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Note, too, that the Singapore problems—typical of what I’ve seen in Singapore Math—are text-lite.The emphasis is on numbers, manipulating numbers, and problem solving.
The standards ask that students understand what it means to add to and subtract from; the difference between parts and a whole; and to be able to demonstrate these understandings in more than one way.
For example, beginning as early as first grade, students are expected to …
Write one letter A, B, or C in each box to represent the story each kid read. Yet the confusion doesn’t arise from the math; it’s the fault of the English.
The problem includes students (who have no names), book titles, letter labels for the books that are different from the titles, all buried in a problem that is meant to be about comparing fractions with unlike denominators.
But to understand whether the confusion stems from the standards or the curriculum, let’s start by recalling what the CCSS actually require.
Any honest reading of the standards must recognize that in grades 4, 5, and 6, the Common Core demand that students master standard algorithms.use a variety of models, including discrete objects and length-based models (e.g., cubes connected to form lengths), to model add-to, take-from, put-together, take-apart, and compare situations to develop meaning for the operations of addition and subtraction, and to develop strategies to solve arithmetic problems with these operations.Add within 100, including adding a two-digit number and a one-digit number, and adding a two-digit number and a multiple of 10, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used.Here’s another example drawn from Singapore Math, in which a drawing is used to help pupils make sense of an elementary subtraction problem: ?– 7 = 5 In this problem, students are encouraged to draw the whole—which is unknown—and to show what they know. In this case, the drawing is used as a tool to better understand what the problem is asking.Here, students are not limited to lining up numbers, carrying the one, or borrowing but are able to use manipulatives or drawings to arrive at answers or illustrate their understanding of what it means to add or take away one.This video gives a clear sense of how a student might use a “10 frame” or number cubes to count and to add, and it shows how useful such a model can be in helping students learn numbers.The standards themselves are unambiguous that students will master the best and most efficient ways to do arithmetic, and any curriculum that does not give top billing to standard algorithms in the pertinent grades is not aligned with the Common Core.Because math users and teachers want more than procedural fluency from students (because they want young people actually to the math problems they answer so that they are ready for more advanced math), the Common Core leave plenty of room for teachers to go beyond the standard algorithm to ensure that students understand how numbers work.Third, Common Core supporters need to understand that even as opponents eagerly pounce on any mistake that anybody makes in the name of the Common Core, that doesn’t mean that we deny or ignore such failures.Failure is an important part of innovation and a necessary step in the quest for excellence.