The author of this paper submits that a mathematics student needs to learn to conjecture and prove or disprove said conjecture. Ergo, the purpose of the paper is to submit the thesis that learning requires doing; only through inquiry is learning achieved, and hence this paper proposes a programme of use of a modified Moore method (MMM) across the mathematics curriculum. The author of this paper has used the MMM in classes including an Introduction to Mathematics (general education liberal arts mathematics required as the minimum class that fulfils the mathematics requirement at Kutztown University of Pennsylvania (KUP)), Fundamentals of Mathematics I & II courses (mathematics for elementary education majors), Calculus I, II, \& III, Set Theory, Linear Algebra, Bridge to Higher Mathematics, Probability and Statistics I & II, Real Analysis I \& II, Topology, Senior Seminar, and Directed Reading. The author of this paper has taught for approximately twenty-five years, much of it at Morehouse College (MC) an historically black liberal arts institution, but now teaches at a comprehensive university in the Pennsylvania State System of Higher Education (PASSHE) where use of the MMM has been met with mixed reception by students and faculty. This paper discusses the techniques used to facilitate learning and the successes or lack thereof of how the methods and materials in the courses taught established a meaningful inquiry-based learning environment, how the method assisted in forging some long-term undergraduate research, and encouraged some undergraduates to delve into research who might not have otherwise embarked on research. So, this paper proposes an approach to mathematics education that centres on exploration, discovery, conjecture, hypothesis, thesis, and synthesis such that the experience of doing a mathematical argument, creating a mathematical model, or synthesising ideas is reason enough for the exercise - - and the joy of mathematics is something that needs to be instilled and encouraged in students by having them do proofs, counterexamples, examples, (informal) arguments, and counter-arguments in any mathematics course. Thus, the MMM used by the author is wholly a derivative of the Moore method and exists because of R. L. Moore, W. H. Mahavier, B. Fitzpatrick, M. Smith, C. Reed, D. Doyle, and other distinguished academics who instructed the author or the author's professors.