CHARACTERISTICS OF PROFESSIONAL DEVELOPMENT AND TEACHER INTERACTIONS IN A MOOC DESIGNED FOR THE TEACHING OF STATISTICS 

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CHARACTERISTICS OF PROFESSIONAL DEVELOPMENT AND TEACHER INTERACTIONS IN A MOOC DESIGNED FOR THE TEACHING OF STATISTICS

ABSTRACT

 

This study investigates to what extent the characteristics of effective face-to-face professional development hold in a MOOC designed for statistics development of secondary teachers and the nature of teachers’ and others’ interactions with materials and with each other in this online professional development. Social theory of learning and connectivism are used to frame participants’ learning as they establish and experience interactions in the network.

The context of this study is a MOOC for educators offered by a large American university and specifically designed for teachers to learn about statistics teaching and the use of statistical investigations in teaching. Qualitative research methods of content analysis are used to identify and describe the enacted characteristics of the MOOC vis-à-vis documented characteristics of effective face-to-face professional development literature. Inductive coding and social network analysis were used to understand the content of participants’ interactions and the

network structure produced by them, respectively.

Findings regarding characteristics of effective professional development show how this MOOC embodied variations on key characteristics of effective face-to-face professional development. Participants’ autonomy is highlighted as a common element that modifies the

characteristics suggested in the literature of face-to-face teachers’ professional development.

Findings regarding the nature of participants’ interactions show that MOOC resources were vehicles for participants’ interactivity with some resources engaging more participants than others, and resources being essential for the creation of organic networks. Discussion starters acted as network expanders who amplified interactivity among participants, while the main instructor took the leadership of interactivity and acted as a concierge throughout this MOOC.

The study also shows how participants interacted with others in forums, exposing that they shared

 

not only their perspectives about resources provided by this MOOC but also their qualifications and their insecurities with respect to statistics content and statistics teaching.

Aligning theoretical perspectives from social theory of learning with connectivism, this study helps to create awareness in the field of teacher professional development regarding new characteristics that emerge when professional development is delivered in large-scale, via the Internet, and free of charge. In this sense, outcomes of the study include a suggested set of characteristics that MOOCs should contain to be an environment for effective professional development for teachers.

For the fields of mathematics education and statistics education, this study presents teachers getting acquainted with the pedagogical approach of teaching statistics through data investigations through this MOOC, exposing their perceptions of this approach and their intentions of further implementation, which can contribute to minimize the lack of training in statistics teaching identified in the literature.

Implications for research highlight the importance of the quality of participants’ posts in MOOC forums, their individualist modes of interaction in this online professional development, and the role MOOC resources play in their practice. Further research is suggested in the areas of investigating the impact of forum prompt content on the quantity of posts made by participants, sentiment analysis of the content of participants’ forum posts, and investigation into the role of the main instructor in MOOCs for teachers’ professional development.

 

 

TABLE OF CONTENTS

List of Figures ………………………………………………………………………………………………………….. ix

List of Tables …………………………………………………………………………………………………………… xii

Acknowledgements …………………………………………………………………………………………………… xv

Chapter 1 Rationale…………………………………………………………………………………………………… 1

Mathematics Curriculum Policy Calls for Statistics at High School …………………………. 2

Challenge in Teaching Statistics at High School ……………………………………………………. 4

The Need for Statistics Professional Development and Support for Teachers ……………. 8

MOOCs as Venues for Teachers’ Professional Development ………………………………….. 10

The Study …………………………………………………………………………………………………………. 12

Organization of this Dissertation …………………………………………………………………………. 14

Chapter 2 Review of Relevant Literature …………………………………………………………………….. 15

Teacher Professional Development ………………………………………………………………………. 15

Characteristics of Effective Professional Development for Teachers ………………………… 17

Content Focus …………………………………………………………………………………………….. 18

Opportunities for Active Learning ………………………………………………………………… 18

Coherence ………………………………………………………………………………………………….. 19

Type of Activity …………………………………………………………………………………………. 20

Duration of Activity ……………………………………………………………………………………. 22

Collective Participation ……………………………………………………………………………….. 23

Concluding Remarks about Characteristics of Effective Professional Development …… 23

Teachers’ Change as An Outcome of Professional Development …………………………….. 24

Teacher Professional Learning …………………………………………………………………………….. 25

The Role of Resources in Teachers’ Learning from Professional Development ….. 27

Teaching Statistics through Data Investigations …………………………………………………….. 29

Use of Primary Data vs Secondary Data ………………………………………………………… 34

Use of Technology Tools …………………………………………………………………………….. 36

Concluding Remarks about Teaching Statistics through Data Investigations …………….. 37

Massive Open Online Courses (MOOCs) ……………………………………………………………… 39

MOOCS for Teachers’ Professional Learning ………………………………………………… 41

Situating the Research Questions in the Literature …………………………………………………. 45

Chapter 3 Theoretical Framework ………………………………………………………………………………. 47

Social Theory of Learning ………………………………………………………………………………….. 47

Connectivism ……………………………………………………………………………………………………. 50

Four Key Principles of Network Learning ……………………………………………………… 53

Engagement Depicted through Connectivism …………………………………………………. 54

Concluding Remarks about Connectivism …………………………………………………………….. 56

Participants’ Interaction in Online Environments …………………………………………………… 57

A Functional Definition for Interaction…………………………………………………………..57

Forms of Interactions in Online Environments ……………………………………………….. 58

Final Remarks …………………………………………………………………………………………………… 60

Chapter 4 Research Design, Methodology and Data Analysis ………………………………………… 62

Context of the Study ………………………………………………………………………………………….. 63

Pilot Study ………………………………………………………………………………………………………… 64

Experimental Data Collection ……………………………………………………………………………… 66

Preliminary Analysis of the Pilot Data ………………………………………………………………….. 68

Participants ………………………………………………………………………………………………… 68

Analyzing Sample Data ……………………………………………………………………………….. 69

How the Structure of the Network was Extracted and Analyzed ……………………….. 73

Important Measurements of SNA………………………………………………………………….. 76

Categories Developed from Coding Using the Pilot Data…………………………………. 79

Current Study ……………………………………………………………………………………………………. 82

Study Participants ……………………………………………………………………………………….. 83

Data Sources ………………………………………………………………………………………………. 84

MOOC Materials ………………………………………………………………………………………… 84

Click Data ………………………………………………………………………………………………….. 84

Demographics ……………………………………………………………………………………………. 85

Discussion Forum Content …………………………………………………………………………… 85

Online Survey …………………………………………………………………………………………….. 85

Interview with MOOC Instructors ………………………………………………………………… 87

The Role of the Researcher ………………………………………………………………………….. 88

Assumptions ………………………………………………………………………………………………. 88

Validity and Reliability ……………………………………………………………………………….. 89

Data Collection Timeline …………………………………………………………………………….. 90

Appropriateness of Data Collection ………………………………………………………………. 91

Data Analysis Preparation …………………………………………………………………………………… 91

Online Survey …………………………………………………………………………………………….. 91

Interviews ………………………………………………………………………………………………….. 93

Interactive Data Analysis …………………………………………………………………………….. 93

Description of the Codes ……………………………………………………………………………… 96

Content of Participants’ Interactions Related to Themselves. ……………………………. 96Content of Participants’ Interactions Related to their Students. …………………………. 100Content of Participants’ Interactions Related to MOOC Materials. ……………………. 102

Codes Distribution………………………………………………………………………………………. 102

Ethical Issues ……………………………………………………………………………………………… 104

Chapter 5 Findings ……………………………………………………………………………………………………. 105

Presence of the Characteristics of Effective Professional Development ……………………. 106

Content Focus …………………………………………………………………………………………….. 107

Opportunities for Active Learning ………………………………………………………………… 116

Coherence ………………………………………………………………………………………………….. 124

Type of the Activity ……………………………………………………………………………………. 136

Duration of the Activity ………………………………………………………………………………. 140

Collective Participation ……………………………………………………………………………….. 148

Summary for the Characteristics of Effective Professional Development –

Answering the First Research Question …………………………………………………………. 157

Participants’ Autonomy ……………………………………………………………………………….. 157

Discussion of the Relationship Among the Characteristics of Effective Professional

Development ……………………………………………………………………………………………… 159

Discussion of the Structural Features of Effective Professional Development and this

MOOC ………………………………………………………………………………………………………. 162

Discussion of MOOC’s Caveat as Venues for Teachers’ Effective Professional

Development ……………………………………………………………………………………………… 163

Chapter 6 Findings ……………………………………………………………………………………………………. 165

The Nature of Participants’ Interactions in Forums with Respect to Materials …………… 167

Which Materials were Vehicles for Participants to Interact with Others in this

MOOC? ……………………………………………………………………………………………… 167

Nature of the Content of Participants’ Posts with Respect to the LOCUS Test,

Gapminder, and Statistical Tasks …………………………………………………………… 169

Discussion about the Nature of the Content of Participants’ Posts with Respect to the LOCUS Test, Gapminder, and Statistical Tasks ……………………………… 219Forum Prompts and their Embedded Requests ……………………………………………….. 222Forum Prompts and the Nature of the Content of Participants’ Posts …………………. 226

Discussion about Forum Prompts and the Nature of the Content of Participants’

Posts ………………………………………………………………………………………………….. 233

Who Started the Discussions in Forums? ……………………………………………………….. 236

Summary of Who Started the Discussions in Forums ………………………………………. 242

Structure of Participants’ Interactions in Forums with Respect to Three

Resources……………………………………………………………………………………………. 243

Summary of the Structure of Participants’ Interactions in Forums with Respect

to Three Resources ………………………………………………………………………………. 254Nature of Participants’ Interactions with Others in Forums …………………………………….. 256

Distribution of Forum Posts as the MOOC Progresses …………………………………….. 257

Discussion about the Distribution of Forum Posts as the MOOC Progresses ………. 262

What Participants Share about Themselves ……………………………………………………. 264

How Participants Interact with Others …………………………………………………………… 283

Discussion about How Participants Interact with Others ………………………………….. 289

Answering the Second Research Question about the Nature of Participants’

Interactions with Respect to Materials and with Others ……………………………………. 290

Nature of Participants’ Interactions with Respect to Materials ………………………….. 291

Nature of Participants’ Interactions with Respect to Others ……………………………… 293

Chapter 7 MOOCs and Professional Learning: Implications and Possibilities ………………….. 295

Conceptualizing a Set of Characteristics for MOOCs To Be Designed as Venues for

Teachers’ Professional Development …………………………………………………………….. 296

MOOCs as Spaces for Professional Learning and their Potential for Teachers’

Communities of Practice ……………………………………………………………………………… 299

Enhanced Interactivity in MOOCs ……………………………………………………………………….. 301

Resources ………………………………………………………………………………………………….. 302

Prompts …………………………………………………………………………………………………….. 303Teachers’ Responsibility for Their Own Professional Development ………………………….306

Taking the Risk of Developing Identity as Statistics Teachers …………………………………. 308

Roles of Others in MOOCs …………………………………………………………………………………. 311

The Role of Super-Posters ……………………………………………………………………………. 311

The Role of the Main Instructor ……………………………………………………………………. 312

Chapter 8 Contributions, Implications for Research, Limitations, and Future Directions ……. 316

Contributions …………………………………………………………………………………………………….. 316

Contributions towards Characterizing MOOCs as Venues for Teachers’

Professional Development …………………………………………………………………….. 316

Contributions towards Participants’ Interactions in MOOCs for Professional

Development ………………………………………………………………………………………. 317

Implications for Research …………………………………………………………………………………… 320

Quality of Participants’ Posts in MOOC Forums …………………………………………….. 321

From Individualist Interaction Towards Cooperation and Collaboration Among

Participants in MOOCs ………………………………………………………………………… 323

MOOCs Addressing Statistics Content and Pedagogical Knowledge ………………… 325

The Role MOOC Resources Play in Teachers’ Practice …………………………………… 326

Implications for Theory ……………………………………………………………………………………… 328

Contributions of Connectivism …………………………………………………………………….. 329

The Need for Further Theoretical Development of Connectivism ……………………… 330

Implications for Methodology……………………………………………………………………………… 333

Limitations ……………………………………………………………………………………………………….. 335

Future Directions ……………………………………………………………………………………………….. 336

MOOCs in Teachers’ Professional Learning Trajectory ………………………………………….. 338

References ……………………………………………………………………………………………………………….. 340

Chapter 1 

 

Rationale

The motivations for this study are the increasing trend of teaching statistics and probability in mathematics school curricula around the world, and the consequent demand for prepared mathematics teachers to implement the directions presented in curriculum policies. Although many countries have started initiatives to prepare their teachers to teach statistics, research indicates that lack of teacher preparation for teaching statistics at the middle and high school level is still an important issue in the education community (Franklin, 2013; Conference Board of the Mathematical Sciences [CBMS] , 2012). The need to offer mathematics teachers and teachers in general, opportunities to develop themselves regarding the teaching of statistics is vital to the successful implementation of curriculum policies.

Massive Open Online Courses (MOOCs) appear to be excellent venues for delivering large-scale professional development for teachers, and more specifically, professional development focused on statistics teaching. MOOCs provide opportunities for teachers from many different parts of the world to interact with peers, to share their experiences, and to learn through interaction with materials and with each other. MOOCs for professional development also have the potential to reach across political and cultural boundaries in order to meet the international need for teachers’ development in school statistics. A MOOC provides the opportunity to establish a community of teachers, and to develop life-long networked learning amongst the participants.

Although MOOCs as professional development for teachers have attracted the interest of researchers regarding geographically dispersed teachers working in online environments, research is still scant in this field. Relatively little is known about the characteristics of MOOCs as effective professional development for teachers, and how these characteristics compare to those of effective programs in the established literature of face-to-face professional development for teachers.

To make the most of the opportunities that MOOCs offer, careful attention needs to be paid to the processes of teachers’ learning in this new professional development venue. Although many researchers have studied the effectiveness of face-to-face professional development (e.g., Blank et al., 2008; Desimone, 2009; Loucks-Horsley, Love, Stiles, Mundry & Hewson, 2010; Borko, Jacobs & Koellner, 2010), research into professional development within a MOOC is still developing. The findings of such studies will inform whether and how MOOCs might be designed and leveraged as globally available, easily accessible, professional development options. There is a definitive need to understand which characteristics of effective professional development hold in MOOCs and how participants interact with others and with materials in this environment.

This chapter provides an overview of what is known in the field regarding the implementation of statistics in schools around the world, and the preparation of mathematics teachers to face this challenge. The chapter highlights the importance of mathematics teachers’ preparation and suggests MOOCs as a potential professional development venue for teachers. It also details the characteristics of this study, its research questions, its assumptions, and its contributions to the fields of professional development of teachers and statistics education.

Mathematics Curriculum Policy Calls for Statistics at High School

Demand for statistical knowledge is increasing around the world. This is related to easy access to large amounts of information and the need for individuals to be able to interpret that information and thus make better decisions informed by data. In tandem with this movement, schools around the world have adapted or redesigned their mathematics curricula in order to include statistics content in their students’ formation. In many different countries such as Australia, the United Kingdom, Portugal, South Africa, Brazil, and the United States, mathematics curriculum policies state that statistics content should be included in elementary and secondary school.

Analysis of the mathematics curriculum policies of these countries has shown that all of them present high school statistics content focused on data handling, data representation, and data interpretation. Some mathematics curricula (e.g. The Australian Curriculum and Reporting Authority, 2010) highlight the importance of data representation and interpretation encouraging students to interpret and investigate data presented in digital media, reports of surveys, and elsewhere. The intention is to help students understand how data was obtained to estimate population parameters and how statistics is used to support a claim. Other mathematics curricula highlight that statistics learning should also develop students as consumers of data (e.g., United

Kingdom, Department of Education [DoE] , 2003). This includes development of student’s understanding of the relationships between a statistical summary, its graphical representation, and its primitive data, thus helping them to construct rational arguments based on information and observations, and convey convincing results by using appropriate statistical terminologies (e.g.,

United Kingdom, Department of Education [DoE] , 2003; Brasil, 2006).

Consequently, statistics teaching should focus on data handling (analysis and interpretation of data) and further methods of organizing, displaying and analyzing data (DoE, 2003a). Mathematics teachers should instruct their pupils to describe, interpret, and compare observed distributions through appropriate graphical representation involving discrete and continuous data, as well as explore relationships in bivariate data (United Kingdom, Department of Education, 2013b). The role of collecting and interpreting data present in national curriculum policies provides an opportunity for mathematics teachers to implement statistics topics using modeling and technologies (e.g., Silva, Fonseca, Martins, Lopes, Fonseca, 2005; Brasil, 2006; Common Core State Standards Initiative [CCSS-M] , 2010).

In the United States, the demand for teaching statistics concepts to students has been addressed with the insertion of statistics topics such as data analysis, probability, and statistics throughout reforms of the elementary and secondary mathematics curriculum (NCTM, 2000).

The statistics strand has been reinforced even more with the release and implementation of the

Common Core (CCSS-M, 2010), focusing on the development of students’ statistics conceptual understanding beginning in grades K-6. American national assessments also include statistics concepts, further demonstrating the need to teach statistics to students.

When focusing on high school statistics, mathematics curriculum policies from many countries afford great opportunities for students to learn statistics and to develop critical thinking skills as they encounter any type of quantitative information or results of statistics investigations. These policies also bring challenges for mathematics teachers in delivering the expected statistical content described in the official documents.

Challenge in Teaching Statistics at High School

Although official guidelines and reforms in Australia, the United Kingdom, Portugal, South Africa, Brazil, and the United States emphasize the importance of teaching statistics, research indicates that teachers experience difficulties in teaching statistical topics to their students (Chadjipadelis, Meletiou-Mavrotheris & Paparistodemou, 2010; Franklin, 2013; CBMS, 2012; Meletiou-Mavrotheris & Mavrotheris, 2007; Begg & Pfannkuch, 2004). The Conference Board of the Mathematical Sciences (CBMS) reports that the majority of K-12 teachers have never taken a formal statistics course (CBMS, 2001; CBMS, 2012). Difficulties in teaching statistical topics may be related to deficits in college curricula. For those who have taken undergraduate statistics courses, these courses typically were not designed to prepare them to teach statistics as required by the curriculum policies (Franklin, 2013; Meletiou-Mavrotheris & Mavrotheris, 2007; Rossman, Medina & Chance, 2006).

Regarding in-service mathematics teachers, literature from many different countries reports their lack of knowledge and lack of confidence in teaching statistics to their students. Research in South Africa shows that many mathematics teachers do not feel confident in teaching statistics (North & Zewotir, 2006; Wessels, 2011); they tend to present statistics in a traditional way, using small, artificial data sets, and without true understanding of the analysis performed with the data. Some authors assert that a consequence of this approach may be a generation of students who have fragmented skills that will interfere with further pursuit of studies in statistics (North & Zewotir, 2006; Wessels, 2011). The lack of statistical knowledge is also seen in more experienced African mathematics teachers; before the implementation of the new South African curriculum, statistics was taught neither in elementary nor secondary school levels (North, Scheiber & Ottaviani, 2010).

Similar deficiencies in knowledge of teaching statistics exist in Brazil. Santos (2005) reported that in a survey of 52 mathematics teachers participating in the program “Teia do Saber” (“Web of Knowledge”, a professional development program) 66% of the teachers had not worked with statistics content before. Mathematics teacher participants in the survey attributed their lack of statistical knowledge to the fact that they did not develop any statistics knowledge during their college preparation, and to the absence of statistics content in the school textbooks used during their formation.

Even when it is part of the curriculum, Carvalho (2006) states that statistics content is usually placed as the last part of a mathematics school program. Consequently, if some mathematics teachers spend more time on non-statistics material early in the year, they might rush through the statistical concepts in order to finish the academic program on time. Similarly, the Portuguese Mathematics Teachers Association (APM, 1998) reports that mathematics teachers usually simplify or exclude statistics content from their teaching. Ponte and Fonseca (2000) describe that, despite the importance of statistics being recognized in the national curriculum, this topic still seems to be marginal to the Portuguese curriculum.

In countries where statistics have been fully implemented, such as Australia, research shows that mathematics teachers still encounter difficulties when dealing with the use and interpretation of data in their classes (Pierce, Chick, & Gordon, 2013). This is particularly evident when dealing with nonstandard representations of data such as a box-plot (Pierce & Chick, 2011). In some cases, mathematics teachers still had difficulty in reading, comparing, or interpreting data even when graphical representations were available to them. As a result of these difficulties, mathematics teachers tend to prefer teaching statistics by using other forms of representation, such as tabular representation.

In some cases teachers see “teaching statistics as the same as teaching mathematics” (Pierce & Chick, 2011a, p. 155). This perspective results in mathematics teachers emphasizing mathematical techniques in statistics classes, reducing the use of real data, and diminishing the explorations of statistical applications in many different areas (Holmes, 2003). Some mathematics teachers tend to be more comfortable with the application of predictable statistics formulas rather than having to address problems that may have more than one way to reach to a solution (Gattuso & Pannone, 2002). An explanation for this could be that statistics presents complex ideas and its problems are highly embedded in a context, which can mislead interpretation or lead to false intuitions during the solving of a statistics problem (Ben-Zvi & Garfield, 2004). Many statistics concepts are abstract and make use of complex notations and different representations that might be confusing for both students and teachers. Teachers also have to face a technological challenge if they decide to teach statistics with any technological device (Batanero, Burrill & Reading, 2011).

Teaching statistics in a fashion similar to teaching mathematics is an approach taken by many mathematics teachers and is described in the literature as a lack of teachers’ content

(subject area) knowledge and teachers’ pedagogical content knowledge (PCK) (Makar &

Confrey, 2003; Meletiou-Mavrotheris & Stylianou, 2003a; Meletiou-Mavrotheris,

Paparistodemou, & Stylianou, 2009). PCK is defined by Shulman (1987) as “the blending of content and pedagogy into an understanding of how particular topics, problems, or issues are organized, represented, and adapted to the diverse interests and abilities of learners, and presented for instruction” (p. 8).

This brief overview of the literature demonstrates that mathematics teachers in many different countries are not prepared to face the challenge of teaching statistics (e.g., Giambalvo & Gattuso, 2008, Franklin, 2013; Lajoie & Romberg, 1998; Batanero, Burrill & Reading, 2011). Quite often, mathematics teachers have not received appropriate preparation in college, do not feel confident in teaching statistical concepts to their students, or reduce the possibilities and potential of a statistical class by teaching statistics through a procedural mathematics class.

Thus, the question at hand is, how do we provide mathematics teachers with appropriate content knowledge and pedagogical knowledge in order to better teach statistics to their students? Professional development provides an opportunity for mathematics teachers to achieve the statistics teaching requirements stated in the curriculum policies, and also for these teachers to prepare to implement fundamental changes in their instructional methods and tools employed in the classroom.

The Need for Statistics Professional Development and Support for Teachers

Content found in the literature reinforces that mathematics teachers need to know the main curriculum guidelines with regard to statistics, the students’ difficulties with the content, and how to organize their teaching in order to promote student learning (Turkman & Ponte, 2000). It is equally necessary that teachers have knowledge about the content they are teaching, develop confidence in the materials used in class and develop links to statistics topics throughout the curriculum (Holmes, 2003; Barnett, 1982). Therefore, professional development opportunities are crucial for supporting mathematics teachers learning and future implementations of statistics concepts in class (Barnett, 1982; North, Scheiber & Ottaviani, 2010; Wessels, 2011).

Literature on professional development provides two main strands regarding opportunities for teachers to develop their statistics knowledge and their skills for teaching. One is teachers taking part in training sessions and engaging with materials provided by many national offices and organizations. Another is described as teachers participating in professionaldevelopment experiences funded by districts, schools, or state programs. These two strands coexist and are important throughout the continual formation of statistics teachers.

In the first strand, many national offices and organizations have provided training, webinars, and projects to promote access, understanding, and use of data aiming to give teachers an opportunity to access and develop materials to further use in their class (Lehohla, 2002; Kong

& Harradine, 2006). Examples of these projects can be found in CensusAtSchool

(http://www.amstat.org/censusatschool/) and ExperimentsAtSchool

(http://www.censusatschool.org.uk/resources/science), with both projects providing tools for students to collect and analyze real data, and support for teachers to integrate this real data into their classes.

For English speakers, projects such as the International Statistical Literacy Project (ISLP – http://iase-web.org/islp/), offers an online repository containing activities created to spread the use of data in statistics class. Initiatives from the American Statistical Association (ASA)/

National Council of Teachers of Mathematics (NCTM) Joint Committee on the Curriculum in Statistics and Probability also contributes to this strand, offering webinars and curate materials for teachers such as peer-reviewed lesson plans for K-12 mathematics teachers

(http://www.amstat.org/education/usefulsitesforteachers.cfm). International efforts such as the World of Statistics website (http://www.worldofstatistics.org/primary-secondary-school-teacherresources/) compile and provide lists of resources for teachers who are interested in teaching statistics to their pupils at many different school levels. Significant resources could be added if National Science Foundation (NSF) research grant initiatives were considered, such as the work of Lane and his group in creating The Rice Virtual Lab in Statistics, a source for a variety of statistics applets (http://onlinestatbook.com/rvls/index.html).

Despite an abundance of materials and content made available to teachers, the reality of teaching statistics in schools shows that the availability of resources, although good, is not enough. Statistics teachers still need professional development to improve their content knowledge, to interact with and learn from their peers, to share their teaching skills, and to improve their statistics teaching.

In the second strand, teachers’ professional knowledge has been nurtured through local and state professional development initiatives that vary in content, duration, and format. The content of these initiatives focuses on increasing teachers’ statistical content knowledge and pedagogical knowledge. Initiatives that focus on advancing teachers’ statistical content tend to center efforts in getting teachers acquainted with statistical big ideas such as use of data, variability, distribution, informal inference, correlation and covariation. Initiatives that focus on advancing mathematics teachers’ pedagogical skills center efforts on developing approaches for teaching statistics through the use of real data. Examples of these approaches make use of statistical investigations, statistical projects, and technological tools. The duration of professional development ranges from short training meetings (i.e., a one-day conference) to extensive methods such as coaching or a multiyear degree program (i.e., a master’s degree). The format of professional development also varies from being delivered face-to-face, to online meetings that happen during school hours, or outside of the school day.

Despite the existence of initiatives that are focused on providing teaching materials and training for teachers, there are still a large number of them who are teaching statistics content while having little or no training in statistics themselves. Consequently, this may limit teacher performance in class, and thus limit the learning opportunities provided to their students. This widespread situation indicates that statistics professional development for teachers should be increased, and Massive Open Online Courses (MOOCs) appear to be excellent venues to host large-scale professional development for teachers. MOOCs provide opportunities for teachers from many different parts of the world to interact with peers, to share their experiences, and to learn through engagement with materials and with each other.

MOOCs as Venues for Teachers’ Professional Development

MOOC is an acronym for Massive Open Online Course, a term coined by George

Siemens and Stephen Downes when running a large online course (Cormier & Siemens, 2010). According to Yuan, Powell and Olivier (2014), the word ‘massive’ means to spread connections with the intent of establishing communities among participants. The word ‘open’ means open enrollment and free of charge, the word ‘online’ emphasizes networked learning across multiple platforms, and the word ‘course’ means participants engaging with materials and peers, sharing resources and generating their own content.

The two most common kinds of MOOCs are cMOOCs and xMOOCs. These terminologies are based on different pedagogical frameworks implemented at these MOOCs. cMOOCs follow the principles of Connectivism (Siemens, 2004; 2005) which is described in detail in Chapter 3 of this study. xMOOCs (extension MOOCs) follow the principles of

Behaviorism and are mainly used by higher education institutions to “extend access to onsite learning activities, resources and events, which are typically based upon the transmission of content and verification of reception model” (O’Toole, 2013, p. 1).

MOOCs for educators or MOOC-Eds emerged as a new type of MOOCs specifically designed to attend to professional development needs of teachers and professionals serving in K12 settings (Kellogg, Booth, & Oliver, 2014). In terms of classification, MOOC-Eds seem to be in the middle of the spectrum of cMOOCs—xMOOCs, combining elements of both perspectives. For instance, MOOC-Eds may use platforms to deliver its course content to a large group of participants as in xMOOCs, and, at the same time they may use activities that afford collaboration among peers as in cMOOCs.

The Friday Institute for Educational Innovation at North Carolina State University is one of the pioneers in offering MOOC-Eds. Their MOOCs are designed to afford teachers selfdirected and flexible learning, peer-support and working from practice as teachers “engage in discussions, respond to participants’ questions, and elaborate on lessons learned” (Kleiman, Wolf, & Frye, 2013, p. 2). Coursera, in partnership with higher education institutions, has also launched a series of MOOCs designed for K-12 teachers (Empson, 2013). Their goal is to include courses that focus on basic and specific topics of teacher training and development.

These new venues for teachers’ professional development seem to attend a demand also observed by researchers of MIT (Seaton, Coleman, Daries, & Chuang, 2015) which informed that from 246899 participants enrolled in 11 MIT MOOCs (MITx) offered in Spring of 2014, 30% of these participants identified themselves as teachers, and other 9% informed working as teachers.

MOOCs for educators seems to be an attractive opportunity to provide cost-effective professional development for teachers. Moreover, they seem to be spaces for teachers’ continuing professional education, providing certification to teachers in different subjects. Thus, MOOCs as new venues of teachers’ professional development presents new opportunities to understand which characteristics of effective professional development hold in this type of MOOC and how participants interact with others and with materials in this environment.

The Study

Curriculum policies presented in the beginning of this chapter emphasize the role of statistics in high school mathematics classrooms. Teachers need a thoughtful and extensive preparation regarding pedagogical and content knowledge in statistics to implement these curriculum policies. The insertion of statistics in high school mathematics curricula and the need to prepare teachers to teach statistics at this level sets the motivation for this study.

A MOOC-Ed for statistics teachers is a promising opportunity for teachers worldwide to develop their professional knowledge by interacting with each other and with resources (course materials). It has the potential to be a venue for teachers’ professional development with teachers participating from different geographical locations, which may help to address the demand for qualified teachers to teach statistics in secondary school. To make the most of the opportunities that this type of MOOC offers, careful attention must be paid to the processes of teachers’ learning in this new professional development venue.

Although many researchers have studied the effectiveness of face-to-face professional development (e.g., Blank et al., 2008; Desimone, 2009; Loucks-Horsley, Love, Stiles, Mundry & Hewson, 2010; Borko et al., 2010), professional development within a MOOC is relatively new and in need of additional research. The findings of such studies would inform whether and how MOOCs might be designed and leveraged as globally available, easily accessible, professional development. There is a definitive need to understand which characteristics of effective professional development hold in MOOCs as a new form of online professional development, and how participants interact with others and with materials in a MOOC for professional development purposes. Thus, the purpose of this study is to answer the following two questions:

To what extent can the characteristics described in the literature on effective face-to-face teachers’ professional development hold in a MOOC designed for statistics development of secondary teachers?

What is the nature of teachers’ and others’ interactions (with materials and with each other) in a MOOC designed for statistical professional development?

In addressing these questions, the position is taken that learning is fundamentally a social experience (Wenger, 1998; 2006) and happens through participation in social practices. Thus, this study makes use of social theory of learning (Wenger, 1998) to describe participants’ engagement in a MOOC focused on professional development of statistics teachers. Connectivism (Siemens,

2005; Siemens & Downes, 2011) is used to frame teachers’ learning through participation as they

establish and experience connections in this professional online environment.

In this study, the online environment will be characterized by a MOOC for Educators (MOOC-Ed) offered by a large American university that has been specifically designed for teachers to learn about statistics teaching and the use of statistical investigations in teaching. As participants in this MOOC, teachers interact with resources (course materials) and with others as they establish and experience connections in this professional online environment. Interactions emerge as an important feature of online professional development, and this construct is particularly important when MOOCs are framed as participative online professional development, as is the MOOC object of this study. A definition of interaction, as well types of interactions relevant to this study are described in detail in Chapter 3.

Organization of this Dissertation

Chapter 1 has described the context of the problem, rationale, purpose of the study, and research questions. Chapter 2 describes the literature review of the main features that lead to an effective form of professional development, teachers’ professional learning, and MOOCs as spaces for teachers’ professional development and professional learning. Chapter 3 presents the Social Theory of Learning and Connectivism as the theoretical framework used in this study aligned with the concept of participants’ interactions with materials and with others in this

MOOC. Chapter 4 describes the methodology and the instruments used in conducting the study. Chapter 5 and Chapter 6 describe the findings for the first and the second research questions, respectively. Chapter 7 is dedicated to MOOC implications. Chapter 8 extends these implications for research, methodology and theory, and concludes this work by presenting avenues for further research.

CHARACTERISTICS OF PROFESSIONAL DEVELOPMENT AND TEACHER INTERACTIONS IN A MOOC DESIGNED FOR THE TEACHING OF STATISTICS

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