Emerging Trends in Statistics Education (2023). ZDM- Mathematics Education

Gail Burrill

Michigan State University, United States

Maxine Pfannkuch

University of Auckland | Waipapa Taumata Rau, Aotearoa New Zealand

Statistics Education Research

Building on previous research, Pfannkuch* (2018) reimagined the teaching and learning of statistics and anticipated possible changes, arguing that curricular approaches should include

(1) immersing students in data-rich environments, statistical investigations, and modeling,

(2) critically evaluating data-based arguments in diverse media, including risk, and

(3) facilitating accessibility of statistical concepts through interactive visualizations, learning how to scaffold students’ reasoning, and providing coherent conceptual pathways.

The Study

• Who: 24 leading members of the statistics education community
• What: described trends they have observed in the field and identified over 200 interesting and relevant papers, special journal editions, and books published between 2017-2022 related to those trends
• How: Using an open coding technique drawn from Grounded Theory (Strauss & Corbin, 1998) and referring to five key background papers published prior to 2017, and considering Pfannkuch (2018), identified papers from those recommended that challenge what should be taught and suggest new ways of thinking about the teaching and learning of statistics (note: were limited by number of characters)
• Results:
• Four emerging themes in statistics education research
• 50 papers that exemplify these trends
• Eight papers identified as particularly important* in defining future directions

Emerging Trends in Statistics Education�

Core considerations:

continuing advances in technology and

dual roles of

• data consumer (those who interact with data-based information produced by someone else), and
• data producer (those that engage in empirical investigations, interpret their own data, and report their conclusions (Gal, 2002).

Emerging Trends in Statistics Education�

Data Science

According to Gould* (2021), data science is not well defined -

• a core of statistical thinking,
• components of computational thinking,
• “a dash of mathematical thinking”

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• Attending to pedagogy Burrill and Dick (2022) give design and implementation principles for scaffolding understanding from hands on to automaticity.
• Utts (2021) addresses general principles related to ethics.
• Weiland (2017) argues that students need to learn about their personal data trail.

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Critical components of a data science course that might be overlooked

• the investigative process
• shifting the focus from the analysis phase, which seems typical, to the question-posing phase as in Arnold & Franklin (2020).

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Computational Thinking

• Computational thinking is an approach to problem solving that attempts to make problems computable
• “Computational thinking is essential” (*Gould 2021).

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• Integrate computing and statistics at all levels (Horton & Hardin, 2021)

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Fergusson, 2022, PHD Thesis

Data Moves (*Erickson, T., Wilkerson, M., Finzer, W., & Reichsman, F., 2019).

Using digital tools to facilitate the manipulation and analysis of large, complex datasets.

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Core data moves:

• filtering,
• grouping,
• summarizing,
• calculating,
• merging/joining, and
• making hierarchy.

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Authors argue data moves should be part of data analysis, identify potential research questions that should be addressed in moving forward, and give recommendations for curriculum and instruction:

• include data moves explicitly as a part of data analysis.
• early assignments should be more computationally demanding—and less “sanitized.”
• use data moves to help students transition between tools.
• consider data moves as part of data literacy.

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Data Investigation Framework (*Lee et al., 2022)

Frame the Problem

• Pose investigative questions
• Consider variability

Consider & Gather Data 

• Attend to issues related to collection, measurement, design, methods, potential biases, and ethical concerns.

Process Data 

• Identify strategies/ techniques for organizing and processing data,
• Consider data moves.

Explore and Visualize Data 

• Create visualizations and measures to reason about the data
• Look for relationships among variables.
• Identify patterns and trends.

Consider Models

• Explore & select models
• Consider variability, uncertainty
• Identify assumptions needed for viable model.

Communicate & Propose Action 

• Create a data story for the intended audience
• Use evidence to justify claims
• Propose possible actions

Illustrating the Framework (*Lee et al., 2022)

An investigative question: How tall do roller coasters in your region of the US tend to be?

Explore/ Visualize Data

Process Data

Answer the question about how tall coasters tend to be, and explore extensions

Consider Models

Data Cards

Software

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Shifting nature of software (Wild 2018):

from point and click interfaces (e.g., TinkerPlots^TM and CODAP) designed for learning statistics

to software that relies on coding, e.g., Rstudio and Shiny apps (Gould, 2021)

or APIs - Application Programming Interfaces, (Fergusson & Wild, 2021) creating building blocks from pieces of code making data accessible to secondary students.

Increasing complexity of coding (e.g., ProDaBi Project)

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Students classified email messages as spam or non-spam using four different technologies (Horton et al., 2022)

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Modeling

• statistical modeling, holistic approach for developing key statistical ideas (*Pfannkuch et al., 2018)
• broadened to include algorithmic predictive modeling, focusing on the effectiveness of a model; e.g., the ProDaBi Project (Fleischer et al. 2022; Podworny et al. 2022), a multigrade curriculum using Jupyter Notebooks to generate decision trees and evaluate results.

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• How secondary teachers understand model building and evaluation; found the evaluation component challenging

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• teachers engaged in predictive modeling involving simple linear regression (Fergusson & Pfannkuch, 2022)

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(Zieffler et al., 2021).

Predictive modeling & young learners

Negotiated rules

• Year 3 have thick fingers. Kindergarten ones have no fingers or just sticks.
• If there are nine or fewer features on the face, the picture was drawn by a Kindergartener. If ten or more features, then by a Year 3.
• Year 3 have eye-shaped eyes and at least one other detail. Kindergarten eyes are balls or dots.

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Oslington et al. (2018).

Student predictions

First graders’ rules to identify who drew a picture of a person., kindergartner or third grader

Emerging Trends in Statistics Education�

Data Formats

New forms of data: e.g.,

• sourced data from public datasets,
• photographs,
• sound,
• wearable sensor technologies,
• computational logs,
• video,
• images,
• overlay tools on maps,
• demographic spatial data sets, …

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Data use by middle and secondary students in the digital age: A status report and future prospects. (*Lee & Wilkerson, 2018)

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Described new and emerging forms of data accessible through emerging technologies; implications for classroom practice, teacher preparation, and educational research

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1. collected through automated means
2. algorithmically-generated
3. non-quantitative
4. curated and publicly-available

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(Englel & Wilhem, 2021)

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Data collection/analysis

Use of eye-tracking technology to collect data and machine learning algorithms for data analysis related to students’ understanding of histograms (Boels et al., 2019)

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Boels et al., 2022. Secondary school students’ strategies when interpreting histograms and case-value plots: An eye-tracking study

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Data collection/analysis

More open analysis methods

Biehler et al. (2018) recommended the use of Grounded Theory (Corbin & Strauss, 1994) or an inductive-enriched Qualitative Content Analysis (Mayring, 2015), ensuring that frameworks for student reasoning arise from the data (e.g., interviews, videos) itself.

 Zieffler et al. (2021) used Grounded Theory to identify themes in teachers’ reasoning by viewing the digital recordings and artifacts of the participants’ work.

Challenges:

• Students may not have a sense of how measurements are taken or what they mean when using automated data collection tools, simulations, or publically-available datasets.
• Simulations may omit variability in algorithmic output,
• Contemporary narrative data visualizations and non-quantitative data may not emphasize or provide simple ways to consider variability. (*Lee & Wilkerson, 2018)

Data collection/analysis

New tools to probe students’ reasoning and actions when analyzing data

• Computer supported data analysis and coding to determine pre-service teachers’ reasoning and actions (Frischemeier & Biehler, 2018);

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Frischemeier & Biehler, 2018

Data collection/analysis

New tools to probe students’ reasoning and actions when analyzing data

• Coding videos of teachers’ reasoning around participatory sensing data in an interactive dashboard data analysis environment;
• use of transition matrices and network graphs to track students’ pathways through the data cycle (Gould et al., 2017)

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Network graphs to illustrate transitions in thinking (Gould et al., 2017)

Representation

• interactive data visualizations allow user to explore data without requiring deep mathematical knowledge;
• promote conceptual understanding beyond graphical representations typically part of the school curriculum (Engel et al., 2020)

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an equity perspective using examples related to the pandemic to describe how formatting, framing, and narrating might uphold hierarchies of power, honor some values over others, and promote certain decisions (Rubel et al., 2021)

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Understanding mean as balance point

(Burrill, 2018)

Ice volume as function of time

Curriculum

• Pfannkuch* (2018)- reimagined curriculum fostering statistical reasoning and argumentation including understanding the context, interrogating data, and using data as evidence for making and supporting claims

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• Andre & Lavicza (2019) argue curricula must respond to the technology; found most split the statistical investigative cycle; early grades ask questions, gather data and reason about the nature of data; higher grades learn calculation techniques and inferential reasoning.

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• *Gould (2021) – introduce data science in secondary schools, argues for “data acumen”;
• *Erickson et al. (2019) – revise K-12 curriculum to build skill with data moves such as filtering, merging two data sets, or making hierarchy;
• Burrill (2020) -integrate data/statistical literacy into the school curriculum;
• Wilkerson & Laina (2018) – suggest the need to consider repurposing publicly available data sets as part of curriculum, to provide opportunities for statistical reasoning

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Questions/Comments?

References not in the ZDM paper

• Boels, L., (2023). Secondary school students’ strategies when interpreting histograms and case-value plots: An eye-tracking study. Dissertation. Freudenthal University
• Fergusson, A. (2022). Towards an integration of statistical and computational thinking. Doctoral Thesis. University of Auckland.

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