‘Concrete’ Manipulatives, Concrete Ideas

Abstract

The notion of 'concrete,' from concrete manipulatives to pedagogical sequences such as 'concrete to abstract,' is embedded in educational theories, research, and practice, especially in mathematics education. In this article, the author considers research on the use of manipulatives and offers a critique of common perspectives on the notions of concrete manipulatives and concrete ideas. He offers a reformulation of the definition of 'concrete' as used in psychology and education and provides illustrations of how, accepting that reformulation, computer manipulatives may be pedagogically efficacious.

Lärares och elevers användande av laborativt material i bråkundervisningen i skolår 4-6 : Vad görs möjligt för eleverna att erfara?

“…Som tidigare nämnts stödjer flertalet studier (se Clements, 1999;Cotter, 2000;Durmus & Karakirik, 2006;Kennedy & Tipps, 1994;Sowell, 1989) användandet av laborativt material eftersom de menar att elevers begreppsliga förmåga kan utvecklas då ett laborativt material används i matematikundervisningen. Ytterligare exempel på studier som visar att det är fördelaktigt att använda laborativt material för att utveckla elevers begreppsliga förmåga är Mochs (2002) studie Manipulatives Work!…”

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

“…Base-ten blocks are very popular in North American classrooms; they are used to help children "see" and operate on foundational concepts in the decimal number system, such as place value and regrouping. Teachers often use manipulatives to ground students' conceptual understanding in mathematics before abstract notation, such as written numerals, is introduced (Clements, 1999;Uttal, Scudder & DeLoache, 1997) [1,2].…”

Materiais manipuláveis e repertório compartilhado em aulas de matemática envolvendo tópicos de geometria

“…Os materiais didáticos têm sido foco de pesquisas em Educação Matemática (PAIS, 2000;CLEMENTS, 1999). Estas pesquisas, em sua maioria, discutem sobre as vantagens e as desvantagens da sua utilização no ensino de Matemática e outras, mais especificamente, no ensino de geometria.…”

“…A dimensão concreta dos materiais manipuláveis é discutida por Clements (1999), por exemplo, quando ele associa esses recursos ao fato de eles poderem ser agarrados ou manipulados com as próprias mãos. De certo modo, suas ideias convergem com as de Reys (1971apud PASSOS, 2006) no sentido de permitirem o toque, a manipulação, o movimento e, devemos acrescentar, o dobrar, frisar, recortar, sobrepor, justapor.…”