MTTC Mathematics

Adaptive reasoning: The capacity to think logically about the relationships among concepts and situations and to justify and ultimately prove the correctness of a mathematical procedure or assertion.

Affordances: The properties of objects, systems, institutions, or environments that potentially enable or facilitate particular actions or behaviors.

Algorithm: A process or set of rules that precisely defines a sequence of operations to be followed, such as when performing calculations.

Attribution: A characteristic or feature of objects that allows for sequencing or classifying, such as length, shape, or color.

Composition: The action of putting together or combining of things as parts or elements of a whole, as in adding parts to obtain a number or arranging shapes to form a larger shape.

Conceptual understanding: An integrated and functional grasp of mathematical concepts, operations, and relations.

Counting: The action of finding the number of elements of a finite set of objects.

Decomposition: The action of separating or resolving anything into constituent parts, such as decomposing 456 into 400+50+6 or a hexagon into four triangles.

Fraction: A number expressible in the form 𝑎/𝑏 where a and b are integers and b is not zero.

Magnitude: The size of a mathematical object; a property which determines whether the object is larger or smaller than other objects of the same kind.

Manipulatives: Objects designed so learners can perceive some mathematical concept by manipulating them.

Arithmetic rack: The original arithmetic rack, also known as a Rekenrek, consists of two rows of 10 beads, each broken into two sets of five. It encourages children to ‘privilege 5’ and ‘think 10’, supporting number sense, math facts, and efficient calculation. Accessible to very young learners, it is used to generate a variety of addition and subtraction strategies.

Base-ten blocks: Blocks used to learn place value, addition, subtraction, multiplication, and division. Base ten blocks consist of cubes (ones place), rods (tens place), flats (hundreds place), and blocks (thousands place). A place value model that involves trading to regroup.

Operation: In this context, a binary operation on numbers, namely a calculation that combines two numbers to produce another number, in particular the four operations addition, subtraction, multiplication, division, together with basic associative, commutative, and distributive properties.

Place value: The value of the place of a digit for a number represented in positional notation. For example, the place value of the 3 in 237 is ten.

Procedural Fluency: Knowledge of procedures, knowledge of when and how to use them appropriately, and skill in performing them flexibly, accurately, and efficiently.

Representations: Ways to symbolize, describe, and refer to mathematical entities. They are used to understand, develop, and communicate mathematical features of objects or operations, as well as connections between different properties. Representations may be visible, such as a number sentence, a display of manipulative materials, or a graph, but may also be internal ways of seeing and thinking about a mathematical idea.

Number line: A picture of a line that serves to model real numbers. Every point of a number line is assumed to correspond to a real number and every real number to a point.

Area model: A rectangular diagram that uses an area interpretation of multiplication to model computations, in particular place-value-based algorithms.

Arrays: An arrangement of objects in rows and columns to model multiplication and division of whole numbers.