Description:
This paper details the research design of a multidisciplinary, multi-method, collaborative research project investigating health communication from the experiences of the early childhood education (ECE) sector during the COVID-19 pandemic. With the rapidly evolving pandemic, the ECE sector was instantly tasked with expanding their required health practices to prevent the spread of infection. It was evident that the sector needed a system to communicate health advice in a timely, consistent and effective manner. Founded on a partnership model based on 'knowledge brokering' theory, this project demonstrates the value of a multidisciplinary research team collaborating with stakeholder organisations to investigate how COVID-19 health information traversed through complexities of organisational layers and diverse communities of families and staff. Detailing our data collection and analysis protocols, we conclude by outlining how our innovative research design is generating actionable and impactful recommendations for both the ECE and health sectors. [Author abstract]
Description:
Collaborative problem solving (CPS) has received much attention recently. However, little is known about how people work in CPS and how to support students working productively in the setting. CPS requires both social and cognitive aspects. This paper focused on the social aspect to examine how students act on their agency in CPS. Using data from a laboratory classroom with a social setting, we analysed the positions that students take when solving an open-ended mathematics problem and their illocutionary force. The results show that students reveal dynamic positions with a combination of different forces. Also, some interactions are more productive in CPS than others.
Description:
To address the upcoming reform curriculum initiative following competency-based learning in Vietnam, this study examines how variations of a contextualized task allow students to experience the mathematical modelling process. We explore how Grade 10 students respond to tasks with different levels of authenticity when they first attempt such tasks. Adapting the Theory of Authentic Task Situations, we designed variations of the Goat Cage task and implemented them with six small groups of students. Results showed that the modelling processes that the students progressed through differed in mathematical models used and real-world considerations, with diverse approaches when solving the more-authentic variation. Not all phases of the modelling process were observed explicitly when they engaged in the tasks. Students showed a positive disposition towards tasks with more authentic contextual information. The study suggests ways to adapt contextualized tasks to make them more authentic, which allows students to experience a holistic modelling process.
Description:
This conceptual paper proposes a model to describe the quality of student dialogue during participative collaborative problem solving. Drawing on the participation metaphor of learning, we argue that the construct of mathematical sophistication is useful to describe the quality. We then present two frameworks, mathematical competencies and mathematical practices, as ways to operationalise the construct in the collaborative problem-solving setting. We argue that by using a networking theories approach, the two frameworks will provide nuances of levels of mathematical sophistication that can be observed in student interaction. In addition, they could provide an analysis of both individual and group contributions to mathematical sophistication in a collaborative task setting. Implications of using two approaches for conceptualising mathematical sophistication for future mathematics education research and teaching practices are provided.
Description:
This conceptual paper proposes a model to describe the quality of student dialogue during participative collaborative problem solving. Drawing on the participation metaphor of learning, we argue that the construct of mathematical sophistication is useful to describe the quality. We then present two frameworks, mathematical competencies and mathematical practices, as ways to operationalise the construct in the collaborative problem-solving setting. We argue that by using a networking theories approach, the two frameworks will provide nuances of levels of mathematical sophistication that can be observed in student interaction. In addition, they could provide an analysis of both individual and group contributions to mathematical sophistication in a collaborative task setting. Implications of using two approaches for conceptualising mathematical sophistication for future mathematics education research and teaching practices are provided.
Description:
Through the lenses of statistical investigations and cognitive demands, we examined bivariate data tasks offered in US high school mathematics textbook series—a popular representative of three curriculum types: traditional, integrated, and hybrid. We developed a framework grounded in literature of association topics for the inclusion and exclusion of tasks. Using the Guidelines for Assessment and Instruction of Statistics Education (GAISE) framework, textbook tasks were coded for four investigation components (formulate questions, collect data, analyze data, and interpret results) and levels of statistical sophistication, as well as levels of cognitive demand as suggested by the Mathematical Complexity framework. Across the three series 582 statistical association tasks, all components of statistical investigation were evident with different levels of treatment: (a) all questions for statistical investigations were provided by textbook authors (b) tasks rarely afforded student opportunities to collect data and (c) nearly all of the tasks required students to analyze data and most required them to interpret results. Tasks in the integrated series were more numerous ( n = 246) and required higher levels of mathematical complexity and statistical sophistication than tasks in the traditional and hybrid series. The vast majority of tasks were coded at the GAISE Level B for analyze data and interpret results and moderate level for mathematical complexity. Further analyses show the concordance between the developmental levels for statistical sophistication and mathematical complexity. Suggestions for curriculum development, content analysis, and future research are provided.
Description:
In recent years, school mathematics has increased its emphasis on functions and functional relationships in dynamic situations (Carlson, Jacobs, Coe, Larsen, & Hu, 2002). Secondary school mathematics curricula support the promotion of conceptual understanding on functions including patterns of change to help student understand the fundamental ideas of calculus (Zeytun, Cetinkaya, & Erbas, 2010). However, research has suggested that undergraduate students show their weak understanding of functions while entry-level university courses do little to address this deficiency. Research on students’ understanding of functions has revealed that even high-performing students have difficulty modeling functional relationships of dynamic functional events. Their difficulties resulted from the lack of abilities in imagining and coordinating the simultaneous changes in variables, namely in determining the rate of change of one variable as it continuously varies in a dependent relationship with another variable (Carlson et al., 2002). This type of abilities is known as covariational reasoning, which involves imagining and coordinating the changes in two quantities simultaneously (Carlson et al., 2002). Dynamic functional situations are recommended to be used in order to promote students’ understanding about the relationship between the rate of change and covariant aspects of functions (Carlson et al., 2002). Many studies were conducted to investigate undergraduate students’ covariational reasoning abilities (eg, Carlson et al., 2002; Johnson, McClintock, & Hornbein, 2017) and prospective and in-service teachers’ covariational reasoning (Yemen-Karpuzcu, Ulusoy, & Işıksal-Bostan 2017; Zeytun et al., 2010), paucity of research is done to explore secondary school students’ covariational reasoning and little is known about their reasoning about the covariant aspects of function in dynamic situations. Therefore, this paper has explored high school students’ covariational reasoning in solving tasks about dynamic situations involving two simultaneously changing quantities. The focus was on students’ ability to reason about covarying quantities and their difficulties in interpreting dynamic functional situations.
Description:
In recent years, school mathematics has increased its emphasis on functions and functional relationships in dynamic situations (Carlson, Jacobs, Coe, Larsen, & Hu, 2002). Secondary school mathematics curricula support the promotion of conceptual understanding on functions including patterns of change to help student understand the fundamental ideas of calculus (Zeytun, Cetinkaya, & Erbas, 2010). However, research has suggested that undergraduate students show their weak understanding of functions while entry-level university courses do little to address this deficiency. Research on students’ understanding of functions has revealed that even high-performing students have difficulty modeling functional relationships of dynamic functional events. Their difficulties resulted from the lack of abilities in imagining and coordinating the simultaneous changes in variables, namely in determining the rate of change of one variable as it continuously varies in a dependent relationship with another variable (Carlson et al., 2002). This type of abilities is known as covariational reasoning, which involves imagining and coordinating the changes in two quantities simultaneously (Carlson et al., 2002). Dynamic functional situations are recommended to be used in order to promote students’ understanding about the relationship between the rate of change and covariant aspects of functions (Carlson et al., 2002). Many studies were conducted to investigate undergraduate students’ covariational reasoning abilities (eg, Carlson et al., 2002; Johnson, McClintock, & Hornbein, 2017) and prospective and in-service teachers’ covariational reasoning (Yemen-Karpuzcu, Ulusoy, & Işıksal-Bostan 2017; Zeytun et al., 2010), paucity of research is done to explore secondary school students’ covariational reasoning and little is known about their reasoning about the covariant aspects of function in dynamic situations. Therefore, this paper has explored high school students’ covariational reasoning in solving tasks about dynamic situations involving two simultaneously changing quantities. The focus was on students’ ability to reason about covarying quantities and their difficulties in interpreting dynamic functional situations.
Description:
To meet the demand of incoming school curriculum reform focusing on competency-based learning in Vietnam, this paper reports on an innovation project on developing secondary mathematics preservice teachers’ (PSTs) mathematical literacy and preparing them to teach mathematics contextually. We developed a curriculum and studied the effectiveness of the implementation of a secondary mathematics PST education program that integrates mathematical literacy (ML) in methods courses. The courses offer the PSTs opportunities to experience ML as active learners and prepare them to teach ML. The preliminary results on a project-based modeling task show that the PSTs begin to develop an understanding of ML when they take real-life considerations into account in solving the authentic problem. Discussion about the tension between simplifying models and reflecting the real problem, and directions for future study are suggested.
Description:
This paper reports on efforts to characterise levels of mathematical sophistication for students in collaborative mathematics problem solving. Using a laboratory classroom in Australia, data were captured with multiple cameras and audio inputs. Students worked individually, in pairs, and in small groups (4 to 6 students). We focused on investigating collaborative work, with the goal of studying the mathematical sophistications of students’ reasoning when solving problems. Drawing from two analytical frameworks to document the mathematical sophistication in students’ exchange, levels of cognitive demands and mathematical practices, this research highlights different aspects of students’ reasoning in solving these tasks.
Description:
This paper reports on efforts to characterise levels of mathematical sophistication for students in collaborative mathematics problem solving. Using a laboratory classroom in Australia, data were captured with multiple cameras and audio inputs. Students worked individually, in pairs, and in small groups (4 to 6 students). We focused on investigating collaborative work, with the goal of studying the mathematical sophistications of students’ reasoning when solving problems. Drawing from two analytical frameworks to document the mathematical sophistication in students’ exchange, levels of cognitive demands and mathematical practices, this research highlights different aspects of students’ reasoning in solving these tasks.
Description:
In this study, we examined non-traditional pathway preservice teachers’ attitudes towards mathematics to inform decision-making on designing the course and the units related to mathematics and how to support the teachers in transitioning smoothly into higher education programs. We adopted a mixed design approach to document teachers’ attitudes towards mathematics. Results show that the teachers revealed positive attitudes towards their mathematical self-ability of the subject, the enjoyment of mathematics, and the utility of the subject
Description:
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.
Description:
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.
Description:
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.
Description:
The research reported here uses a pre/post-test 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.
Description:
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.
Description:
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.