Subitizing is the process of recognizing and naming the number of objects in a set.

Conceptual subitizing refers to using pattern recognition to quickly determine the number of objects in a set, such as seeing 2 things and 2 things and knowing this makes 4 things in all.

Perceptual subitizing refers to instantly recognizing and naming the number of objects in a set.

Superposition is the act of placing one item on top of another.

Take apart situations refer to addition/subtraction situations in which a total quantity is taken apart to make two quantities (which do not have to be equal). These situations generally have several solutions. For example: Joey has 5 marbles to put in his 2 pockets. How many can he put in his left pocket and how many in his right pocket?

Tangram is a puzzle consisting of seven flat shapes, called tans, which are put together in different ways to form distinct geometric shapes.

Teacher effectiveness refers to the impact of teachers’ actions and behaviors on the accomplishments and/or learning outcomes of the children they teach.

Teacher-guided instruction refers to teachers’ planning and implementing experiences in which they provide explicit information, model or demonstrate skills, and use other teaching strategies in which they take the lead.

Teacher-initiated learning experiences refer to classroom experiences that are determined by the teacher’s goals and direction, but ideally also reflect children’s active engagement.

Teacher quality refers to the positive actions and behaviors of teachers, particularly with regard to their interactions with young children.

Thinking about parts level refers to a level of thinking that occurs when preschoolers can place shapes contiguously to form pictures in which several shapes play a single role (e.g., a leg might be created from three contiguous squares) but use trial and error and do not anticipate creation of new geometric shapes.

Training refers to the educational activities that take place outside of the formal education process. Such efforts may include coaching, mentoring, or workshops.

Unitizing refers to finding or creating a mathematical unit as it occurs in numerical, geometric, and spatial contexts.

Virtual manipulatives refer to manipulatives accessed through learning software and composed of digital “objects” that resemble physical objects and can be manipulated, usually with a mouse, in the same ways as

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