
Paper Title
or Section 
Authors 
Pages 
DOI 

Table of Contents 

526 


PMENA History and Goals 

27 


PMENA Steering Committee 

28 


Conference Chairs 

29 


PMENA 42 Contributors 

30 


PMENA 42 Review Process & Reviewers 

3134 


PMENA 42 Strands 

3537 


Preface / Prólogo 
Ana Isabel Sacristán & José Carlos
CortésZavala 
3843 
10.51272/pmena.42.20203 

Special Tribute / Homenaje especial 

44 


Tribute to Eugenio Filloy†: A pioneer
and driving force of Mathematics Education as a
discipline / Homenaje a Eugenio Filloy†: Un pionero
impulsor de la disciplina de la Matemática Educativa 
Ana Isabel Sacristán et al. 
4567 
10.51272/pmena.42.20202 

PLENARY LECTURES 

68 


Reflections on digital technologies in
mathematics education across cultures 
Celia Hoyles, Carolyn Kieran, Teresa Rojano,
Ana Isabel Sacristán, María Trigueros 
6992 
10.51272/pmena.42.20201 

Educational neuroscience: past, present
and future prospects 
Stephen R. Campbell 
93100 
10.51272/pmena.42.20204 

Eyetracking mathematical
representations – finding links between vision and
reasoning 
Ulises Xolocotzin, Matthew Inglis, Ana María
Medrano Moya 
101107 
10.51272/pmena.42.20205 

SPECIAL LECTURES 

108 


Mental mathematics in the classroom:
Content, practices and Papert’s Mathland 
Jérôme Proulx 
109119 
10.51272/pmena.42.20206 

Construction of arithmeticalgebraic
thinking in a sociocultural instructional approach /
Construction d’une pensée arithémicoalgébrique dans une
approche socioculturelle de l’enseignement 
Fernando Hitt 
120142 
10.51272/pmena.42.20207 

Understanding teachers’ professional
development through their interaction with resources: a
multilingual project 
Luc Trouche 
143154 
10.51272/pmena.42.20208 

RESEARCH COLLOQUIA 

155 


Research Colloquia: Conceptions and
consequences of what we call argumentation,
justification and proof 
Michelle Cirillo, Kristen N. Bieda 
156158 
10.51272/pmena.42.20209 

Research Colloquia: Research tools for
collectivity: Tracking mathematics classes 
Jennifer S. Thom, Florence Glanfield, Joyce
Mgombelo, Jérôme Proulx, Lynn McGarvey, Jo Towers 
159161 
10.51272/pmena.42.202010 

WORKING GROUPS 

162 


Working Group: Implementing and
researching mathematics contentfocused coaching models 
Cynthia Callard, Cynthia Carson, Ryan
Gillespie, Julie Amador, Jeffrey Choppin, Stephanie Martin 
163165 
10.51272/pmena.42.202011 

Embodied mathematical imagination and
cognition (EMIC) working group 
Mitchell J. Nathan, Avery Harrison, Hannah
Smith, Erin Ottmar, Dor Abrahamson, Caro WilliamsPierce 
166168 
10.51272/pmena.42.202012 

Working Group: Complex connections:
reimagining units construction and coordination 
Beth L. MacDonald, Steven Boyce, Cameron
Byerley, Diana L. Moss, Claudia BertoloneSmith, Jeffrey
A. Grabhorn 
169170 
10.51272/pmena.42.202013 

Working Group: Didactic contrasts
between Calculus and Analysis / Grupo de trabajo:
Contrastes didácticos entre cálculo y análisis 
Fabio Augusto Milner, José Ramon Jiménez
Rodríguez 
171174 
10.51272/pmena.42.202014 

Working group on gender and sexuality in
mathematics education: Informing methodology with theory 
Katrina PiatekJimenez, Brent Jackson, Ana
Dias, Weverton Ataide Pinheiro, Harryson Gonçalves,
Jennifer Hall, Elizabeth Kersey, Angela HodgeZickerman 
175177 
10.51272/pmena.42.202015 

Working Group: Mathematical Play: Across
Ages, Context, and Content 
David Plaxco, Paul Reimer, Caro
WilliamsPierce, Amy Ellis, Susanna MolitorisMiller,
Amber Simpson, Michelle Zandieh, Matt Mauntel, Mohammad
Fatih Dogan 
178180 
10.51272/pmena.42.202016 

Working Group: Mathematics teacher
educators using selfbased methodologies 
Elizabeth SuazoFlores, Jennifer Ward, Sue
Ellen Richardson, Melva Grant, Dana Cox, Signe E.
Kastberg, Olive Chapman 
181184 
10.51272/pmena.42.202017 

New Working Group: Teaching mathematics
for social justice in the context of University
Mathematics Content and Methods courses 
Eva Thanheiser, Frances K Harper, Christa
Jackson, Naomi Jessup, Crystal KalinecCraig, Cathery Yeh,
Amanda Sugimoto 
185188 
10.51272/pmena.42.202018 

Working Group: Statistics education
across social and political boundaries: Similarities,
differences and points for building community 
Ana Luisa Gómez Blancarte, Blanca Rosa Ruiz
Hernandez, M. Alejandra Sorto, Travis Weiland 
189191 
10.51272/pmena.42.202019 

Algebra, Algebraic Thinking and Number
Concepts 




Research Reports 

192 


Supporting students’ meanings for
quadratics: Integrating RME, quantitative reasoning and
designing for abstraction 
Mustafa M. Mohamed, Teo Paoletti, Madhavi
Vishnubhotla, Steven Greenstein, Su San Lim 
193201 
10.51272/pmena.42.202020 

Unit transformation graphs: A case study 
Anderson Norton, Catherine Ulrich, Sarah
Kerrigan 
202210 
10.51272/pmena.42.202021 

Learning difficulties to build zero and
one, based on Von Neumann / Dificultades de aprendizaje
para construir el cero y el uno, con base en Von Neumann 
María Leticia Rodríguez González, Eugenio
Filloy Yagüe, Bernardo Gómez Alfonso 
211226 
10.51272/pmena.42.202022 

Introducing inverse function to high
school students: Relating convention and reasoning 
Irma E. Stevens, Inah Ko, Teo Paoletti,
Nicolas Boileau, Patricio Herbst 
227235 
10.51272/pmena.42.202023 

Framework for representing a
multiplicative object in the context of graphing 
Halil I. Tasova, Kevin C. Moore 
236245 
10.51272/pmena.42.202024 

A conceptual analysis of the equal sign
and equation –the transformative component 
Yufeng Ying 
246254 
10.51272/pmena.42.202025 

Algebra, Algebraic Thinking and Number
Concepts: Brief Research Reports 

255 


Mental constructions of invariant
subspace developed by an APOS teaching design /
Construcciones mentales sobre subespacio invariante
desarrolladas en una propuesta de enseñanza desde la
teoría APOE 
Irenisolina AnteloLópez, César Fabián
RomeroFélix 
256264 
10.51272/pmena.42.202026 

Assessing students' understanding of
fraction multiplication 
Pavneet Kaur Bharaj, Erik Jacobson, Jinqing
Liu, Fatimah Ahmad 
265269 
10.51272/pmena.42.202027 

Students’ understandings of the
transformations of functions 
Camille S. Burnett 
270274 
10.51272/pmena.42.202028 

Didactic sequence for the learning of
place value in second grade elementary students in a
multigrade school / Secuencia didáctica para el
aprendizaje del valor posicional en alumnos de segundo
ciclo de primaria de una escuela multigrado 
Fátima del Carmen CastañedaHernández, Erika
GarcíaTorres 
275282 
10.51272/pmena.42.202029 

Intertextuality and semiosis processes
in the algebraic resolution of verbal problems /
Intertextualidad y procesos de semiosis en la resolución
algebraica de problemas verbales 
Juan Manuel Córdoba Medina, Eugenio Filloy
Yagüe 
283290 
10.51272/pmena.42.202030 

Examining students’ reasoning about
multiple quantities 
Nicole Panorkou, Erell Germia 
291295 
10.51272/pmena.42.202031 

Investigating the learning sequence of
decimal magnitude and decimal operations 
Erik Jacobson, Patricia A. Walsh, Pavneet
Kaur Bharaj 
296300 
10.51272/pmena.42.202032 

Levelzero covariational reasoning in
secondary school mathematics / El nivel cero del
razonamiento covariacional en la educacion secundaria 
José Ramón JiménezRodríguez 
301304 
10.51272/pmena.42.202033 

Decomposing, composing and recomposing
numbers in numerical equalities: algebraic thinking
based on structure sense / Descomposición, composición y
recomposición de números en igualdades numéricas:
pensamiento algebraico basado en un sentido de
estructura 
Cesar Martínez Hernández, Carolyn Kieran 
305313 
10.51272/pmena.42.202034 

Intuition in Linear Transformation: some
difficulties / La intuición en la transformación lineal:
algunas dificultades 
Osiel RamírezSandoval 
314323 
10.51272/pmena.42.202035 

A study of contradictions as a lever for
continuing education: A case involving algebraic
generalization activities / Étude de contradictions
comme levier de formation continue: un exemple autour
d’activités de généralisation algébrique 
Mélanie Tremblay, Mireille Saboya 
324338 
10.51272/pmena.42.202036 

The allocation of sense to the quotative
division of fractions / La asignación de sentido a la
división cuotativa de fracciones 
Angel TotolhuaTlaque, Marta Elena
Valdemoros 
339346 
10.51272/pmena.42.202037 

Expressions of mathematical
generalization among children in grade five of primary
school / Expresiones de generalización matemática en
niños de quinto grado de primaria 
Genny Rocío Uicab Ballote, Teresa Rojano
Ceballos, Montserrat García Campos 
347355 
10.51272/pmena.42.202038 

Children’s integer division: Extending
analogies and direct modeling 
Nicole M. WessmanEnzinger 
356361 
10.51272/pmena.42.202039 

Foundational algebraic reasoning in the
schemes of middle school students with learning
disabilities 
Jerry A. Woodward 
362370 
10.51272/pmena.42.202040 

“H is not a number!” Examining how
number influences variable 
Karen Zwanch 
371375 
10.51272/pmena.42.202041 

Algebra, Algebraic Thinking and Number
Concepts: Poster Presentations 

376 


Epistemic analysis of a lesson on linear
equations of a Mexican textbook / Análisis epistémico de
una lección sobre ecuaciones lineales en un libro de
texto mexicano 
Graciela Rubi AcevedoCardelas, Ramiro
ÁvilaGodoy, Ana Guadalupe del CastilloBojórquez 
377 
10.51272/pmena.42.202042 

A proposal for teaching mathematics to
high school students from modeling approach / Una
propuesta de enseñanza de las matemáticas para alumnos
de preparatoria desde la modelización 
Armando Agustín ChavezSalazar, Parameters
and system of linear equations 
378379 
10.51272/pmena.42.202043 

Parameters and system of linear
equations / Parámetros en sistemas de ecuaciones
lineales 
Luis Enrique Hernández, Claudia Acuña Soto 
380381 
10.51272/pmena.42.202044 

Introducing variables to grade 4 and 5
students and the misconceptions that emerged 
Jenna R. O’Dell, Todd Frauenholtz 
382 
10.51272/pmena.42.202045 

Elementary Algebraic thinking with
patterns in two variables 
Adam R. Scharfenberger, Leah M. Frazee 
383384 
10.51272/pmena.42.202046 

Student’s strategies to solve ratio
comparison problems in elementary school / Estrategias
de los estudiantes para resolver problemas de
comparación de razones en primaria 
VázquezGómez, Sofía, SepúlvedaVega,
Francisco 
385387 
10.51272/pmena.42.202047 

The advanced tacitly nested number
sequence: Why does it matter in the middle grades? 
Karen Zwanch 
388389 
10.51272/pmena.42.202048 

Curriculum, Assessment & Related Topics 




Research Reports 

390 


What makes a mathematics lesson
interesting to students? 
Leslie Dietiker, Rashmi Singh, Meghan
Riling, Hector I. Nieves 
391399 
10.51272/pmena.42.202049 

Identifying opportunities to engage in
literacy practices: A framework for analyzing curriculum
materials 
Ethan Smith 
400408 
10.51272/pmena.42.202050 

Designing mathematics learning
environments for multilingual students: Results of a
redesign effort in introductory Algebra 
William Zahner, Kevin Pelaez, Ernesto
Calleros 
409416 
10.51272/pmena.42.202051 

Curriculum, Assessment & Related Topics:
Brief Research Reports 

417 


Characterizing coherence within enacted
mathematics lessons 
Jaepil Han, Meghan Riling, Hector I. Nieves,
Leslie Dietiker, Rashmi Singh 
418422 
10.51272/pmena.42.202052 

An analysis of coordinate systems
presented in grade 68 textbooks 
Hwa Young Lee, Lino Guajardo 
423428 
10.51272/pmena.42.202053 

Types of problems linked to the
development of algebraic reasoning in chilean primary
education / Tipos de problemas vinculados al desarrollo
del razonamiento algebraico en la educación básica
chilena 
Ana Luisa Llanes Luna, Silvia Elena Ibarra
Olmos, Luis R. PinoFan 
429437 
10.51272/pmena.42.202054 

Review of slope in calculus textbooks 
Susan Bateman, Kevin LaForest, Deborah
MooreRusso 
438447 
10.51272/pmena.42.202055 

Computational thinking practices as a
frame for teacher engagement with mathematics curriculum
materials 
Kathryn M. Rich 
448452 
10.51272/pmena.42.202056 

Broader intentions: Exploring the role
of aims for school mathematics in teacher curricular
decision making 
Andrew Richman 
453457 
10.51272/pmena.42.202057 

Curriculum, Assessment & Related Topics:
Poster Presentations 

458 


Secondary math methods syllabi across
cultures 
Paula Guerra Lombardi, Viviana González,
Woong Lim, Rafael Méndez Romero 
459460 
10.51272/pmena.42.202058 

Mathematics instruction during
prospective teachers’ perfoRmancebased assessment in
special education classrooms 
Katherine Baker, Danielle Lane 
461462 
10.51272/pmena.42.202059 

Locating a productive climate: Measuring
student computational fluency in a tier 2 system 
Monica Mendoza, Rachel Lambert, Tomy Nguyen 
463 
10.51272/pmena.42.202060 

Teacher’s collaboration with freshmen
undergraduates to improve feedback practices through
cogenerative dialogues 
Mitchelle M. Wambua, Nicole L. Fonger 
464465 
10.51272/pmena.42.202061 

Equity and Justice 




Research Reports 

466 


Critically analyzing and supporting
difficult situations (cards): a tool to support equity
commitments 
Anne Marie Marshall, Andrea McCloskey, Brian
R. Lawler, Theodore Chao, The MathEd Collective 
467475 
10.51272/pmena.42.202062 

Between the boundaries of knowledge:
theorizing an eticemic approach to mathematics
education 
Lee Melvin Peralta 
476484 
10.51272/pmena.42.202063 

Measuring high school students’ funds of
knowledge for learning mathematics 
Tiffini PruittBritton, Candace Walkington 
485492 
10.51272/pmena.42.202064 

Predicting the mathematics pathways of
english language learners: a multilevel analysis 
Cristina Runnalls 
493499 
10.51272/pmena.42.202065 

Why theorizing affect matters for
mathematics education research 
Ryan Ziols 
500511 
10.51272/pmena.42.202066 

Equity and Justice: Brief Research Reports 

512 


Student engagement and gender identity
in undergraduate introduction to proof 
Emmanuel Barton Odro 
513517 
10.51272/pmena.42.202067 

Reconciling tensions in equity discourse
through an antihierarchical (anarchist) theory of
action 
David M. Bowers, Brian R. Lawler 
518524 
10.51272/pmena.42.202068 

Bearing witness to mathematical ghosts:
the ethics of teachers seeking justice 
Grace A. Chen 
525529 
10.51272/pmena.42.202069 

Rural parents’ views on their
involvement in their children’s mathematics education 
Daniel L. Clark 
530535 
10.51272/pmena.42.202070 

An ethnography of re/humanizing (math)
pedagogies at a predominantly latinx california high
school 
Emma C. Gargroetzi 
536540 
10.51272/pmena.42.202071 

Supporting the whole student: blending
the mathematical and the social emotional 
Sara Gartland 
541545 
10.51272/pmena.42.202072 

Nonbinary people’s views of gender and
mathematics 
Jennifer Hall, Travis Robinson, Limin Jao 
546550 
10.51272/pmena.42.202073 

An historical exploration of achievement
gap rhetoric: A critical discourse analysis of federal
education legislation 
Michelle Hawks 
551556 
10.51272/pmena.42.202074 

Community mathematics project: Tutoring
lowincome parents to make sense of mathematics 
Denisse M. Hinojosa, Emily Bonner, Crystal
KalinecCraig 
557562 
10.51272/pmena.42.202075 

Gender differences in number strategy
use for students solving fraction story problems 
Cassandra Quinn, Susan B. Empson, Victoria
R. Jacobs 
563567 
10.51272/pmena.42.202076 

Social norms conducive to women’s
learning in inquiryoriented abstract algebra 
Kaitlyn Stephens Serbin, Sara Brooke
Mullins, Marilin Annie Kelley, Estrella Johnson 
568572 
10.51272/pmena.42.202077 

Differences in mathematical ability
beliefs between teachers and mathematicians in higher
education 
Yasemin CopurGencturk, Han Du, Ian Thacker 
573577 
10.51272/pmena.42.202078 

Products of white institutional space:
An analysis of whiteness in online mathematics tasks 
Blake O'Neal Turner 
578581 
10.51272/pmena.42.202079 

Tensions of responsibility in critical
mathematics: defining teacher responsibility and student
agency 
Trevor T. Warburton 
582586 
10.51272/pmena.42.202080 

Exploring culture in mathematics
education from the perspectives of preservice teachers
of color 
Dorothy Y. White, Luz A. Maldonado
Rodríguez, Juanita M. Silva, Christian J. Anderson 
587591 
10.51272/pmena.42.202081 

Translanguaging to ensure latinx
mathematics learners thrive 
Craig Willey, Hector Morales, Jr. 
592597 
10.51272/pmena.42.202082 

Equity and Justice: Poster Presentations 

598 


MIM: Mathematics education responsive to
diversity: A NorwegianCanadian and American research
collaboration 
Annica Andersson, Beth HerbelEisenmann,
Hilja Lisa Huru, David Wagner 
599600 
10.51272/pmena.42.202083 

Prospective mathematics teachers’
conceptualizations of equity 
Kanita K. DuCloux, Corey M. Wadlington 
601602 
10.51272/pmena.42.202084 

Blackness and whiteness in Appalachian
mathematics classrooms 
Sean P. Freeland 
603604 
10.51272/pmena.42.202085 

Mathematics problems and real world
connections: How political is too political? 
Paula Guerra, Raisa Lopez, Elisa Pereyra 
605606 
10.51272/pmena.42.202086 

Conceptualizing access knowledge for
teaching mathematics 
Rachel Lambert 
607 
10.51272/pmena.42.202087 

Facilitating mathematics teacher
educators’ conversations on inequities in mathematics
classrooms 
Leslie E.J. Nielsen, Kanita K. DuCloux,
Dorothy Y. White 
608609 
10.51272/pmena.42.202088 

Mathematics identity and sense of
belonging of developmental mathematics students 
Francis Nzuki 
610611 
10.51272/pmena.42.202089 

Critical mathematics education for
subsaharan african youth: towards epistemic freedom 
Oyemolade Osibodu 
612613 
10.51272/pmena.42.202090 

“Ya me conforme”: Resisting dominant
narratives in mathematics classrooms 
Kevin Pelaez, William Zahner 
614615 
10.51272/pmena.42.202091 

Capturing the high ground in learning
disabled mathematics education research 
Thomas E. Ricks 
616 
10.51272/pmena.42.202092 

A narrative inquiry of GEMS women’s
experience with STEM 
Lili Zhou, Sue Ellen Richardson 
617618 
10.51272/pmena.42.202093 

Geometry and Measurement 




Research Reports 

619 


Understanding instructional capacity for
high school geometry as a systemic problem through
stakeholder interviews 
Claudine Margolis, Michael Ion, Patricio
Herbst, Amanda Milewski, Mollee Shultz 
620627 
10.51272/pmena.42.202094 

Geometry and Measurement 




Research Reports 

619 


Understanding instructional capacity for
high school geometry as a systemic problem through
stakeholder interviews 
Claudine Margolis, Michael Ion, Patricio
Herbst, Amanda Milewski, Mollee Shultz 
620627 
10.51272/pmena.42.202094 

Development of space reasoning in early
ages through variation activities / Diseño de
actividades para el desarrollo de razonamiento espacial
en edades tempranas a través de manipulativos 
Yudi Andrea Ortiz Rocha, Ivonne Twiggy
Sandoval Cáceres, Ana Isabel Sacristán 
628645 
10.51272/pmena.42.202095 

Interpretive model of the
conceptualization of the congruence of polygons (MICP) /
Modelo Interpretativo de la Conceptualización de la
Congruencia de Polígonos (MICP) 
Cristian Andrey Peña Acuña, Mirela
RigoLemini 
646661 
10.51272/pmena.42.202096 

Children’s durational organization of
evereyday experiences: a mathematical perspective of a
linguistic study 
Amy Smith 
662669 
10.51272/pmena.42.202097 

Geometry and Measurement: Brief Research
Reports 

670 


Acknowledging noncircular
quantifications of angularity 
Hamilton L. Hardison 
671675 
10.51272/pmena.42.202098 

Prospective high school mathematics
teachers’ uses of diagrams and geometric transformations
while reasoning about geometric proof tasks 
Karen Hollebrands, Deniz Ozen Unal 
676680 
10.51272/pmena.42.202099 

Interactions with geometric figures: A
case with graduate students 
Mario MayorgaSánchez, Gonzalo Zubieta 
681688 
10.51272/pmena.42.2020100 

Using designbased tasks to teach area
measurement 
Edward S. Mooney, Jeffrey E. Barrett 
689693 
10.51272/pmena.42.2020101 

Selfinstructions for applying writing
in geometry problem resolution / Autoinstrucciones para
aplicar la escritura en la resolución de problemas de
geometría 
Luz Graciela Orozco Vaca 
694701 
10.51272/pmena.42.2020102 

Difficulties to justify geometric
propositions when solving loci problems with GeoGebra /
Dificultades para justificar proposiciones geométricas
al resolver problemas de lugares geométricos con
GeoGebra 
José Luis Soto Munguía, Manuel Alfredo Urrea
Bernal, César Fabián Romero Félix 
702710 
10.51272/pmena.42.2020103 

Spatial imagination to work on 3D space
using a figural device / Imaginación espacial para
trabajar objetos en el espacio 3D usando un dispositivo
figural 
Beatriz Alejandra Veloz Díaz, Claudia
Margarita Acuña Soto 
711719 
10.51272/pmena.42.2020104 

Enhancing spatial abilities through
exposer to computeraid design programs 
Ashley M. Williams, Robert M. Capraro 
720725 
10.51272/pmena.42.2020105 

Geometry and Measurement: Poster
Presentations 

726 


“A square is not long enough to be a
rectangle”: exploring prospective elementary teachers’
conceptions of quadrilaterals 
Pavneet Kaur Bharaj, Dionne Cross Francis 
727728 
10.51272/pmena.42.2020106 

Growth in mathematical understanding and
spatial reasoning with programming robots 
Krista Francis, Stefan Rothschuh, Brent
Davis 
729730 
10.51272/pmena.42.2020107 

Funky protractors created by prospective
teachers 
Hamilton L. Hardison, Hwa Young Lee 
731732 
10.51272/pmena.42.2020108 

Gestures in geometry: how do gestures
contribute to engagement and vocabulary acquisition
through game play? 
Avery Harrison, Renah Razzaq, Erin Ottmar,
Ivon Arroyo 
733734 
10.51272/pmena.42.2020109 

Navigating complexities in definitions
of length and area 
Eryn M. Stehr, Jia He 
735736 
10.51272/pmena.42.2020110 

A research approach on the role of space
in the construction of conic sections 
Luis Carlos VargasZambrano, Gisela
MontielEspinosa 
737738 
10.51272/pmena.42.2020111 

Instructional Leadership, Policy, and
Institutions/Systems 




Research Reports 

739 


Elementary mathematics teacher agency:
Examining teacher and ecological capacity 
Phi Nguyen, Sheunghyun Yeo, Wenmin Zhao,
Corey Webel 
740748 
10.51272/pmena.42.2020112 

Instructional Leadership, Policy, and
Institutions/Systems: Brief Research Reports 

749 


Using transcript analysis to predict
students’ selfreported happiness in elementary
mathematics classrooms: Methodological considerations 
Pamela Catherine Callahan, Blake O’Neal
Turner, Casey Archer, Monica Anthony 
750754 
10.51272/pmena.42.2020113 

Instructional Leadership, Policy, and
Institutions/Systems: Poster Presentations 

755 


A collaborative selfstudy to forefront
issues of identity and equity in mathematics methods
courses 
Katherine Baker, Monica Gonzalez, Kathleen
Nitta, Jennifer Ward, Naomi Jessup, Tracy Dobie, Erin
Smith 
756757 
10.51272/pmena.42.2020114 

A model for mathematics instructional
improvement at scale 
Alison Castro Superfine, Benjamin Michael
Superfine 
758759 
10.51272/pmena.42.2020115 

Evolution of elementary math leaders’
collaborative plans for schoollevel change 
Brendan Dames, Corey Webel 
760 
10.51272/pmena.42.2020116 

Continuous improvement lesson study with
mathematics teacher educators 
Lara K. Dick, Melissa M. Soto, Mollie H.
Appelgate, Dittika Gupta 
761762 
10.51272/pmena.42.2020117 

Mathematical Knowledge for Teaching 




Research Reports 

763 


Survey of preservice teachers’
pedagogical content knowledge for students’
multiplicative reasoning 
Christine K. Austin, Karl W. Kosko 
764771 
10.51272/pmena.42.2020118 

Teachers’ attention to and flexibility
with referent units 
Yasemin CopurGencturk, Ibrahim Burak Olmez 
772780 
10.51272/pmena.42.2020119 

Teachers’ review of tasks as a tool for
examining secondary teachers’ mathematical knowledge for
teaching 
Michelle Morgan King, Adam Ruff, Alees Lee,
Robert Powers, Jodie Novak 
781789 
10.51272/pmena.42.2020120 

Inductive reasoning in mathematics
teachers when resolving generalization tasks /
Razonamiento inductivo en maestros de matemáticas al
resolver tareas de generalización 
Karina NuñezGutiérrez, Guadalupe
CabañasSánchez 
790802 
10.51272/pmena.42.2020121 

An approach to density in decimal
numbers: A study with preservice teachers / Un
acercamiento a la densidad en los números decimales: un
estudio con profesores en formación 
Mayra SuárezRodríguez, Olimpia Figueras 
803819 
10.51272/pmena.42.2020122 

Experienced secondary teachers’
decisions to attend to the independent variable in
exponential functions 
Melissa Troudt, Lindsay Reiten, Jodie Novak 
820828 
10.51272/pmena.42.2020123 

Mathematical Knowledge for Teaching: Brief
Research Reports 

829 


A classroom experience: vector concept /
Una experiencia de clase: concepto vector 
Viana GarcíaSalmerón, Flor
RodríguezVásquez 
830839 
10.51272/pmena.42.2020124 

Exploring the interwoven discourses
associated with learning to teach mathematics in a
making context 
Steven Greenstein, Doris Jeannotte, Eileen
Fernández, Jessica Davidson, Erin Pomponio, Denish Akuom 
840844 
10.51272/pmena.42.2020125 

Elementary teachers’ discourse about
mathematical reasoning 
Doris Jeannotte, Stéphanie Sampson, Sarah
Dufour 
845849 
10.51272/pmena.42.2020126 

Language: a hidden resource in preparing
bilingual preservice teachers 
Gladys H. Krause, Juanita Silva, Jair J.
Aguilar 
850859 
10.51272/pmena.42.2020127 

Introducing fraction multiplication. A
study on teacher’s pedagogical knowledge / Introducir la
multiplicación de fracciones. Un estudio sobre el
conocimiento didáctico del profesor 
David Alfonso Páez, Indira V. Medina
Mendoza, María Guadalupe Pérez Martínez 
860869 
10.51272/pmena.42.2020128 

Mathematics teachers’ perception of
inductive reasoning and its teaching 
Landy Sosa Moguel, Eddie Aparicio Landa 
870874 
10.51272/pmena.42.2020129 

Defining key developmental
understandings in congruence proofs from a
transformation approach 
Julia St. Goar, Yvonne Lai 
875879 
10.51272/pmena.42.2020130 

Using task design methodology to unpack
teachers’ (mis)conceptions about procedural and
conceptual knowledge 
Angelica Monarrez, Mourat Tchoshanov 
880884 
10.51272/pmena.42.2020131 

Mathematical Knowledge for Teaching: Poster
Presentations 

885 


A study on the relationship between
tutor’s content knowledge and their tutoring decisions 
Jose Saul Barbosa, Christopher James Duffer 
886887 
10.51272/pmena.42.2020132 

Novice teachers interpretation of
fractions 
Brian Bowen 
888889 
10.51272/pmena.42.2020133 

Advancing reasoning and proof in
secondary mathematics classrooms: instructional modules
for supporting teachers 
Orly Buchbinder, Sharon McCrone 
890891 
10.51272/pmena.42.2020134 

Technological knowledge of mathematics
preservice teachers at the beginning of their
methodology courses / Conocimiento tecnológico de los
futuros maestros de matemáticas al iniciar sus cursos de
metodología 
Yency ChoqueDextre, Juliette
MorenoConcepción, Omar HernándezRodríguez, Wanda
VillafañeCepeda, Gloriana González 
892894 
10.51272/pmena.42.2020135 

Exploring mathematics teacher educators’
avenues for professional growth: A review of the
research literature 
Dana Olanoff, Priya Vinata Prasad, Rachael
M. Welder 
895897 
10.51272/pmena.42.2020136 

1/2, 1/3 or 2/4? Interpretation of
elementary school teachers’ answers to an evaluation /
¿1/2, 1/3 o 2/4? Interpretación de respuestas de
docentes de nivel básico a una evaluación 
Armando Paulino Preciado Babb, María Estela
Navarro Robles 
898900 
10.51272/pmena.42.2020137 

The ideas of Giordano Bruno as a
teaching alternative 
Felipe de Jesús Matías, Aurora Gallardo 
901903 
10.51272/pmena.42.2020138 

Mathematical Processes and Modeling 



< 
Research Reports 

904 


Exploring secondary students’ proving
competencies through clinical interviews with smartpens 
Michelle Cirillo, Jenifer Hummer 
905913 
10.51272/pmena.42.2020139 

Developing a framework for
characterizing student analogical activity in
mathematics 
Michael D. Hicks 
914921 
10.51272/pmena.42.2020140 

How mathematical modeling enables
learning? 
Sindura Subanemy Kandasamy, Jennifer Czocher 
922930 
10.51272/pmena.42.2020141 

Establishing a Cartesian coordination in
the Ant Farm Task: The case of Ginny 
Hwa Young Lee, Hamilton L. Hardison, Sindura
Kandasamy, Lino Guajardo 
931939 
10.51272/pmena.42.2020142 

Prospective K8 teachers’ problem
posing: Interpretations of tasks that promote
mathematical argumentation 
Marta T. Magiera 
940948 
10.51272/pmena.42.2020143 

Mathematical knowledge and skills of
university students when solving a MEA / Conocimientos y
habilidades matemáticas de estudiantes universitarios al
realizar una MEA 
Iván I. RodríguezGonzález, Verónica
VargasAlejo, Luis E. MonteroMoguel 
949965 
10.51272/pmena.42.2020144 

Mathematical Processes and Modeling: Brief
Research Reports 

966 


Model eliciting activity for hypothesis
testing with engineering students/ Actividad provocadora
de modelos para prueba de hipótesis con estudiantes de
ingeniería 
Sergio Damian CamachoAguilar, Martha Aguiar
Barrera, Humberto Pulido Gutiérrez 
967975 
10.51272/pmena.42.2020145 

An analysis of students’ mathematical
models for Music 
Kimberly Corum, Melike Kara, Emma Talbot,
Tatiana Ilina 
976980 
10.51272/pmena.42.2020146 

Beyond patterns: making sense of
patternsbased generalizations through empirical
reconceptualization 
Amy B. Ellis, Elise Lockwood 
981985 
10.51272/pmena.42.2020147 

Creativityinprogress rubric on problem
solving at the postsecondary level 
Gulden Karakok, Houssein El Turkey, Miloš
Savić, Gail Tang, Emily CilliTurner, Paul Regier 
986990 
10.51272/pmena.42.2020148 

A quantitative reasoning study of
studentreported difficulties when solving related rates
problems 
Thembinkosi P. Mkhatshwa 
991995 
10.51272/pmena.42.2020149 

Secondary teachers’ differing views on
who should learn proving and why 
Samuel Otten, Mitchelle M. Wambua, Rajendran
Govender 
9961000 
10.51272/pmena.42.2020150 

The role of the researcher’s questions
in a clinical interview on students’ perceived problem
solving 
Reyhan Safak, Karoline Smucker, Azita
Manouchehri 
10011004 
10.51272/pmena.42.2020151 

Proportional thinking: a comparative
study among fourth and fifth grade children / El
pensamiento proporcional: un estudio comparativo entre
niños de cuarto y quinto de primaria 
Mike Saldaña Guerrero, Sofia K. Vázquez
Gómez 
10051013 
10.51272/pmena.42.2020152 

Stages in using proof techniques:
Student development in the transition to proof 
V. Rani Satyam 
10141022 
10.51272/pmena.42.2020153 

Attend to structure and the development
of mathematical generalizations in a dynamic geometry
environment 
Xiangquan Yao 
10231027 
10.51272/pmena.42.2020154 

Mathematical Processes and Modeling: Poster
Presentations 

1028 


How to pose it: developing a
problemposing framework 
José N. Contreras 
10291030 
10.51272/pmena.42.2020155 

Domain appropriateness and skepticism in
viable argumentation 
Robert Ely, David Yopp, Anne E. Adams 
10311032 
10.51272/pmena.42.2020156 

Examining justification of thirdgrade
children when they engaged in equalsharing problems 
Hochieh Lin 
10331034 
10.51272/pmena.42.2020157 

A content focused task schematization
around mathematical modeling problems: quantities 
Ayse Ozturk 
10351036 
10.51272/pmena.42.2020158 

Exploring high school students’
validation methods in the mathematical modeling process 
Ayse Ozturk 
10371038 
10.51272/pmena.42.2020159 

Prompting quantitative reasoning
patterns with mathematical modeling problems 
Patti Brosnan, Ayse Ozturk 
10391040 
10.51272/pmena.42.2020160 

Making sense of senseless things: an
enactivist analysis of harmony and dissonance in problem
solving 
Erin Pomponio, Steven Greenstein, Denish
Akuom 
10411042 
10.51272/pmena.42.2020161 

Talking in mathematics ‒ do we know how? 
Pauline Tiong 
10431044 
10.51272/pmena.42.2020162 

Development of the mathematic modeling
process in mathematics undergraduate students /
Desarrollo del proceso de modelación matemática en
estudiantes de licenciatura en matemáticas 
Jesús David Berrio Valbuena, Zuriel
Fitzgerald Peña Ubarne, Maria de los Ángeles Torrenegra
Giraldo 
10451047 
10.51272/pmena.42.2020163 

Didactic sequence for learning problem
solving concerning the use of relative extrema /
Secuencia didáctica: el aprendizaje de resolución de
problemas referentes al uso de extremos relativos 
Paulina Villalón Valdez, Claudia Margarita
Orozco Rodríguez, Fernando Ignacio Becerra López, Juana
Adriana Ascencio Escamilla 
10481050 
10.51272/pmena.42.2020164 

Secondary teachers’ practical
rationality of mathematical modeling 
Wenmin Zhao, Samuel Otten 
10511052 
10.51272/pmena.42.2020165 

Miscellaneous Topics 




Research Reports 

1053 


Numerical estimation skills, epistemic
cognition and climate change: mathematical skills and
dispositions that can support science learning 
Ian Thacker 
10541062 
10.51272/pmena.42.2020166 

Miscellaneous Topics: Brief Research Reports 

1063 


Utilizing mathematics to examine sea
level rise as an environmental and a social issue 
Debasmita Basu, Nicole Panorkou 
10641068 
10.51272/pmena.42.2020167 

Sources of evolution of university
students’ views on mathematical creativity 
Emily CilliTurner, Miloš Savić, Gail Tang,
Houssein El Turkey, Gulden Karakok 
10691073 
10.51272/pmena.42.2020168 

Learning to pose problems within dynamic
geometry environments: a self study involving Varignon’s
problem 
José N. Contreras 
10741079 
10.51272/pmena.42.2020169 

A largescale study on teacher noticing 
Yasemin CopurGencturk, Jessica Rodrigues 
10801084 
10.51272/pmena.42.2020170 

Reasoning about the rate of change while
linking CO2 pollution to global warming 
Darío A. González 
10851093 
10.51272/pmena.42.2020171 

Miscellaneous Topics: Poster Presentations 

1094 


Posing problems about geometric
situations: A study of prospective secondary mathematics
teachers 
José N. Contreras 
10951097 
10.51272/pmena.42.2020172 

Comprehension of complex mathematical
tasks within the scholarized cultural environment in
thirdgrade / Entendimiento de tareas matemáticas
complejas dentro del entorno cultural escolarizado, en
3° grado de primaria 
Uriel Escobar, Felipe Tirado 
10981099 
10.51272/pmena.42.2020173 

Transformations of figures in O’dam
embroidery´s / Transformaciones de figuras en morrales
O’dam 
Erika Janeth Frayre Larreta, Alicia López
Betancourt 
11001102 
10.51272/pmena.42.2020174 

You say brutal, I say thursday: isn’t it
obvious? 
Sarah Sword, Anne Marie Marshall, Michael
Young 
11031104 
10.51272/pmena.42.2020175 

Kindergarten students’ spatial thinking:
practices on debugging of building blocks 
Lili Zhou, Sezai Kocabas 
11051106 
10.51272/pmena.42.2020176 

Precalculus, Calculus, or Higher Mathematics 




Research Reports 

1107 


Two prospective middle school teachers
reinvent combinatorial formulas: permutations and
arrangements 
Joseph Antonides, Michael T. Battista 
11081116 
10.51272/pmena.42.2020177 

Report of a classroom experience for the
development of distribution models / Experiencia en el
aula para el desarrollo de modelos para el reparto 
María José Aviña González, Angelina Alvarado
Monroy 
11171129 
10.51272/pmena.42.2020178 

Constrasting social and
sociomathematical norms of two groups of students in a
postsecondary Precalculus class 
David Fifty, Orly Buchbinder, Sharon McCrone 
11301138 
10.51272/pmena.42.2020179 

Students’ reasoning about
multivariational structures 
Steven R. Jones, Haley P. Jeppson 
11391147 
10.51272/pmena.42.2020180 

“Dyslexia is naturally commutative”:
Insider accounts of dyslexia from research
mathematicians 
Rachel Lambert, Edmund Harriss 
11481155 
10.51272/pmena.42.2020181 

What Is a Function? 
Alison Mirin, Keith Weber, Nicholas
Wasserman 
11561164 
10.51272/pmena.42.2020182 

Understanding the roles of proof through
exploration of unsolved conjectures 
Jeffrey Pair, Gabe Calva 
11651171 
10.51272/pmena.42.2020183 

Precalculus, Calculus, or Higher
Mathematics: Brief Research Reports 

1172 


Towards a didactic distinction between
Calculus and Analysis. The case of the notion of
variable / Hacia una distinción didáctica entre el
Cálculo y el Análisis. El caso de la noción de variable 
María Teresa Dávila Araiza, Agustín Grijalva
Monteverde 
11731181 
10.51272/pmena.42.2020184 

Constructing rates of change through a
units coordinating lens: The story of Rick 
Jeffrey A. Grabhorn, Steven Boyce 
11821185 
10.51272/pmena.42.2020185 

Detection of difficulties in endowing
the notions of change and variation with meaning through
iteration / Detección de dificultades en la dotación de
significado de las nociones de cambio y variación
mediante iteración 
Arturo E. Meléndez, Eugenio Filloy, Luis
Puig 
11861193 
10.51272/pmena.42.2020186 

Function identity and the fundamental
theorem of calculus 
Alison Mirin 
11941198 
10.51272/pmena.42.2020187 

Undergraduate mathematics majors’
problem solving and argumentation 
Hannali Pajela, Sarah Roberts, Mary E.
Brenner 
11991203 
10.51272/pmena.42.2020188 

Teachersintraining’s reflections on
the teaching of calculus to people with distinct
characteristics / Profesores en formación que
reflexionan sobre la enseñanza del cálculo a personas
con características diferenciadas 
Sandra Evely Parada Rico, Cristian Leonardo
Echeverría Ballesteros 
12041212 
10.51272/pmena.42.2020189 

From recursion to induction: students’
generalization practices through the lens of
combinatorial games 
Cody L. Patterson, Lino Guajardo, Emma Yu 
12131217 
10.51272/pmena.42.2020190 

Students’ understanding of linear
algebra concepts underlying a procedure in a quantum
mechanics task 
Kaitlyn Stephens Serbin, Megan Wawro 
12181222 
10.51272/pmena.42.2020191 

“Solving versus relating”: Preservice
teachers’ conflicting images of formulas and dynamic
contexts 
Irma E. Stevens 
12231227 
10.51272/pmena.42.2020192 

Precalculus, Calculus, or Higher
Mathematics: Poster Presentations 

1228 


First fundamental theorem of calculus:
How do engineering students interpret and apply it? /
Primer teorema fundamental del cálculo: ¿cómo lo
interpretan y aplican estudiantes de ingeniería? 
Omar Arenas Bonifacio, Ernesto Alonso
Sánchez Sánchez 
12291231 
10.51272/pmena.42.2020193 

The variation, covariation and the
reference system in the construction of Cartesian ideas
/ La variación, la covariación y el sistema de
referencia en la construcción de ideas cartesianas 
Itzel González Rodríguez, José David
Zaldívar Rojas 
12321234 
10.51272/pmena.42.2020194 

Mathematical modeling for studying the
concept of integral through an authentic problem /
Modelación matemática para el estudio del concepto de
integral a través de un problema auténtico 
Shirley Johana Toloza Peña, Jorge Enrique
Fiallo Leal 
12351237 
10.51272/pmena.42.2020195 

Statistics and Probability 




Research Reports 

1238 


Comparison strategies by quotient and
the urn model in the choice of probabilities /
Estrategias de comparación por cociente y el modelo de
urna en la elección de probabilidades 
Maribel AguasHidalgo, Ricardo
QuinteroZazueta 
12391253 
10.51272/pmena.42.2020196 

Highschool students’ probabilistic
reasoning when working with random intervals 
Sandra Areli Martínez Pérez, Ernesto A
Sánchez Sánchez 
12541261 
10.51272/pmena.42.2020197 

Covariational reasoning patterns of high
school students in problems of correlation and linear
regression / Patrones de razonamiento covariacional de
estudiantes de bachillerato en problemas de correlacion
y regresión lineal 
Miguel Medina, Eleazar Silvestre 
12621279 
10.51272/pmena.42.2020198 

Types of orchestrations in a case study
of a statistics constructionist teaching practice /
Tipos de orquestación en un estudio de caso de una
enseñanza construccionista de la estadística 
Perla Marysol RuizArias, Ana Isabel
Sacristán 
12801297 
10.51272/pmena.42.2020199 

High school students’ misconceptions
about significance testing with a repeated sampling
approach 
Ernesto Sánchez Sánchez, Víctor N. García
Rios, Eleazar Silvestre Castro, Guadalupe Carrasco Licea 
12981306 
10.51272/pmena.42.2020200 

Statistics and probability: Brief Research
Reports 

1307 


Fundamental statistical ideas in primary
/ Ideas fundamentales de estadística en primaria 
Santiago Inzunza 
13081316 
10.51272/pmena.42.2020201 

Reasoning about association for
categorical data using contingency tables and mosaic
plots 
Sheri E. Johnson 
13171321 
10.51272/pmena.42.2020202 

Students’ “multisample distribution”
misconception about sampling distributions 
Kiya L. Eliason, Steven R. Jones 
13221330 
10.51272/pmena.42.2020203 

Conditional probability in early
childhood: a case study 
Brigitte Johana Sánchez Robayo, Jesse L. M.
Wilkins 
13311335 
10.51272/pmena.42.2020204 

The impact of selfcollected data on
students’ statistical analysis 
Karoline Smucker, Azita Manouchehri 
13361340 
10.51272/pmena.42.2020205 

Statistics and Probability: Poster
Presentations 

1341 


Decisionmaking problem for interpreting
algebraic inequalities / Problemas de toma de decisión
para interpretar las inecuaciones algebraicas 
Sharon Samantha Membreño Estrada, Claudia
Margarita Acuña Soto 
13421343 
10.51272/pmena.42.2020206 

Model eliciting activity for learning
statistical techniques for process control / Actividad
provocadora de modelos para el aprendizaje de técnicas
estadísticas de control de procesos 
Ponce Vega Luis Martin, Aguiar Barrera
Martha Elena, Gutiérrez Pulido Humberto 
13441346 
10.51272/pmena.42.2020207 

The role of simulation in solving
probability tasks 
Karoline Smucker 
13471348 
10.51272/pmena.42.2020208 

Student Learning and Related Factors 




Research Reports 

1349 


Mathematics anxiety as a mediator for
gender differences in 2012 PISA mathematics scores 
Jennifer Cox, Erik Jacobson 
13501359 
10.51272/pmena.42.2020209 

Elementary students and their
selfidentified emotions as they engaged in mathematical
problem solving 
Jenna R. O’Dell, Todd Frauenholtz 
13601368 
10.51272/pmena.42.2020210 

Student Learning and Related Factors: Brief
Research Reports 

1369 


A culture of change: Students stories in
undergraduate reform math 
John Bragelman, Wesley Maciejewski 
13701373 
10.51272/pmena.42.2020211 

Discovering square roots: Productive
struggle in middle school mathematics 
Cindy Cattey, Cody Patterson 
13741378 
10.51272/pmena.42.2020212 

Everyday experiences and school
knowledge of mathematics. An enactive approach /
Experiencias cotidianas y conocimientos escolares de
matemáticas. una aproximación enactivista 
Edda N. Jimenez de la Rosa y Barrios 
13791385 
10.51272/pmena.42.2020213 

Moving towards meaning making in
multiplication: A preliminary report of an intervention
in number sense 
Rachel Lambert, Monica Mendoza, Tomy Nguyen 
13861389 
10.51272/pmena.42.2020214 

Gender differences in attitudes towards
mathematics and STEM major choice: The importance of
mathematics identity 
Dalton Marsh, Sheree Sharpe 
13901394 
10.51272/pmena.42.2020215 

Investigating selfefficacy, test
anxiety, and performance in college Algebra 
Yuliya Melnikova, Valerie Long, Russell S.
Stocker 
13951398 
10.51272/pmena.42.2020216 

Monopolizing teacher attention: A case
of multilingual learners’ competence embodied in social
formations 
Isaac T NicholsPaez 
13991404 
10.51272/pmena.42.2020217 

Mothercentered understanding of
mathematical interactions with children: Pursuing
positive intent 
Sam Prough 
14051409 
10.51272/pmena.42.2020218 

Didactic purposes and functions of
security and doubt in mathematical contents / Fines y
funciones didácticas de la seguridad y la duda en
contenidos matemáticos 
Mirela RigoLemini, María Alejandra
BernalPinzón, Esperanza Carolina OrozcodelCastillo 
14101418 
10.51272/pmena.42.2020219 

Comparing transfer and nontransfer
college students’ mathematics professional vision 
Sarah A. Roberts, Hannali Pajela 
14191423 
10.51272/pmena.42.2020220 

Spontaneous mathematical moments between
caregiver and child during an engineering design project 
Amber Simpson, Qiu Zhong 
14241428 
10.51272/pmena.42.2020221 

Manifestations of bias within preservice
teachers professional noticing of children’s
mathematical thinking 
Jonathan Thomas, Taylor Marzilli, Brittney
Sawyer, Cindy Jong, Molly H. Fisher 
14291433 
10.51272/pmena.42.2020222 

Middle school students’ contextualized
geometric spatial understandings 
Jennifer Wilhelm, Merryn Cole, Emily
Driessen, Samantha Ringl 
14341438 
10.51272/pmena.42.2020223 

Student Learning and Related Factors: Poster
Presentations 

1439 


Preschoolaged children’s emergent
dispositions with respect to mathematics 
James E. R. Beyers, Megan Sytsma 
14401441 
10.51272/pmena.42.2020224 

A preliminary model of influences on
adolescents’ perceptions of usefulness in school
mathematics 
Tracy E. Dobie, Rachel Francom 
14421443 
10.51272/pmena.42.2020225 

Exploring the relationship between math
anxiety, working memory and teacher practices 
Luke Duncan, Karen High 
14441445 
10.51272/pmena.42.2020226 

Problem posing in partitive and
quotitive division 
Amanda Lake Heath, L. Jeneva Clark 
14461447 
10.51272/pmena.42.2020227 

Modal continuity in Deaf students’
signed mathematical discourse 
Christina M. Krause, Dor Abrahamson 
14481449 
10.51272/pmena.42.2020228 

Adolescents’ mathematics identities in a
math circle 
Rileigh Luczak 
14501451 
10.51272/pmena.42.2020229 

Tutoring lab attendance and time spent
on homework: Impact on student performance in college
algebra 
Yuliya Melnikova, Valerie Long, Courtlyn
Adams 
14521453 
10.51272/pmena.42.2020230 

Student inquiry in interesting lessons 
Hector I. Nieves, Rashmi Singh, Leslie
Dietiker 
14541455 
10.51272/pmena.42.2020231 

Problem solving dispositions in rural
communities 
Frederick A. Peck, Mary Alice Carlson,
Adewale Adeolu, Sara Killeen, Katherine McWalters 
14561457 
10.51272/pmena.42.2020232 

The effects of worked example formats on
student learning of Algebra 
Hannah Smith, Avery Harrison, Jenny YunChen
Chan, Erin Ottmar 
14581459 
10.51272/pmena.42.2020233 

Teacher Education (Pre‑service) 




Research Reports 

1460 


Using video analysis to improve
preservice elementary teachers’ noticing skills 
Liza Bondurant, Lisa Poling, Diana Moss 
14611468 
10.51272/pmena.42.2020234 

Counterstories of preservice elementary
teachers: strategies for successful completion of their
math content sequence 
Anne Cawley, Hazar Eldick, Samantha Cano 
14691476 
10.51272/pmena.42.2020235 

Productive seeds in preservice teachers’
reasoning about fraction comparisons 
Ian Whitacre, Kelly Findley, Sebnem Atabas 
14771484 
10.51272/pmena.42.2020236 

Didaticmathematical knowledge and
competence of prospective secondary school mathematics
teachers on linear variation / Conocimientos y
competencias didácticomatemáticos de futuros profesores
de matemáticas de secundaria sobre variación lineal 
Karina Jaquelin Herrera García, María Teresa
Dávila Araiza 
14851502 
10.51272/pmena.42.2020237 

What does it mean to be me? A preservice
mathematics teacher’s identity development during an
education abroad program 
Blair Izard 
15031509 
10.51272/pmena.42.2020238 

Classroom events on problem solving with
Geogebra anticipated by future mathematics teachers 
Alexánder Hernández, Josefa PerdomoDíaz,
Matías CamachoMachín 
15101518 
10.51272/pmena.42.2020239 

Latinx paraeducators lived mathematical
experiences 
David Slavit, Gisela ErnstSlavit 
15191526 
10.51272/pmena.42.2020240 

Modeling to understand the world around
us and our place in it: If the world were a village 
Eva Thanheiser, Brenda Rosencrans, Brittney
Ellis, Amanda Sugimoto, Torrey Kulow, Molly Robinson 
15271534 
10.51272/pmena.42.2020241 

Investigating elementary preservice
teachers’ conceptions of mathematical creativity 
Anne N. Waswa, Kevin C. Moore 
15351543 
10.51272/pmena.42.2020242 

Teacher Education (Preservice) Brief
Research Reports 

1544 


The use of mixedreality simulations as
a tool for preparating preservice teachers and their
perceptions and opinions / Uso de simulacion de
realidadmixta como herramienta en la formación de
maestros: percepciones y opiniones 
Jair J. Aguilar, James A. Telese 
15451555 
10.51272/pmena.42.2020243 

Preservice teachers’ operationalization
of cognitive demand across context 
Monica Anthony, Margaret Walton, William
Viviani 
15561560 
10.51272/pmena.42.2020244 

Reflective conversation as a means to
develop knowledge in future mathematics teachers 
Eddie AparicioLanda, Landy SosaMoguel 
15611566 
10.51272/pmena.42.2020245 

Realtime coaching with secondary
preservice teachers: The practices of mathematics
teacher educators 
Fran Arbaugh, Raymond LaRochelle, Seonmi Do,
Azaria Cunningham, Kevin Voogt, Michelle Cirillo, Kristen
N. Bieda 
15671571 
10.51272/pmena.42.2020246 

Frameworks for noticing in mathematics
education research 
Dominique Banner 
15721576 
10.51272/pmena.42.2020247 

Prospective elementary teachers’ use of
contextual knowledge when solving problematic word
problems 
José N. Contreras 
15771584 
10.51272/pmena.42.2020248 

Using strip diagrams to support
prospective middle school teachers’ explanations for
fraction multiplication 
Eric CorderoSiy 
15851589 
10.51272/pmena.42.2020249 

Preservice teachers’ patterns of
questioning while tutoring students with learning
disabilities in Algebra 1 
Anna F. DeJarnette, Casey Hord 
15901594 
10.51272/pmena.42.2020250 

Preservice elementary teachers
navigating tensions related to classroom social dynamics
through hypothetical teaching scenarios 
Tracy E. Dobie, Lauren BarthCohen, Rachel
Francom, Kevin Greenberg, José Gutiérrez 
15951600 
10.51272/pmena.42.2020251 

Error patterns in prospective K8
teachers’ posing of multistep addition and subtraction
word problems 
Ali Foran, Rachael M. Welder 
16011605 
10.51272/pmena.42.2020252 

Conceptual and procedural learning in
preservice mathematics teachers during a conversation /
Aprendizaje conceptual y procedimental en profesores de
matemáticas en formación durante una conversación 
Karla Gómez Osalde, Eddie Aparicio Landa,
Landy Sosa Moguel 
16061614 
10.51272/pmena.42.2020253 

Prospective teachers’ strategies for
evaluating nonstandard angular measurement tools 
Hamilton L. Hardison, Hwa Young Lee 
16151619 
10.51272/pmena.42.2020254 

Preservice teachers’ developing
instructional strategies for English language learners
in secondary mathematics 
Brittany Caldwell, Salvador Huitzilopochtli 
16201623 
10.51272/pmena.42.2020255 

Preservice secondary mathematics
teachers’ evolution of communally agreedon criteria for
proof 
YiYin Ko, Dalton Edgecomb, Nathan Kooi 
16241628 
10.51272/pmena.42.2020256 

Analyzing how reflective discussions in
a content course influence prospective teachers’ beliefs 
Alexa W.C. LeeHassan 
16291633 
10.51272/pmena.42.2020257 

Can confidence in mathematical
afirmationsinfluence negatively in the advance of the
discipline? Why? / ¿La confianza en afirmaciones
matemáticas puede influir negativamente en el avance de
la disciplina? ¿Por qué? 
Benjamín MartínezNavarro, Mirela
RigoLemini 
16341642 
10.51272/pmena.42.2020258 

Preservice teachers analysis of the use
of history in mathematics lessons 
Michael S Meagher, Asli ÖzgünKoca 
16431647 
10.51272/pmena.42.2020259 

Preservice teachers’ perceptions of a
lesson study connecting multicultural literature with
culturally responsive mathematics teaching 
Alesia Mickle Moldavan 
16481652 
10.51272/pmena.42.2020260 

Conceptual systems when implementing
modeleliciting activities / Sistemas conceptuales al
implementar actividades provocadoras de modelos 
Luis E. MonteroMoguel, Verónica
VargasAlejo, Iván I. RodríguezGonzález 
16531661 
10.51272/pmena.42.2020261 

Explicit teaching of questioning in math
methods course: Preservice teachers’ attempts to ask
probing questions 
Susie Morrissey, Ozgul Kartal, Gorjana
Popovic 
16621666 
10.51272/pmena.42.2020262 

Supporting fractions as measures in an
online mathematics methods course 
Diana Moss, Steven Boyce, Beth L. MacDonald,
Claudia BertoloneSmith 
16671671 
10.51272/pmena.42.2020263 

Preparing to elicit student thinking:
Supporting PST questioning in an university teaching
experience 
Sheila Orr, Kristen Bieda 
16721676 
10.51272/pmena.42.2020264 

Prospective teachers’ interpretations of
mathematical reasoning 
Hyejin Park, Marta T. Magiera 
16771681 
10.51272/pmena.42.2020265 

Resources that preservice and inservice
teachers offer in collaborative analysis of student
thinking 
Cody L. Patterson, Hiroko K. Warshauer, Max
L. Warshauer 
16821686 
10.51272/pmena.42.2020266 

Prospective elementary teachers’ content
knowledge of decimal magnitude and place value 
Rachel Starks, Ziv Feldman 
16871691 
10.51272/pmena.42.2020267 

Teachers candidates’ implementations of
equitable mathematics teaching practices: An examination
of divergent paths 
Angela Stoltz, Imani Goffney, Kelly K. Ivy,
Tarik Buli, Ebony Terrell Shockley 
16921697 
10.51272/pmena.42.2020268 

Exploring shifts in a student’s
graphical shape thinking 
Madhavi Vishnubhotla, Teo Paoletti 
16981702 
10.51272/pmena.42.2020269 

Exploring preservice teachers’
pedagogical content knowledge of teaching fractions 

17031707 
10.51272/pmena.42.2020270 

Teacher Education (Preservice): Poster
presentations 

1708 


Future teachers of basic geometry:
Crossroads between the knowledge of two school cultures
of mathematics 
Alejandra AvalosRogel, Marleny Hernández
Escobar 
17091711 
10.51272/pmena.42.2020271 

Developing prospective teachers’
representational fluency of whole number multiplication
using array representations 
Neet Priya Bajwa, Jennifer M. Tobias, Dana
Olanoff, Rachael M. Welder 
17121713 
10.51272/pmena.42.2020272 

The power of caring and funds of
knowledge in teacher learning 
Jessica Davidson, Eileen Fernández 
17141715 
10.51272/pmena.42.2020273 

Prospective teachers’ affordances and
challenges of seeing students’ mathematical strengths 
Monica Gonzalez, Katherine Baker, Kathleen
Nitta, Erin Smith, Tracy Dobie, Naomi Jessup, Jennifer
Ward 
17161717 
10.51272/pmena.42.2020274 

The UTE model: Animating preservice
teachers’ visions for student engagement 
Jonathan Gregg, Raymond LaRochelle, Azaria
Cunningham, Seonmi Do, Kristen Bieda, Fran Arbaugh 
17181719 
10.51272/pmena.42.2020275 

SEE math (support and enrichment
experiences in mathematics) program 
Crystal KalinecCraig, Emily P. Bonner 
17201721 
10.51272/pmena.42.2020276 

Preservice elementary education
teachers’ solutions for word problems: Using strip
diagram vs. algebraic approach 
Melike Kara, Kimberly Corum 
17221723 
10.51272/pmena.42.2020277 

Designing pedagogies of practice for a
critical practicebased teacher education 
Joshua H. Karr 
17241725 
10.51272/pmena.42.2020278 

Documenting adaptive expertise through
the evolving use of an enactment tool 
Joshua H. Karr, Erin E. Baldinger, Matthew
P. Campbell, Sean P. Freeland 
17261727 
10.51272/pmena.42.2020279 

Evaluation of a software solution for
refreshing preservice teachers’ mathematics content
knowledge 
Anjali Khirwadkar, Steven Khan, Joyce
Mgombelo 
17281729 
10.51272/pmena.42.2020280 

Professional teacher noticing as
embodied activity 
Karl W. Kosko, Jennifer Heisler, Enrico
Gandolfi 
17301731 
10.51272/pmena.42.2020281 

Distinctions in preservice teachers’
assetbased noticings of middle school students’
mathematical strengths 
Brian R. Lawler, Dorothy Y. White 
17321733 
10.51272/pmena.42.2020282 

Mathematics is everywhere: intersection
of PST perceptions and nonmathematicseducation faculty
perceptions and observable actions 
Mary Elizabeth Riley Lloyd 
17341735 
10.51272/pmena.42.2020283 

Creative mathematical reasoning and
content as an evaluative framework for preservice
teacher experiences 
Tami S. Martin, Craig J. Cullen 
17361737 
10.51272/pmena.42.2020284 

Textbook use of children’s thinking to
support prospective elementary teachers’ geometric
understanding 
Brooke Max, Rachael Welder 
17381739 
10.51272/pmena.42.2020285 

Using multiple strategies tasks to
explore preservice teachers’ persistence 
Amanda Jo Meiners, Kyong Mi Choi, Dae Hong 
17401741 
10.51272/pmena.42.2020286 

Advancing understanding of equity with
case study dilemmas: Lessons from preservice teachers 
Alesia Mickle Moldavan, Monica Gonzalez 
17421743 
10.51272/pmena.42.2020287 

Relationship between not knowing and
successful problem solving among preservice secondary
mathematics teachers 
Gulshat Shakirova, Mourat Tchoshanov, Kevin
Fierro 
17441745 
10.51272/pmena.42.2020288 

Fostering student teachers’ spatial
reasoning: the robotics Mars challenge 
Mawuli Kofi Tay, Armando Paulino
PreciadoBabb 
17461747 
10.51272/pmena.42.2020289 

Teacher Education (Inservice) /
Professional Development 




Research Reports 

1748 


Methodology for the design of didactic
sequences for secondary mathematics in a technological
context / Metodología para el diseño de secuencias
didácticas para matemática de secundaria en un contexto
tecnólogico 
Jamil Fabiola Alvarado Sánchez, José Luis
Soto Munguía 
17491764 
10.51272/pmena.42.2020290 

Coaches’ and teachers’ noticing through
annotations: Exploring analytic stance across coaching
cycles 
Julie M. Amador, Ryan Gillespie, Jeffrey
Choppin, Cyndi Carson 
17651773 
10.51272/pmena.42.2020291 

Articulating effective middle grades
instructional practices in a teacherresearcher alliance 
Joe Champion, Angela R Crawford, Michele
Carney 
17741781 
10.51272/pmena.42.2020292 

Studying a synchronous online course
using a community of inquiry framework 
Jeffrey Choppin, Julie Amador, Cynthia
Callard, Cynthia Carson 
17821790 
10.51272/pmena.42.2020293 

“I must be a glutton for punishment”:
Teachers’ emotions related to videorecording of
mathematics instruction 
Dionne Cross Francis, Jinqing Liu, Ayfer
Eker, Pavneet K. Bharaj, Kemol Lloyd, Ji Hong, Mihyun Jeon 
17911799 
10.51272/pmena.42.2020294 

Reconciling local contexts and external
conceptual resources in mathematics teachers’
collaborative sensemaking 
Nadav Ehrenfeld, Katherine Schneeberger
McGugan, Samantha A. Marshall, Brette Garner 
18001808 
10.51272/pmena.42.2020295 

Examining how teachers enact the
suggestions of a coach: Critique of a methodology 
Ryan Gillespie, Julie M. Amador, Jeffrey
Choppin 
18091817 
10.51272/pmena.42.2020296 

Changes in practicing secondary
teachers’ professional noticing over a longterm
professional development program 
Raymond LaRochelle, Sloan HillLindsay,
Susan Nickerson, Lisa Lamb 
18181827 
10.51272/pmena.42.2020297 

An exploration of mathematics teacher
leaders in PMENA proceedings from 19842019 
Evthokia Stephanie Saclarides, Courtney
Baker, Allison Mudd, Stefanie Livers, Kristin Harbour,
Margret Hjalmarson 
18281836 
10.51272/pmena.42.2020298 

Teacher Education (Inservice) /
Professional Development: Brief Research Reports 

1837 


A collaborative professional development
model: promoting shifts in classroom practice 
Pavneet Kaur Bharaj, Enrique Galindo,
Jinqing Liu, Gina Borgioli Yoder 
18381842 
10.51272/pmena.42.2020299 

Selfefficacy and the kernel of content
knowledge 
L. Jeneva Clark, Peggy Bertrand, Amanda Lake
Heath 
18431847 
10.51272/pmena.42.2020300 

Contributing factors to secondary
mathematics teachers’ professional identity 
Jennifer Cribbs, Jianna Davenport, Lisa
Duffin, Martha Day 
18481852 
10.51272/pmena.42.2020301 

Mathematics teachers’ perceptions of
their instruction for multilingual learners through
professional development experiences 
Cameron Dexter Torti, Sarah A. Roberts,
Julie A. Bianchini 
18531857 
10.51272/pmena.42.2020302 

A framework for the facilitation of
online professional development to support instructional
change 
Nicholas Fortune, Ralph Chikhany, William
Hall, Karen Allen Keene 
18581862 
10.51272/pmena.42.2020303 

Influences on earlycareer mathematics’
teachers vision of teaching with technology: a
longitudinal study 
Suzanne R. Harper, Dana C. Cox 
18631867 
10.51272/pmena.42.2020304 

Mathematics specialists and teacher
leaders: an ongoing qualitative synthesis 
Margret A. Hjalmarson, Evthokia Stephanie
Saclarides, Kristin Harbour, Stefanie Livers, Courtney K.
Baker 
18681872 
10.51272/pmena.42.2020305 

Towards reflection on the practice in a
learning community of higherlevel mathematics teachers 
Miguel Ángel HuertaVázquez, Olimpia
Figueras 
18731877 
10.51272/pmena.42.2020306 

The evolution of teachers’ conceptions
of teaching mathematical modeling through participation
in lesson study 
Jenifer Hummer 
18781886 
10.51272/pmena.42.2020307 

Characterizing feedback given among
mathematics teachers: classroom observations 
Erin E. Krupa, Mika Munakata 
18871891 
10.51272/pmena.42.2020308 

Examining inservice teachers’
diagnostic competence 
Jinqing Liu, Erik Jacobson, Pavneet Kaur
Bharaj 
18921896 
10.51272/pmena.42.2020309 

The design, implementation, and impact
of a collaborative responsive professional development
(CRPD) model 
Jinqing Liu, Enrique Galindo, Gina Borgioli
Yoder, Pavneet Kaur Bharaj 
18971901 
10.51272/pmena.42.2020310 

Position and sensemaking in rehearsal
debrief discussions 
Jen Munson, Erin E. Baldinger, Sarah Larison 
19021906 
10.51272/pmena.42.2020311 

Aisspommootsiio’pa – A collaboration to
improve teaching and learning mathematics at the Kainai
nation 
Armando Paulino Preciado Babb, Jodi Harker 
19071911 
10.51272/pmena.42.2020312 

“This is you. This is your family”: Case
study on attending to mathematical language development 
Eric CorderoSiy, Sam Prough, Elzena
McVicar, Hala Ghousseini, Elham Kazemi 
19121916 
10.51272/pmena.42.2020313 

Teachers’ cognitive processes during the
teaching of fractions and multiplicative problems / Los
procesos cognitivos de profesores durante la enseñanza
de fracciones y problemas multiplicativos 
Marta Ramírez Cruz, Marta Elena Valdemoros
Álvarez 
19171925 
10.51272/pmena.42.2020314 

Challenges influencing secondary
mathematics teacher’s transition towards teaching with
virtual manipulatives 
Lindsay Reiten 
19261930 
10.51272/pmena.42.2020315 

How facilitators define, design, and
implement effective early childhood mathematics
professional development 
Alexis Spina, Meghan Macias, Paul N. Reimer 
19311935 
10.51272/pmena.42.2020316 

The design and implementation of an
intervention to support and Retain early career
mathematics teachers 
Lisa Amick, Maria Campitelli, Paula
Jakopovic, Judy Kysh, Dawn Parker, April Pforts, Travis
Weiland, Laura J Wilding 
19361940 
10.51272/pmena.42.2020317 

Collaborative learning within an
informal community: How online spaces can catalyze
change 
Heather West, Robin Keturah Anderson, Amanda
Kates 
19411945 
10.51272/pmena.42.2020318 

Teacher Education (Inservice) /
Professional Development: Poster presentations 

1946 


Selfdirected learning for rural
mathematics teachers 
Robin Keturah Anderson, Kelly L. Boles 
19471948 
10.51272/pmena.42.2020319 

Exploring video coaching practices of
online mathematics coaches 
Cynthia Carson, Jeffrey Choppin 
19491950 
10.51272/pmena.42.2020320 

Elementary teachers’ beliefs about
teaching mathematics and science: Implications for
Argumentation 
AnnaMarie Conner, Claire Miller, Jenna
Menke, Yuling Zhuang 
19511952 
10.51272/pmena.42.2020321 

The semiosphere: A lens to look at
lesson study practices in their cultural context 
Carola Manolino 
19531954 
10.51272/pmena.42.2020322 

From terrified to comfortable: a
fourthgrade teacher’s journey in teaching coding 
Jenna Menke, Claire Miller 
19551956 
10.51272/pmena.42.2020323 

Getting a foot in the door: Examining
mathematics coaches’ Strategies for gaining access to
classrooms 
Jen Munson, Evthokia Stephanie Saclarides 
19571958 
10.51272/pmena.42.2020324 

Coteaching as professional development:
A study of secondary mathematics teachers partnering to
transition practice 
Jessica Tybursky Nuzzi 
19591960 
10.51272/pmena.42.2020325 

One teacher’s learning to facilitate
argumentation: focus on the use of repeating 
Hyejin Park, AnnaMarie Conner, Laura M.
Singletary, Jonathan K. Foster, Yuling Zhuang 
19611962 
10.51272/pmena.42.2020326 

Developing argumentation practices for
teachers 
Sam Prough, Eric Siy, Hala Ghousseini 
19631964 
10.51272/pmena.42.2020327 

Remote engagement in early mathematics
professional development: Using tangible artifacts to
mediate participation 
Paul N. Reimer, Aileen Rizo, Steve Pauls 
1965 
10.51272/pmena.42.2020328 

Promoting coaches’ learning through
doing the math together 
Evthokia Stephanie Saclarides, Britnie
Delinger Kane 
19661967 
10.51272/pmena.42.2020329 

Challenges in improving and measuring
mathematics discussion leading practice 
Meghan Shaughnessy, Nicole Garcia, Jillian
Peterson Mortimer, Kristen D’Anna Pynes 
19681969 
10.51272/pmena.42.2020330 

A mathematics teacher’s curricular
decisions 
Elizabeth SuazoFlores 
19701971 
10.51272/pmena.42.2020331 

From highly receptive to highly
skeptical: Engaging all teachers through responsive PD
facilitation 
Christine Taylor, Jean S. Lee 
19721973 
10.51272/pmena.42.2020332 

Teaching and Classroom Practice 




Research Reports 

1974 


A case of shared authority during a
student demonstration in a mathematics classroom 
Sunghwan Byun, Lee Melvin Peralta, Beth
HerbelEisenmann 
19751983 
10.51272/pmena.42.2020333 

High school mathematics teachers’
orientations toward engagement 
Amanda Jansen, Kelly Curtis, Amanda Mohammad
Mirzaei, Cathy Cullicott, Ethan Smith, James Middleton 
19841992 
10.51272/pmena.42.2020334 

Supporting english learner students’
development of the mathematics register through an
instructional intervention 
Richard Kitchen, Libni B. Castellón, Karla
Matute 
19932000 
10.51272/pmena.42.2020335 

Disentangling the role of context and
community in teacher professional development uptake 
Karen Koellner, Nicora Placa, Nanette Seago,
Grace Yormak 
20012008 
10.51272/pmena.42.2020336 

Supporting inclusion of students that
typically struggle with mathematics in cognitively
demanding smallgroup discourse 
Kristy Litster 
20092016 
10.51272/pmena.42.2020337 

Profiling productive mathematical
teaching moves in 4th8th mathematics classrooms 
Kathleen Melhuish, Sharon K. Strickland,
Brittney Ellis, Simon Byeonguk Han, Autumn Pham, Eva
Thanheiser 
20172025 
10.51272/pmena.42.2020338 

Teaching and Classroom Practice: Brief
Research Reports 

2026 


Practices of facilitators when planning
mathematical modeling activities in an informal setting 
Adewale, A.S 
20272031 
10.51272/pmena.42.2020339 

Exploring teachers’ constructions of
equity in mathematics education: an ecological approach 
Megan Brunner 
20322036 
10.51272/pmena.42.2020340 

Preservice teachers’ perceptions of
depictions of mathematics teaching practice when
enduring individual characteristics are introduced 
Lawrence M. Clark, Blake O’Neal Turner,
Kristyn Lue 
20372041 
10.51272/pmena.42.2020341 

Instructional tensions faced while
engaging high school geometry students in SMP3 tasks 
Kimberly Conner, Brooke Krejci 
20422046 
10.51272/pmena.42.2020342 

Mathematics instructors’ attention to
instructional interactions in discussions of teaching
rehearsals 
Lindsay Czap, Sally Ahrens, Alyson E.
Lischka 
20472051 
10.51272/pmena.42.2020343 

Orchestrating both student authority and
accountability to the discipline when guiding students
presenting a proof 
Mette Andresen, Bettina Dahl 
20522056 
10.51272/pmena.42.2020344 

Reviewing the literature on flipped
mathematics instruction: a qualitative metaanalysis 
Ruby L. Ellis, Jaepil Han, Zandra de Araujo,
Samuel Otten 
20572061 
10.51272/pmena.42.2020345 

Connecting ideas and gesturing during
wholeclass discussions 
Jonathan K. Foster 
20622066 
10.51272/pmena.42.2020346 

One teacher’s analysis of her
questioning in support of collective argumentation 
Jonathan K. Foster, Yuling Zhuang, AnnaMarie
Conner, Hyejin Park, Laura M. Singletary 
20672071 
10.51272/pmena.42.2020347 

STEM instructors’ noticing and
responding to student thinking 
Jessica R. Gehrtz 
20722076 
10.51272/pmena.42.2020348 

Hybrid environments of learning:
Potential for student collaboration and distributed
knowledge 
Veronica Hoyos, Estela Navarro, Victor J.
Raggi 
20772081 
10.51272/pmena.42.2020349 

Embracing proving into everyday lesson
by problem posing 
Hangil Kim 
20822086 
10.51272/pmena.42.2020350 

Profiling the use of public records of
students’ mathematical thinking in 4th8th mathematics
classrooms 
Christina Koehne, Eva Thanheiser, Sharon
Strickland, Autumn Pham, Ruth Heaton, Kathleen Melhuish 
20872091 
10.51272/pmena.42.2020351 

An instructor’s actions for maintaining
the cognitive demands of tasks in teaching mathematical
induction 
Vladislav Kokushkin, Marcie Tiraphatna 
20922096 
10.51272/pmena.42.2020352 

Relationships with mathematics: the
importance of agency and authority 
Tanya LaMar 
20972104 
10.51272/pmena.42.2020353 

Articulating the student mathematics in
student contributions 
Laura R. Van Zoest, Shari L. Stockero, Keith
R. Leatham, Blake E. Peterson, Joshua M. Ruk 
21052109 
10.51272/pmena.42.2020354 

Making addition Visual: Subitizing and
scaffolding 
Tina Rapke, Matthew Cheung, Heather Bourrie 
21102114 
10.51272/pmena.42.2020355 

Linking a mathematician’s beliefs and
instruction: a case study 
Rachel Rupnow 
21152120 
10.51272/pmena.42.2020356 

Operationalizing access for students:
making meaning of tasks, contexts and language 
Amanda Sugimoto, Eva Thanheiser, Kate
Melhuish, M. Alejandra Sorto, Autumn Pham 
21212125 
10.51272/pmena.42.2020357 

Mathematics teachers’ epistemic
dispositions and their relationship with teacher
instruction and student learning: a systematic research
synthesis 
Ian Thacker, Richard Rasiej 
21262132 
10.51272/pmena.42.2020358 

District certified culturally responsive
teachers and their elementary mathematics teaching
practice: a multicase study 
Casedy A. Thomas 
21332137 
10.51272/pmena.42.2020359 

Documenting mathematical language:
distinctionmaking and registerfitting 
David Wagner, Karla Culligan 
21382142 
10.51272/pmena.42.2020360 

Teaching and Classroom Practice: Poster
Presentations 

2143 


Uses of the free math textbook in
elementary schools in Mexico / Usos del libro de texto
gratuito de matemáticas en las escuelas primarias de
México 
Miguel DíazChávez 
21442145 
10.51272/pmena.42.2020361 

What matters to middle school
mathematics teachers: results from a threeyear
professional development program 
Laura B. Kent 
21462147 
10.51272/pmena.42.2020362 

Translanguaging moves in elementary
mathematics classroom number talks: understanding
linguistic repertoires 
Luz A. Maldonado Rodríguez, Gladys Krause,
Melissa AdamsCorral 
21482149 
10.51272/pmena.42.2020363 

Using translanguaging to reexamine and
deconstruct earlier findings about bilingual mathematics
education. 
Sitaniselao Stan Manu 
21502151 
10.51272/pmena.42.2020364 

Alternatives to mathematics class
discussions: inclusive ways to connect and expand
children’s ideas 
José Martínez Hinestroza 
21522153 
10.51272/pmena.42.2020365 

Learning through activity (LTA) in
superior education: The case of the HeineBorel theorem 
Rogelio Meana Chávez, Juan Gabriel Herrera
Alva 
21542155 
10.51272/pmena.42.2020366 

Mathematics teacher educators as
culturally responsive pedagogues: Introducing a
framework for “growing CRP” 
Kathleen Nolan, Lindsay Keazer 
21562157 
10.51272/pmena.42.2020367 

Beginning teachers’ equitable and
ambitious number talks 
Byungeun Pak, Brent Jackson, Jillian Cavanna 
21582159 
10.51272/pmena.42.2020368 

The interplay between a visual task and
elementary students’ mathematical discourse 
Zachary Pearson, Azita Manouchehri 
21602161 
10.51272/pmena.42.2020369 

A university instructor’s orchestration
for supporting his students’ programming for mathematics 
Marisol SantacruzRodríguez, Ana Isabel
Sacristán, Chantal Buteau, Joyce Mgombelo, Eric Muller 
21622163 
10.51272/pmena.42.2020370 

Technology 




Research Reports 

2164 


The effects of a technology course with
collaborative design on prospective teachers’ knowledge
and beliefs 
Jon D. Davis 
21652173 
10.51272/pmena.42.2020371 

Investigating undergraduate students’
generalizing activity in a computational setting 
Elise Lockwood, Adaline De Chenne 
21742182 
10.51272/pmena.42.2020372 

Middle school students’ development of
an understanding of the concept of function 
Michael S Meagher, Jennifer Lovett, Allison
McCulloch 
21832191 
10.51272/pmena.42.2020373 

Technology: Brief Research Reports 

2192 


Developing TPACK for makerspaces to
support mathematics teaching and learning 
Kimberly Corum, Sandy Spitzer, Lynn Nichols,
Kristin Frank 
21932197 
10.51272/pmena.42.2020374 

Integrating digital resources to the
documentation system of a mathematics teacher in a
Mexican rural primaryschool / Integración de recursos
digitales al sistema documental de una profesora de
matemáticas en una primaria rural de méxico 
Homero EnríquezRamírez, Ana Isabel
Sacristán 
21982207 
10.51272/pmena.42.2020375 

Enhancing students’ spatial reasoning
skills with robotics intervention 
Krista Francis, Stefan Rothschuh, Dana
Poscente, Brent Davis 
22082212 
10.51272/pmena.42.2020376 

Teachers’ problem posing in
paperandpencil and GeoGebra / Planteamiento de
problemas por profesores en papelylápiz y GeoGebra 
Lucero Hernández Cruz, Cesar Martínez
Hernández, Rodolfo Rangel Alcántar, Norma Angélica Barón
Ramírez 
22132221 
10.51272/pmena.42.2020377 

Preservice teachers’ perspectives on
technology integration in kindergarten through eighth
grade mathematics 
Monte Meyerink, Fenqjen Luo, Ciara Burgal 
22222227 
10.51272/pmena.42.2020378 

Prospective teachers’ approaches to
problemsolving activies with the use of a dynamic
geometry system 
Daniel Ortiz May 
22282232 
10.51272/pmena.42.2020379 

Designing for an integrated STEM+C
experience 
Nicole Panorkou, Toni York 
22332237 
10.51272/pmena.42.2020380 

Integrated STEM education through
gamebased learning 
Micah Stohlmann 
22382242 
10.51272/pmena.42.2020381 

Embodiment as a Rosetta stone:
Collective conjecturing in a multilingual classroom
using a motion capture geometry game 
Michael I. Swart, Kelsey E. Schenck, Fangli
Xia, Doy Kim, Oh Hoon Kwon, Mitchell J. Nathan, Candace
Walkington 
22432251 
10.51272/pmena.42.2020382 

Theory and Research Methods 




Research Reports 

2252 


Ranking the cognitive demand of
fractions tasks 
Sarah Kerrigan, Anderson Norton, Catherine
Ulrich 
22532261 
10.51272/pmena.42.2020383 

Analyzing teacher learning in a
community of practice centered on video cases of
mathematics teaching 
Youngjun Kim, Victoria D. Bonaccorso,
Mustafa M. Mohamed, Helene S. Leonard, Joseph DiNapoli,
Eileen Murray 
22622269 
10.51272/pmena.42.2020384 

An invitation to conversation:
addressing the limitations of graphical tasks for
assessing covariational reasoning 
James Drimalla, Brady A. Tyburski, Cameron
Byerley, Steven Boyce, Jeffrey Grabhorn, Christopher
Orlando Roman, Kevin C. Moore 
22702278 
10.51272/pmena.42.2020385 

Four component instructional design
(4C/ID) model confirmed for secondary tertiary
mathematics 
Carol H. Wade, Christian Wilkens, Gerhard
Sonnert, Philip M. Sadler 
22792287 
10.51272/pmena.42.2020386 

Teacher questioning strategies in
supporting validity of collective argumentation:
explanation adapted from habermas' communicative theory 
Yuling Zhuang, AnnaMarie Conner 
22882296 
10.51272/pmena.42.2020387 

Theory and Research Methods: Brief Research
Reports 

2297 


Pseudoempirical, internalized, and
interiorized covariational reasoning 
Steven Boyce 
22982302 
10.51272/pmena.42.2020388 

Learning from teaching: a new model of
teacher learning 
Yasemin CopurGencturk, Jessica Rodrigues 
23032307 
10.51272/pmena.42.2020389 

Design and validation of two measures:
competence and selfefficacy in mathematical modeling /
Diseño y validación de instrumentos de medición de
competencias y autoeficacia de modelización matemática 
Jennifer A. Czocher, Sindura Subanemy
Kandasamy, Elizabeth Roan 
23082316 
10.51272/pmena.42.2020390 

Gesture in proof and logical reasoning 
Laurie D. Edwards 
23172324 
10.51272/pmena.42.2020391 

Making meaning of learning trajectories
amidst multiple metaphors 
Nicole L. Fonger, Amy Ellis 
23252329 
10.51272/pmena.42.2020392 

Differences in students with learning
disabilities’ (LD) units construction/coordination and
subitizing 
Beth L. MacDonald, Jessica H. Hunt, Kerry
Jordan 
23302335 
10.51272/pmena.42.2020393 

Putting the “M” back into STEM:
Considering how units coordination relates to
computational thinking 
Beth L. MacDonald, Colby TofelGrehl,
Kristin A. Searle, Andrea M. Hawkman, Mario I. Suárez 
23362340 
10.51272/pmena.42.2020394 

Whose problem, whose practice?
Negotiating the focus of researchpractice partnerships
within school mathematics 
Charles Munter, Cassandra Quinn, Phi Nguyen 
23412345 
10.51272/pmena.42.2020395 

Theory and Research Methods: Poster
Presentations 

2346 


FALA framework: A learning progression
for novice teachers’ use of formative assessment 
Carolyn Mitten 
23472348 
10.51272/pmena.42.2020396 

A theorymethodology framework for
conceptualizing a culturally responsive
mathematics/teacher education 
Kathleen Nolan 
23492350 
10.51272/pmena.42.2020397 

A conceptualized framework for assessing
factors that maintain and lower cognitive demand during
task enactment 
Joshua M. Ruk 
23512352 
10.51272/pmena.42.2020398 

Building a robot: making mathematics
visible in a nonformal STEM learning environment 
V. Rani Satyam, Amber Simpson, Joseph
DiNapoli, Xiangquan Yao 
23532354 
10.51272/pmena.42.2020399 

Author’s Index / Indice de autores 


