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| Basic facts for addition and multiplication refer to combinations where both addends or both factors are less than 10 |
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| Mastery of a basic fact means that a child can givea quick response (in about 3 sec) without resorting to non-efficient means, such as counting |
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| Teaching students facts well does not require much more than flashcards and timed tests |
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| developing quick and accurate recall with the basic facts is a developmental process |
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| the reality that many studetns in 4th and 5th grades have not mastered addition and subtraction facts and that students in middle school and beyond do not know thier multiplication facts strongly suggests that memorizing facts simply does not work wellT |
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| struggling learners and studentss with disabilities often have difficulty memorizing many isolated facts, but can be successful using strtategies |
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| excessive use of drill of basic facts doesnot cause unnecessary anxiety and undermine students interest in doing mathematics |
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| in order to guide students to use effective strategies it is not necessary for teachers to know as many strategies as possible |
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| research has found that when a strong emphasis is placed on students solving problems not only do they become better problem solvers but they also master more basic facts than sutdents in a fact drill proram |
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| STORY PROBLEMSN PROVIDE CONTEXT THAT CAN HELP STUDENTS UNDERSTAND THE SITUATION AND APPLY FLEXIBLE STRATEGIES FOR DOING THE COMPUTATION |
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| Childdren do not need lots of opportunities to make strategies their own |
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| perhaps the most important strategy for basic facts is the make 10 strategy |
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| story problems using two numbers taht can make 10 or that ask how many are needed to mae 10 can assist this process |
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| The ten frame is not a very useful tool for teaching 10 facts |
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| knowing combinations that make 10 do not help with basic fact mastery or foundation for working on addition with higher numbers as well as understanding place value concepts |
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| know facts and derived facts |
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| one more than and two more than |
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| Reinforcing reasoning strategies |
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| the up ove r10 reasoning strategy is important but does not deserve significant attention in teaching addition and subtraction facts |
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| the big idea of developing reasoning strategies is to help students move away from counting and become more efficient until they are able to recall facts quiclky and correctly |
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| subtraction as think addition |
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| when students see 9-4 as a teacher you want students to think spontaneously "four and what makes nine" |
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| if think addition is tobe used effectively it is not essential that addition facts |
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| when a teacher uses a story problem there will be a high probablility that the studetns will think 5 and how many make 12 |
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| the take from the 10 reasoning strategy is well known in the United States but is not consistently used in high performing countries |
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| the commutative property is not very important for multiplication facts |
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| facts that have 2 as a factor are equivalent to the addition doubles and should already be known by the students |
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| studetns will not need help realizing that not only is 2X7 double 7 but so is 7x2 |
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| teachers should regulary use rules that sound arbitraty and without reason such as any number multiplied by zero is zero |
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| the concepts behing multiplying by zeros and ones can best be developed through flashcards |
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| the close fact reasoning is critically imprtant because it can be used for any fact and it reinforces students sense of numbers and relationships among numbers |
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| story problems provide context that can help students understand the situation and apply flexibible strategies for doing the computation |
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| the array plays a large part in helping studetns establish multiplication facts and relationships |
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| mastery of multiplication facts and connections between multiplication and division are not the key elements of division fact mastery |
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| drill does not strengthen memory and should not be used |
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| flash cards are among the most useful approaches to fact strategy practice |
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| Drill is not apropriate after students have developed reasoning strategies |
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