# Proceedings

• ### MODELING SCATTERPLOT DATA AND THE SIGNAL-NOISE METAPHOR:<br>TOWARDS STATISTICAL LITERACY FOR PRE-SERVICE TEACHERS

The idea of data being a mixture of signal and noise is perhaps one of the most fruitful and fundamental ideas of statistics. To enable future mathematics teachers to educate students to become statistically literate, we propose an integrative approach connecting central topics of school mathematics with the signal-noise idea. A course on modeling functional relationships-a core topic in any mathematics curriculum-confronts students with the signal-noise idea when looking at the deviation between model and data. We provide empirical evidence that students of such a course acquire implicitly important statistical thinking skills.

• ### TOWARDS A SUITABLY DESIGNED INSTRUCTION ON STATISTICAL REASONING: UNDERSTANDING SAMPLING DISTRIBUTION WITH TECHNOLOGY

Earlier studies on sampling distribution, its founding concepts, misconceptions about sampling distributions, and the use of simulation highlighted that (1) learning of statistics requires an understanding of multifaceted issues and relations among them; (2) learning may be examined in terms of task, technique, theory, and learner's profile, each of which is influenced by instructional context; and (3) learning environments should be designed to stimulate flexible travelling along the network of these issues. Considering these emerging findings we attempt to outline a possible instructional design to teach sampling distribution with technology. Suggestions for training teachers in statistics education are included.

• ### TEACHER TRAINING PROGRAM ON TEACHING ARITHMETIC MEAN BY USING THE VISUAL APPROACH- A CASE STUDY

This paper describes an action research carried out over eight days on an elementary mathematics teacher in the United Arab Emirates. The effectiveness of a short teacher training program using the visual approach in teaching the concept of arithmetic mean was examined. The teacher was trained to teach a sixth grade class using a visual approach that focused on teaching the conceptual understanding of the arithmetic mean. Results showed some positive effects of the short training program on students' conceptual understanding of arithmetic mean. Some misconceptions related to arithmetic mean were found among students in pre and post testing.

• ### TRAINING TEACHERS TO DEVELOP STATISTICAL THINKING

In this paper I argue that to improve teachers' statistical content and pedagogical content knowledge, teachers need to experience the game of statistics, build key statistical concepts related to transnumeration thinking, reasoning with statistical models, and consideration of variation, and understand how students develop their statistical reasoning. The implication of requiring teachers to have substantive and deep knowledge of statistics is discussed.

• ### PREPARING SCHOOL TEACHERS TO DEVELOP STUDENTS' STATISTICAL REASONING

In this paper we discuss how two different types of professional development projects for school teachers are based on the same framework and are used to prepare knowledgeable and effective teachers of statistics. The first example involves a graduate course for masters' students in elementary mathematics education at the University of Haifa, Israel. The second example is a graduate course for in-service secondary mathematics teachers, at the University of Minnesota, United States of America. The framework used is based on six instructional design principles described by Cobb and McClain (2004). Our view of such a classroom is a learning environment for developing a deep and meaningful understanding of statistics and helping students develop their ability to think and reason statistically "Statistical Reasoning Learning Environment" (SRLE).

• ### A MODEL OF LEARNING TO TEACH STATISTICAL INQUIRY

Although the inquiry process is a foundational practice in statistics, it is rarely taught in school. This paper introduces a tentative model to describe primary teachers' evolving experiences in learning to teach statistical inquiry.

• ### DEVELOPING NEW STATISTICAL CONTENT KNOWLEDGE WITH SECONDARY SCHOOL MATHEMATICS TEACHERS

This paper describes a pilot study exploring the acquisition of new statistical content knowledge by teachers, which is now needed as a result of curriculum change. The teachers involved in the study formed a professional learning community where their learning needs with respect to changes in the statistics curriculum were identified and workshops presented to help meet these needs. In the paper teachers' understanding of new statistical content knowledge and learning experiences are reported. Initial findings support previous research into how teachers learn and show that new content knowledge is not automatically gained through their participation in professional development.

• ### NAVIGATING LAYERS OF UNCERTAINTY IN TEACHING STATISTICS THROUGH CASE DISCUSSION

The dynamics of an online case discussion among a group of fifteen prospective secondary mathematics teachers are described. During the discussion, participants offered and debated conjectures about general pedagogy, statistical content, and content-specific pedagogy. Their collective discourse showed that cases can help catalyze online conversations in which prospective teachers challenge one another's claims and interpretations. It also suggested that discussion moderators may need to help participants consider factors in addition to teacher explanations when analyzing the path of students' statistical learning. The paper closes by suggesting that a carefully-sequenced case-based curriculum may have the potential to build prospective teachers' statistical knowledge and challenge persistent misconceptions.

• ### SHAPING K-12 STATISTICS EDUCATION IN THE UNITED STATES

In recent years, three key documents have been influential in focusing attention on statistics and data analysis in the Pre-K-12 mathematics curriculum in the United States. We examine how these three documents come together with a collective potential to shape the future direction of Pre-K-12 statistics education, and we describe the specific contributions made by the document Guidelines for Assessment and Instruction in Statistics Education (GAISE) Report: A Pre-K-12 Curriculum Framework.

• ### INSTRUCTING FUTURE TEACHERS OF STATISTICS:<br>THE BENEFITS OF EN-ACTIVE, ANALOGUE MODELLING

I report on special features of a course on statistics and probabilities at my university, where future teachers of mathematics in primary school are instructed on en-active representations of statistical situations and on their analogue modelling. I also report on empirical work with future mathematics teachers of primary school in Baden W&uuml;rttemberg who have been instructed to introduce simple, en-active representations of statistical concepts in the classroom.