Whole number computations are a critical skill that serves as a foundation upon which higher-order concepts in mathematics are taught to children. To facilitate their instruction, educators often use multiple representations to support a child's cognition. Representations with physical manipulatives are widely studied through a graduated…

Students hold many misconceptions as they transition from arithmetic to algebraic thinking, and these misconceptions can hinder their performance and learning in the subject. To identify the errors in Algebra I which are most persistent and pernicious in terms of predicting student difficulty on standardized test items, the present study assessed…

Formal algebras are among the most powerful and general mechanisms for expressing quantitative relational statements; yet, even university engineering students, who are relatively proficient with algebraic manipulation, struggle with and often fail to correctly deploy basic aspects of algebraic notation (Clement, 1982). In the cognitive tradition,…

This document was prepared to assist teachers in Virginia in three ways: (1) by assessing student achievement on the competencies adopted by the State Board of Education; (2) by diagnosing student errors in mathematics; and (3) by prescribing instructional activities designed to promote student mastery of skills assessed in the competency program.…

A survey of 42 faculty members in the Virginia Community College System (VCCS) was conducted to aid in the development of a spelling course for VCCS students; 21 questionnaires were returned. The survey investigated causes of spelling problems, possible solutions, most common types of errors, curricula in which students have most spelling…