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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“On the contrary, Bloom discovered that an educator could reach all learners in a classroom if he makes use of formative assessments, feedback, remedial procedures, and if he provides individual instruction to the individual student (Bloom, 1984).”
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“While structured, one-on-one support services can have large effects on student outcomes,theyare oftencostlytoimplementanddifficult toscale uptothe studentpopulation at large (Bloom 1984).”
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“Based on the famous Bloom’s two sigma result [6], one-to-one tutoring presents better learning effects than group (conventional) tutoring.”
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“Meta-analyses conducted by Walberg (1984) and Bloom (1984) have confirmed the effectiveness of adjusting instruction to address the individual needs of students.”
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“There is evidence that the gains from tutoring, when compared to classroom instruction, are generally in the range of 0.4 to 2.0 standard deviation units, depending on the expertise of the tutor ( Bloom, 1956, 1984; Cohen, Kulik, & Kulik, 1982; Corbett, 2001; Graesser & Person, 1994).”
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“This feature is based, in part, on the finding that the most effective tutoring is provided one-to-one by a skilled-human tutor who tailors the interaction to the specific capabilities, progress and needs of the tutee in order to achieve mastery at each stage (B. S. Bloom, 1984).”
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“…focused on individual academic needs and learning aspects, and also demonstrated the strongly positive effects of tutoring on academic outcomes at the individual student level (see Bloom, 1984; Cohen, Kulik, & Kulik, 1982; Juel, 1996; McArthur, Stasz, & Zmuidzinas, 1990; Topping & Whitley, 1990).”
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“OTSL is a form of one-to-one tutoring, and so can benefit from analysis of this highly effective (Bloom, 1984) but extremely expensive form of pedagogy.”
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“Several studies and meta-analyses conducted in the 1980s and 1990s reported positive influences of productive, higher-order questions on student achievement (Redfield and Rousseau 1981; Wise and Okey 1983; Bloom 1984; Hamaker 1986; Walberg 1999). The influences on achievement ranged from 12 to 27 percentile points gai…”
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“While summative assessments are useful for categorization, ranking, and licensing, and can even be motivating in some instances, they are not optimal for providing detailed and timely feedback which is essential for learning (Bloom, 1984, Shute, 2008; Sadler, 1989).”
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Craig, S. D., Driscoll, D. M., & Gholson, B. (2004) · Journal of educational multimedia and hypermedia · Cited by 75
TEx-Sys model for building intelligent tutoring systems
Stankov, S., Rosić, M., Žitko, B., & Grubišić, A. (2007) · Computers & Education · doi:10.1016/j.compedu.2007.10.002 · Cited by 74
Pressley, M. G., Gaskins, I. W., Solic, K., & Collins, S. (2006) · Journal of Educational Psychology · doi:10.1037/0022-0663.98.2.282 · Cited by 78
“Consistent with the finding that the very maximum achievement benefits come from one-on-one tutoring (Bloom, 1984), teacher scaffolding is a large part of every student’s day at Benchmark, often resulting in de facto one-on-one tutoring as students do their in-class assignments.”
BackgroundKnowledge and Situational Feedback in a Learning Environment for Algebra Story Problem Solving
Nathan, M. J. (1998) · Interactive Learning Environments · doi:10.1080/1049482980050110 · Cited by 74
“Student modeling and the expert-like feedback that ITSs attempt to provide are intended to bring about the large gains brought about by human tutoring (Bloom, 1984).”
BackgroundEvaluation of animalwatch: An intelligent tutoring system for arithmetic and fractions
Beal, C. R., Arroyo, I., Cohen, P. R., & Woolf, B. P. (2010) · Cited by 74
Not Too Late: Improving Academic Outcomes among Adolescents
Guryan, J., Ludwig, J., Bhatt, M. P., Cook, P. J., Davis, J. M. V., Dodge, K., Farkas, G., Fryer, R. G., Mayer, S., Pollack, H., et al. (2023) · American Economic Review · doi:10.1257/aer.20210434 · Cited by 77
Ai-Driven Personalized Learning Systems: Enhancing Educational Effectiveness
Katiyar, N., Awasthi, M. V. K., Pratap, D. R., Mishra, M. K., Shukla, M. N., singh, M. R., & Tiwari, M. (2024) · doi:10.53555/kuey.v30i5.4961 · Cited by 108
AdELE: A Framework for Adaptive E-Learning through Eye Tracking
García-Barrios, V. M., Gütl, C., Preis, A., Andrews, K., Pivec, M., Mödritscher, F., & Trummer, C. (2004) · Cited by 73
My science tutor: A conversational multimedia virtual tutor.
Ward, W., Cole, R., Bolaños, D., Buchenroth-Martin, C., Svirsky, E., & Weston, T. (2013) · Journal of Educational Psychology · doi:10.1037/a0031589 · Cited by 81
ICT Supporting the Learning Process: The Premise, Reality, and Promise
Lai, K. (2008) · Springer eBooks · doi:10.1007/978-0-387-73315-9_13 · Cited by 74
“For example, Bloom (1984) reported a general difference in achievement of two standard deviations favouring tutoring.”
BackgroundAn Economic Appraisal of MOOC Platforms: Business Models and Impacts on Higher Education
Belleflamme, P., & Jacqmin, J. (2015) · CESifo Economic Studies · doi:10.1093/cesifo/ifv016 · Cited by 80
“In the context of MOOCs, the Internet facilitates the implementation of a mastery learning environment thanks to the use of tests and possible remedial systems (Bloom, 1984).”
BackgroundSocial Robots for (Second) Language Learning in (Migrant) Primary School Children
Konijn, E. A., Jansen, B., Bustos, V. M., Hobbelink, V. L. N. F., & Preciado, D. F. (2021) · International Journal of Social Robotics · doi:10.1007/s12369-021-00824-3 · Cited by 80
The importance and perspectives of international studies in educational effectiveness
Creemers, B. (2006) · Educational Research and Evaluation · doi:10.1080/13803610600873978 · Cited by 71
“It was also the basis for Bloom’s concept of mastery learning (Bloom, 1984) and is also related to ‘‘direct instruction’’ as described by Rosenshine (1983).”
BackgroundSmart MOOC integrated with intelligent tutoring: A system architecture and framework model proposal
Yılmaz, R., Yurdugül, H., Yılmaz, F. G. K., Şahi̇n, M., Sulak, S., Aydın, F., Tepgeç, M., Müftüoğlu, C. T., & Oral, Ö. (2022) · Computers and Education Artificial Intelligence · doi:10.1016/j.caeai.2022.100092 · Cited by 88
Comparison of Reading Intervention Approaches for Students with Mild Disabilities
Marston, D., Deno, S. L., Kim, D., Diment, K., & Rogers, D. (1995) · Exceptional Children · doi:10.1177/001440299506200103 · Cited by 71
Chi, M., VanLehn, K. A., & Litman, D. J. (2010) · Lecture notes in computer science · doi:10.1007/978-3-642-13388-6_27 · Cited by 70
“Human one-on-one tutoring is one of the most effective educational interventions in that tutored students often perform significantly better than students in classroom settings[4].”
BackgroundAttali, Y. (2015) · Computers & Education · doi:10.1016/j.compedu.2015.08.011 · Cited by 70
Instructional Grouping for Reading for Students with LD
Vaughn, S. R., Hughes, M. T., Moody, S. W., & Elbaum, B. E. (2001) · Intervention in School and Clinic · doi:10.1177/105345120103600301 · Cited by 70
Simulating Human Tutor Dialog Moves in AutoTutor
Person, N. K., Graesser, A. C., Kreuz, R. J., Victoria, V., & Parkway, N. (2003) · Cited by 70
Suzuki, R., Salehi, N., Lam, M. S., Marroquin, J. C., & Bernstein, M. S. (2016) · CHI Conference on Human Factors in Computing Systems · doi:10.1145/2858036.2858121 · Cited by 69
A Web-Based Intelligent Tutoring System for Computer Programming
Butz, C. J., Song, H., & Maguire, R. B. (2004) · Web Intelligence · doi:10.1109/wi.2004.15 · Cited by 69
Yusuf, B., Walters, L. M., & Sailin, S. N. (2020) · International Journal of Emerging Technologies in Learning (iJET) · doi:10.3991/ijet.v15i03.11849 · Cited by 68
“Comparisons between robots and humans are rare in the literature; so, no meta-analysis data were available to compare the cognitive learning effect size [43], [44].”
BackgroundEducational technology: what it is and how it works
Dron, J. (2021) · AI & Society · doi:10.1007/s00146-021-01195-z · Cited by 68
Inferring what the student knows in one-to-one tutoring: The role of student questions and answers
Person, N. K., Graesser, A. C., Magliano, J. P., & Kreuz, R. J. (1994) · Learning and Individual Differences · doi:10.1016/1041-6080(94)90010-8 · Cited by 68
Leveraging Parents through Low-Cost Technology
Bergman, P., & Chan, E. W. (2019) · The Journal of Human Resources · doi:10.3368/jhr.56.1.1118-9837r1 · Cited by 79
“In contrast to the intervention tested here, this set of tools often includes high-touch interventions, such as intensive tutoring (Bloom 1984; Cook et al. 2015; Fryer 2017) or one-on-one advising (Oreopoulos and Petronijevic 2018), but their scale may be limited by high costs.”
ResultIreson, J., & Rushforth, K. (2009) · Research Papers in Education · doi:10.1080/02671520903191170 · Cited by 67
“In contrast, experimental studies such as those of Mischo and Haag (2002) and Bloom (1984) found that tutoring raised achievement.”
ResultLearnersourcing Personalized Hints
Glassman, E. L., Lin, A., Cai, C. J., & Miller, R. C. (2016) · ACM Conference on Computer Supported Cooperative Work (CSCW) · doi:10.1145/2818048.2820011 · Cited by 67
A possible future for next generation adaptive learning systems
Essa, A. (2016) · Smart Learning Environments · doi:10.1186/s40561-016-0038-y · Cited by 77
“In order to set the stage for our discussion of Deep Learner Models, let's review an important implication of Bloom's findings in " The 2-Sigma Problem " (Bloom 1984).”
BackgroundInstructional design for distance learning
Jacqueline Bourdeau, B., & Bates, A. (1996) · Journal of Science Education and Technology · doi:10.1007/bf01677124 · Cited by 67
“tive as mastery learning and one-to-one tutoring ( Bloom, 1984 ).”
Background
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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