Call for Chapters for APME 2016
Annual Perspectives in Mathematics Education (APME) 2016:
Mathematical Modeling and Modeling Mathematics
Deadline March 1, 2015
The 2016 Annual Perspectives in Mathematics Education (APME) volume: Mathematical Modeling and
Modeling Mathematics will consist of chapters that represent current thinking and promising practices
devoted to effectively incorporating models and mathematical modeling in the teaching and learning of
mathematics K–12. The focus on mathematical modeling in the Common Core State Standards for
Mathematics (CCSSM) (National Governors Association Center for Best Practices & Council of Chief
State School Officers, 2010) is of particular interest because it had not been given explicit and detailed
attention in previous U.S. standards documents for school mathematics. Additionally, mathematical
modeling holds a privileged place in the CCSSM as it is the only topic that is both a conceptual category
and a Standard for Mathematical Practice.
In light of the heightened attention to using models and mathematical modeling in school
mathematics, both nationally and internationally, this volume will examine the benefits and challenges of
implementing modeling through multiple lenses—clarifying constructs; task and curriculum design
considerations, especially in a digital world; effective instructional practices, including elaborating
equitable and culturally relevant pedagogies; student learning; assessment of modeling experiences; and
supporting teachers’ learning.
Chapter manuscripts should make strong links between research and practice and highlight
important issues as they relate to implementing models and mathematical modeling in the classroom. Each
chapter should appeal to a broad audience, which may include mathematics educators in a variety of
capacities, such as curriculum designers/developers, assessment developers, teachers, teacher leaders,
professional development leaders, mathematics teacher educators, and researchers. Suggested topics for the
2016 APME include, but are not limited to:
Understanding Models and Modeling
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Describe and discuss the terms and constructs associated with models and modeling. What are the
various meanings associated with “model,” “modeling,” “building a model,” “using a model,” etc.?
How are these terms used similarly and differently across grades, contexts, and strands of mathematics
(e.g., algebra, geometry, statistics)? What role do models and modeling serve in teaching and learning
and/or in mathematics as a discipline?
How is modeling related to problem solving? To mathematizing? To applied mathematics? For each
comparison, how are the ideas similar? How are they different?
Describe and illustrate the differences between and among types of modeling such as descriptive,
analytic, deterministic, and stochastic.
Discuss the historical development and role of mathematical modeling in school mathematics.
Discuss connections between the Common Core State Standards for Mathematics and the Next
Generation Science Standards in terms of mathematical modeling. How is “modeling” used in each
document? How can curricula and instruction leverage these connections?
Modeling-based Curriculum Materials and Resources
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How does the treatment of models and modeling in the U.S. compare with the treatment in curricula of
other countries?
How can existing curriculum be used or adapted to support the teaching of mathematical modeling?
Discuss how modeling might play out in a curriculum at a particular grade or grade band with attention
to how the practice of modeling mathematics connects to the other Standards for Mathematical
Practice.
The accessibility of modeling software, even at the elementary grades, through visual programming
languages such as “Scratch” has opened more widely connections between mathematics and
computational thinking. How can this access be leveraged to help students learn the art of
mathematical modeling? How can this access be leveraged to allow students to design simulations and
investigate the behavior of models whose mathematical analysis may be beyond their understanding?
The ready availability of large data sets on the Internet allows for the classroom experience to be
realistic and meaningful. How can such data sets be used effectively in the K-12 classroom? What
connections to the CCSSM are most readily made when using such data sets?
Discuss findings from innovative uses of models and/or modeling within digital environments, using
current technologies and tools for modeling; as part of project-based learning; as part of STEMfocused schools; as part of a computer science curriculum; and in conjunction with integrated,
connected, or theme-based curricula. What technologies exist (or need to be developed) that facilitate
model building and how should they be incorporated into the curriculum?
What innovative opportunities for teaching, learning, and engaging in mathematical modeling are
afforded by new technologies (e.g., mobile technologies, GPS-enabled technologies)? By emerging
deeply digital instructional materials?
Teaching and Learning with Modeling
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What can a modeling and models perspective contribute to theories of learning mathematics?
Discuss and explore how models and modeling tend to be used at various grade levels.
Describe and illustrate how the practice of mathematical modeling can support problem-based learning
that enables students to develop important mathematics.
Discuss findings for ways models and modeling can support (or limit) students in engaging in other
mathematical practices or processes in learning and doing mathematics.
What interdisciplinary approaches are effective for teaching and learning mathematical modeling, and
what are their distinguishing features?
Discuss findings on effective practices and/or approaches for teaching and learning with models and
modeling, as well as challenges and/or limitations. Discuss findings on effective levels of scaffolding
for modeling activities, particularly in the introductory phase of learning mathematical modeling.
Discuss findings on how students learn from and with models and/or modeling. Discuss the differences
in using mathematical modeling as a strategy for motivating and learning a topic in mathematics and
using mathematical modeling as a strategy for motivating the continued study of mathematics
(modeling as a means to an end and as an end in itself).
Mathematics can be used to understand processes or phenomena, and mathematical models can be
used to predict outcomes or generate solutions. How can mathematical modeling be used as part of
offering students opportunities to think critically with mathematics?
How do students make connections or negotiate between mathematical models (of real world
situations) and their own experiences or firsthand knowledge of the real world?
What are the affective components of mathematical modeling in the students’ sense of the subject of
mathematics and themselves as learners and users of mathematics and mathematical thinking?
How can mathematical modeling support teaching mathematics for social justice?
Discuss ways models, modeling contexts, and modeling and can be used as part of equitable and/or
culturally relevant pedagogies. How can modeling be used to integrate students’ out-of-school
practices, connect with their family and community resources and backgrounds, and/or explore issues
of social justice?
Assessing Mathematical Modeling
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How should mathematical modeling be assessed? What can we learn from other disciplines in this
regard? In particular, in the English Language Arts Standards, the assessment of open-ended student
writing projects is commonplace. How can this help inform the assessment of mathematical
modeling?
What learning progressions and assessment tasks are appropriate for different courses and grade
levels?
Describe how students’ work with models and modeling can be assessed (formatively and/or
summatively) or used as a tool for making students’ thinking more visible as part of assessment.
Explore how students’ responses to models and modeling activities can be used to gain insights into
their mathematical thinking.
Supporting Teachers’ Learning about Mathematical Modeling
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What does research and/or the wisdom of practice suggest about the mathematical knowledge for
teaching (MKT) that supports effective teaching of mathematical modeling or modeling mathematics
at particular grades or grade bands?
Discuss supporting prospective and practicing teachers’ conceptions of [models and] modeling and
how they learn to integrate [models and] modeling into their instructional practice.
Discuss the professional development of in-service teachers with regards to mathematical modeling?
What does research say about their current background in mathematical modeling? What supports are
most effective for improving their knowledge of mathematical modeling and their teaching of
mathematical modeling?
Details for Submission
Interest in submitting a chapter manuscript to this APME volume should be indicated by submitting an
Intention to Submit form to Christian.Hirsch@wmich.edu by March 1, 2015.
The full chapter manuscript is to be submitted electronically by May 1, 2015 to the same email address.
Late or partial manuscripts cannot be considered. All chapter submissions will be blind peer-reviewed
and authors will receive feedback within 8 weeks.
Details regarding submission requirements will be sent once your Intention to Submit form is received.
Generally speaking, the submitted manuscript will require:
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use of standard word processing software, such as Microsoft Word, with a font size of 12 (preferably
Times New Roman)
an abstract of 200 words or less. You may wish to refer to your Intention to Submit form and edit what
you have already provided as a possible abstract
all material be double-spaced, including abstract, quoted matter, lists, tables, notes, references, and
bibliographies. Manuscripts should not exceed 3,500 words (14 pages), including the references
a separate cover sheet with manuscript title and name(s) of author(s) in the order of authorship and
including affiliations. The lead author should provide full contact information. Because initial
decisions on submitted manuscripts will be made during the summer, lead authors should ensure some
appropriate means of contact, or designate another individual to receive information.
not referencing your own work in a way that compromises the blind-review process. All blinded
references can be re-inserted should your work be accepted for publication.
all references cited in the manuscript be listed at the end of the manuscript using the Chicago Manual
of Style, 16th edition. NCTM uses the humanities style, which gives the full names of all authors and
editors.