Teaching arithmetic to low-performing, low-SES first graders

The origin of counting: A study of the early meaning of ‘one’, ‘two’ and ‘three’ among Basque- and Spanish-speaking children

“…Behavioural studies on children's counting skills have shown that prior to the emergence of logical reasoning abilities (conservation, transitivity and seriation) that Piaget stated as prerequisites of the basic numeracy (Bouwmeester & Sijtsmal, 2004;Butterworth, 2005;Kamii & Kysh, 2006;Kamii et al, 2005;Labinowicz, 1980;Piaget & Szeminska, 1965), children's numerical performance seems to be coherent with the grasp of the procedural principles of counting (Bryant, 1996;Gallistel & Gelman, 1992;Gelman & Gallistel, 1978;Gelman & Meck, 1983). But, even preceding this earliest understanding, analysing the activity that children between 30 and 42 months old display when they are requested to gather sets of no more than four objects, there is no alternative but to admit that such young children have interiorized an essential counting understanding (Le Corre & Carey, 2007;Le Corre & Carey, 2008;Sarnecka & Carey, 2008;Sarnecka & Lee, 2009;Villarroel et al, 2009;Wynn, 1992).…”

“…From this standpoint, basic numeracy is the final consequence of internal cognitive development which prompts the subject to grasp the logico-mathematical knowledge (Bryant, 1996;Kamii, Rummelsburg & Kari, 2005). Neither the observance of the reality and the characteristic of objects (physical knowledge) nor acceptance of social conventions (social-conventional knowledge) provoke the mathematical foundation of numbers, mainly owing to the fact that number sense consists of mental relationships which have their source in an individual's mind and in the experience that the individual has with real objects (Kamii & Kysh, 2006;Kamii et al, 2005;Labinowicz, 1980;Piaget, 1971).…”

Research in Early Childhood Science Education

“…9.7 ; Kamii, Rummelsburg, & Kari, 2005 ) children try to pull one block after another out of the tower without making it fall. 9.7 ; Kamii, Rummelsburg, & Kari, 2005 ) children try to pull one block after another out of the tower without making it fall.…”

Supporting the collaboration of special educators and general educators to teach students who struggle with mathematics: An overview of the research

“…Incorporated in this group of learning theories are a wide range of views that focus primarily on how the individual constructs understanding through various cognitive processes including low-level processes (e.g., attention, perception, encoding, storage, and retrieval of knowledge) and higher order processes, such as metacognition (Lever-Duffy, McDonald, & Mizell, 2005;Schunk, 2008). Of the studies reviewed, the instruction primarily focused on memory (Cade & Gunter, 2002;Greene, 1999), one or more cognitive and/or metacognitive processes often combined with a self-reflection/regulation component (Baxter, Woodward, & Olson, 2005;Butler, Beckingham, & Lauscher, 2005;Fuchs, Fuchs, Hamlett, & Appleton, 2002;Fuchs, Fuchs, & Prentice, 2004;Ives, 2007;Kramarksi, Mevarech, & Arami, 2002 1 ;Kroesbergen, Van Luit, & Naglieri, 2003;Naglieri & Johnson, 2000;van Garderen, 2007;Van Luit & Naglieri, 1999) or understanding of a mathematical content (Butler, Miller, Crehan, Babbitt, & Pierce, 2003;Cass, Cates, Smith, & Jackson, 2003;Jitendra, DiPipi, & Perron-Jones, 2002;Kamii, Rummelsburg, & Kari, 2005;Kaufman, Handl, & Thony, 2003;Maccini & Hughes, 2000;Witzel, Mercer, & Miller, 2003;Woodward & Brown, 2006;Xin, Jitendra, & Deatline-Buchman, 2005).…”