Language syntax is discussed, followed by an overview of algbraic syntax. Evaluating algebraic expressions was chosen as the means to investigate the psychological basis of syntactic skills. Subjects' ability to perform evaluative tasks appropriately using standard algebraic notation was ascertained; then similar tasks were presented using a nonce, or artificial, notation designed to display the propositional or deep structure character of algebraic expressions while distorting the surface cues of ordinary notion. Data from three ten-item instruments (included in appendices) were analyzed for 517 subjects in grades 9, 11, first-year calculus, and fourth-year engineering; and professional engineers in Vancouver, British Columbia. Covariates were computing experience and past algebraic achievement. Most subjects (93.6%) demonstrated competence in the regular notation algebra tasks. Both subjects using propositional referents and those using surface cues in syntactic decision making were generally successful (91.0%) at the five simple nonce algebra items, but complex nonce algebra items were more difficult (66.3% was the mean percentage correct). Close nonce notation was significantly more difficult than spaced nonce notation. Variation among respondents was substantial, and individual differences are extensively discussed, as are implications for research. (MNS)