Place value refers to the meaning of a digit in a written number as determined by its placement within the number.

Pre-service education refers to the formal education and training that one receives prior to having formal responsibility for a group of children.

Primary mathematics/focused mathematics time refers to a dedicated instructional time focused on mathematics as the primary goal.

Professional development is an umbrella term including both formal education and training.

Prompting thought processes refers to a particular feedback strategy for mathematics instruction that asks students to explain their thinking or actions.

Providing information refers to clarifying incorrect answers or providing very specific information about the correct answer.

Put together situations refer to addition/subtraction situations in which two quantities are put together to make a third quantity.

Relating and ordering refers to mathematical processes of comparing and placing in order.

Relating parts and wholes level refers to a level of thinking that occurs when children combine pattern block shapes to make composites that they recognize as new shapes and to fill puzzles, with growing intentionality and anticipation.

Scaffolding refers to an instructional strategy in which the teacher provides information and assistance that allow children to perform at a higher level than they might be able to do on their own. It extends knowledge rather than verifying prior or existing knowledge.

Secondary (embedded) mathematics refers to a form of integration through which teaching and exposure to mathematics content is an ancillary activity. One or more subjects other than mathematics, such as literacy or science, are the primary goals of the activity.

Spatial orientation refers to knowing where one is and how to get around in the world. Children have cognitive systems that are based on their own position and their movements through space, as well as external references. They can learn to represent spatial relations and movement through space using both of these systems, eventually mathematizing their knowledge.

Spatial visualization/imagery refers to the process that occurs when there is understanding and performing imagined movements of two-dimensional and three-dimensional objects. To do this requires creating a mental image and manipulating it, showing the close relationship between these two cognitive abilities.

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