Criteria for High-Quality Capstone Courses
The 15 criteria included as part of this evaluative tool were found to be generally present in effective capstone courses. Using this tool, which includes these criteria and the accompanying rating scale, evaluators can gain insight into the possible effectiveness of a course. A template (Excel 28kb), which allows curriculum developers and evaluators to determine an average score for a course curriculum description, is provided as an additional tool for judging the effectiveness of one or more courses. Promising courses would have an average score that approaches 2 and should demonstrate consistency across most criteria. (Ratings of 3 are extremely rare in these courses and generally are found only in very focused and specific course descriptions. For example, computer math courses generally rated 3s in the technology criterion – II.G.)
I. Students should solidify and increase mathematical knowledge and skills at and above the level of Algebra II or its equivalent.
- The course description indicates that opportunities will be provided for students to reinforce and increase their fluency with arithmetic and algebraic processes.
- The course description indicates that opportunities will be provided for continued experience with functions that include linear, quadratic, and exponential and possibly extend to some advanced functions, such as logarithmic, trigonometric, higher-degree polynomial, or piecewise-defined functions.
- The course description offers students new insight into mathematics by including topics from non-traditional areas—such areas might include finite or discrete mathematics, statistical reasoning and inference, computer applications, analytic geometry, non-Euclidean geometry, or geometric probability.
II. Students should deepen and enrich the ways they think about mathematics to elevate its study well beyond rote memorization to a process of analysis and interpretation that enables the learner to grapple with a range of complex questions, topics, and issues.
- The course description provides opportunities for students to think conceptually, in addition to procedurally, about mathematics.
- The course description requires students to justify approaches to and results of problems with compelling mathematical arguments and encourages the application of solid reasoning in multiple contexts and across disciplines.
- The course description provides students with opportunities to deepen their understanding of mathematical reasoning and supports the development of expertise in using the appropriate type of reasoning for a given situation.
- The course description encourages experimental thinking, inquisitiveness, and evaluation of problem solving processes.
- The course description includes situations that engage students in the use of abstraction and generalization.
- The course description includes opportunities to see connections among the branches of mathematics.
- The course description provides opportunities for the effective use of modern technologies, such as graphing and algebraic calculators or software, data gathering probes, or computer-assisted sampling.
III. Students should develop an appreciation for and experience with a variety of applications of mathematics across disciplines and in practical situations.
- The course description includes a focus on solving non-routine problems that are of interest to students who do not currently plan to follow a mathematics-intensive postsecondary pathway in college or work.
- The course description provides opportunities for students to determine the key elements of a problem, translate them into related mathematics, apply relevant mathematical strategies to solve problems, and communicate results using terminology that is understandable, correct, and appropriate for the situation.
- The course description provides students with problems that can be solved in more than one way and with the opportunity to evaluate the effectiveness and efficiency of particular solution methods.
- The course description encourages student persistence when solving problems, including those problems that require extended time and/or the gathering of information for their solutions.
- The course description requires students to visually represent a situation using mathematical diagrams or representations and to apply common sense to evaluate the reasonableness of solutions for practical problems in terms of the context.
The following rating system will be used to judge the quality of a course curriculum:
- 0 = There is no basis in the course description for evaluation of this criterion.
- 1 = Criterion is not suggested overtly but is implied in the course description. OR = Criterion is partially suggested in the course description.
- 2 = Criterion is clearly or strongly suggested by the course description.
In a few cases there may be a need for a higher rating:
- 3 = Course description requirements satisfy and go beyond the scope of this criterion reference.
In using these criteria to evaluate a number of capstone courses, including those courses identified as strong, Achieve was able also to get a sense of the criteria themselves. Reviewers found the strongest representations of the criteria in these effective courses to be in the areas of non-traditional topics (I.C), use of technology (II.G), and non-routine problems (III.A). The criteria with the weakest representation, when judged against these courses, were algebraic function review (II.B), the use of abstraction and generalization (II.E), connections among the branches of mathematics (II.F), and problems with multiple possible solutions (III.C). This group of criteria received an average score of around 1.5, slightly lower than others. Capstone course designers might use this information when thinking about topics to be included in effective course curricula.