MFAS Glossary of STEM Education Terminology

The cardinality of a set refers to the number of elements (or objects) contained in the set.

When counting a set of objects, the last number word used corresponds to the cardinality of the set.

A strategy for combining (i.e., adding or subtracting) numbers that involves combining tens with tens and ones with ones. These partial sums are then combined to get a final result. For example, in order to subtract 43 from 97, a student may subtract 90 - 40 getting 50. Then the student subtracts three from seven getting four. To complete the problem, the student adds four to 50, getting a final answer of 54.

A strategy for combining (i.e., adding or subtracting) numbers that involves adjusting one number to compensate for changes made in another number. For example, in order to add 38 + 9, the student adds two to 38 to make it 40 but subtracts two from nine making it seven. Then the student combines 40 and seven getting a final answer of 47.

Determining the cardinality of an organized set of objects, such as the array of eight dots on a domino, almost instantly. Sets that are perceptually subitized are immediately combined.

The ability to maintain that the cardinality of a set is the same regardless of the distribution or orientation of the objects in the set.

After combining objects from one or more sets, the child counts the objects starting with "one" to determine the sum.

The child counts backward from the a starting quantity given in the problem using the number of counting words given by a change quantity given in the problem. The child keeps track of the number of counting words spoken (often using fingers) to find the unknown in the problem.

The child counts backward from a starting quantity until a result given in the problem is reached. The child keeps track of the number of counting words spoken (often using fingers) to reach the result to find the unknown in the problem.

To count the total number of objects in two or more sets, the child begins counting from the total of the first set. For example, if the first set contains five objects, the child begins the count with "six" and continues until the remaiing objects are counted.

The child counts forward from the first addend given in a problem using the number of counting words given by the second addend in the problem. The child keeps track of the number of counting words spoken (often using fingers) to find the unknown in the problem.

The child counts forward from the larger addend given in a problem using the number of counting words given by the smaller addend in the problem to reach a total. The child keeps track of the number of counting words spoken (often using fingers).

The child counts forward from a starting quantity given in the problem until the total is reached. The child keeps track of the number of counting words spoken (often using fingers) to reach the total.

Strategies that involve the use of counting rather than modeling to solve word problems.

A computational strategy in which a student decomposes numbers into other numbers for which known number facts can be applied. For example, to add five and four, the student decomposes five into one and four. The student knows that the sum of two fours is eight so the sum of five and four is one more than eight.

A strategy for solving problems in which a known number fact is used to find an unknown sum, difference, product, or quotient. For example, a student may know that the sum of two fives is ten. Therefore, the sum of five and six must be one more than ten since six is one more than five.

Using objects (including fingers) to represent quantities in word problems.

The quantity that a number represents contains the quantities represented by all preceding numbers. For example, 14 contains 13 (as well as 12, 11, 10, 9, …).

A strategy for combining (i.e., adding or subtracting) numbers that involves combining numbers in increments. For example, in order to add 46 + 35, a student may add 40 + 30 getting 70 and then add 70 + 6 to get 76. The student then adds 76 + 4 getting 80 and finally adds the one that is leftover from the five, getting 81.

The child models the addends in the problem with objects and after combining the objects, counts all of them to determine the sum.

The child models the starting quantity with a set of objects and then adds additional objects to the set until the total is reached. The objects added to the set are then counted to find the unknown in the problem.

Objects from two different sets are paired until the smaller set is exhausted. By doing so, the larger set can be identified. Also, the remaining objects from the larger set can be counted in order to determine the difference between the cardinality of the sets.

A problem in which the number of objects in groups and a total number of objects are given. The unknown is the number of groups.

A principle of counting in which a distinct and unique word name is applied to each object counted.

A problem in which a number of groups containing the same number of objects and a total number of objects are given. The unknown is the number of objects in each group.

Determining the cardinality of a small collection of objects almost instantly.

The child models the starting quantity with a set of objects and then removes a given number of objects from this set. The remaining objects are then counted to find the unknown in the problem.

The child models the starting quantity with a set of objects and then removes objects from this set until the total is reached. The objects removed from the set are then counted to find the unknown in the problem.

A principle of counting in which the word names used for counting are applied in a consistent order. For example, a child demonstrating stable order will count, "one, two, three four, five, etc." rather than "one, three, four, two, six, five, etc."

The ability to perceive the number of objects in a set almost immediately and without explicitly counting.

Carpenter, T.P.,  Fennema, E.H., Franke, M.L., Levi, L., & Empson, S.B. (1999). Children's mathematics: Cognitively guided instruction. Portsmouth, NH: Heinemann.

Clements, D.H. and Sarama, J. (2009). Learning and teaching early math: The learning trajectories approach. New York: Taylor & Francis.

Gelman, R. & and Gallistel, C.R. (1978). The child's understanding of number. Cambridge, MA: Harvard University Press.