Journal Manuscripts by Dung Tran
Repeated sampling approaches to inference that rely on simulations have recently gained prominenc... more Repeated sampling approaches to inference that rely on simulations have recently gained prominence in statistics education, and probabilistic concepts are at the core of this approach. In this approach, learners need to develop a mapping among the problem situation, a physical enactment, computer representations, and the underlying randomization and sampling processes. We explicate the role of probability in this approach and draw upon a models and modeling perspective to support the development of teachers' models for using a repeated sampling approach for inference. We explicate the model development task sequence and examine the teachers' representations of their conceptualizations of a repeated sampling approach for inference. We propose key conceptualizations that can guide instruction when using simulations and repeated sampling for drawing inferences.
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This study examined the alignment of three selected U.S. high school textbooks series with the Co... more This study examined the alignment of three selected U.S. high school textbooks series with the Common Core State
Standards for Mathematics (CCSSM) regarding the treatment of statistical association. A framework grounded in the
literature for inclusion and exclusion of reasoning about association topics was developed, and textbook entries were
compared with the CCSSM learning expectations (LEs). Across the three series, about 77–90% of the 582 association
problems addressed two numerical variables. All CCSSM LEs were covered by two of the three series. However,
additional association LEs not found in the CCSSM were included in the textbooks. Implications for curriculum revision
and development, and content analysis are suggested. The study challenges the notion of CCSSM-aligned curricula
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This commentary highlights the contribution that careful and systematic analyses of curriculum or... more This commentary highlights the contribution that careful and systematic analyses of curriculum or content standards can make to questions and issues important in the mathematics education field. We note the increased role that curriculum standards have played as part of a standards-based education reform strategy. We also review different methods used by researchers to compare and analyze the Common Core State Standards for Mathematics, each method designed for a particular purpose. Finally, we call upon mathematics education researchers to engage in careful analysis of curriculum standards and to share their findings in ways that can inform public debate as well as support education professionals in improving student learning opportunities.
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The choice and context of authentic problems—such as designing a staircase or a soda can—illustra... more The choice and context of authentic problems—such as designing a staircase or a soda can—illustrate the modeling process in several stages.
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School Science and Mathematics, 2015
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Conference Manuscripts by Dung Tran
Mô hình hoá toán học là cầu nối giữa toán học ở nhà trường và các vấn đề trong cuộc sống hàng ngà... more Mô hình hoá toán học là cầu nối giữa toán học ở nhà trường và các vấn đề trong cuộc sống hàng ngày. Tuy nhiên, các bài toán bằng lời, một hình thức phổ biến của các tình huống mô hình hoá toán học trong nhà trường thường ít xác thực, dẫn đến thái độ thiếu tích cực của học sinh đối với các bài toán thực tế. Bài báo này trình bày khái niệm tính xác thực và các tiêu chí cho một nhiệm vụ toán học xác thực. Chúng tôi sẽ sử dụng một ví dụ để minh hoạ quá trình chuyển đổi một vấn đề toán học thường găp trong nhà trường sang vấn đề mô hình hoá xác thực. Một số đề nghị cho việc thiết kế và tích hợp các tình huống xác thực vào trong lớp học sẽ được bàn luận.
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Statistics receives attention through global curriculum. Some have designed professional developm... more Statistics receives attention through global curriculum. Some have designed professional development for teachers to develop their statistical content and pedagogy, typically on a small local scale. Online courses can expand the number of teachers involved and create communities beyond school or district lines. For a " massive " and " open " course, there are many design challenges to meet the needs of participants with varied backgrounds in teaching statistics. We will share how a Massive Open Online Course for Educators (MOOC-Ed) designed in the USA, but offered and taken by educators from around the world, including Australia and New Zealand, presents design challenges for how to best impact teachers' learning and classroom practices. For this paper, we will focus on course design principles, the design and implementation of a framework for supporting students' approaches to statistical investigations and a task guide to assist teachers in evaluating, designing, and implementing worthwhile statistical tasks. We will share participants' engagement with the course and evidence we have collected suggesting impacts on their classroom practice. Statistics receives attention through global curriculum (ACARA, 2012; CCSSM, 2010). Some have designed professional development for teachers to develop their statistical content and pedagogy, typically on a small local scale (cf. Darling-Hammond et al., 2009). Online courses can expand the number of teachers involved and create communities beyond school or district lines (Kim, 2015). Indeed, with advances in technology and interest in offering alternatives to traditional professional development, the number of online professional development opportunities has increased. The USA National Research Council (2007) claimed that: " Growing numbers of educators contend that online teacher professional development (OTPD) has the potential to enhance and even transform teachers' effectiveness in their classrooms and over the course of their careers. " (p. 2) MOOCs are designed and delivered to serve different target populations and provide diverse experiences for learners (Clark, 2013). For a " massive " and " open " course, there are many design challenges to meet the needs of participants with varied backgrounds in teaching statistics and working in different educational contexts. Capturing the potential for MOOCs to serve as large-scale professional development, teams have created MOOCs for Educators (MOOC-Eds) in the USA. As leaders of one of these teams, we designed a course focusing on teaching statistics to assist mathematics and statistics teachers in developing content understanding and pedagogical strategies for improving practice, and forming local and global communities of educators. This course was offered to and taken by educators from around the world, including those from Australia and New Zealand, presenting design challenges for how to best impact teachers' learning and classroom practices worldwide. Our question guiding this design and research is " To what extent does a MOOC in teaching statistics offer opportunities for mathematics and statistics teachers to engage in professional learning and impact their teaching statistics practices? " For this paper, we will focus on course design principles, the design and implementation of a framework for supporting students' approaches to statistical investigations and a task guide to assist teachers in evaluating, designing, and implementing worthwhile statistical tasks. We will share participants' engagement with the course and evidence we have collected suggesting impacts on their classroom practice. Course Design Principles MOOC-Eds are specifically designed to help educators meet their professional learning needs, so it is assumed that participants are motivated and self-directed. This MOOC-Ed was built using design principles of effective online learning and professional development (Kleiman, Wolf, & Frye, 2014) that emphasize: (a) self-directed learning, (b) peer-supported learning, (c) job-connected learning, and (d) learning from multiple voices. Most typical MOOC participants review material individually and some engage in discussion forums (Kim, 2015). We will highlight two of the design principles that
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With online learning becoming a more viable and attractive option for students and teachers aroun... more With online learning becoming a more viable and attractive option for students and teachers around the world, we discuss how one effort in the U.S. is focused on designing, implementing, and evaluating MOOCs designed for professional development of mathematics teachers. We share design principles and learning opportunities, and discuss how these MOOCs have impacted engagement of educators, and impacts participants report for changes to teaching practices.
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Educators lament consistent observations of students’ suspension of reality and sense-making when... more Educators lament consistent observations of students’ suspension of reality and sense-making when solving word problems. These problems mainly focus on mathematics targeted at elementary and middle school levels, such as arithmetic or proportional reasoning. This study examines high school students’ modelling competencies when they are confronted with more or less authentic tasks. An adapted version of the theory of authentic task situations (Palm, 2009) was used for design and implementation of variations of the same tasks to high school students as they worked in small groups. Results showed that students’ mathematical modelling competencies differed in both mathematical models used and considerations of real-world aspects, with more diverse approaches when solving more authentic variations. Students also showed a positive disposition towards authentic tasks.
Các nhà nghiên cứu cảm thấy đáng tiếc khi quan sát thấy học sinh thường bỏ qua yếu tố thực tế và ít vận dụng suy luận hợp lý khi giải quyết các bài toán bằng lời. Những bài toán này chủ yếu tập trung vào nội dung toán ở cấp I và II như phép tính số học hay suy luận tỉ lệ. Nghiên cứu này xem xét năng lực mô hình hoá của học sinh khi các em giải quyết các nhiệm vụ toán học với nhiều mức độ xác thực. Lý thuyết nhiệm vụ toán học xác thực (Palm, 2009) được điều chỉnh và sử dụng để thiết kế và phân công các nhiệm vụ cho các nhóm nhỏ học sinh. Kết quả cho thấy các em bộc lộ năng lực mô hình hoá toán học khác nhau, bao gồm mô hình toán học được sử dụng cũng như các yếu tố thực tế được xem xét, trong đó học sinh có nhiều tiếp cận khi giải quyết nhiệm vụ xác thực hơn. Nghiên cứu cũng cho thấy học sinh bộc lộ thái độ tích cực hơn cho các nhiệm vụ này.
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The research reported here uses a pre/post model and stimulated recall interviews to assess teach... more The research reported here uses a pre/post model and stimulated recall interviews to assess teachers' statistical reasoning about comparing distributions, when enrolled in a graduate-level statistics education course. We discuss key aspects of the course design aimed at improving teachers' learning and teaching of statistics, and the resulting different ways of reasoning about comparing distributions that teachers exhibited before and after the course.
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Simulation approaches to inference have gained prominence in statistics education. In this paper ... more Simulation approaches to inference have gained prominence in statistics education. In this paper we combine a theoretical analysis of the ways researchers and curriculum developers have represented models of simulation processes with an empirical analysis of the ways teachers represent models of the process they believe would be helpful to students. Our results cumulate in suggestions for a more explicit framework for using a simulation approach to inference.
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The research reported here uses common items to assess statistical reasoning of teachers enrolled... more The research reported here uses common items to assess statistical reasoning of teachers enrolled in a graduate-level education course to evaluate their reasoning about sampling variability. In particular, we discuss key aspects of a purposeful course design aimed at improving teachers' learning and teaching of statistics, and the resulting different ways of reasoning about sampling variability that teachers exhibited before and after the course.
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Journal Manuscripts by Dung Tran
Standards for Mathematics (CCSSM) regarding the treatment of statistical association. A framework grounded in the
literature for inclusion and exclusion of reasoning about association topics was developed, and textbook entries were
compared with the CCSSM learning expectations (LEs). Across the three series, about 77–90% of the 582 association
problems addressed two numerical variables. All CCSSM LEs were covered by two of the three series. However,
additional association LEs not found in the CCSSM were included in the textbooks. Implications for curriculum revision
and development, and content analysis are suggested. The study challenges the notion of CCSSM-aligned curricula
Conference Manuscripts by Dung Tran
Các nhà nghiên cứu cảm thấy đáng tiếc khi quan sát thấy học sinh thường bỏ qua yếu tố thực tế và ít vận dụng suy luận hợp lý khi giải quyết các bài toán bằng lời. Những bài toán này chủ yếu tập trung vào nội dung toán ở cấp I và II như phép tính số học hay suy luận tỉ lệ. Nghiên cứu này xem xét năng lực mô hình hoá của học sinh khi các em giải quyết các nhiệm vụ toán học với nhiều mức độ xác thực. Lý thuyết nhiệm vụ toán học xác thực (Palm, 2009) được điều chỉnh và sử dụng để thiết kế và phân công các nhiệm vụ cho các nhóm nhỏ học sinh. Kết quả cho thấy các em bộc lộ năng lực mô hình hoá toán học khác nhau, bao gồm mô hình toán học được sử dụng cũng như các yếu tố thực tế được xem xét, trong đó học sinh có nhiều tiếp cận khi giải quyết nhiệm vụ xác thực hơn. Nghiên cứu cũng cho thấy học sinh bộc lộ thái độ tích cực hơn cho các nhiệm vụ này.
Standards for Mathematics (CCSSM) regarding the treatment of statistical association. A framework grounded in the
literature for inclusion and exclusion of reasoning about association topics was developed, and textbook entries were
compared with the CCSSM learning expectations (LEs). Across the three series, about 77–90% of the 582 association
problems addressed two numerical variables. All CCSSM LEs were covered by two of the three series. However,
additional association LEs not found in the CCSSM were included in the textbooks. Implications for curriculum revision
and development, and content analysis are suggested. The study challenges the notion of CCSSM-aligned curricula
Các nhà nghiên cứu cảm thấy đáng tiếc khi quan sát thấy học sinh thường bỏ qua yếu tố thực tế và ít vận dụng suy luận hợp lý khi giải quyết các bài toán bằng lời. Những bài toán này chủ yếu tập trung vào nội dung toán ở cấp I và II như phép tính số học hay suy luận tỉ lệ. Nghiên cứu này xem xét năng lực mô hình hoá của học sinh khi các em giải quyết các nhiệm vụ toán học với nhiều mức độ xác thực. Lý thuyết nhiệm vụ toán học xác thực (Palm, 2009) được điều chỉnh và sử dụng để thiết kế và phân công các nhiệm vụ cho các nhóm nhỏ học sinh. Kết quả cho thấy các em bộc lộ năng lực mô hình hoá toán học khác nhau, bao gồm mô hình toán học được sử dụng cũng như các yếu tố thực tế được xem xét, trong đó học sinh có nhiều tiếp cận khi giải quyết nhiệm vụ xác thực hơn. Nghiên cứu cũng cho thấy học sinh bộc lộ thái độ tích cực hơn cho các nhiệm vụ này.
iterations of coding yielded an emergent coding scheme that helps capture the nuances of children’s reasoning with multiple types of fractions representations. Initial results from the
interview analyses suggest variation in children’s reasoning across four categories: (a) model types, (b) children use of representations and representational fluency, (c) connectedness of children’s informal to formal reasoning type, and (d) meanings of fractions. We discuss the challenges of negotiating first-order versus second-order models of children’s meaning of
fractions, and the relationship between children’s representational fluency and conceptions of fractions