Helping Students Develop Statistical Reasoning: Implementing a Statistical Reasoning Learning Environment (SRLE) Dani Ben-Zvi 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 1/7/20112

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 1/7/20113

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 1/7/20114

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 co- learner, an enculturator, or a facilitator, rather than as a conduit of knowledge in a teacher-centered classroom 1/7/20115

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 1/7/20116

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) 729/6/11

1. Focus on central statistical ideas 8 Big ideas DistributionVariabilityCenter Data SamplingCovariation 29/6/11

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 9 Number of lost milk teeth The distances students can jump Class survey Body measurements 29/6/11

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 1029/6/11

Types of classroom activities 11 Group data investigations (projects) Inquiry-based guided activities 29/6/11

The data investigation cycle (PCAIC) P ose question and conjecture C ollect data A nalyze I nterpret and make conclusions C ommunicate

4. Appropriate technological tools 1329/6/11

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. 14 What do you think and why? What would happen if? 29/6/11

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 15 ARTIST Website 29/6/11

Aspect of the Course “Traditional” Statistics Class SRLE Class Focus of courseSkills and procedures, covering content Big ideas, developing statistical reasoning and thinking Role of textbook Use for examples or homework problems and to review for test Read and take notes to prepare for class CenterTeacher centeredStudent centered Role of the teacher Delivers knowledge by telling and explaining Facilitates developing of knowledge through discussion and activities Role of technology To compute or check answers, construct graphs To explore data, illustrate concepts, generate simulations, test conjectures, and collaborate 1/7/201116

Aspect of the Course “Traditional” Statistics Class SRLE Class Discourse Teacher answers questions Teacher poses questions and guides a discussion. Students present arguments, answer other students’ questions, and are asked if they agree or disagree with answers. Data Small data sets to illustrate and practice procedures. Rich, real data sets to engage students in thinking and reasoning and making conjectures. Data sets are generated by the students. AssessmentFocuses on computations, definitions and formulas; on short answers and multiple choice tests. Tests. Uses a variety of methods, assesses reasoning and thinking. Formal and informal assessment is an integral part of learning and is aligned with learning methods and goals. Students may be asked to explain their reasoning and justify their conclusions. 1/7/201117

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. 1829/6/11

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 ( 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 1/7/201119

Summary: Key elements Big ideasData sets Classroom activities Technological tools Classroom discourse Alternative assessment 1/7/ SRLE

Additional Reading 21

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), 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–

Obrigado! For further questions: Dani Ben-Zvi The University of Haifa, Israel

The Connections learning environment Hands-on small- groups activities Final project presentation Presentation preparation Minds-on: whole- class discussions Investigations using Excel Scaffolding instructional activities 24