## Key Ideas > [!abstract] Core Concepts > > - **Foundation before progression**: Students must achieve firm grasp of each concept before advancing to more complex topics (Bloom, 1968) > - **Individual development over age-based progression**: Learning based on understanding rather than chronological age or curriculum timeline (Guskey, 2007) > - **Missing prerequisite knowledge, not cognitive disability**: Very small percentage have disabilities; most lack foundational skills (Bloom, 1976) ## Definition **Mastery Approach**: Educational method ensuring students have firm understanding of foundational concepts before progressing to advanced topics, prioritising individual development over age-based curriculum progression (Bloom, 1968; Guskey, 2007). ## Connected To [[Prior Knowledge]] | [[Diagnostic Questions]] | [[Explicit Teaching]] | [[Formative Assessment]] | [[Low-Floor High-Ceiling]] | [[Fluency]] | [[Implementation Fidelity]] --- ## The conveyor belt problem Traditional education operates like a conveyor belt, creating systematic failure (Bloom, 1968). Age-based progression delivers content regardless of individual learning needs or understanding. Once a unit is completed and assessed, the curriculum moves on without ensuring all students have grasped the material (Carroll, 1963). This approach causes knowledge gaps to accumulate, especially for students struggling to keep pace (Guskey, 2007). Each new concept rests on incomplete understanding of previous material. Without secure foundations, the accumulated difficulties eventually prevent further progress. ## Mathematics as foundation building Mathematics education requires building a solid foundation. Each concept builds upon previous ones, making secure foundational knowledge essential (National Mathematics Advisory Panel, 2008). Most student difficulties stem not from an inability to understand complex concepts, but from a lack of fundamental skills and knowledge (Bloom, 1976). A very small percentage have cognitive disabilities that prevent mainstream curriculum engagement; the majority are missing [[Prior Knowledge|prerequisite knowledge]] that the curriculum assumes they possess (Guskey, 2007). This reframes the issue from student deficiency to instructional challenge (Bloom, 1976). ## Core elements of mastery model Mastery learning incorporates several components that work together to ensure student understanding (Guskey, 2007; Bloom, 1968). [[Diagnostic Questions]] serve as pre-assessments to identify knowledge gaps before teaching begins. High-quality [[Explicit Teaching]] provides systematic, evidence-based initial instruction. [[Formative Assessment]] monitors progress through regular checks during learning. When assessments reveal gaps, corrective instruction addresses them immediately through high-quality reteaching. [[Low-Floor High-Ceiling]] extension activities challenge students who achieve mastery early whilst others consolidate understanding. ## The 2 sigma problem: evidence for mastery learning Bloom (1984) examined the effectiveness of one-to-one tutoring compared to conventional classroom instruction, finding that tutored students performed two standard deviations better than classroom students. This "2 sigma effect" represents a massive improvement, moving the average tutored student from the 50th to the 98th percentile. The research identified several factors contributing to tutoring effectiveness: immediate feedback on errors, correction of mistakes before they embed, active student participation in learning, and individualised pacing matched to student needs. Bloom challenged educators to find practical methods approaching tutoring effectiveness for group instruction. Whilst individual tutoring for all students is impractical, the research identifies specific elements that can be incorporated into classroom instruction: frequent formative assessment to monitor understanding, immediate corrective feedback when errors occur, mastery learning approaches ensuring students understand before progression, and increased opportunities for active student participation. Combining several of these elements can produce substantial achievement gains approaching those of tutoring (Bloom, 1984). ## Practice philosophy > [!cite] > Novices practise until they can get it right. Experts practise until they cannot get it wrong. > > _- School superintendent, 1902_ Fluency and automaticity require extensive practice beyond initial success, ensuring knowledge remains accessible under pressure and in new contexts (Ericsson & Kintsch, 1995; Logan, 1988). ## Implementation principles Effective implementation of mastery learning requires adherence to several principles (Guskey, 2007). Students must achieve mastery before progression; the timeline should not advance if students have not secured understanding (Bloom, 1968). Diagnostic assessment identifies missing prerequisites (Guskey, 2007), whilst high-quality reteaching addresses problems revealed by formative assessment (Bloom, 1976). The approach maintains high expectations: all students can achieve mastery with appropriate time and support (Bloom, 1968). ## References Bloom, B. S. (1968). Learning for mastery. *Evaluation Comment*, 1(2), 1-12. Bloom, B. S. (1976). *Human characteristics and school learning*. McGraw-Hill. Bloom, B. S. (1984). The 2 sigma problem: The search for methods of group instruction as effective as one-to-one tutoring. *Educational Researcher*, 13(6), 4-16. https://doi.org/10.3102/0013189X013006004 Carroll, J. B. (1963). A model of school learning. *Teachers College Record*, 64(8), 723-733. Ericsson, K. A., & Kintsch, W. (1995). Long-term working memory. *Psychological Review*, 102(2), 211-245. https://doi.org/10.1037/0033-295X.102.2.211 Guskey, T. R. (2007). Closing achievement gaps: Revisiting Benjamin S. Bloom's "Learning for Mastery". *Journal of Advanced Academics*, 19(1), 8-31. https://doi.org/10.4219/jaa-2007-704 Logan, G. D. (1988). Toward an instance theory of automatization. *Psychological Review*, 95(4), 492-527. https://doi.org/10.1037/0033-295X.95.4.492 National Mathematics Advisory Panel. (2008). *Foundations for success: The final report of the National Mathematics Advisory Panel*. U.S. Department of Education.