REPORT
Interactive Technologies in STEM Teaching and Learning
Preliminary Guidelines for Using
Interactive Mobile Technologies in
Early Elementary Mathematics
Josephine Louie, Catherine McCulloch, Pam Buffington,
Marian Pasquale, Jennifer Stiles, Amy Busey
Introduction
Interactive mobile technologies such as iPads, Chromebooks, and other handheld
computing devices are becoming increasingly pervasive in K–12 classrooms in the United
States.1 How can these tools be used to support ambitious learning and teaching goals,
particularly in mathematics in the early grades?
In November 2014, 35 education researchers, district and school leaders,
and teachers met in Auburn, Maine, as part of the Research + Practice
Collaboratory, a five-year project funded by the National Science
Foundation to share knowledge and ideas about the opportunities that
interactive mobile technologies currently offer to support mathematics
learning among young students. Focusing on learning and teaching issues
rather than on technology infrastructure requirements, participants at the
Interactive Mobile Technologies Inquiry Group, or ITIG, also discussed the
learning approaches and arrangements that may be needed to maximize
these opportunities. From this meeting emerged a set of preliminary
guidelines to promote mathematical thinking among young students with access to
interactive mobile technology in their classrooms. This report presents these guidelines, the
rationale behind them, and additional resources.
Auburn, Maine, is currently the site of a collaborative effort among public-school teachers
and administrators; the Interactive STEM team at EDC, which is a major partner in the
Research + Practice Collaboratory; and Maine university researchers to investigate and build
local capacity in the use of one-to-one iPads to support mathematics learning in grades K–3.
1 Herold, B. (2015, February 26). Mobile devices for schools generating “huge momentum,” analysts say. Education
Week. Retrieved from http://blogs.edweek.org/edweek/DigitalEducation/2015/02/mobile_devices_schools_momentum.
html?cmp=ENL-DD-NEWS1
EDC
Learning
transforms
lives.
This document is created by Education Development Center, Inc. Copyright 2015.
Supported by the National Science Foundation (grant DRL-1238253). Opinions expressed
in this resource are those of the contributors and not necessarily those of the foundation.
Learn more at interactivestem.org and researchandpractice.org.
REPORT | 2
Auburn is also the home of the Leveraging Learning Institute, an annual conference organized
by the Auburn School Department to support educators from around the country who are
implementing iPad initiatives in their classrooms. The ITIG meeting was held in Auburn to
involve educators and researchers participating in the Auburn district collaboration and the
November 2014 Leveraging Learning Institute.
The 35 participants at the meeting included 13 teachers, principals, and district leaders and
22 researchers and technical assistance providers. Table 1 shows the participants by role,
and Appendix A lists their names and affiliations. Seven of the
13 Maine educators and 12 of the 22 researchers and technical
Table 1. ITIG participants by role
assistance providers have been involved with the Research +
Total
35
Practice collaboration in Auburn or with the Collaboratory project
School or district-based educators
13
more broadly. Visit the Interactive STEM website to view reports
on the strategies used at the ITIG meeting to elicit the preliminary
Teachers
5
guidelines and to learn more about participants’ experiences.
School principals
2
Math coaches
1
Technology coaches
3
District leaders
2
Educational researchers and technical
assistance providers
College or university
22
8
Non-university organization
14
Note: See the list of participants and their affiliations in Appendix A.
The mathematical thinking that the preliminary guidelines aim
to foster includes conceptual understandings of mathematical
ideas and the display of core mathematical practices as outlined
by the Standards for Mathematical Practice from the Common
Core State Standards.2 Readers should view these guidelines as
a “beta” resource: They build on the research evidence and field
experience shared by the meeting participants but will evolve
as knowledge grows. The guidelines may also serve as broad
conjectures that draw from prior research and current practice to
guide further study.
Development of the Preliminary Guidelines
In a series of panel presentations and small-group discussions over the two-day meeting, ITIG
members explored multiple questions, such as:
»»
»»
»»
What are the affordances of using interactive mobile technology to support mathematics
learning and teaching?
What are key concerns and challenges in using these technologies to support the
development of mathematical content and practices in K–3 classrooms?
What design considerations for implementing these technologies have emerged from the
experience, craft knowledge, and research shared during this meeting?
The ideas that ITIG participants shared were documented in slide presentations, video and
audio recordings, and notes taken during small-group discussions. Before, during, and after the
meeting, participants circulated resources relevant to the meeting’s topics (see Appendix B).
Drawing upon meeting discussions as well as these resources, meeting organizers summarized
the major ideas that surfaced and drafted a set of guidelines for implementing interactive
mobile technologies to support the development of mathematical thinking in K–3 classrooms.
These draft guidelines were then sent to all meeting participants for review and comment. This
report synthesizes the ideas and resources that emerged from this process.
2 National Governors Association Center for Best Practices, Council of Chief State School Officers (2010). Common Core State
Standards–Mathematics. Washington D.C.: Author.
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The Preliminary Guidelines
Five broad guidelines arose from the insights shared during and after the meeting (Table
2). Guideline 1 focuses on understanding and making best use of the features of interactive
mobile technologies that are well suited to promote mathematical thinking in young learners.
Guidelines 2 and 3 describe the pedagogical environments that may be necessary to foster
mathematical thinking with interactive mobile technologies. Guidelines 4 and 5 highlight the
individual and organizational supports that teachers may need to enact guidelines 1–3.
Table 2. Preliminary guidelines for implementing interactive mobile technologies to support the development of
mathematical thinking in K–3 classrooms
1. Take advantage of the
affordances of interactive
mobile technologies
to support conceptual
learning. Key affordances
include digital technology’s
capacities to:
a. Provide dynamic, multisensory representations of mathematical ideas.
2. Keep learning at the
forefront:
a. Know the learning goals.
b. Record and respond to user data.
c. Make student thinking visible and more widely shared.
d. Facilitate shared learning activities.
b. Understand relevant learning progressions.
c. Understand uses and activities that are developmentally appropriate.
d. Integrate digital with nondigital activities.
e. Provide opportunities for thoughtful, reflective practice.
3. Create a classroom culture
of exploration and sharing:
a. Encourage students to take risks and persist in the face of challenges.
b. Set norms by which students can take the lead in their learning.
c. Support students in building knowledge from what they already know.
d. Foster collaboration.
4. Provide teachers with
supports to use new
tools and to transform
instruction:
a. Offer opportunities to learn math content, math practices, and new technologies.
b. Promote teacher learning through collaboration with peers.
c. Enable teacher learning through small, iterative steps, ongoing over time.
d. Envision adults as facilitators of learning.
5. Establish organizational
arrangements to
support effective use of
technology:
a. Build adequate time for math instruction with interactive technologies.
b. Facilitate regular access to research.
c. Allow alternate teaching arrangements.
d. Ensure principal support for teacher development and classroom change.
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Guideline 1: Take advantage of the affordances of interactive mobile
technologies to support conceptual learning.
At the ITIG meeting, several participants presented ideas about the unique attributes of
interactive mobile technologies and the opportunities they offer to students to develop deeper
understandings of mathematical concepts. These participants recommended that educators
become familiar with the affordances of these technologies and take advantage of them in the
classroom. Key affordances include digital technology’s capacities to do the following.
Provide dynamic, multisensory representations of mathematical ideas. Meeting participants
discussed the dynamic, interactive digital tools that are available today on devices such as
iPads and other computer platforms and that can help students build their mathematical
knowledge. Like physical manipulatives, these digital tools or virtual manipulatives can help
students see, hear, and physically interact with abstract mathematical concepts and processes
through concrete demonstrations and tactile activities (e.g., with animations or games
that relate the numeral 5 with a picture of five blocks or animals, or with illustrations that
depict the process of addition by showing numerals change as objects are
added to a group or a line). Such tools can help students develop deeper
understandings of mathematical concepts by helping them access numerical
quantities and relationships through varied representations.
Notably, digital tools or virtual manipulatives can be even more powerful
than their physical counterparts. Meeting participants described how digital
technologies can overcome constraints of space and time in the classroom.
For example, digital simulations can depict minute amounts as well as
extremely large quantities; distances near and far; and long-term change
processes, such as aging or decay. Screen technologies can aid student
learning by providing multiple representations of mathematical concepts,
and they can also help to focus students’ attention on mathematical
processes. For example, a Web program might require students to rotate and manipulate a set
of geometric shapes before solving a problem with the shapes, thereby helping students to
focus on the problem’s geometric concepts and transformations. Screen applications such as
open number lines and number racks can also serve as general-purpose, flexible, and dynamic
tools that students can use to approach a variety of mathematics problems. (See the resources
in Appendix B, section 1.a.)
Record and respond to user data. Another important affordance of interactive mobile
technologies is the capacity to capture students’ verbal and behavioral responses to tasks or
problems and the potential this offers as a scaffold for furthering student learning. Meeting
participants stressed the importance of observing students’ strategies at solving problems
rather than the answers alone. Digital tools and devices collect a continuous stream of
data that may then be used to guide students’ attempts to navigate new mathematical
terrain. Because the path along which students learn new mathematical concepts may not
be linear, digital recordings of how students approach problems can provide teachers and
students—as well as “intelligent” adaptive learning systems on the devices themselves—
with detailed information to clarify the barriers students may face as they learn. Interactive
mobile technologies therefore offer important aids for gathering and managing data about
the complex pathways students may take as they try to master mathematical concepts and
practices. They also have the potential to provide individualized formative feedback to
students based on the data received and to help guide adjustments to students’ ongoing
learning experiences. (See resources in Appendix B, section 1.b.)
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Make student thinking visible and more widely shared. Several meeting participants who are
current classroom educators described the positive student responses they observe when
students use recording devices through educational apps or the iPad camera to document
their problem-solving approaches and to share their thinking with others. Multisensory
recordings allow students to review, reflect on, and critique their own as well as other
students’ text-based, pictorial, or spoken artifacts. The ease with which recordings can be
shared exposes students to different ways to solve problems and allows them to spot and
often correct their own misconceptions and errors. The ability to produce video and audio
recordings of their own work can help students view themselves as creators of their own
mathematical ideas and can be highly engaging. When repeated over time, recordings of
students’ mathematical thinking can provide students with proof of their own learning and may
offer encouragement and fuel motivation. (See resources in Appendix B, section 1.c.)
Facilitate shared learning activities. Meeting participants and the resources they distributed
emphasize the important role that social interactions play in learning and how interactive
mobile technologies can provide engaging ways to facilitate shared learning activities.
Participants described the value of having students interact with digital media in conjunction
with other students or adults. Significant learning can occur when students play games,
work together to solve problems, and create new ideas or solutions in shared digital spaces.
Interactive mobile technologies can provide dynamic mathematical stimuli around which
students may collaboratively engage, and they can support the sharing and distribution of
student work that are often needed for productive collaboration. (See resources in Appendix
B, section 1.d.)
Guideline 2: Keep learning at the forefront.
Meeting participants emphasized that interactive mobile technologies can play important roles
in mathematical learning only when learning goals are clear and technologies are strategically
harnessed to support these goals. Mathematical learning does not arise when students simply
have access to new technology tools; teachers must help establish learning targets for students
and know when and how to integrate technology to support achievement of these targets.
Know the learning goals. A recurring theme throughout the meeting was how critical it is for
teachers to have a clear understanding of the mathematical learning goals they want students
to achieve. Without such understandings, it is less likely the technology used in the classroom
will support strong student outcomes. New interactive digital tools and mobile apps are
continually coming online to serve different purposes. Working in contexts awash with digital
choices, several Maine educators described how important it is for educators to evaluate and
select these new digital tools to maximize alignment with learning targets. (See resources in
Appendix B, section 2.a.)
Understand relevant learning progressions. Reaching a learning target is typically a multistep
process, and the paths that students take vary. Meeting participants reflected on the learning
trajectories or pathways students take on their way to learning mathematical concepts, ideas,
and practices. Educators need to understand what the milestones may be for different learning
targets to select the digital tools that can best support students in meeting these milestones.
(See Appendix B, section 2.b.)
Understand uses and activities that are developmentally appropriate. Just as it is important
for teachers to choose and integrate digital tools aligned with student learning goals, it is
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important for teachers to select tools that match where students are in their
cognitive, socio-emotional, or physical development. Meeting participants raised
the point that some screen representations and activities can be enlightening for
some students but distracting or cognitively overwhelming for others.3 Even when
teachers identify specific digital resources that are appropriate for the learning
goals and developmental stages of individual students, they may still need to
help students focus on the most important components of the digital activities to
prevent distraction from core mathematical tasks. (See Appendix B, section 2.c.)
Integrate digital with nondigital activities. Meeting participants observed a limit
in how much students may stay engaged with digital tools as part of mathematics
lessons. Teachers need to mix on-screen time with off-screen time (including
discussion, movement, written expression, and manipulating physical objects)
to keep young students engaged and focused on learning. Based on current research, one
participant recommended a 5-to-1 ratio of nondigital to digital activities in the classroom. (See
Appendix B, section 2.d.)
Provide opportunities for thoughtful, reflective practice. Meeting participants noted the
importance of repeated practice in student learning but also acknowledged a downside when
repetition triggers disengagement and turns off student thinking. Digital technologies provide
students with the opportunity for repeated practice, keeping their minds “on” by presenting
ideas from multiple perspectives. Teachers, however, may wish to look for or tailor screen
activities to promote more reflective practice. (See Appendix B, section 2.e.)
Guideline 3. Create a culture of exploration and sharing.
To maximize the opportunities that technology offers to support strong mathematical
thinking, educators need to create and support classrooms where students are expected to
investigate, explore, invent, and generate mathematical ideas—both on-screen and off-screen,
independently and with peers. Participants suggested that interactive mobile technologies
cannot take the lead in developing young mathematical thinkers, but they can play an
important supporting role when classroom foundations are in place.
Encourage students to take risks and persist in the face of challenges. Multiple meeting
participants agreed that risk-taking and persistence in struggle are necessary for solving
mathematical problems and the development of strong mathematical thinking. They
suggested that students and teachers will not realize the full benefits of interactive mobile
technologies in mathematics learning unless habits of risk-taking and persistence are
embedded in daily work and applied to digital screen activities. (See Appendix B, section 3.a.)
Set norms by which students can take the lead in their learning. To develop strong
mathematical thinkers, teachers need to let students follow their own interests and come up
with their own solutions as they explore mathematical ideas and problems. This approach
should also apply in the use of interactive mobile technologies: students should be given
some freedom to play with digital tools and applications to engage their thinking during
mathematical activities. Empowering students to explore mathematics with technology
can help them see that knowledge and authority do not reside solely in the teacher or the
3 For example, apps that allow students to change the colors and shapes of objects when engaged in counting activities may
be helpful when such functions allow students to explore grouping patterns, but they may also prove distracting when such
choices become activities in themselves and pull students’ attention away from the mathematical tasks at hand.
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technology. Strong mathematical thinkers view themselves as agents in their own learning and
mathematical problem solving. (See Appendix B, section 3.b.)
Support students in building knowledge from what they already know. To help students
navigate new fields of learning, meeting participants discussed how teachers need to help
students connect new ideas and activities with prior knowledge and experiences. As students
explore mathematical concepts and problems using interactive mobile technologies, teachers
need to provide a bridge between past and present mathematical tasks and tools to bolster
students’ understandings and to keep them oriented toward learning goals. (See Appendix B,
section 3.c.)
Foster collaboration. Meeting participants discussed research indicating that collaboration and
social interactions can promote strong learning. Collaboration can help students see multiple
perspectives, which in turn can help deepen understandings of mathematical concepts and
ideas. As discussed above, interactive mobile technologies can facilitate shared learning
experiences and collaboration by providing recording channels and digital spaces that allow
students to share their work easily, and by providing activities in which students can distribute
roles. (See Appendix B, section 3.d.)
Guideline 4. Provide teachers with supports to use new tools and to
transform instruction.
Teachers play a seminal role in the classroom and need training to use technology effectively.
This training cannot focus solely on learning how to use new technological tools, which can
become obsolete very quickly. Teachers need to learn how new technologies may support or
enhance student learning of specific content and practices and how to adapt and expand their
pedagogical approaches to incorporate a variety of tools.
Offer opportunities to learn mathematical content, mathematical practices, and new
technologies. To help students develop deep understandings of mathematical content and
practices, teachers must have strong knowledge of the content and practices themselves
and should therefore have opportunities to strengthen this knowledge where it is weak.
Teachers also need to understand the trajectories that students may follow in pursuing specific
mathematical learning objectives and to learn pedagogical approaches that can help students
navigate these pathways. Further, when teachers have access to new technologies, they need
guidance and practice in integrating these technologies into instruction and in learning how
different digital tools may support different mathematical learning goals. (See Appendix B,
section 4.a.)
Promote teacher learning through collaboration with peers. Meeting participants described
how significant teacher learning can occur through collaboration with colleagues. They
therefore recommended that schools and districts help provide and structure opportunities for
peer collaboration that is focused on professional learning. (See Appendix B, section 4.b.)
Enable teacher learning through small, iterative steps, ongoing over time. Learning to
teach in new ways with new and ever-evolving technologies can be a challenge. Meeting
participants surmised that an effective way to help teachers change their instructional
approaches to incorporate new technological tools productively is to support teachers in
making small changes over time. Participants suggested that the time frames required for
meaningful change are typically on the order of months or years rather than days or weeks.
A more incremental process that includes opportunities for teachers to assess, reflect on,
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and adjust new learning and teaching strategies with interactive technologies may lead to
deeper understandings of what will work best with different students in their contexts and may
promote more sustained changes in professional practice. (See Appendix B, section 4.c.)
Envision adults as facilitators of learning. Meeting participants noted that if the overarching
goal is to promote students’ abilities to become independent mathematical thinkers, then
teachers may need to learn how and when to be a “guide on the side” rather than to serve
solely as a traditional “sage on the stage.” With the introduction of interactive technologies in
the classroom, opportunities arise for teachers and students to work together in new ways and
for students to engage in more active knowledge construction. For resources, see Appendix B,
section 4.d.
Guideline 5. Establish organizational arrangements to support effective use
of technology.
As new technologies become available for use in the classroom, organizational arrangements
such as school routines, schedules, and staffing structures may need to change to help
students and teachers take full advantage of the learning opportunities that the new tools
bring.
Build adequate time for math instruction with interactive technologies. Meeting participants
suggested that students need to be able to explore mathematical concepts and ideas to
become mathematical thinkers and that such exploration requires time. Teachers and schools
should therefore build in time for such activity during mathematics lessons, as well as time
that may be needed for students and teachers to become familiar with new interactive
technologies that can support mathematics learning but may require additional exploration to
learn how to use. (See Appendix B, section 5.a.)
Facilitate regular access to research. Teachers and administrators at the meeting described
their strong interest in current research and the guidance that it may provide to strengthen
their daily work in learning and teaching. They noted, however, that they don’t have easy
access to research literature or the time or capacity to read research papers—particularly those
that are highly technical. And research organizations that publish practitioner-specific materials
often charge fees that teachers must pay for themselves. Meeting participants encouraged
both school and educational research communities to find ways to help teachers stay current
with research on mathematics education and interactive technology and the practical
implications they offer to improve classroom instruction. (See Appendix B, section 5.b.)
Allow alternate teaching arrangements. Mathematics teaching with interactive technology
is most effective when teachers have knowledge and confidence in these domains. Meeting
participants encouraged schools and districts to consider alternate teaching arrangements
to help build teacher capacity and to deploy school assets in the most beneficial ways. For
example, team teaching may help educators pool their strengths and work together to build
professional knowledge. School leaders may also consider allowing teachers who have a
particular passion or expertise in mathematics to focus on mathematics instruction in the early
grades. (See Appendix B, section 5.c.)
Ensure principal support for teacher development and classroom change. As leaders
who manage staff and set the overall vision of learning and teaching within their schools,
principals play a critical role in supporting teachers who work on the frontlines to integrate
new educational technologies in the classroom and to improve student learning outcomes.
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Principals and other instructional leaders must understand and promote the many affordances
of interactive technologies to enhance strong mathematical thinking in early grades, the
learning and teaching strategies that can best develop such thinking, and the organizational
structures that can allow such strategies to thrive. (See Appendix B, section 5.d.)
Conclusion
These guidelines are preliminary because they draw on knowledge shared among the
participants at the Interactive Technologies Inquiry Group meeting in November 2014 but
do not emerge from a comprehensive review of the literature nor a rigorous analysis of
existing practice. Consequently, the guidelines can be seen as conjectures that may provide
practical suggestions for classroom educators but that need further validation through
research and testing.
The first guideline encourages educators to understand and harness the special affordances
and dynamic opportunities that interactive technologies may offer student understandings of
mathematics concepts and practices. The second guideline encourages teachers to identify
clear mathematical learning objectives and to select technology tools to help meet these
objectives. As digital tools and apps grow in functionality, availability, and entertainment
value, educators need to keep primary learning goals in the forefront to prevent specific apps
or the technology itself from becoming the focus of student learning. The third guideline
recommends that schools and teachers create classroom cultures in which students are
expected to explore their own mathematical ideas and work with peers to solve problems.
A conjecture underlying this guideline is that interactive technologies can help to support
mathematical thinking among students only when this type of classroom culture is in place.
The fourth and fifth guidelines describe the individual and organizational supports that
teachers may need to learn to use interactive technologies in ways that foster mathematical
thinking among students.
Only the first guideline focuses exclusively on the features and affordances of interactive
technologies. The others focus on the instructional elements that need to be in place for
ambitious mathematics learning and teaching to occur. The emphasis on pedagogical,
cultural, and organizational requirements for strong mathematics learning indicates a belief
among meeting participants that interactive technologies by themselves cannot foster
strong mathematical thinking among students. Interactive technologies are engaging and
multifaceted aids in the classroom, but basic approaches toward mathematics learning and
teaching need primary attention.
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Appendix A.
Interactive Mobile Technologies in Early Mathematics Classrooms:
ITIG Participants
Damian Bebell, Assistant Research Professor, Boston College, Boston, MA
Bronwyn Bevan, Director, Institute for Research and Learning, Exploratorium, San Francisco, CA
Pam Buffington, Managing Project Director, Education Development Center, Inc., Gardiner, ME
Amy Busey, Research Associate, Education Development Center, Inc., Waltham, MA
Kara Carpenter, Co-Founder, Teachley, New, York, NY
Lisa Coburn, Grade 1 Teacher/Team Leader Pre-K–2, Washburn School, Auburn, ME
Jere Confrey, Joseph D. Moore Distinguished University Professor, North Carolina State University,
Cary, NC
Karen DeCarolis, Grade 1 Teacher, Crescent Park School, Bethel, ME
Sue Dorris, Administrator, East Auburn Community School, Auburn, ME
Bernadette Doykos, Research Associate, University of Southern Maine, Gorham, ME
Amber Eliason, Math Coach, Washburn School, Auburn, ME
Cathy Fosnot, CEO, New Perspectives on Learning, New London, CT, and Professor Emeritus of
Childhood Education, City College of New York, New York, NY
Jen Helms, Researcher, Inverness Research, Denver, CO
Lisa Hogan, Technology Integrator, Freeport High School, Freeport, ME
Shannon Larsen, Assistant Professor of Elementary Mathematics and Education, University of Maine
at Farmington, Farmington, ME
Linda Laughlin, Proficiency-Based Coordinator, RSU 18, Oakland, ME
Tiffany Lee, Research Scientist, University of Colorado, Boulder, School of Education, Boulder, CO
Ashley Lewis Presser, Senior Research Associate, Education Development Center, Inc., New, York, NY
Josephine Louie, Research Scientist, Education Development Center, Inc., Waltham, MA
Kelly McCormick, Associate Professor of Mathematics Education, University of Southern Maine,
Gorham, ME
Catherine McCulloch, Project Director, Education Development Center, Inc., Waltham, MA
Carol Miller, Technology Coach K–6, Auburn School Department, Auburn, ME
Heather Mitchell, Researcher, Inverness Research, Lopez Island, WA
Patricia Moyer Packenham, Professor of Mathematics Education and Leadership Programs,
Utah State University, Logan, UT
Mike Muir, Multiple Pathways Director, Auburn School Department, Auburn, ME
Marian Pasquale, Senior Research Scientist, Education Development Center, Inc., Waltham, MA
Laura Shaw, Principal, Washburn School, Auburn, ME
Patrick Shields, Executive Director, SRI International, Menlo Park, CA
Steve Spodaryk, Lead Technology Engineer, TERC, Cambridge, MA
Denyell Suomi, Grade 1 Teacher, Belgrade Central School, Belgrade, ME
Shawn Towle, NCSM Leader and Mathematics Teacher, Falmouth Middle School, Falmouth, ME
Phil Vahey, Director of Mathematics Learning Systems, SRI International, Menlo Park, CA
Brenda Wight, Grade 3 Teacher, Crescent Park School, Bethel, ME
Kerri Wingert, Graduate Researcher, University of Washington, Seattle, WA
Cathy Wolinsky, Instructional Technology Integrator K–4, Yarmouth Elementary School, Yarmouth, ME
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Appendix B.
Resources
The resources provided in this section were shared by participants at the Interactive Mobile
Technologies Inquiry Group meeting and the Interactive STEM team at EDC, and they are
organized by the topics discussed under each guideline. These resources do not represent
a thorough or complete literature review of the topics. Instead, they are resources the
contributors find informative, thought-provoking, or potentially useful for readers who may be
interested in exploring a topic further. Although some resources may be relevant for multiple
topics, they are listed only once.
1. Affordances of interactive technologies
a. Capacities to represent mathematical ideas and practices
Ginsburg, H. P., Carpenter, K., & Labrecque, R. (2011). Introduction to MathemAntics: Software for
children from 3 (age) to 3 (grade). Retrieved from http://www.tc.columbia.edu/i/a/document/18999_
Ginsburg_Carpenter_Labrecque_2011_WhitePaper.pdf
Ginsburg, H. P., Jamalian, A., & Creighan, S. (2013). Cognitive guidelines for the design and evaluation
of early mathematics software: The example of MathemAntics. In L. D. English & J. T. Mulligan
(Eds.), Reconceptualizing early mathematics learning (pp. 83–120). Dordrecht, Netherlands: Springer
Netherlands.
Math Learning Center. (n.d.). Free Apps from MLC. Retrieved from http://catalog.mathlearningcenter.
org/apps
Moyer-Packenham, P. S., & Westenskow, A. (2013). Effects of virtual manipulatives on student
achievement and mathematics learning. International Journal of Virtual and Personal Learning
Environments, 4(3), 35–50. Retrieved from http://doi.org/10.4018/jvple.2013070103
Sarama, J., & Clements, D. H. (2009). “Concrete” computer manipulatives in mathematics education.
Child Development Perspectives, 3(3), 145–150.
Vahey, P., Knudsen, J., Rafanan, K., & Lara-Meloy, T. (2013). Curricular activity systems supporting the
use of dynamic representations to foster students’ deep understanding of mathematics. In C. Mouza
& N. Lavigne (Eds.). Emerging technologies for the classroom: A learning sciences perspective,
(15–30). New York, NY: Springer.
b. Capacities to provide student feedback
Blair, K. P. (2013). Learning in critter corral: Evaluating three kinds of feedback in a preschool math
app. Proceedings of the 12th International Conference on Interaction Design and Children (pp.
372–375). New York, NY, USA: ACM.
Sedig, K., & Liang, H.-N. (2006). Interactivity of visual mathematical representations: Factors affecting
learning and cognitive processes. Journal of Interactive Learning Research, 17(2), 179–212.
c. Capacities to document and share student thinking
Vahey, P., Lara-Meloy, T., Moschkovich, M., & Velazquez, G. (2010). Representational technology for
learning mathematics: An investigation of teaching practices in Latino/a classrooms. Proceedings of
the 2010 International Conference of the Learning Sciences: Vol. 1 (pp. 285–292).
Yelland, N., & Kilderry, A. (2010). Becoming numerate with information and communications
technology in the 21st century. International Journal for the Early Years, 18(2), 91–106.
Hattie, J., & Timperley, H. (2007). The power of feedback. Review of Educational Research, 77(1),
81–112. doi: 10.3102/003465430298487
d. Capacities to support collaborative learning
Meltzoff, A. N., Kuhl, P. K., Movellan, J., & Sejnowski, T. J. (2009). Foundations for a new science
of learning. Science, 325, 284–288. Retrieved from http://www.ncbi.nlm.nih.gov/pmc/articles/
PMC2776823/
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Penuel, W. R., Pasnik, S., Bates, L., Townsend, E., Gallagher, L. P., Llorente, C., & Hupert, N. (2009). Preschool teachers can use a media-rich curriculum to prepare low-income children for school success:
Results of a randomized controlled trial. New York, NY & Menlo Park, CA: Education Development
Center, Inc., & SRI International.
Roschelle, J., & Leinwand, S. (2011). Improving student achievement by systematically integrating
effective technology. NCSM Journal of Mathematics Education Leadership, 13(2), 3–9.
Sarama, J. (2004). Technology in early childhood mathematics: Building blocks as an innovative
technology-based curriculum. In D. H. Clements, J. Sarama, & A.-M. DiBiase (Eds.), Engaging young
children in mathematics: Standards for early childhood mathematics education (pp. 361–375).
Mahwah, NJ: Lawrence Erlbaum Associates.
2. Mathematics learning and teaching strategies
a. Importance of setting clear learning targets
Heath, G. (2002). Using applets in teaching mathematics. Mathematics and Computer Education,
36(1), 43–52.
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c. Developmental appropriateness of interactive technologies
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d. Allocation of time with digital and nondigital activities
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e. Need for thoughtful, reflective practice
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3. Classroom culture
a. Importance of promoting risk-taking and persistence in face of struggle
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b. Need to build student agency and ownership over learning
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d. Role of student collaboration in mathematics learning
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4. Teacher supports
a. Teacher content and pedagogical knowledge in mathematics and technology
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b. Role of collaboration in professional learning
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5. Organizational arrangements
a. Instructional time for early mathematics learning and technology use
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b. Access to current educational research
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d. Role of principals in mathematics learning and technology use
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Educational Administration Quarterly, 46(1) 31–56Appendix A. Interactive Mobile.