Electronic Supplementary Material
Kuzle, A., & Biehler, R. (2015). Examining mathematics mentor teachers’
practices in professional development courses on teaching data analysis:
implications for mentor teachers’ programs. ZDM Mathematics Education,
47(1). doi: 10.1007/s11858-014-0663-2.
Online Resource 1: Brief descriptions of the five mentors’ one-day PDs
PD and its
title
PD 1: Data
analysis with
dynamic tools
PD 2: Data
analysis for the
secondary
mathematics and
science classroom
using the software
Fathom
PD 3:1 Fathom: An
interactive
computer
program for our
school?
Structure
Introduction:
 participant introduction (previous experiences and expectations)
 two inputs:
 Introduction: statistics and probability in the state standards
 Statistics—particularly diagrams in primary school: On what
can we build the secondary curriculum?
Block I:
 learning Fathom basics with eFathom
 solving a given problem using Excel, Fathom, and by hand
(stationary learning)
 reflection on the three tools with respect to time, visualization, and
ease of use
Block II:
 consolidation of technical skills in Fathom by working on a new
problem
Reflection and closure:
 discussion about implementation of Fathom in school
 reflection on the day with respect to teachers’ expectations
Introduction:
 input
 Data collection and various approaches for creating diagrams
without PC
Block I:
 input on Fathom—a short trip through a new statistical program
 learning Fathom basics with eFathom
Block II:
 filling in a survey whose results served as a dataset for data
analysis activities with Fathom
 first steps in using Fathom for creating statistical graphs
Block III:
 critical analysis of statistical graphs (role of previous knowledge for
what will be seen in graphs)
Reflection and closure:
 query as evaluation of the PD on implementation of Fathom in
school
Introduction:
 input
 Statistics and probability in the state standards and the
curriculum: new emphases, and teaching statistics using
Fathom
Block I:
 demonstration of Fathom affordances with a focus on data
1 PDs 3 and 4 were planned together, but were separately implemented by
the two teams. The two slightly differed, which explains differences in the
table.
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PD 4: Fathom: an
interactive
computer
program for our
school?
PD 5: Data
collection and
data analysis in
the mathematics
classroom—a PD
for mathematics
mentor teachers2
collection and data analysis
 learning Fathom basics by solving a given problem with the help of
mentors and/or prepared help cards
Block II:
 a theoretical input on boxplots incl. creating a “human boxplot”
 creating boxplots with Fathom and interpreting them
Reflection and closure:
 discussion about implementation of Fathom in school and open
questions
 reflection on the day with respect to teachers’ expectation
Introduction:
 input
 Statistics and probability in the state standards and the
curriculum: new emphases, and teaching statistics using
Fathom
Block I:
 input on Fathom—a short trip through a new statistical program
 learning Fathom basics by solving a given problem with either
eFathom or with the help of prepared help cards (here the teachers
decided on the self-learning option)
Block II:
 demonstration of Fathom affordances with a focus on comparing
numerical and categorical data
 working on selected tasks on the basis of the previous input
Reflection and closure:
 mentor’s talk on the usefulness of Fathom
Introduction:
 two inputs
 Implementation of Fathom in teaching statistics incl.
demonstration of Fathom affordances (e.g., diagrams,
distributions of mean values, boxplots)
 Statistics: On the path towards new task culture? (standards,
data analysis cycle, comparison of schoolbook tasks, goals for
statistics teaching and learning)
Block I/III:
– parallel workshops
 Workshop 1: learning Fathom basics with eFathom followed by
solving a task using Fathom
 Workshop 2: task culture in data analysis (e.g., solving tasks with
different foci, such as analysis of two categorical characteristics,
population pyramid, boxplots, points of concurrency)
Block II:
 input (with discussion) on teaching data analysis with a particular
attention to the content goals of statistics, and the process goals for
using digital media in schools
Reflection and closure:
 discussion about implementation of Fathom in school and
comparison with Excel (opportunities and obstacles)
2 PD was organized for other mathematics mentor teachers from the region
and lasted 7 hours.
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Online Resource 2: Coding scheme for analyzing DZLM design principles
Category: Design
Subcategory: Training
principle
practices
Learner-orientation Needs and concern
alignment
Case-based
learning
Mentors consider
participants’ concerns and
needs with respect to the
topic of the PD, and use
these as an input to arrange
training activities.
Considering teachers’
individual prerequisites
Mentors consider the
individual prerequisites of
the participants, which
influence their subjectmatter and methodological
decisions.
Focus on active learning
The mentors organize
activities in a manner that
allows participating
teachers to become active
members in a teaching–
learning context of the PD.
In addition, the participants
can also be active members
during the planning and
implementation phase of
the PD.
The mentors focus on
participating teachers’
experiences in which they
attain their expertise.
Focus on teachers’
experiences
Using examples from
student work
Competence
development
Description
Explicit development of
competences
Implicit development of
competences
The mentors use different
student artifacts using
various tools (e.g.,
handouts, videos), which
serve as a context for
subject-matter or
methodological activities
and discussions.
The mentors explain what
competences are promoted,
and how goals for their
long-term teaching–
learning practices are
coherent.
The mentors focus solely on
the activity itself ignoring
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its over-reaching purpose.
Application of
various
instructional
formats
Stimulating
collaboration
Methodological diversity The mentors create
interactive teaching–
learning opportunities for
the participating teachers
through which they actively
engage in PD
implementation, foster
collaboration, development
of competences, and/or
focus on student thinking
and learning.
Short-term
The mentors focus on
collaboration
creating possibilities for
discursive activities
relevant to participating
teachers (e.g., their teaching
practices).
Sustainable long-term
collaboration
Fostering (self-)
reflection
Reflection on teaching
practices
The mentors focus on
creating an environment
that fosters long-term
collaboration (e.g.,
constitution of tandems,
planning groups, PLCs).
The mentors prompt
teachers to reflect on their
teaching practices. This
serves as a basis for
considering an
implementation of the
newly introduced PD ideas
into their mathematics
lessons.
Reflection on the task
The mentors foster
reflection on different task
dimensions (e.g.,
competences, alternative
solution paths,
differentiation
possibilities).
Reflection on the
transfer possibilities
The mentors prompt
teachers to critically
consider to what extent the
newly introduced ideas fit
their daily classroom work
(e.g., practices, routines).
Reflection on student
The mentors prompt
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work
teachers to think about
student solutions and
possible student thinking.
In this way they can better
understand them, and
anticipate their thinking
among others.
Reflection on beliefs
The mentors encourage
teachers to think about
whether, and to what
extent, the newly presented
ideas fit their goals for
student learning, and their
own beliefs about
mathematics, and teaching
mathematics.
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