When Theories Don't Add Up: Disentangling he Manipulatives Debate

McNeil, Nicole M.; Jarvin, Linda

doi:10.1080/00405840701593899

Cited by 152 publications

(133 citation statements)

References 30 publications

(26 reference statements)

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“…On average, each student improved by 4 marks out of 18. This finding is consistent with previous studies that support the use of multiple representations in Mathematics lessons, such as by McNeil and Jarvin (2007), Stylianou (2010), Ahmad et al (2010) and Cope (2015).…”

Section: Discussionsupporting

confidence: 83%

“…In the recent years, there have been numerous studies that experiment with steering away from the normal 'chalk and board' and symbol-oriented algebraic lessons using multiple representations. However, teachers need to be careful when choosing representatives; minimise the use of manipulatives that are common to the students outside school, such as toys to not make the students think of the activity as simple play (McNeil and Jarvin, 2007). McNeil and Jarvin also proposed that teachers take time to build the connection between the informal and formal understandings.…”

Section: Introductionmentioning

confidence: 99%

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Using Visual Representations as an Alternative in Teaching Simultaneous Equations

Nordin¹,

Tengah²,

Shahrill³

et al. 2017

International Conference on Education

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Abstract:It is widely known that students normally struggle in the mathematics topic of algebra. They tend to steer away from algebraic problems such as solving linear equation with one variable, let alone simultaneous equations, which require them to determine the values of two variables. This action research study investigates the effect of replacing the common symbolic representations with pictorial (static visual) representations in simultaneous equations lessons of 38 low-performing Year 10 students. The data for the study was collected by means of pre-and post-tests and facilitated by three worksheets as the intervention instruments. During the lessons, pictorial representations were used in solving simultaneous equations questions. These entailed drawing several pictorials that were given in the equations. In particular, drawings of burgers, fries, cheese slices, gift boxes and sweets were used as these were generally relatable to the students in real-life. The students were then provided with fresh worksheets and subsequently translated their workings from the pictorial part to x and y. And thus forms the symbolic part of the intervention. From the students' pre-test and posttest scores, it was evident that the pictorial representations helped the students in making significant improvements in the topic.

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Section: Discussionsupporting

confidence: 83%

Section: Introductionmentioning

confidence: 99%

Using Visual Representations as an Alternative in Teaching Simultaneous Equations

Nordin¹,

Tengah²,

Shahrill³

et al. 2017

International Conference on Education

View full text Add to dashboard Cite

show abstract

“…Finally, with even the best designed manipulatives, it is unreasonable to expect young children to make the relation between the concrete material and the mathematics concept it represents without explicit guidance (Ball, 1992;McNeil & Jarvin, 2007). Studies of children's symbolic reasoning consistently find that children under the age of 5 have trouble abstracting the meaning of a symbol without instruction (e.g., DeLoache et al, 1999).…”

Section: Explicitly Explain the Relation Between The Manipulatives Anmentioning

confidence: 99%

What Makes Mathematics Manipulatives Effective? Lessons From Cognitive Science and Montessori Education

et al. 2015

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Manipulatives are ubiquitous in early childhood classrooms; yet, findings regarding their efficacy for learning mathematics concepts are inconsistent. In this article, we present four general principles that have emerged from cognitive science about ways to ensure that manipulatives promote learning when used with young children. We also describe how Montessori instruction offers a concrete example of the application of these principles in practice, which may, in turn, explain the high levels of mathematics achievement among children who attend Montessori programs during early childhood. The general principles and concrete examples presented in this article should help early childhood programs maximize the benefits of using manipulatives for developmentally appropriate mathematics instruction.

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“…Although their value is apparent on the surface, recent research has demonstrated that the conditions under which students learn and apply knowledge with manipulatives is complex and as yet, not well understood (McNeil & Jarvin, 2007) [3]. Moreover, because manipulatives are ubiquitous in North American mathematics classrooms in the early elementary years, and because teachers often have an unquestioning faith in their benefits for student learning (e.g., Moyer, 2001) [4], the study of how manipulatives are best used in mathematics instruction is a critical issue in education.…”

Section: Introductionmentioning

confidence: 99%

“…Research evidence points to the benefits of manipulatives under specific conditions, including the instructional context, the prior knowledge of the student, and the learning objectives (Laski, Jor'dan, Daoust & Murray, 2015; Marley & Carbonneau, 2014;McNeil & Jarvin, 2007;Trespalacios, 2010) [3,[5][6][7]. The focus of our research is on the instructional context, specifically on lesson sequencing and instructional guidance.…”

Section: Introductionmentioning

confidence: 99%

Effects of Instructional Guidance and Sequencing of Manipulatives and Written Symbols on Second Graders’ Numeration Knowledge

2017

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Concrete objects used to illustrate mathematical ideas are commonly known as manipulatives. Manipulatives are ubiquitous in North American elementary classrooms in the early years, and although they can be beneficial, they do not guarantee learning. In the present study, the authors examined two factors hypothesized to impact second-graders' learning of place value and regrouping with manipulatives: (a) the sequencing of concrete (base-ten blocks) and abstract (written symbols) representations of the standard addition algorithm; and (b) the level of instructional guidance on the structural relations between the representations. Results from a classroom experiment with second-grade students (N = 87) indicated that place value knowledge increased from pre-test to post-test when the base-ten blocks were presented before the symbols, but only when no instructional guidance was offered. When guidance was given, only students in the symbols-first condition improved their place value knowledge. Students who received instruction increased their understanding of regrouping, irrespective of representational sequence. No effects were found for iterative sequencing of concrete and abstract representations. Practical implications for teaching mathematics with manipulatives are considered.

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When Theories Don't Add Up: Disentangling he Manipulatives Debate

Cited by 152 publications

References 30 publications

Using Visual Representations as an Alternative in Teaching Simultaneous Equations

Using Visual Representations as an Alternative in Teaching Simultaneous Equations

What Makes Mathematics Manipulatives Effective? Lessons From Cognitive Science and Montessori Education

Effects of Instructional Guidance and Sequencing of Manipulatives and Written Symbols on Second Graders’ Numeration Knowledge

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