In mathematics, conceptual understanding is the ability to grasp the meaning behind mathematical concepts. Many students see math as a procedural discipline based on step-by-step problem-solving; in reality, though, math is basically a set of concepts and theorems dealing with relationships between variables. Informal assessment tools for conceptual understanding in adult learners, should test to see if the learners are approaching the material critically and philosophically. Some such tools include checklists, graded class discussions, and one-on-one interviews.
In mathematics, procedural skills are the abilities needed to manipulate mathematical information. These skills include fact recall, symbol usage, algorithm use, and ordering. Informal assessment tools for the procedural skills of adult math learners, should be able to test all of these skills. Some such tools include short quizzes, student-generated test questions, and class discussions.
Problem-solving is the ability to obtain the correct answer to a mathematical problem through the use of a demonstrable thought process. Problem-solving is used in algebra, trigonometry, calculus, and other mathematical disciplines. With informal assessment of adult students' problem-solving skills, you evaluate problem-solving without the use of tests or even assigned problems. Some tools that can be used to this end include group brainstorming sessions and problem-solving challenges.
Application and integration refer to the use of mathematical concepts to deal with problems in other fields. Mathematical concepts and procedures are frequently applied to solve problems in science, engineering, and finance. Informal assessment tools for an adult learner's ability to integrate mathematics with other subjects should test a student's ability to identify ways math can be used in other subjects. Such tools include independent research projects, class discussions, and technology-aided assignments.