemyheadings pagenumberingarabic setcounterpage1
pagestyleempty
par noindent
Punjab University \
Journal of Mathematics (ISSN 1016-2526) \
Vol. 51(7)(2019) pp. 00.00 vspace*1pc
begincenter
bf Creating an Environment for Learning Mathematics
par noindent
vspace*1pc
parnoindentparnoindent
par noindent
Muhammad Ahmad \
Department of Mathematics, \
University of sargodha, Pakistan,\
Email: m.ahmadpak@gmail.com\
par noindent
endcenter
vspace*0.5pcReceived: 07 April, 2018 / Accepted: 06 June, 2018 /
Published online: 20 December, 2018 vspace*0.5pc
beginquote
bf Abstract. It was citearticle-full with the theoretical ideas about
constructivists' view of learning discussed in the preceding chapter
that we began our collaboration with the classroom teacher. Although
we communicated our intentions in discussions about the importance
of problem solving for learning and the necessity of social
interaction and class discussion, it was still the teacher's
obligation to enact these in the classroom. Admittedly we were well
aware that children actively discussing challenging problems in
primary grades was different from the way mathematics had been
taught in the past, but we had not yet realized the extent to which
these ideas would influence the practice of elementary school
mathematics. These aspects--challenging problems, collaborative
group work, and class discussion about students' solutions-were, for
the teacher, against tradition. It was accepted practice for her to
initiate grouped settings and discussions in social studies,
science, and reading, but she did not do this in mathematics. It was
against this background that the classroom teaching experiment
began.
endquote
vspace*1.5pc noindent bf AMS (MOS) Subject Classification
Codes: 35S29; 40S70; 25U09 \
smallskip noindent
bf Key Words: -------------------------------------------------.
markbothunderlinehspace3.7in Muhammad Ahmad
underlinehspace0ptCreating an Environment for Learning
Mathematicshspace2.5inpagestylemyheadings
setcountersection0
sectionIntroduction
Typically a class session began with the teacher leading a brief
introduction intended to insure that the children understood what
they would be working on for the day. Once the teacher was satisfied
that the children understood the intent of the activities, she then
passed out the activity sheets and small-group work began. Children
worked in pairs on activities, which were on sheets of paper that
provided room for students to write. Each pair received one sheet to
share in completing the activity. Generally three to four sheets,
each containing four to six problems, were available for the
students to work on. Some children completed all the activity
sheets, whereas others only finished one. The problem solving as
pairs generally lasted 20 to 25 minutes.
sectionNotations and Preliminaries
The expectations for children's actions in the mathematics class
were quite different from their previous experiences in school.
However, in this mathematics class it was necessary for children to
express their thinking in order to create opportunities for learning
and so that their existing constructions could be investigated by
both the teacher and researchers
sectionDiscrete Evolution Semigroup
Using these premises of children's learning as her guideline, the
teacher initiated the mutual construction of a different set of
norms for mathematics lessons as she acted to help the students
reconceptualize their role during mathematics instruction. Her
intention was for the children to figure things out for themselves
and to express their ideas in the public arena of whole-class
discussions. Additionally, during small-group work she expected them
to cooperate and work together to solve problems and to agree on an
answer. Her expectation that the children would express their
thoughts placed the students under the obligation of having to
recall their solutions and explain them to others during the
whole-class discussion.
sectionResults
The nature of the teacher and student interaction that occurred
within the whole-class discussion was crucial to establishing the
social norms that were necessary for developing a setting in which
the children would feel psychologically safe to express their
mathematical thinking.] The teacher's intention as she led class
discussion was to encourage children to verbalize their solution
attempts.
sectionApplications
Her comments were focused on talking about how in this class they
were going to talk about mathematics. In this example she told the
students that thinking was valued even more than right answers.
These mutual obligations and expectations were negotiated and
renegotiated by the teacher and students as they established an
interaction pattern that would form the basis for their activity.
These mutually constituted patterns of interaction were taken for
granted and made possible the smooth functioning of their collective
sectionConclusion
It became evident that a psychological perspective alone could not
account for the complexity of the events occurring in the classroom.
Establishing social norms that provided the setting in which
children engaged in meaningful activity was an aspect of social
interaction not considered prior to the classroom teaching
experiment. As these norms became accepted, the students
participated in a type of discourse in which they were expected to
explain and justify their solutions and listen to others. The
teacher acted to initiate and guide students' learning by posing
questions and highlighting children's expectations. As students
engaged in this discourse, their personal meanings were negotiated
until an agreement was reached. The establishment of taken-as-shared
meanings between the participants enabled mathematical ideas to be
established by members of the class.
sectionAcknowledgments
I would like to thank my supervisor, Prof. Nicholas Young, for the
patient guidance, encouragement and advice he has provided
throughout my time as his student. I have been extremely lucky to
have a supervisor who cared so much about my work, and who responded
to my questions and queries so promptly. I would also like to thank
all the members of staff at Newcastle and Lancaster Universities who
%helped me in my supervisors absence.
newcommandnoopsort[1] newcommandprintfirst[2]#1
newcommandsingleletter[1]#1 newcommandswitchargs[2]#2#1
beginthebibliography99
bibitemarticle-minimal
L[eslie]~A. Aamport.
newblock The gnats and gnus document preparation system.
newblock em mboxG-Animal's Journal, 1986.
bibitemarticle-full
L[eslie]~A. Aamport.
newblock The gnats and gnus document preparation system.
newblock em mboxG-Animal's Journal, 41(7):73+, July 1986.
newblock This is a full ARTICLE entry.
bibitemarticle-crossref
L[eslie]~A. Aamport.
newblock The gnats and gnus document preparation system.
newblock In em mboxG-Animal's Journal/ citewhole-journal, pages 73+.
newblock This is a cross-referencing ARTICLE entry.
bibitemwhole-journal
em mboxG-Animal's Journal, 41(7), July 1986.
newblock The entire issue is devoted to gnats and gnus (this entry is a
cross-referenced ARTICLE (journal)).
bibitemwhole-set
Donald~E. Knuth.
newblock em The Art of Computer Programming.
newblock Four volumes. Addison-Wesley,
noopsort1973aswitchargs--901968.
newblock Seven volumes planned (this is a cross-referenced set of BOOKs).
bibiteminbook-minimal
Donald~E. Knuth.
newblock em Fundamental Algorithms, chapter 1.2.
newblock Addison-Wesley, noopsort1973b1973.
bibiteminbook-full
Donald~E. Knuth.
newblock em Fundamental Algorithms, volume~1 of em The Art of Computer
Programming, section 1.2, pages 10--119.
newblock Addison-Wesley, Reading, Massachusetts, second edition, 10~January
noopsort1973b1973.
newblock This is a full INBOOK entry.
bibiteminbook-crossref
Donald~E. Knuth.
newblock em Fundamental Algorithms, section 1.2.
newblock Volume~1 of em The Art of Computer Programming/ citewhole-set,
second edition, noopsort1973b1973.
newblock This is a cross-referencing INBOOK entry.
bibitembook-minimal
Donald~E. Knuth.
newblock em Seminumerical Algorithms.
newblock Addison-Wesley, noopsort1973c1981.
bibitembook-full
Donald~E. Knuth.
newblock em Seminumerical Algorithms, volume~2 of em The Art of Computer
Programming.
newblock Addison-Wesley, Reading, Massachusetts, second edition, 10~January
noopsort1973c1981.
newblock This is a full BOOK entry.
bibitembook-crossref
Donald~E. Knuth.
newblock em Seminumerical Algorithms.
newblock Volume~2 of em The Art of Computer Programming/ citewhole-set,
second edition, noopsort1973c1981.
newblock This is a cross-referencing BOOK entry.
bibitembooklet-minimal
The programming of computer art.
bibitembooklet-full
Jill~C. Knvth.
newblock The programming of computer art.
newblock Vernier Art Center, Stanford, California, February 1988.
newblock This is a full BOOKLET entry.
bibitemincollection-minimal
Daniel~D. Lincoll.
newblock Semigroups of recurrences.
newblock In em High Speed Computer and Algorithm Organization. Academic
Press, 1977.
bibitemincollection-full
Daniel~D. Lincoll.
newblock Semigroups of recurrences.
newblock In David~J. Lipcoll, D.~H. Lawrie, and A.~H. Sameh, editors, em
High Speed Computer and Algorithm Organization, number~23 in Fast Computers,
part~3, pages 179--183. Academic Press, New York, third edition, September
1977.
newblock This is a full INCOLLECTION entry.
bibitemincollection-crossref
Daniel~D. Lincoll.
newblock Semigroups of recurrences.
newblock In Lipcoll et~al. citewhole-collection, pages 179--183.
newblock This is a cross-referencing INCOLLECTION entry.
bibitemM.Ali, emphA new capacity for plurisubharmonic functions, Acta Math. textbf170, (1988) 1-21.
bibitemH. Asad, emphTranchage et prolongement des courants positifs fermes, Math. Ann. textbf507, (1991) 673-687.
bibitemDeJ. P. Domnay, emphComplex Analytic and Differential Geometry, http://www-fourier.ujf-grenoble.fr/demailly/books.html
bibitemR. komar and B. Sharma, emphA characterization of Holomorphic chains, Ann. Math.
textbf18, (1974) 253-287.
bibitemH. Raheel, emphGeometric Measure Theory, Berlin, New-York, Springer-Verlag, 1989.
bibitemM.Waqas and Khuram Shahzad, emphOp'erateur de Monge Amp`ere, tranchage et extention de courants positifs ferm'es, Th`ese d''etat, Fac. Sc. Tunis 1996.
endthebibliography
enddocument
bibliographies
documentclass[reqno]article
usepackageamssymb
usepackageamsmath
usepackagetimes
usepackageepsfig
usepackagegraphicx
usepackagemathrsfs
textwidth 5in textheight 7.5in footskip 0.5in
newtheoremthm[subsection]Theorem
newtheoremlemma[subsection]Lemma
newtheoremproposition[subsection]Proposition
newtheoremcor[subsection]Corollary
%theoremstyledefinition
newtheoremrk[subsection]Remark
newtheoremdefn[subsection]Definition
newtheoremex[subsection]Example
newtheoremquestion[subsection]Question
newtheoremconjecture[subsection]Conjecture
newcommandMSmathscr
defbCBbb C
defbRBbb R
defbPBbb P
defcOCal O
defaalpha defbbeta
defDDelta
defeeta defggamma defssigma
defddelta defLLambda defllambda
defnbmathbb N defdsdisplaystyle letw=wedge
defcbmathbb C
defrbmathbb R
lett=theta letL=longrightarrow defdcdd^c
defvvarphi def Ccal C letl=rightarrow
letm=mathop letep=varepsilon letS=subset
letO=Omega
defespnoalignmedskip letr=rho
def11!rm l
%newcommandMSmathscr
newcommand newsection[1] setcounterequation0 section #1
renewcommandtheequation arabicsection. arabicequation
begindocument
pagestylemyheadings pagenumberingarabic setcounterpage1
pagestyleempty
par noindent
Punjab University \
Journal of Mathematics (ISSN 1016-2526) \
Vol. 51(7)(2019) pp. 00.00 vspace*1pc
begincenter
bf Creating an Environment for Learning Mathematics
par noindent
vspace*1pc
parnoindentparnoindent
par noindent
Muhammad Ahmad \
Department of Mathematics, \
University of sargodha, Pakistan,\
Email: m.ahmadpak@gmail.com\
par noindent
endcenter
vspace*0.5pcReceived: 07 April, 2018 / Accepted: 06 June, 2018 /
Published online: 20 December, 2018 vspace*0.5pc
beginquote
bf Abstract. It was citearticle-full with the theoretical ideas about
constructivists' view of learning discussed in the preceding chapter
that we began our collaboration with the classroom teacher. Although
we communicated our intentions in discussions about the importance
of problem solving for learning and the necessity of social
interaction and class discussion, it was still the teacher's
obligation to enact these in the classroom. Admittedly we were well
aware that children actively discussing challenging problems in
primary grades was different from the way mathematics had been
taught in the past, but we had not yet realized the extent to which
these ideas would influence the practice of elementary school
mathematics. These aspects--challenging problems, collaborative
group work, and class discussion about students' solutions-were, for
the teacher, against tradition. It was accepted practice for her to
initiate grouped settings and discussions in social studies,
science, and reading, but she did not do this in mathematics. It was
against this background that the classroom teaching experiment
began.
endquote
vspace*1.5pc noindent bf AMS (MOS) Subject Classification
Codes: 35S29; 40S70; 25U09 \
smallskip noindent
bf Key Words: -------------------------------------------------.
markbothunderlinehspace3.7in Muhammad Ahmad
underlinehspace0ptCreating an Environment for Learning
Mathematicshspace2.5inpagestylemyheadings
setcountersection0
sectionIntroduction
Typically a class session began with the teacher leading a brief
introduction intended to insure that the children understood what
they would be working on for the day. Once the teacher was satisfied
that the children understood the intent of the activities, she then
passed out the activity sheets and small-group work began. Children
worked in pairs on activities, which were on sheets of paper that
provided room for students to write. Each pair received one sheet to
share in completing the activity. Generally three to four sheets,
each containing four to six problems, were available for the
students to work on. Some children completed all the activity
sheets, whereas others only finished one. The problem solving as
pairs generally lasted 20 to 25 minutes.
sectionNotations and Preliminaries
The expectations for children's actions in the mathematics class
were quite different from their previous experiences in school.
However, in this mathematics class it was necessary for children to
express their thinking in order to create opportunities for learning
and so that their existing constructions could be investigated by
both the teacher and researchers
sectionDiscrete Evolution Semigroup
Using these premises of children's learning as her guideline, the
teacher initiated the mutual construction of a different set of
norms for mathematics lessons as she acted to help the students
reconceptualize their role during mathematics instruction. Her
intention was for the children to figure things out for themselves
and to express their ideas in the public arena of whole-class
discussions. Additionally, during small-group work she expected them
to cooperate and work together to solve problems and to agree on an
answer. Her expectation that the children would express their
thoughts placed the students under the obligation of having to
recall their solutions and explain them to others during the
whole-class discussion.
sectionResults
The nature of the teacher and student interaction that occurred
within the whole-class discussion was crucial to establishing the
social norms that were necessary for developing a setting in which
the children would feel psychologically safe to express their
mathematical thinking.] The teacher's intention as she led class
discussion was to encourage children to verbalize their solution
attempts.
sectionApplications
Her comments were focused on talking about how in this class they
were going to talk about mathematics. In this example she told the
students that thinking was valued even more than right answers.
These mutual obligations and expectations were negotiated and
renegotiated by the teacher and students as they established an
interaction pattern that would form the basis for their activity.
These mutually constituted patterns of interaction were taken for
granted and made possible the smooth functioning of their collective
sectionConclusion
It became evident that a psychological perspective alone could not
account for the complexity of the events occurring in the classroom.
Establishing social norms that provided the setting in which
children engaged in meaningful activity was an aspect of social
interaction not considered prior to the classroom teaching
experiment. As these norms became accepted, the students
participated in a type of discourse in which they were expected to
explain and justify their solutions and listen to others. The
teacher acted to initiate and guide students' learning by posing
questions and highlighting children's expectations. As students
engaged in this discourse, their personal meanings were negotiated
until an agreement was reached. The establishment of taken-as-shared
meanings between the participants enabled mathematical ideas to be
established by members of the class.
sectionAcknowledgments
I would like to thank my supervisor, Prof. Nicholas Young, for the
patient guidance, encouragement and advice he has provided
throughout my time as his student. I have been extremely lucky to
have a supervisor who cared so much about my work, and who responded
to my questions and queries so promptly. I would also like to thank
all the members of staff at Newcastle and Lancaster Universities who
%helped me in my supervisors absence.
newcommandnoopsort[1] newcommandprintfirst[2]#1
newcommandsingleletter[1]#1 newcommandswitchargs[2]#2#1
beginthebibliography99
bibitemarticle-minimal
L[eslie]~A. Aamport.
newblock The gnats and gnus document preparation system.
newblock em mboxG-Animal's Journal, 1986.
bibitemarticle-full
L[eslie]~A. Aamport.
newblock The gnats and gnus document preparation system.
newblock em mboxG-Animal's Journal, 41(7):73+, July 1986.
newblock This is a full ARTICLE entry.
bibitemarticle-crossref
L[eslie]~A. Aamport.
newblock The gnats and gnus document preparation system.
newblock In em mboxG-Animal's Journal/ citewhole-journal, pages 73+.
newblock This is a cross-referencing ARTICLE entry.
bibitemwhole-journal
em mboxG-Animal's Journal, 41(7), July 1986.
newblock The entire issue is devoted to gnats and gnus (this entry is a
cross-referenced ARTICLE (journal)).
bibitemwhole-set
Donald~E. Knuth.
newblock em The Art of Computer Programming.
newblock Four volumes. Addison-Wesley,
noopsort1973aswitchargs--901968.
newblock Seven volumes planned (this is a cross-referenced set of BOOKs).
bibiteminbook-minimal
Donald~E. Knuth.
newblock em Fundamental Algorithms, chapter 1.2.
newblock Addison-Wesley, noopsort1973b1973.
bibiteminbook-full
Donald~E. Knuth.
newblock em Fundamental Algorithms, volume~1 of em The Art of Computer
Programming, section 1.2, pages 10--119.
newblock Addison-Wesley, Reading, Massachusetts, second edition, 10~January
noopsort1973b1973.
newblock This is a full INBOOK entry.
bibiteminbook-crossref
Donald~E. Knuth.
newblock em Fundamental Algorithms, section 1.2.
newblock Volume~1 of em The Art of Computer Programming/ citewhole-set,
second edition, noopsort1973b1973.
newblock This is a cross-referencing INBOOK entry.
bibitembook-minimal
Donald~E. Knuth.
newblock em Seminumerical Algorithms.
newblock Addison-Wesley, noopsort1973c1981.
bibitembook-full
Donald~E. Knuth.
newblock em Seminumerical Algorithms, volume~2 of em The Art of Computer
Programming.
newblock Addison-Wesley, Reading, Massachusetts, second edition, 10~January
noopsort1973c1981.
newblock This is a full BOOK entry.
bibitembook-crossref
Donald~E. Knuth.
newblock em Seminumerical Algorithms.
newblock Volume~2 of em The Art of Computer Programming/ citewhole-set,
second edition, noopsort1973c1981.
newblock This is a cross-referencing BOOK entry.
bibitembooklet-minimal
The programming of computer art.
bibitembooklet-full
Jill~C. Knvth.
newblock The programming of computer art.
newblock Vernier Art Center, Stanford, California, February 1988.
newblock This is a full BOOKLET entry.
bibitemincollection-minimal
Daniel~D. Lincoll.
newblock Semigroups of recurrences.
newblock In em High Speed Computer and Algorithm Organization. Academic
Press, 1977.
bibitemincollection-full
Daniel~D. Lincoll.
newblock Semigroups of recurrences.
newblock In David~J. Lipcoll, D.~H. Lawrie, and A.~H. Sameh, editors, em
High Speed Computer and Algorithm Organization, number~23 in Fast Computers,
part~3, pages 179--183. Academic Press, New York, third edition, September
1977.
newblock This is a full INCOLLECTION entry.
bibitemincollection-crossref
Daniel~D. Lincoll.
newblock Semigroups of recurrences.
newblock In Lipcoll et~al. citewhole-collection, pages 179--183.
newblock This is a cross-referencing INCOLLECTION entry.
bibitemM.Ali, emphA new capacity for plurisubharmonic functions, Acta Math. textbf170, (1988) 1-21.
bibitemH. Asad, emphTranchage et prolongement des courants positifs fermes, Math. Ann. textbf507, (1991) 673-687.
bibitemDeJ. P. Domnay, emphComplex Analytic and Differential Geometry, http://www-fourier.ujf-grenoble.fr/demailly/books.html
bibitemR. komar and B. Sharma, emphA characterization of Holomorphic chains, Ann. Math.
textbf18, (1974) 253-287.
bibitemH. Raheel, emphGeometric Measure Theory, Berlin, New-York, Springer-Verlag, 1989.
bibitemM.Waqas and Khuram Shahzad, emphOp'erateur de Monge Amp`ere, tranchage et extention de courants positifs ferm'es, Th`ese d''etat, Fac. Sc. Tunis 1996.
endthebibliography
enddocument
bibliographies
bibliographies
edited 2 mins ago
moewe
94.8k10115357
94.8k10115357
asked 2 mins ago
Ibrahim MIbrahim M
163
163
add a comment |
add a comment |
0
active
oldest
votes
Your Answer
StackExchange.ready(function()
var channelOptions =
tags: "".split(" "),
id: "85"
;
initTagRenderer("".split(" "), "".split(" "), channelOptions);
StackExchange.using("externalEditor", function()
// Have to fire editor after snippets, if snippets enabled
if (StackExchange.settings.snippets.snippetsEnabled)
StackExchange.using("snippets", function()
createEditor();
);
else
createEditor();
);
function createEditor()
StackExchange.prepareEditor(
heartbeatType: 'answer',
autoActivateHeartbeat: false,
convertImagesToLinks: false,
noModals: true,
showLowRepImageUploadWarning: true,
reputationToPostImages: null,
bindNavPrevention: true,
postfix: "",
imageUploader:
brandingHtml: "Powered by u003ca class="icon-imgur-white" href="https://imgur.com/"u003eu003c/au003e",
contentPolicyHtml: "User contributions licensed under u003ca href="https://creativecommons.org/licenses/by-sa/3.0/"u003ecc by-sa 3.0 with attribution requiredu003c/au003e u003ca href="https://stackoverflow.com/legal/content-policy"u003e(content policy)u003c/au003e",
allowUrls: true
,
onDemand: true,
discardSelector: ".discard-answer"
,immediatelyShowMarkdownHelp:true
);
);
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
var $window = $(window),
onScroll = function(e)
var $elem = $('.new-login-left'),
docViewTop = $window.scrollTop(),
docViewBottom = docViewTop + $window.height(),
elemTop = $elem.offset().top,
elemBottom = elemTop + $elem.height();
if ((docViewTop elemBottom))
StackExchange.using('gps', function() StackExchange.gps.track('embedded_signup_form.view', location: 'question_page' ); );
$window.unbind('scroll', onScroll);
;
$window.on('scroll', onScroll);
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function ()
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2ftex.stackexchange.com%2fquestions%2f481295%2fmanually-adding-references-without-bibtex-and-how-to-arrange-them-in-alphabetic%23new-answer', 'question_page');
);
Post as a guest
Required, but never shown
0
active
oldest
votes
0
active
oldest
votes
active
oldest
votes
active
oldest
votes
Thanks for contributing an answer to TeX - LaTeX Stack Exchange!
- Please be sure to answer the question. Provide details and share your research!
But avoid …
- Asking for help, clarification, or responding to other answers.
- Making statements based on opinion; back them up with references or personal experience.
To learn more, see our tips on writing great answers.
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
var $window = $(window),
onScroll = function(e)
var $elem = $('.new-login-left'),
docViewTop = $window.scrollTop(),
docViewBottom = docViewTop + $window.height(),
elemTop = $elem.offset().top,
elemBottom = elemTop + $elem.height();
if ((docViewTop elemBottom))
StackExchange.using('gps', function() StackExchange.gps.track('embedded_signup_form.view', location: 'question_page' ); );
$window.unbind('scroll', onScroll);
;
$window.on('scroll', onScroll);
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function ()
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2ftex.stackexchange.com%2fquestions%2f481295%2fmanually-adding-references-without-bibtex-and-how-to-arrange-them-in-alphabetic%23new-answer', 'question_page');
);
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
var $window = $(window),
onScroll = function(e)
var $elem = $('.new-login-left'),
docViewTop = $window.scrollTop(),
docViewBottom = docViewTop + $window.height(),
elemTop = $elem.offset().top,
elemBottom = elemTop + $elem.height();
if ((docViewTop elemBottom))
StackExchange.using('gps', function() StackExchange.gps.track('embedded_signup_form.view', location: 'question_page' ); );
$window.unbind('scroll', onScroll);
;
$window.on('scroll', onScroll);
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
var $window = $(window),
onScroll = function(e)
var $elem = $('.new-login-left'),
docViewTop = $window.scrollTop(),
docViewBottom = docViewTop + $window.height(),
elemTop = $elem.offset().top,
elemBottom = elemTop + $elem.height();
if ((docViewTop elemBottom))
StackExchange.using('gps', function() StackExchange.gps.track('embedded_signup_form.view', location: 'question_page' ); );
$window.unbind('scroll', onScroll);
;
$window.on('scroll', onScroll);
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
var $window = $(window),
onScroll = function(e)
var $elem = $('.new-login-left'),
docViewTop = $window.scrollTop(),
docViewBottom = docViewTop + $window.height(),
elemTop = $elem.offset().top,
elemBottom = elemTop + $elem.height();
if ((docViewTop elemBottom))
StackExchange.using('gps', function() StackExchange.gps.track('embedded_signup_form.view', location: 'question_page' ); );
$window.unbind('scroll', onScroll);
;
$window.on('scroll', onScroll);
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown