The purpose of this study was to explore a cognitive approach to analyzing students' written responses to mathematics performance assessments to inform learning, instruction, and assessment design and development. The existing data used in this study were seventh grade students' written responses to, and item scores on, four released mathematics performance tasks used for state assessment. The students' written work included anchor, practice, and qualifying sets of papers used for rater training. The Rasch item parameters from a measurement model based on item response theory were also collected for data analysis. Grounded on Mislevy's evidentiary assessment argument, as well as advanced knowledge of cognitive research on problem solving, this study used a written protocol approach to investigate the cognitive complexity of mathematics performance tasks and the quality of scoring rubrics for those tasks. A quantitative analysis of the cognitive aspects of students' responses was also conducted using cognitive scoring rubrics based on four cognitive components suggested from research on mathematical problem solving. The findings of this study suggest that a cognitive approach to analyzing students' written responses to mathematics performance assessments can provide (a) empirical evidence that supports (or refutes) claims about the cognitive complexity of these assessments; (b) cognitive evidence to validate scoring methods to ensure that cognitive aspects of task performance will be assessed; and (c) rich, meaningful, and diagnostic assessment information about student learning in mathematics. The results of this study have educational implications suggesting that this cognitive approach can be used to provide (a) a useful framework for obtaining cognitive evidence as feedback to decisions about task revision, deletion, or inclusion when designing and developing performance assessments; (b) a useful approach to inform scoring rubric development and scoring as well as rater training; and (c) a method for analyzing students' thinking and reasoning from their written work to inform teachers of student learning and instruction in the context of the classroom. The limitations of this are discussed and suggestions for future research are also given in this study. [The dissertation citations contained here are published with the permission of ProQuest LLC. Further reproduction is prohibited without permission. Copies of dissertations may be obtained by Telephone (800) 1-800-521-0600. Web page: http://www.proquest.com/en-US/products/dissertations/individuals.shtml.]