Less is known about the components of effective mathematics instruction than about the components of effective reading instruction, because research in math is less extensive than in reading. However, conclusions still can be drawn from some very good studies that do exist, as well as from typical grade level expectations in math. As is true for reading, there is no single "best" program for teaching mathematics. Rather, certain key abilities involved in learning math need to be addressed in instruction, with the importance of different abilities shifting somewhat across the elementary and secondary grades.
Because progress in math builds heavily upon previously learned skills, it is important for instruction to be clear, unambiguous, and systematic, with key prerequisite skills taught in advance. For instance, children should not be expected to develop automatic recall of addition facts if they do not understand the basic concept of addition or the meaning of the addition sign. It is also essential for children to have sufficient practice to acquire new skills. For example, although manipulatives such as cubes or rods can be very helpful in developing basic concepts, many children will not spontaneously progress from accurately solving facts with manipulatives to automatic recall of facts. Instead, most children benefit from practice activities focused specifically on helping them to memorize facts. Similarly, learning computational algorithms such as those used in long division or two-digit multiplication often requires considerable practice.
Scientific investigators interested in learning disabilities have identified several patterns that may be found in youngsters with math disabilities. Some of these children have difficulties that revolve primarily around automatic recall of facts, coupled with good conceptual abilities in mathematics; this pattern characterizes some children with reading disabilities. Another common pattern involves difficulties with computational algorithms; yet a third pattern involves visual-spatial difficulties, such as difficulty lining up columns or with learning spatial aspects of math, such as geometry. Although effective general education instruction can help to prevent low math achievement in many children, some youngsters with genuine math disabilities will require more intensive, long-term instruction in order to be successful.
Effective Kindergarten through Grade Four Instruction
At these grade levels, general education instruction in mathematics should include development of the following math-related abilities: concepts and reasoning (e.g., basic number concepts, meaning of operations such as addition, geometric concepts); automatic recall of number facts (e.g., memorization of basic addition facts such as 3 + 4 so that children know answers instantly instead of having to count); computational algorithms (the written procedure or series of steps for solving more complex types of calculation, e.g., for two-digit addition with regrouping, calculation starts in the right-hand column and tens are "carried" from the ones to the tens column); functional math (e.g., practical applications such as time and money); and verbal problem-solving (e.g., solving word problems).Because progress in math builds heavily upon previously learned skills, it is important for instruction to be clear, unambiguous, and systematic, with key prerequisite skills taught in advance. For instance, children should not be expected to develop automatic recall of addition facts if they do not understand the basic concept of addition or the meaning of the addition sign. It is also essential for children to have sufficient practice to acquire new skills. For example, although manipulatives such as cubes or rods can be very helpful in developing basic concepts, many children will not spontaneously progress from accurately solving facts with manipulatives to automatic recall of facts. Instead, most children benefit from practice activities focused specifically on helping them to memorize facts. Similarly, learning computational algorithms such as those used in long division or two-digit multiplication often requires considerable practice.
Scientific investigators interested in learning disabilities have identified several patterns that may be found in youngsters with math disabilities. Some of these children have difficulties that revolve primarily around automatic recall of facts, coupled with good conceptual abilities in mathematics; this pattern characterizes some children with reading disabilities. Another common pattern involves difficulties with computational algorithms; yet a third pattern involves visual-spatial difficulties, such as difficulty lining up columns or with learning spatial aspects of math, such as geometry. Although effective general education instruction can help to prevent low math achievement in many children, some youngsters with genuine math disabilities will require more intensive, long-term instruction in order to be successful.
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