Helping Students
Develop Statistical Reasoning:
Implementing a Statistical Reasoning
Learning Environment (SRLE)
Dani Ben-Zvi
dbenzvi@univ.haifa.ac.il
The University of Haifa, Israel
Encontro Interamericano de Educação Estatística
The Challenge of Learning and
Teaching Statistics
• Current research studies suggest very
different ways of teaching than traditional
lectures (Garfield and Ben-Zvi, 2007)
• Leaving familiar teaching methods to try
active learning techniques is challenging
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Statistical Reasoning Learning Environment
SRLE
• A model for an interactive, introductory
statistics course that is designed to develop
students’ statistical reasoning
• This model is built on the socio-constructivist
theory of learning
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Building on socio-constructivist
principles of learning
• New knowledge and understandings are based
on the existing knowledge and beliefs we
already have and are grounded in our
experiences (e.g., Cobb, 1994; Piaget, 1978)
• People learn by constructing knowledge
(rather than by receiving knowledge) while
interacting with adults or peers (Vygotsky,
1978)
• We learn by doing
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Implication of current theories of learning
• Good instructional practice consists of designing
student-centered learning environments that
stimulate students to construct knowledge and
understanding
• Activities that provide students many opportunities to
think, reason, and reflect on their learning, as well as
discussing and reflecting with their peers
• The teacher is cast as an instructional coach, a colearner, an enculturator, or a facilitator, rather than as a
conduit of knowledge in a teacher-centered classroom
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Why change?
• A student-centered approach is more effective in
helping students build a deep understanding of
statistics and to be able to transfer what they
have learned in subsequent classes or in the real
world
• Students in the “teaching is telling” approach
rarely have a chance to develop a deep
understanding of what they have “learned,” and
quickly forget it after they complete a course
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Principles of a Statistical Reasoning
Learning Environment (SRLE)
1. Focus on central statistical ideas
2. Use real and motivating data sets
3. Design classroom activities to support
development of students’ reasoning
4. Use of appropriate technological tools
5. Promote classroom discourse
6. Use alternative methods of assessment
(Cobb and McClain, 2004)
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1. Focus on central statistical ideas
Distribution
Covariation
Variability
Big
ideas
Sampling
Center
Data
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2. Use Real and Motivating Data
• Data should be the focus for statistical learning (Franklin
and Garfield, 2006)
• Throughout a course, students need to consider methods
of data collection and production and how these methods
affect the quality of the data and the types of analyses
that are appropriate
• Interesting data sets motivate students to engage in
activities, especially ones that ask them to make
conjectures and think about a data set before analyzing it
Number of lost
milk teeth
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The distances
students can
jump
Class survey
Body
measurements
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3. Classroom activities
• Use of carefully designed, research-based
activities that promote student learning
through collaboration, interaction, discussion,
data, and interesting problems
(Bransford, Brown, & Cocking, 2000)
• Activities that promote active learning
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Types of classroom activities
Group data
investigations
(projects)
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Inquiry-based
guided
activities
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The data investigation cycle (PCAIC)
Pose question and conjecture
Communicate
Collect data
Analyze
Interpret and make conclusions
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4. Appropriate technological tools
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5. Promote classroom discourse
Engage students in sustained exchanges that focus on
significant statistical ideas:
• Learn to question each other
• Explain their reasoning and justify
their answers and arguments
• Express their views, even if they are tentative.
Create a safe classroom climate.
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6. Alternative assessment
Teachers:
• Become knowledgeable about alternative methods of
assessment
• Learn about student projects as a form of authentic
assessment
Types of assessments:
• Statistical literacy (e.g., critique a graph in a newspaper)
• Statistical reasoning (e.g., write a meaningful short essay)
• Feedback to each other or the instructor
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Aspect of the
Course
“Traditional” Statistics
Class
SRLE Class
Focus of course
Skills and procedures,
covering content
Big ideas, developing statistical
reasoning and thinking
Role of textbook
Use for examples or
Read and take notes to prepare for
homework problems and
class
to review for test
Center
Teacher centered
Student centered
Role of the
Delivers knowledge by
Facilitates developing of knowledge
teacher
telling and explaining
through discussion and activities
Role of
To compute or check
To explore data, illustrate concepts,
technology
answers, construct graphs
generate simulations, test
conjectures, and collaborate
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Aspect of
the Course
“Traditional”
Statistics Class
SRLE Class
Discourse
Teacher answers
Teacher poses questions and guides a
questions
discussion. Students present arguments,
answer other students’ questions, and are
asked if they agree or disagree with answers.
Data
Small data sets to
Rich, real data sets to engage students in
illustrate and practice thinking and reasoning and making conjectures.
procedures.
Assessment
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Data sets are generated by the students.
Focuses on
Uses a variety of methods, assesses reasoning
computations,
and thinking. Formal and informal assessment
definitions and
is an integral part of learning and is aligned
formulas; on short
with learning methods and goals. Students
answers and multiple
may be asked to explain their reasoning and
choice tests. Tests.
justify their conclusions.
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Moving to a SRLE
Moving to SRLE approach is faced with many challenges: students,
colleagues, and institution, instructors. (Garfield and Ben-Zvi, 2008)
Some teachers:
• View statistics as mathematics
• Teach statistics in terms of computations and formulas
• lack experience in analyzing and exploring real and messy data
• Believe there is a single correct answers to most statistics
problems
• Are not comfortable with open-ended discussions
• Are not comfortable with the inquiry-based pedagogical
methods
• Do not understand the important big ideas of statistics and data
analysis.
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Moving to a SRLE
• The first step: Align current course and
materials with the components of a SRLE and
pick a starting point
• Sample activities in the AIMS Website
(http://www.tc.umn.edu/~aims)
• Careful and steady change over a period of
time may lead to a successful implementation
of a SRLE in a statistics course, rather than
trying a radical, all at once change
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Summary: Key elements
Big ideas
Alternative
assessment
Data sets
SRLE
Classroom
discourse
Classroom
activities
Technological
tools
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Additional Reading
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Read more about theses ides:
• Garfield J., & Ben-Zvi, D. (2009). Helping students develop
statistical reasoning: Implementing a Statistical Reasoning
Learning Environment. Teaching Statistics, 31(3), 72-77.
• Ben-Zvi, D., & Garfield, J. (Editors) (2004). The challenge of
developing statistical literacy, reasoning, and thinking.
Dordrecht, the Netherlands: Kluwer Academic Publishers.
• Garfield, J., & Ben-Zvi, D. (2007). How students learn statistics
revisited: A current review of research on teaching and learning
statistics. International Statistical Review, 75(3), 372–396.
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Obrigado!
For further questions:
Dani Ben-Zvi
dbenzvi@univ.haifa.ac.il
The University of Haifa, Israel
The Connections learning environment
Presentation
preparation
Final project
presentation
Hands-on smallgroups activities
Scaffolding
instructional
activities
Investigations
using Excel
Minds-on: wholeclass discussions
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