We take K.OA.3 and K.CC.6 and consider them together, then rather than K.CC.6, unfortunately, suggests activities to evolve these concepts that would bore a With these three concepts before moving on to addition and subtraction in Grade 1. Should comprise the Big Three of Kindergarten and you can go plenty deep Than he than to thank his parents that the cookies were distributedĬounting, that two quantities are equal is a critically important concept, followed in developmental sequence by one quantity is A child is more likely to complain that his brother got more cookies Within the realm of a kindergartner's experience are the ideas of equal, lessĪnd more. K.CC.6 states `` Identify whether the number of objects in one group is greater than, less than, or equal to the number of objects in another group, e.g., by using matching and counting strategies.'' Math textbooks and workbooks are filled with dull, pointless questions. Many math questions are solved and then quickly forgottenīecause they lack this dimensionality. Possibilities, list them all or draw them all, and that's it theĪ well-conceived question will be remembered, not for the answer, but for the Past the obvious answers to the question. What makes the flower problem particularly shallow is that it creates no open paths for forward learning Task of the educator and of the curriculum, and math questions should Kindergartner's experiences, and at that age, coalescing a child'sĪmorphous experiences by way of a well formulated question is a parallel More importantly, though, the flower question is pretty far removed from a The point that the question is sexist, but there, we said it anyway. This is aīlog about mathematics, not gender issues, so we shouldn't be raising Unsettling, and worse than the apple problem we used. Ways to distribute five flowers among grandma's two vases is particularly The way we've been teaching addition all these years stillĬCSSI's example (Table 1 in the Standards), to figure out all possible Shouldn't be posed just because it can be, especially at such a youngĪge the purpose of the question needs be clear.Ĭoncepts are neither taught nor reinforced by decomposition additionĬoncepts are introduced by putting two groups together and counting the What then, is the pedagogical theory behind assigning such a task to a kindergartner? We think there is none. And their instincts would be correct it's not a mathematically important result that 23 + 19 and 11 + 31 both add to 42. That fascinating, they'll say ``duh'', because they saw 5 apples allĪlong. Mathematical abstraction that both 2 + 3 is 5 and 4 + 1 is 5, and isn't If you try to impress on a kindergartner the The apples, because no matter how the apples are separated, the total remains the same. Kindergartner will be impressed that there are myriad ways to separate Separate groups and record numbers and equations, but the intent of the You can force them to draw pictures of the Learning to recognize common and distinct characteristics, so a commonĮxercise is to groups things together that share a characteristic, not separate them. Kindergartners are at an age of concrete thinking, where they are Groups is an abstraction any intelligent kindergartner will want to put Cézanne, why would you want me to separate 5 apples into two groups? That's [As we try to put ourselves into a kindergartner's mind, we'd be thinking (but writing with an adult mind's language), As the problem proceeds, no matter how they are separated, a kindergartner will likely only perceive all 5 apples as one group. Let's say a problem begins with 5 apples and asks a kindergartner to place them into two bowls in various ways (see footnoteīelow). ``pairs'', does it really mean ``groups''? Is it an introduction to oddĪnd even numbers? The commutative property? Transitivity?Īlgebra? Combinatorics? Or to impress on the kindergartner that both 4 Common Core standard K.OA.3 states, `` Decompose numbers less than or equal toġ0 into pairs in more than one way, e.g., by using objects or drawings,Īnd record each decomposition by a drawing or equation (e.g., 5 = 2 + 3Īlthough it falls under the general heading of addition and subtraction, the mathematical concept that thisĮxercise is supposed to teach kindergartners is mystifying.
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