Do we need a “diagnostic tool” to determine what kids do not know or do we need to use the research of the past 20 years to study what children do know and then develop activities and tasks that challenge and develop that knowledge????
“The difficulty of conceptualizing standards for three- to six-year-olds’ mathematics education stems from the fact that subjects such as mathematics, science, and social studies are not yet differentiated in three- to six-year-olds’ thinking. For example, when young children serve coffee or go shopping in their pretend play, it is impossible to categorize this activity as mathematics, science, or social studies.
When they paint, likewise, the activity inseparably involves mathematics (e.g., three brushes for three different colors), science (e.g., the drying of paint), and art. A better guide than a subject-matter approach one that emphasizes the logico-mathematical foundation of all knowledge. The principle of teaching that flows from this conceptualization is to encourage children to think logico-mathematically because it is by thinking, or by being mentally active, that children build logico-mathematical knowledge.
Kamii and colleagues offer these two activities. Download the full article here: Kamii and Fives
One of the principles of teaching given in the NAEYC/ NCTM position statement is “Integrate mathematics with other activities and other activities with mathematics” (2002, 8). An example given in that document illustrating this principle is to say, when children are lining up, that those wearing something red can get in line first, those wearing blue can get in line second, and so on. This is probably an example of encouraging children to categorize things and to put them in temporal sequence. But from our research we do not believe or see evidence that logico-mathematical relationships develop in this kind of sterile, bit-by-bit way.
Logico-mathematical relationships are messier and more complex, and they develop in interrelated ways.
Developing activities that challenge children to think logico -mathematically in their play ( see Line Up Fives )may be a more fruitful focus of our efforts than trying to specify standards that may well be off the mark. Play has long been valued in early childhood education, and we will do well to analyze it with depth and precision not only in card games but also in other kinds of play that naturally appeal to young children.”
Constance Kamii wrote the words above in 2004. There are still valid today as we continue to worry, fret and sweat over “standards” and “diagnostic tools and tests” instead of attending to the learning of children… We keep insisting on weighing the horse not attending to its emotional, social and intellectual growth….Observe and listen, then discuss with colleagues before you make assumptions about what children do and do not understand…. Video conversations and explanations and watch carefully what young children say and think….. send me your clips, I will review with you. come to a Summer Institute, I will show you what I mean and send you back to school with clips to practice.
The “game” lining up the fives is one way to develop logico -mathematical thinking. It is highly engaging and very spatial….. I share it with parents in my public events. I let students develop variations to challenge themselves.
Thank you Constance… This is definitely one of the pieces of the puzzle that is early numeracy…..