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DRAFT: NOT FOR DISTRIBUTION WITHOUT AUTHOR CONSENT
TO BE PUBLISHED (in 2011) in C. Batenero et al., (Eds.), Teaching statistics in school
mathematics. Challenges for teaching and teacher education. New York: Springer. [This
book is the outcome of the ICMI-18 Study conference from Monterrey Mexico June 2008]
TEACHING TEACHERS TO TEACH STATISTICAL INVESTIGATIONS
Katie Makar and Jill Fielding-Wells
The University of Queensland Australia
k.makar@uq.edu.au, j.wells2@uq.edu.au
Wild and Pfannkuch (1999) described the investigation cycle as a dimension of statistical thinking
that statisticians use for inquiry; it includes five key elements (PPDAC): Problem, Plan, Data,
Analysis, and Conclusion. Despite its importance for the discipline, the statistical investigation
cycle is given little attention in schools. Teachers face unique challenges in teaching statistical
inquiry, with elements unfamiliar to many mathematics classrooms: Coping with uncertainty,
encouraging debate and competing interpretations, and supporting student collaboration. This
chapter highlights ways for teacher educators to support teachers’ learning to teach statistical
inquiry. Results of two longitudinal studies are used to formulate recommendations to develop
teachers’ proficiency in this area.
1. Introduction
Wild (1994) defined statistics as an inquiry process “concerned with finding out about the
real world by collecting, and then making sense of, data” (p. 164). Despite calls for more
emphasis on the investigative process (Moore, 1997), the focus in school statistics
continues to be on calculations, procedures, and graphs (Sorto, 2006). Some countries now
include statistical inquiry or investigations (implicitly or explicitly) in their national
curriculum or curriculum standards (for example, see Davies, 2007; NCTM, 2000;
Australian Curriculum, Assessment and Reporting Authority, 2009; and New Zealand
Ministry of Education, 2007), but it is uncertain the extent to which schools in these
countries have successfully implemented statistical investigations.
Statistical inquiry put forward by Wild and Pfannkuch (1999) described five steps in the
investigative cycle (PPDAC): Problem, Plan, Data, Analysis, and Conclusions (Figure 1).
Little research has focused on the whole inquiry process (Lavigne and Lajoie, 2007).
Instead, much of the research in statistics education has centered on data analysis,
predominantly with well-defined problems in which many of the difficult decisions have
been obscured. In his review of research in statistics education, Shaughnessy (2007, p. 963)
emphasized the implications of this issue:
Most of the current statistics education in the United States places a heavy emphasis on the
DAC parts of the Investigative cycle, but precious little time is devoted in classrooms to the PP
parts. If students are given only prepackaged statistics problems, in which the tough decisions
of problem formulation, design and data production have already been made for them, they
will encounter an impoverished, three-phase investigative cycle and will be ill-equipped to deal
with statistics problems in their early formation stages.
This chapter overviews key understandings that teacher educators need to know in
order to develop teachers’ proficiency in teaching statistical inquiry. We focus in particular
on the investigation cycle (see Pfannkuch & Ben-Zvi, this volume, for further discussion of
developing teachers’ statistical thinking more broadly). An example of a statistical
investigation in a middle school classroom is used to illustrate each step of the investigative
DRAFT: NOT FOR DISTRIBUTION WITHOUT AUTHOR CONSENT
TO BE PUBLISHED (in 2011) in C. Batenero et al., (Eds.), Teaching statistics in school
mathematics. Challenges for teaching and teacher education. New York: Springer. [This
book is the outcome of the ICMI-18 Study conference from Monterrey Mexico June 2008]
cycle. Challenges encountered in teaching investigations are discussed to alert teacher
educators to key areas to focus their work with teachers. Two longitudinal studies are used
to highlight ways that researchers have approached supporting teachers to develop this
proficiency.
2. What is a Statistical Investigation?
Fig 1 The investigative cycle in statistical inquiry (Wild & Pfannkuch, 1999)
Wild and Pfannkuch’s (1999) landmark paper described four dimensions of thinking used
in statistical inquiry of authentic problems: Phases of the investigative process (PPDAC,
Figure 1), types of thinking used, ongoing and iterative mental questioning (interrogating),
and dispositions required. Problems in school statistics are frequently well-structured,
where the planning, data collection, analysis and conclusion are streamlined and
unproblematic. Most problems in life, however, are ill-structured. In ill-structured
problems, the problem definition or solution pathways have a number of ambiguities that
need to be addressed (King & Kitchener, 1994). They are unresolved, often with conflicting
evidence, requiring students to consider potential causes of the problem, and generate
multiple ideas on how to solve it (Walker & Leary, 2008). Ill-structured problems often
require discussion to negotiate which characteristics of a phenomenon can be measured to
address the problem under investigation. For example, if the question being addressed is,
“Which brand of bubble gum is the best?”, then students will need to debate qualities
valued in bubble gum that might qualify as ‘best’ and identify possible measures to capture
these qualities. Statistical inquiry situates statistical investigations within these complex
settings.
Example of a Statistical Investigation: Exploring Flight
Below we give a brief example of a statistical investigation embedded in a middle school
science unit designed to develop students’ understanding of forces used in flight.
Problem. The driving question for this unit was “What is the best design for a loopy
aircraft?” In the unit, students constructed a loopy aircraft (made by affixing a paper loop to
DRAFT: NOT FOR DISTRIBUTION WITHOUT AUTHOR CONSENT
TO BE PUBLISHED (in 2011) in C. Batenero et al., (Eds.), Teaching statistics in school
mathematics. Challenges for teaching and teacher education. New York: Springer. [This
book is the outcome of the ICMI-18 Study conference from Monterrey Mexico June 2008]
each end of a plastic straw). In performing initial test flights, they immersed themselves in
the problem and debated and clarified the issue of ‘best’ within the driving question. They
defined ‘best’ as the aircraft able to fly the greatest distance. Once clarified, students
extended understanding of the science of flight through research and direct teaching.
Plan. In the second investigation step, students considered factors that could be altered
on the loopy aircraft. They defined three variations (each) for the width, length and
placement of loops on the straw, requiring construction of 27 aircraft. The students
developed measurement protocols and a sampling design that would limit unexplained
variability and anomalies (by flying each plane 5 times).
Data Collection. Once data collection was planned, students recorded flight distances of
five flights for each of the twenty-seven aircraft constructed. Upon reviewing the data, the
students recognized a need to ‘clean’ the data as measurements had been inconsistently
recorded with a mixture of meters and centimeters.
Data Analysis. When faced with 135 data points, students initially made superficial
judgments about the best design (such as the single plane flying the greatest distance). In
discussing this issue, they decided to add the five flight distances together to create a single
measure for each aircraft and moderate the effect of anomalies. The teacher used this
opportunity to introduce the mean. Students used Tinkerplots (Konold & Miller, 2005) to
generate distributions of the mean distances to compare flights for each variable; for
example, the distribution of distances of planes with narrow wings could be compared to
those with medium and wide wings.
Conclusions. Students used means to draw conclusions about the most advantageous
width, length and placement. Because the optimal width, length, and placement differed
from the aircraft that flew the furthest, a student raised the possibility that interactions
between variables had not been considered (a concept students might encounter in a second
university statistics course). Inherent in this insight was the potential to initiate a new, more
sophisticated PPDAC cycle with design modifications to further improve distance. At the
end of the unit, students wrote a final report articulating their findings, conclusions, and
justification.
3. Assisting Teachers with Statistical Investigations
By breaking down the PPDAC cycle into its five phases, we draw on the literature to
identify key issues to consider in teaching statistical investigations.
Problem
The problem posing phase is essential in the investigation cycle as the investigation
question acts as the initial ‘hook’ and driving focus for the investigation. Research indicates
that a critical aspect of this phase is for teachers to learn “to use the driving question to
orchestrate a project” (Marx, et al. 1994, p. 535). Questions developed for statistical
investigations need to be:
Interesting, challenging and relevant (Crawford, Krajcik, & Marx, 1998; Groves &
Doig, 2004). The Flight unit was motivating to students as it tapped into their interest in
paper planes and was of a low-stakes competitive nature. The level of cognitive
engagement was challenging, but attainable for middle school students.
DRAFT: NOT FOR DISTRIBUTION WITHOUT AUTHOR CONSENT
TO BE PUBLISHED (in 2011) in C. Batenero et al., (Eds.), Teaching statistics in school
mathematics. Challenges for teaching and teacher education. New York: Springer. [This
book is the outcome of the ICMI-18 Study conference from Monterrey Mexico June 2008]
Statistical in nature (Makar & Confrey, 2002; Makar & Rubin, 2009; Arnold, 2008b).
Questions need to be answered through gathering and interpreting data. In the Flight
Unit, the students collected data to justify and defend their choice of ‘best’ aircraft.
Furthermore, the data offered sufficient complexity to generate interesting results.
Ill-structured and ambiguous (Borasi, 1992). Depth of investigation can be achieved by
using questions which are ill-defined as they enable negotiation by students. Vague
words such as ‘typical’, ‘best’, ‘largest’ and ‘most appropriate’ are particularly useful
as they need definition. For example, “What is the best design for a loopy aircraft?”
raised issues such as whether ‘best’ was an aircraft that flew the farthest, the most
accurately, or spent the longest time airborne, each of which would lead the
investigation into separate statistical areas.
There is significant scope here to assist teachers with the skills needed to develop problems
worthy of investigation, or to guide students to do so (Allmond & Makar, forthcoming-
2010). One particularly critical aspect is the knowledge and understanding of statistical
procedures that teachers require. In order to ensure that an investigation will develop
statistical knowledge, teachers require a certain depth of knowledge and experience to plan
and conduct statistical investigations (Arnold, 2008a).
Planning
School statistics often results in students being presented with data manufactured to
demonstrate a pre-determined result. Students utilize cues to decide which statistics to use,
for example by the topic of the preceding lesson. Teachers and students have little
experience with the reasoning and decision-making needed for planning data collection,
recording methods, and appropriate statistical analyses. Research suggests that statistical
content knowledge is viewed by teachers as the largest threat to perceptions of their
competence (Hills, 2007) and thus suggests that developing solid statistical understandings
in teachers would empower more investigative approaches. With better statistical
knowledge and experience, teachers can give students more control in planning
investigations and support them to make essential methodological decisions about, for
example, the use of populations and/or sample sizes, and validity and reliability of data
collection and analysis (Fielding-Wells, forthcoming-2010).
Data Collection
Investigations enable students to choose their method of data collection, providing them
with authentic feedback of their planning decisions that will generate deeper knowledge of
methodology and efficiency (Krajcik et al., 1998). Teachers accustomed to directing
students’ methodology can be helped to recognize the deeper learning opportunities that
arise when students are allowed to face problems and deliberate ways to resolve issues that
arise during data collection.
Data Analysis
In most classrooms, data analysis is the entry point of student learning in statistics. Data
presented to students have usually been cleaned and carefully selected to illustrate the
lesson purpose. In reality, data are more complex. Issues that arise in managing complex
DRAFT: NOT FOR DISTRIBUTION WITHOUT AUTHOR CONSENT
TO BE PUBLISHED (in 2011) in C. Batenero et al., (Eds.), Teaching statistics in school
mathematics. Challenges for teaching and teacher education. New York: Springer. [This
book is the outcome of the ICMI-18 Study conference from Monterrey Mexico June 2008]
data can springboard discussions about treatment of outliers, errors, and unanticipated
results. Allowing students to represent their own data also encourages the process of
changing data representations to reveal alternate insights (Cobb, 1999). While time
constraints are a valid concern for teachers, when students are allowed to identify errors
and inefficiencies and negotiate alternate activities, it develops depth of understanding,
along with perseverance and efficiency.
Conclusion
The ability to communicate and critique statistical processes is necessary for the
development of statistical literacy (Gal, 2002). In the conclusion phase, students interpret
their results, reflect on the process, and draw critical inferences. At this time, teachers need
to draw upon skillful questioning techniques and understanding of statistical analyses in
order to facilitate students’ reasoning and assist them to connect their conclusions to the
evidence they’ve collected..
Other Issues
Through participation in the entire PPDAC cycle, students deepen understandings of the
complexity of statistical processes. However, teachers need to allow students to make their
own mistakes and support students in managing many of the challenges that arise. In doing
so, they develop students’ resilience and motivation as they implement plans and actions
which result in improved understanding of their world. As a result, there is necessarily less
order in the classroom that teachers find counter-intuitive to teaching, and the noise and
increased difficulty monitoring student on-task behavior confronts existing classroom
norms.
4. Challenges in Teaching Statistical Investigations
Developing students’ inquiry skills requires teachers to proficiently engage students in
statistical inquiry and support them through the investigative cycle. Those involved in
teacher education and professional development must understand the nature of these
challenges in order to support and validate teachers’ experiences in learning to teach
statistical inquiry. For example, teachers are typically frustrated with initial attempts at
implementation (R. Anderson, 2002). “There is a danger that … initial difficulties with
implementation and disappointment with student performance can lead to a premature
rejection of [these] new pedagogies” (Krajcik et al., 1998, p. 341). Researchers have
identified a number of issues to consider when supporting teachers to teach inquiry – in
statistics, mathematics and the sciences:
Envisioning inquiry. Teachers often have difficulty envisioning inquiry in the
classroom. Providing resources for teachers to use with students, allowing time to plan
and learn collaboratively with other teachers, and creating opportunities to observe
students in learning inquiry (R. Anderson, 2002; J. Anderson, 2005) will support them
to develop this vision.
New teaching practices. Teachers take on new roles when teaching inquiry, often
requiring unfamiliar skills (Arnold, 2008a; Crawford, 2000; Ponte, 2001). These roles
highlight the diversity and complexity of teaching inquiry, reflecting shifts in the nature
of teacher-student interactions. For example, the teacher takes on the role of motivator,
DRAFT: NOT FOR DISTRIBUTION WITHOUT AUTHOR CONSENT
TO BE PUBLISHED (in 2011) in C. Batenero et al., (Eds.), Teaching statistics in school
mathematics. Challenges for teaching and teacher education. New York: Springer. [This
book is the outcome of the ICMI-18 Study conference from Monterrey Mexico June 2008]
modeler of inquiry practice, collaborator and mentor. Teaching practices are extended
with teachers becoming learners and innovators. Teacher educators can alert teachers to
these new practices and discuss their implications.
Managing uncertainties. Teachers need support to manage ambiguities and limitations
in applying mathematical ideas. This will help them develop an ability in students to
recognize the tentativeness of results, dependence on context, and that outcomes can be
continually improved (Borasi, 1992). Experience as learners in conducting statistical
investigations gives teachers direct experience in managing uncertainties.
Validation and support. Emotional support and validation are needed for teachers to
cope with new teaching practices, competing time and curricular pressures, and
frustration (Marx et al., 1994). The discomfort and risk-taking needed by teachers
necessitates non-judgmental observations of their teaching, particularly in initial
attempts (Hills, 2007).
Creating a classroom culture of inquiry. Teachers need guidance to engender a culture
of inquiry in their classroom. Extended time is needed to develop effective student
collaborative relationships and to learn to engage students in meaningful discussions
(Crawford, Krajcik, & Marx, 1998).
Content knowledge. Disciplinary knowledge is central to teachers’ ability to cope with
the unexpected issues endemic to inquiry (Arnold, 2008a). Teacher educators should
embed opportunities to develop teachers’ content knowledge in investigations to model
how teachers should develop students’ content knowledge.
Accountability. Support from teacher educators coupled with informal pressure or
accountability is important for continuing improvement (Guskey, 2002).
Teaching teachers to incorporate statistical investigations into their classrooms is an
ongoing challenge. Workshops or short-term professional development programs are not
sufficient to sustain innovation. In these next two sections, we describe two projects aimed
at developing teachers’ practices over time which address many of the challenges we
highlighted above. Both projects engage long-term scaffolds that assist teachers in
embracing the curriculum and pedagogies associated with statistical investigations.
Additionally, they focus on shifting teachers’ epistemological beliefs about statistics from a
set of methods and calculations, towards statistics as an investigative data-rich process of
understanding the world. The first project, based on collaboration among researchers in the
European Union, focuses on developing an online community of practice to support
teachers in embracing statistical investigations (see also Meletiou-Mavrotheris & Serrado,
this volume). The second project, based on a longitudinal study in Australia, works with
teachers both individually within their classrooms and collectively through regular
professional development over several years to support their move to inquiry-based
teaching in statistics. We use the diverse approaches of these projects to suggest ways to
develop teachers’ proficiency with teaching statistical investigations.
5. The EarlyStatistics (ES) Project
The aim of the project was to support teachers’ knowledge of statistical investigations
through online interactions and six modules that guided them through readings, teaching
activities, and reflections. The online modules addressed key phases of a statistical
DRAFT: NOT FOR DISTRIBUTION WITHOUT AUTHOR CONSENT
TO BE PUBLISHED (in 2011) in C. Batenero et al., (Eds.), Teaching statistics in school
mathematics. Challenges for teaching and teacher education. New York: Springer. [This
book is the outcome of the ICMI-18 Study conference from Monterrey Mexico June 2008]
investigation (problem-posing, data collection, data analysis and interpretation), initial
experiences in teaching statistical investigations, and reflections on their learning
(EarlyStatistics Consortium, 2008; Meletiou-Mavrotheris et al, 2008b).
The EarlyStatistics project design (Meletiou-Mavrotheris et al, 2008a) embraced
characteristics of effective learning environments (National Research Council, 2000)—
learning-centered, knowledge-centered, assessment-centered, and community-centered. It
developed key ideas of statistical problem-solving using the GAISE framework (Franklin et
al., 2007) through increasingly sophisticated levels of problem-posing, data collection, data
analysis, and interpretation, with a focus throughout on variability concepts. Statistical tools
such as Fathom (Finzer, 2005) and Tinkerplots were central to the work.
To support teachers towards expertise with statistical investigations, project modules
provided teachers with exemplars, classroom activities, and reflections (Table 1). These
activities occurred through interactions with an online community of practice.
Table 1 Iterative stages in EarlyStatistics project
Stage
Aim
Initial moment
Preparation before classroom
intervention
Analysis of:
Statistical and probabilistic content
Official curriculum
Students’ ideas
Models of intervention
Experimental moment
During classroom intervention
Activity:
Plan their own scenario
Implement and report on classroom
intervention
Reflection and Assessment moment
After classroom intervention
Reflect and assess:
Statistical and probabilistic content developed
Students’ learning outcomes
Classroom dynamics
With an emphasis on reflection and teacher community embedded in experiences that build
teachers’ understanding and teaching repertoire of key ideas in statistics, the EarlyStatistics
project highlighted the diverse ways that teachers adapt to teaching statistical
investigations. For example, in their reflections, teachers focused on the significance of
problem solving in statistics, the difficulties of developing well-chosen statistical activities,
the importance of creating a classroom environment that engaged students, or the
challenges of envisioning and implementing statistical investigations (Azcarate et al.,
2008).
6. Developing Expertise in Teaching Statistical Inquiry (DETSI)
The aim of this study was to understand development of primary teachers’ confidence,
commitment, and expertise as they gained experience with teaching inquiry in a supportive
environment. Throughout the study, teachers designed (or modified published units) and
taught 3-4 inquiry units per year to their students.
DRAFT: NOT FOR DISTRIBUTION WITHOUT AUTHOR CONSENT
TO BE PUBLISHED (in 2011) in C. Batenero et al., (Eds.), Teaching statistics in school
mathematics. Challenges for teaching and teacher education. New York: Springer. [This
book is the outcome of the ICMI-18 Study conference from Monterrey Mexico June 2008]
Outcomes of the study produced a model (Makar, 2008) to describe the diversity of
teachers’ evolving experiences in teaching statistical inquiry over time, with four phases to
describe common patterns in the teachers’ classroom focus (Figure 2).
Fig 2 A model of learning to teach statistical inquiry
Orientation Cycle
The Orientation cycle represented teachers’ initial experience in teaching statistical inquiry.
Being able to envision the inquiry process in a classroom setting was by far the most
challenging hurdle for the teachers in this cycle. Teachers typically found their first unit
quite difficult as they wrestled with unexpected learning outcomes that surfaced. They
often blamed themselves for not anticipating outcomes rather than seeing this as the nature
of inquiry. During their initial experiences, it was apparent that the teachers’ main concerns
were in envisioning what statistical inquiry is, coming up with an interesting problem, and
engaging with structural aspects of their classroom (e.g., group work, eliciting and
supporting student independence). Addressing these challenges became a focus of their
teaching in the next cycle.
Exploration Cycle
After the teachers experienced what a statistical inquiry looked like in their classrooms,
they reacted to problems that had emerged. For example, they also could see a range of
potential directions in different phases of the investigative cycle (Figure 1) and responded
to changing classroom management issues that arose in each of these cycles. The teachers
continued to find logistical aspects challenging, like organizing and coordinating group
work, and helping students develop independence. Their growing experience helped them
modify their teaching styles to begin to address these issues.
DRAFT: NOT FOR DISTRIBUTION WITHOUT AUTHOR CONSENT
TO BE PUBLISHED (in 2011) in C. Batenero et al., (Eds.), Teaching statistics in school
mathematics. Challenges for teaching and teacher education. New York: Springer. [This
book is the outcome of the ICMI-18 Study conference from Monterrey Mexico June 2008]
Consolidation Cycle
By the next stage, the teachers had developed a ‘big picture’ of what was involved in
teaching a statistical investigation and worried less about micro-issues (e.g., classroom
management, logistical issues). They found it easier to design and locate rich driving
questions to initiate the inquiry process, and in many cases, a new interest was emerging to
deepen students’ understandings of content by better structuring teaching of more subtle
aspects of the inquiry process. Interviews with the teachers highlighted their changing
approaches to teaching inquiry, as well as elements that still challenged them.
At first I just thought that [posing a question] would be a pretty logical kind of a thing, but
when the kids had to pose their own, and then collect the data to answer that, and then analyze
and interpret it, that was hard for them to make that connection. I think we did one big
investigation, it was all of those parts, and when they got to the end, they’d forgotten what the
question was! … If I did this again next year, … every time we would [keep] looking at the
question and breaking it down [asking], ‘What do we want to find out here?’ And keeping [the
question] visible the whole way through.
As this comment illustrates, teachers in this phase felt more comfortable now negotiating
the balance between student decision-making and providing scaffolding to help their
inquiry stay focused and insightful. There was improved interest in supporting student
learning, such as helping students make connections between the question being posed, the
data they collected, and the conclusions being drawn (Hancock, Kaput & Goldsmith,
1992). The teachers needed to experience this issue firsthand in their own classrooms to
better envision their roles in scaffolding students in this process. The Consolidation cycle
occurred after the teachers had taught with inquiry for a year or more and again emphasizes
the non-trivial nature of learning to teach statistical investigations.
Commitment Cycle
After two years, some teachers were clearly committed to including statistical inquiry as a
regular part of their teaching, as well as working to help other teachers develop and
improve their teaching of inquiry. Many teachers confessed that they could now ‘see
inquiry questions everywhere’ and their commitment to statistical inquiry was clear.
7. Implications for Teaching Teachers to Teach Statistical Investigations
The process of learning to teach statistical investigations is complex. Research has been
clear in the need to develop teachers’ confidence with teaching statistical inquiry, but few
opportunities exist for them to gain this critical experience. The two projects presented in
this chapter—the EarlyStatistics (ES) Project and the Developing Expertise in Teaching
Statistical Inquiry (DETSI) Project—were diverse in their approaches to supporting
teachers to teach statistical investigations, but common elements suggest key characteristics
are needed in teaching teachers to teach statistical investigations.
1. Long-term support and resources. Both projects highlighted the importance of
providing ongoing support and exemplary resources as teachers develop proficiency in
teaching statistical investigations. This requires a shift from more traditional modes of
teacher learning through workshops or coursework.
DRAFT: NOT FOR DISTRIBUTION WITHOUT AUTHOR CONSENT
TO BE PUBLISHED (in 2011) in C. Batenero et al., (Eds.), Teaching statistics in school
mathematics. Challenges for teaching and teacher education. New York: Springer. [This
book is the outcome of the ICMI-18 Study conference from Monterrey Mexico June 2008]
2. Engaging in statistical investigations as learners. Opportunities to experience statistical
investigations as learners provide teachers with deeper understandings of complex
statistical processes, such as the interrogating of data, modes of thinking, dispositions
required, uncertainties and ambiguities encountered, and multiple interpretations and
decisions made in each phase of a statistical investigation. These are often new
experiences for teachers who are accustomed to mathematical structures and procedures
that are more deterministic and predictable in their outcomes.
3. Learning embedded in teachers’ classrooms. A key success of these projects was their
ability to situate teachers’ learning to teach statistical investigations within their own
classrooms. The EarlyStatistics project supported teachers’ classroom experiences
remotely, yet engaged their classroom experiences as central to their learning to teach
statistical investigations. They didn’t just read about statistical investigations but also
implemented a statistical investigation and reflected on their teaching. The DETSI
project partnered teachers and researchers within the teachers’ classrooms over a
number of years. Researchers played the role of a peer mentor in supporting teachers’
development. These projects both connected teachers’ learning to their own schools and
maximized opportunities for teachers to transfer their learning to their classroom
practices.
4. Statistical content knowledge. Although the EarlyStatistics (ES) project was more
explicit in developing teachers’ statistical content knowledge, both projects provided
opportunities for teachers to deepen their understandings of the ‘big ideas’ in
statistics—variation, average, sampling, chance, and inference (Watson, 2006). The ES
project developed these understandings through professional reading of statistics
education literature while the DETSI project developed statistical understandings by
addressing concepts as they emerged within the statistical investigations teachers’
learned and taught over time.
5. Collaboration. Teacher communities were key contributors to the success of both
projects. By engaging teachers in collaboration with their peers and university
researchers, the projects supported teacher professionalism and explicitly valued
teachers’ classroom expertise. The validation, collegiality, sharing of resources and
experiences, and accountability as part of a learning community supported teachers in
addressing challenges they encountered, particularly in their initial experiences teaching
statistical investigations.
6. Reflection. Finally, both projects provided teachers with time and opportunities for
reflection on their learning to teach statistical investigations. Reflection is a powerful
yet under-utilized tool for deepening learners’ knowledge and understandings. In the
case of statistical investigations, these reflections—both individual and communal—
allowed teachers to recognize and attend to key contributors to their learning and
improved the potential that they would apply these understandings to their students’
learning.
Although there were also significant differences in the way that these two projects were
conducted, these common elements point to the need to be more conscious of the
complexities in teachers’ learning to teach statistical investigations. If as a field we
acknowledge and come to recognize the changing needs of teachers as they develop their
DRAFT: NOT FOR DISTRIBUTION WITHOUT AUTHOR CONSENT
TO BE PUBLISHED (in 2011) in C. Batenero et al., (Eds.), Teaching statistics in school
mathematics. Challenges for teaching and teacher education. New York: Springer. [This
book is the outcome of the ICMI-18 Study conference from Monterrey Mexico June 2008]
expertise in teaching statistical investigations over time (Makar, 2008), it will provide new
windows of opportunity for improving research and practice in this area.
Acknowledgements: This research and writing was funded by the Australian Council for
Research (LP0776703), Education Queensland, and The University of Queensland.
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