Reverse-scaffolding algebra: empirical evaluation of design architecture

Chase, Kiera; Abrahamson, Dor

doi:10.1007/s11858-015-0710-7

Cited by 14 publications

(16 citation statements)

References 33 publications

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“…Specifically, students could be too scaffolded and have little space to develop their abilities. To avoid this situation, many researchers proposed allowing students to seek help during word problem-solving (Chase and Abrahamson 2015;Roll et al 2014). For example, Cheng et al (2015) designed a Scaffolding Seeking system to encourage elementary students to solve word problems by themselves by expressing their thinking first, instead of receiving and potentially abusing scaffolds.…”

Section: Related Workmentioning

confidence: 99%

Enhancing achievement and interest in mathematics learning through Math-Island

Yeh

Cheng

Chen

et al. 2019

RPTEL

134

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Conventional teacher-led instruction remains dominant in most elementary mathematics classrooms in Taiwan. Under such instruction, the teacher can rarely take care of all students. Many students may then continue to fall behind the standard of mathematics achievement and lose their interest in mathematics; they eventually give up on learning mathematics. In fact, students in Taiwan generally have lower interest in learning mathematics compared to many other regions/ countries. Thus, how to enhance students' mathematics achievement and interest are two major problems, especially for those low-achieving students. This paper describes how we designed a game-based learning environment, called Math-Island, by incorporating the mechanisms of a construction management game into the knowledge map of the elementary mathematics curriculum. We also report an experiment conducted with 215 elementary students for 2 years, from grade 2 to grade 3. In this experiment, in addition to teacher-led instruction in the classroom, students were directed to learn with Math-Island by using their own tablets at school and at home. As a result of this experiment, we found that there is an increase in students' mathematics achievement, especially in the calculation and word problems. Moreover, the achievements of low-achieving students in the experimental school outperformed the low-achieving students in the control school (a control group in another school) in word problems. Moreover, both the lowachieving students and the high-achieving students in the experimental school maintained a rather high level of interest in mathematics and in the system.

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Section: Related Workmentioning

confidence: 99%

Enhancing achievement and interest in mathematics learning through Math-Island

Yeh

Cheng

Chen

et al. 2019

RPTEL

134

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“…At least, from your subjective perspective, Condition 2 demands of you to develop a new phenomenological and conceptual construction of what a circle is from a mathematical perspective (Abelson & diSessa, 1986; Papert, 1980; Piaget & Inhelder, 1969; Wilensky & Papert, 2010). More generally, the available means of production we have learned to access and use in fulfilling an activity task are instrumental in forming our conceptions of the objects we produce and perceive (Baird, 2004; Chase & Abrahamson, 2015; Meira, 1998; Rosenbaum & Abrahamson, 2016). …”

Section: Learning Is Moving In New Ways: Designing For the Emergence mentioning

confidence: 99%

Making sense of movement in embodied design for mathematics learning

Abrahamson

Bakker

2016

Cogn. Research

Self Cite

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Embodiment perspectives from the cognitive sciences offer a rethinking of the role of sensorimotor activity in human learning, knowing, and reasoning. Educational researchers have been evaluating whether and how these perspectives might inform the theory and practice of STEM instruction. Some of these researchers have created technological systems, where students solve sensorimotor interaction problems as cognitive entry into curricular content. However, the field has yet to agree on a conceptually coherent and empirically validated design framework, inspired by embodiment perspectives, for developing these instructional resources. A stumbling block toward such consensus, we propose, is an implicit disagreement among educational researchers on the relation between physical movement and conceptual learning. This hypothesized disagreement could explain the contrasting choices we witness among current designs for learning with respect to instructional methodology for cultivating new physical actions – whereas some researchers use an approach of direct instruction, such as explicit teaching of gestures, others use an indirect approach, where students must discover effective movements to solve a task. Prior to comparing these approaches, it may help first to clarify key constructs. In this theoretical essay we draw on embodiment and systems literature as well as findings from our design research so as to offer the following taxonomy that may facilitate discourse about movement in STEM learning: (1) distal movement is the technologically extended effect of physical movement on the environment; (2) proximal movement is the physical movements themselves; and (3) sensorimotor schemes are the routinized patterns of cognitive activity that become enacted through proximal movement by orienting on so-called attentional anchors. Attentional anchors are goal-oriented phenomenological objects or enactive perceptions (“sensori-”) that organize proximal movement to effect distal movement (“-motor”). All three facets of movement must be considered in analyzing embodied learning processes. We demonstrate that indirect movement instruction enables students to develop new sensorimotor schemes including attentional anchors as idiosyncratic solutions to physical interaction problems. These schemes are, by necessity, grounded in students’ own agentive relation to the world while also grounding target content such as mathematical notions.

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“…As many articles testify, technology can be sometimes used as soft scaffolds, for example to promote dialogue among students or future teachers (Abdu et al, 2015). But it can also be used for mathematical exploration and feedback (Chase & Abrahamson, 2015;Dove & Hollenbrand, 2014;Kazak et al 2015).…”

Section: What Is Scaffolded?mentioning

confidence: 99%

“…Some emphasize dialogue (Abdu et al, this issue;Bell & Pape, 2012, Kazak et al, 2015Kolikant & Broza, 2011), others teacher strategies (Makar et al, 2015;Pfister et al, 2015;Stender & Kaiser, 2015), teacher practices (Abdu et al, 2015), or the specific nature of computer tools (Chase & Abrahamson, 2015;Kazak et al, 2015). The key idea behind the aforementioned artefacts (solution plans etc.)…”

Section: How Does Scaffolding Take Place?mentioning

confidence: 99%

Scaffolding and dialogic teaching in mathematics education: introduction and review

Bakker

Smit

Wegerif

2015

ZDM Mathematics Education

117

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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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Reverse-scaffolding algebra: empirical evaluation of design architecture

Abstract: how you can disappoint them if you betray some secret too early? Twelve year olds are different; they got used to imposed solutions, they ask for solutions without trying. (Freudenthal 1971, p. 424).

Cited by 14 publications

References 33 publications

Enhancing achievement and interest in mathematics learning through Math-Island

Enhancing achievement and interest in mathematics learning through Math-Island

Making sense of movement in embodied design for mathematics learning

Scaffolding and dialogic teaching in mathematics education: introduction and review

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