“…by simulated teaching experience (Webel, Conner and Zhao, 2018) or by multiple solution method and designed student responses (Evans and Swan, 2014;Evans and Ayalon, 2016). The use of Concept Cartoons that indirectly mix together content-centered and student-centered approaches might also help overcome the unwanted weak relation between content-related noticing and anticipation of other alternatives or continuations that was reported for primary school teachers by Hoth et al (2016) as well as teacher's narrow focus on their own ideas instead on students' reasoning (Visnovska and Cobb, 2015). To illustrate better the potential of Concept Cartoons in relation to formative assessment and the referred study, I have prepared a Concept Cartoon on the word problem W5 (see Figure 6), inspired by the most frequent incorrect solution procedure (presented in the figure by Peter) and by three correct solution procedures gained within the study and listed in Tables 2, 5.…”
The contribution focuses on issues related to the implementation of formative assessment methods into inquiry based teaching, by means of issues related to solving twelve multiple-step arithmetic word problems based on operations with natural and rational numbers. These word problems have multiple correct solution procedures and the presented qualitative exploratory empirical study investigates how varied and how usual might be correct solution procedures provided by diverse groups of solvers -future primary school teachers attending diverse university mathematics courses of diverse forms and/or time extent. According to written data collected from 149 solvers, six notions are introduced in the paper: majority, minority and even solution procedures, and majority, minority and mixed solvers. Issues regarding minority solvers are recognized as an important element for implementing formative assessment methods. All the six notions are illustrated in the paper by samples of solution procedures and diagrams of relative frequency. Implications are given for formative assessment within any kind of education involving multiple-step word problems, regardless of the extent of implemented inquiry.
“…by simulated teaching experience (Webel, Conner and Zhao, 2018) or by multiple solution method and designed student responses (Evans and Swan, 2014;Evans and Ayalon, 2016). The use of Concept Cartoons that indirectly mix together content-centered and student-centered approaches might also help overcome the unwanted weak relation between content-related noticing and anticipation of other alternatives or continuations that was reported for primary school teachers by Hoth et al (2016) as well as teacher's narrow focus on their own ideas instead on students' reasoning (Visnovska and Cobb, 2015). To illustrate better the potential of Concept Cartoons in relation to formative assessment and the referred study, I have prepared a Concept Cartoon on the word problem W5 (see Figure 6), inspired by the most frequent incorrect solution procedure (presented in the figure by Peter) and by three correct solution procedures gained within the study and listed in Tables 2, 5.…”
The contribution focuses on issues related to the implementation of formative assessment methods into inquiry based teaching, by means of issues related to solving twelve multiple-step arithmetic word problems based on operations with natural and rational numbers. These word problems have multiple correct solution procedures and the presented qualitative exploratory empirical study investigates how varied and how usual might be correct solution procedures provided by diverse groups of solvers -future primary school teachers attending diverse university mathematics courses of diverse forms and/or time extent. According to written data collected from 149 solvers, six notions are introduced in the paper: majority, minority and even solution procedures, and majority, minority and mixed solvers. Issues regarding minority solvers are recognized as an important element for implementing formative assessment methods. All the six notions are illustrated in the paper by samples of solution procedures and diagrams of relative frequency. Implications are given for formative assessment within any kind of education involving multiple-step word problems, regardless of the extent of implemented inquiry.
“…A review of literature on scaffolding in mathematics education by Bakker, Smit and Wegerif (2015) found that there are studies focusing on social scaffolding (e.g., Makar, Bakker & Ben-Zvi, 2015), there are studies concerning learners' dispositions and mathematical problem solving skills (e.g., Toh et al, 2014), and studies concerning the teachers who are involved in scaffolding (e.g., Visnovska & Cobb, 2015). An important conclusion made by Bakker, Smit and Wegerif (2015) from their review is that diagnosis of the learning process, especially of the disadvantaged learners, is needed and should be an ongoing process.…”
The current practice of pedagogy and assessment, particularly in the blended learning mode, necessitates learners to be highly motivated and independent in order to be able to take full autonomy of their learning. By using scaffolding techniques, an instructor can identify learning difficulties at different stages of the learning process and take corrective measures to achieve optimal results. This paper discusses the use of scaffolding techniques in a mathematics classroom and investigates students' responsiveness towards this technique by analyzing the students' performance in the final examination. Suggestions are given on how the instructions can be modified to have a better scaffolding in future.
“…What is scaffolded is their pedagogical content knowledge about geometry (Nason et al) and their practices of eliciting and interpreting children's arithmetical thinking (Sleep & Boerst) respectively. We think that research about scaffolding teachers is worth conducting (see also Visnovska & Cobb, 2015), especially if the aim is to teach them how to scaffold their students (practice what you preach). One skill that many teachers struggle with is design (Nason et al), hence more research on how to scaffold teachers to redesign their curriculum seems timely.…”
This article has two purposes: firstly to introduce this special issue on scaffolding and dialogic teaching in mathematics education and secondly to review the recent literature on these topics as well as the articles in this special issue. First we define and characterise scaffolding and dialogic teaching and provide a brief historical overview of the scaffolding metaphor. Then we present a review study of the recent scaffolding literature in mathematics education (2010)(2011)(2012)(2013)(2014)(2015) based on 21 publications that fulfilled our criteria and 14 articles in this special issue that have scaffolding as a central focus. This is complemented with a brief review of the recent literature on dialogic teaching. We critically discuss some of the issues emerging from these reviews and provide some recommendations. We argue that scaffolding has the potential to be a useful integrative concept within mathematics education, especially when taking advantage of the insights from the dialogic teaching literature.
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