The DOI matches its Crossref record; 25 of the 25 references it cites were found in a registry or an index.
The 2 Sigma Problem: The Search for Methods of Group Instruction as Effective as One-to-One Tutoring
Abstract
T w o University of Chicago doctoral students in education, Anania (1982, 1983) and Burke (1984), completed dissertations in which they compared student learning under the following three conditions of instruction: 1. Conventional. Students learn the subject matter in a class with about 30 students per teacher. Tests are given periodically for marking the students. 2. Mastery Learning. Students learn the subject matter in a class with about 30 students per teacher. The instruction is the same as in the conventional class (usually with the same teacher). Formative tests (the same tests used with the conventional group) are given for feedback followed by corrective procedures and parallel formative tests to determine the extent to which the students have mastered the subject matter. 3. Tutoring. Students learn the subject matter with a good tutor for each student (or for two or three students simultaneously). This tutoring instruction is followed periodically by formative tests, feedback-corrective procedures, and parallel formative tests as in the mastery learning classes. It should be pointed out that the need for corrective work under tutoring is very small.
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In the citing paper
“skills vary within individuals based on goals, emotional states, and contextual supportsproducing a child's developmental range”
From Malleability, plasticity, and individuality: How children learn and develop in context1 (2019) · cites this paper as Bloom, 1984
In the citing paper
“a child's performance within that range can be optimized under conditions of high, personalized support”
From Malleability, plasticity, and individuality: How children learn and develop in context1 (2019) · cites this paper as Bloom, 1984
In the citing paper
“Bloom found that students who received effective one-on-one tutoring through a mastery learning framework performed two standard deviations better than students who did not.”
From Malleability, plasticity, and individuality: How children learn and develop in context1 (2019) · cites this paper as Bloom, 1984
In the citing paper
“One-to-one tutoring is an effective teaching method (Bloom, 1984).”
From Towards the Pedagogical Steering of Large Language Models for Tutoring: A Case Study with Modeling Productive Failure (2025) · cites this paper as Bloom, 1984
In the citing paper
“We believe that the increased learning from structured AI tutoring is largely due to its ability to offer personalized feedback on demand—just as one-on-one tutoring from a (human) expert is superior to classroom instruction15.”
From AI tutoring outperforms in-class active learning: an RCT introducing a novel research-based design in an authentic educational setting (2025) · cites this paper as [15]
In the citing paper
“While the advantages of personalized instruction are clear, this model of education cannot scale to meet the needs of a large number of students15.”
From AI tutoring outperforms in-class active learning: an RCT introducing a novel research-based design in an authentic educational setting (2025) · cites this paper as [15]
In the citing paper
“Working with an expert personal tutor is generally regarded as the most efficient form of education15.”
From AI tutoring outperforms in-class active learning: an RCT introducing a novel research-based design in an authentic educational setting (2025) · cites this paper as [15]
In the citing paper
“More focused effort on developing computer-based tutoring systems in particular started following the findings of Bloom (Bloom, 1984)—students who received tutoring in addition to group classes fared two standard deviations better than those who only participated in group classes.”
From Proactive and reactive engagement of artificial intelligence methods for education: a review (2023) · cites this paper as Bloom, 1984
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“Usually, that kind of effectiveness or efficiency effect would be the result of individualized, human tutored instruction (e.g., Bloom, 1984) and yet, we had more than twenty students in a class that met for less than two hours per week, showing such results.”
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“Mastery learning focuses on achieving a certain level of competency before learning subsequent information (Tyler, 2013) and as such has been widely investigated as a strategy for improving student outcomes (Bloom, 1984).”
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“Human-to-human tutoring enhances learning by .4 to 2.3 standard deviation units compared to classroom controls and other suitable controls (Bloom, 1984; Cohen et al., 1982).”
BackgroundInfluentialCan Tutors Monitor Students' Understanding Accurately?
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“3 SD above the average student in a traditional transmission-based classroom (Bloom, 1984; Cohen, Kulik, & Kulik, 1982).”
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“Previous work has shown that students learn more when they receive individualized, rather than group-level, instruction (Bloom, 1984).”
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“It was found that IE methods had an average gain of 0.48 ±.0.14 SD, which was two standard deviations above the traditional course which received and average gain of 0.23 ±.0.04 SD. Bloom (1984, p. 4) states:”
InfluentialLepper, M. R., & Woolverton, M. (2002) · Improving Academic Achievement · doi:10.1016/b978-012064455-1/50010-5 · Cited by 180
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“There is much evidence that academic learning seldom goes beyond committing facts and definitions to memory (Bloom, 1984; diSibio, 1982; Schmeck, 1988a, 1988b; Spiro, 1977).”
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Sayed, W. S., Noeman, A. M., Abdellatif, A., Abdel-Razek, M., Badawy, M. G., Hamed, A., & El-Tantawy, S. (2022) · Multimedia Tools and Applications · doi:10.1007/s11042-022-13076-8 · Cited by 169
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“3160492 has been well established with experiments involving human tutors [3].”
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“Equally interesting is that when the new methods were compared with mastery methods (Bloom, 1984) they produced a 40 % increase in learning.”
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“Bloom (1984) has shown that the vast majority of students (approximately 98 percent) do better when they receive private tutoring instead of classroom instruction.”
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InfluentialSuccess for All: First-Year Outcomes of a Comprehensive Plan for Reforming Urban Education
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“because both the content and style of the instruction can be continuously adapted to best meet the needs of the situation (Bloom, 1984).”
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“Know what you must accomplish, when you should escalate and when you should simply walk away (Clark, 2005) The above described principles and procedures are themselves declarative and procedural knowledge that has been codified into an easily expressible form.”
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“Some researchers have even deemed it the gold standard of pedagogy and learning (Bloom, 1984).”
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“ITSs can facilitate mastery learning (Bloom, 1984) by creating experiences in which the difficulty of the task or specific problems is adapted to the individual student.”
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“Benefits of personalization are well established across the domains of education (Bloom, 1984; Anderson 29 et al., 2001) and healthcare (Beevers and McGeary, 2012; Cesuroglu et al.”
BackgroundGrouping Practices and Reading Outcomes for Students with Disabilities
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“Bloom’s explanation for these findings was that the continual feedback and corrective process that occurs between instructors and students in tutorials provides the reinforcement and encouragement students require to stay actively involved in the learning process ( Bloom, 1984 ).”
BackgroundResultThe Cognitive and Academic Benefits of Music to Children: Facts and fiction
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“…music has an intrinsic value as a great cultural invention, it has the ability to function as a vehicle for emotional expression and communication (Reimer, 1999; Trevarthen & Malloch, 2002), and is a positive activity that can be participated in by children of all cultures, ages, and abilities.”
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“If these individual learning systems are further complemented by collaborative learning tools and online mentoring from regular instructors, effect sizes on the order of two standard deviation units, as suggested by Bloom (1984), may someday be possible.”
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“For example, (Anderson et al. 1995) report an effect size of 1.0 in studies that lasted for one semester, and Bloom (1984) reports an effect size of 2.0 for one-on-one human tutoring.”
BackgroundInfluentialInforming and Performing: A Study Comparing Adaptive Learning to Traditional Learning
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A Survey of Robot-Assisted Language Learning (RALL)
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“While learners might find it more fun and comfortable to interact in a group [107], those who receive one-on-one tutoring usually score much better than those who receive classroom education [17].”
BackgroundTeaching scientific thinking skills: Students and computers coaching each other
Reif, F., & Scott, L. A. (1999) · American Journal of Physics · doi:10.1119/1.19130 · Cited by 138
Wauters, K., Desmet, P., & Noortgate, W. V. D. (2010) · Journal of Computer Assisted Learning · doi:10.1111/j.1365-2729.2010.00368.x · Cited by 137
“Therefore, adaptive learning systems are developed aimed at optimizing learning conditions (Bloom 1984; Wasson 1993; Lee 2001; Verdú et al. 2008).”
BackgroundThe Teaching and Learning Toolkit
Higgins, S. (2018) · Cambridge University Press eBooks · doi:10.1017/9781139519618.004 · Cited by 136
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“The common method to calculate it in the ITS community is to subtract the control group’s mean score from the experimental group’s mean score and divide by the standard deviation of the scores of the control group ( Bloom 1984 ).”
MethodPrivate Tutoring: how prevalent and effective is it?
Ireson, J. (2004) · London Review of Education · doi:10.1080/1474846042000229458 · Cited by 134
“Bloom (1984) found that students in receipt of tutoring in school spent more time on task and had more positive attitudes towards learning, when compared with students who followed normal lessons.”
BackgroundResultInfluentialHeterogeneity of variance in experimental studies: A challenge to conventional interpretations.
Bryk, A. S., & Raudenbush, S. W. (1988) · Psychological Bulletin · doi:10.1037/0033-2909.104.3.396 · Cited by 134
“Further, in many cases, the nature of these differential effects is substantively interesting and can be crucial to evaluating the efficacy of treatments (e.g., see Bloom, 1984; Bryk, 1978).”
BackgroundCook, P., Dodge, K., Farkas, G., Fryer, R., Guryan, J., Ludwig, J., Mayer, S., Pollack, H., & Steinberg, L. (2014) · National Bureau of Economic Research · doi:10.3386/w19862 · Cited by 130
Correlates of leisure‐time reading
Greaney, V., & Hegarty, M. (1987) · Journal of Research in Reading · doi:10.1111/j.1467-9817.1987.tb00278.x · Cited by 133
Proactive and reactive engagement of artificial intelligence methods for education: a review
Mallik, S., & Gangopadhyay, A. (2023) · Frontiers in Artificial Intelligence · doi:10.3389/frai.2023.1151391 · Cited by 139
“More focused effort on developing computer-based tutoring systems in particular started following the findings of Bloom [109] - students who received tutoring in addition to group classes fared two standard deviations better than those who only participated in group classes.”
MethodRevisioning models of instructional development
Gustafson, K. L., & Branch, R. M. (1997) · Educational Technology Research and Development · doi:10.1007/bf02299731 · Cited by 131
Rosé, C. P., & Ferschke, O. (2016) · International Journal of Artificial Intelligence in Education · doi:10.1007/s40593-016-0107-y · Cited by 145
“Interest in discussion-based learning in the AI in Education community is typically motivated by the famous finding that expert human tutors are highly successful at educating students (Bloom 1984; Cohen et al. 1982).”
BackgroundMean What You Say: Defining and Integrating Personalized, Blended and Competency Education.
Patrick, S. K., Kennedy, K., & Powell, A. (2013) · Cited by 128
Metacognition reconsidered: Implications for intervention research
Reeve, R. A., & Brown, A. L. (1985) · Research on Child and Adolescent Psychopathology · doi:10.1007/bf00912721 · Cited by 128
“In a recent paper, Bloom (1954) suggested that one of the most challenging problems for educational researchers is to devise group teaching techniques that are as effective as oneto one tutoring.”
BackgroundApplying Cognitive Theory to Statistics Instruction
Lovett, M. C., & Greenhouse, J. B. (2000) · The American Statistician · doi:10.1080/00031305.2000.10474545 · Cited by 128
“Similarly, the sizable learning gains exhibited by students learning from human tutors is largely attributed to the rich feedback tutors can give (Bloom 1984).”
BackgroundConstraint-Based Tutors: A Success Story
Mitrović, A., Mayo, M., Suraweera, P., & Martin, B. (2001) · Lecture notes in computer science · doi:10.1007/3-540-45517-5_103 · Cited by 127
“It is well known that one-on-one human tutoring is much more effective than traditional classroom instruction, providing an increase of two standard deviations in learning performance [4].”
BackgroundAttitudes, Study Habits, and Academic Performance of Junior High School Students in Mathematics
Etcuban, J. O., Capuno, R. G., Necesario, R., Espina, R. C., Padillo, G. G., & Manguilimotan, R. P. (2019) · International Electronic Journal of Mathematics Education · doi:10.29333/iejme/5768 · Cited by 124
“Good study habits are the productive ones, which help in improving the academic performance of the students or produce positive results (Bloom, 1984; Ogbodo, 2010).”
BackgroundKERMIT: A Constraint-Based Tutor for Database Modeling
Suraweera, P., & Mitrović, A. (2002) · Lecture notes in computer science · doi:10.1007/3-540-47987-2_41 · Cited by 124
“The common method to calculate the effect size in the ITS community is to subtract the control group’s mean gains score from the experimental group’s mean gain score and divide by the standard deviation of the gain scores of the control group [ 2 ].”
MethodModelling Human Teaching Tactics and Strategies for Tutoring Systems: 14 Years On
du Boulay, B., & Luckin, R. (2015) · International Journal of Artificial Intelligence in Education · doi:10.1007/s40593-015-0053-0 · Cited by 124
“The paper found that not all of the reasons above applied in practice, that intelligent tutoring systems were now in some respects approaching the effectiveness of “ordinary” human tutors and that the effectiveness of the latter were rather less than the gold-standard of individual expert tutoring (Bloom, 1984).”
BackgroundPerceptive animated interfaces: first steps toward a new paradigm for human-computer interaction
Cole, R. A., Vuuren, S. V., Pellom, B. L., Hacıoğlu, K., Ma, J., Movellan, J. R., Schwartz, S., Wade-Stein, D., Ward, W., & Yan, J. (2003) · Proceedings of the IEEE · doi:10.1109/jproc.2003.817143 · Cited by 123
“…Object Identifier 10.1109/JPROC.2003.817143 Keywords—Animation, conversational agents, dialogue system, electronic books, human–computer interaction, interactive books, literacy teaching, machine perception, spoken language, tools for cognitive disabilities, virtual humans, vocabulary tutors.”
BackgroundInfluentialLearner modelling: systematic review of the literature from the last 5 years
Abyaa, A., Idrissi, M. K., & Bennani, S. (2019) · Educational Technology Research and Development · doi:10.1007/s11423-018-09644-1 · Cited by 131
“There has long been a consensus that individualized learning is the most effective learning approach (Oen and Sweany 1971; Bloom 1984).”
BackgroundA Systematic Literature Review of Intelligent Tutoring Systems With Dialogue in Natural Language
Paladines, J., & Ramírez, J. (2020) · IEEE Access · doi:10.1109/access.2020.3021383 · Cited by 143
“For reference, students working one-on-one with expert human tutors often score 2.0 higher than students working on the same topic in classrooms [106].”
BackgroundInfluentialAn Intelligent Tutoring System for Entity Relationship Modelling
Suraweera, P., & Mitrović, A. (2004) · International Journal of Artificial Intelligence in Education · doi:10.3233/irg-2004-14(3-4)07 · Cited by 122
Cohen, G. L., & Steele, C. M. (2002) · Elsevier eBooks · doi:10.1016/b978-012064455-1/50018-x · Cited by 123
Why Students Learn More From Dialogue- Than Monologue-Videos: Analyses of Peer Interactions
Michelene, T. H., Kang, S., & Yaghmourian, D. L. (2016) · Journal of the Learning Sciences · doi:10.1080/10508406.2016.1204546 · Cited by 131
“79, based on a meta-review (VanLehn, 2011), and the level of learning achieved by tutees is often considered the gold standard (Bloom, 1984).”
BackgroundMethodInfluentialThe link between flipped and active learning: a scoping review
Li, R., Lund, A., & Nordsteien, A. (2021) · Teaching in Higher Education · doi:10.1080/13562517.2021.1943655 · Cited by 152
“In our study, 14% of the 155 included articles refer to Bloom ([1956] 1984) taxonomy.”
BackgroundThe life cycle of large language models in education: A framework for understanding sources of bias
Lee, J., Hicke, Y., Yu, R., Brooks, C., & Kizilcec, R. F. (2024) · British Journal of Educational Technology · doi:10.1111/bjet.13505 · Cited by 119
Nicholson, P. (2007) · Springer eBooks · doi:10.1007/978-1-4020-4914-9_1 · Cited by 116
Research on Group-Based Mastery Learning Programs: A Meta-Analysis
Guskey, T. R., & Pigott, T. (1988) · The Journal of Educational Research · doi:10.1080/00220671.1988.10885824 · Cited by 116
Brown, B. W., & Saks, D. H. (1986) · American Journal of Education · doi:10.1086/443863 · Cited by 114
Cognitive Perspectives in Psychology
Winn, W. (2013) · doi:10.4324/9781410609519-11 · Cited by 162
“The evidence that this is the case is compelling (Bloom, 1984, 1987; Kulik, 1990a, 1990b). However, enough time typically comes to mean the length of a unit, module or semester and mastery means mastery of performance not of high-level skills such as problem solving. There is a considerable body of opinion that expert…”
BackgroundInfluentialLearning Theories for Engineering Education Practice
Newstetter, W., & Svinicki, M. D. (2014) · Cambridge University Press eBooks · doi:10.1017/cbo9781139013451.005 · Cited by 119
Metadata
- Authors
- BLOOM, B. S.
- Affiliations
- Northwestern University (US)
- Corresponding author
- BLOOM, BENJAMIN S.
- Venue
- Educational Researcher
- Published
- 1984-06
- Volume
- 13
- Issue
- 6
- Pages
- 4-16
- ISSN
- 0013-189X (ISSN-L)
- 1935-102X
- OpenAlex
- W2172010324
- Cited by
- 2,734
- References
- 25
- Citations by year
- 2026: 195 · 2025: 144 · 2024: 131 · 2023: 99 · 2022: 103 · 2021: 84 · 2020: 129 · 2019: 88 · 2018: 122 · 2017: 79 · 2016: 97 · 2015: 119 · 2014: 112 · 2013: 107 · 2012: 103
- FWCI
- 39.22
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- Educational Researcher (publishedVersion)
- Topics
- Social Sciences › Psychology › Developmental and Educational Psychology › Innovative Teaching and Learning Methods
- Physical Sciences › Computer Science › Artificial Intelligence › Intelligent Tutoring Systems and Adaptive Learning
- Social Sciences › Psychology › Developmental and Educational Psychology › Learning Styles and Cognitive Differences
- Keywords
- group instruction, one-on-one tutoring, learning mastery, conventional instruction, corrective procedures, academic performance, tutoring effectiveness
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