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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“Bloom’s 2-sigma problem (Bloom, 1984) – the challenge to achieve, through more efficient teaching methods, at least the same 2 sigma difference that is seen between achievements of those taught in conventional classroom settings and those taught via one-to-one tutoring – remains unmet after nearly…”
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InfluentialRetrieval Algorithms Optimized for Human Learning
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Chou, C., Lai, K.-H. R., Chao, P.-Y., Tseng, S., & Liao, T.-Y. (2018) · Computers & Education · doi:10.1016/j.compedu.2018.07.010 · Cited by 54
A development environment for distributed synchronous collaborative programming
Boyer, K. E., Dwight, A. A., Fondren, R. T., Vouk, M. A., & Lester, J. C. (2008) · ACM Conference on Innovation and Technology in Computer Science Education (ITiCSE) · doi:10.1145/1384271.1384315 · Cited by 50
“2 Distributed Tutoring One-on-one tutoring has been shown to be highly effective for student learning [6].”
BackgroundThe Effects of Politeness-Related Instruction on Medical Tutoring
Bromme, R., Brummernhenrich, B., Becker, B.-M., & Jucks, R. (2012) · Communication Education · doi:10.1080/03634523.2012.691979 · Cited by 49
“…Theory; Computer-Mediated Communication; Expert Layperson Communication One-to-one tutoring, the interaction between a knowledgeable tutor and a less knowledgeable tutee in a learning setting, has proven to be a very effective form of instruction (e.g., Bloom, 1984; Cohen, Kulik, & Kulik, 1982).”
BackgroundInterpretable Knowledge Tracing: Simple and Efficient Student Modeling with Causal Relations
Minn, S., Vie, J.-J., Takeuchi, K., Kashima, H., & Zhu, F. (2022) · Proceedings of the AAAI Conference on Artificial Intelligence · doi:10.1609/aaai.v36i11.21560 · Cited by 56
Mastery Learning and Instructional Design
Gagné, R. M. (2008) · Performance Improvement Quarterly · doi:10.1111/j.1937-8327.1988.tb00003.x · Cited by 49
Uther, M., Zipitria, I., Uther, J., & Singh, P. (2005) · IEEE International Conference on Wireless, Mobile and Ubiquitous Technology in Education (WMUTE) · doi:10.1109/wmte.2005.46 · Cited by 49
“research, a personalised tutoring approach has been shown to be a particularly successful strategy to train learners [10].”
BackgroundDesigning Adaptive Instructional Environments: Insights from Empirical Evidence
Durlach, P. J., & Ray, J. M. (2011) · Defense Technical Information Center (DTIC) · doi:10.21236/ada552677 · Cited by 49
“One-on-one education and training by a human mentor is the epitome of adaptive instruction, and has been shown to be superior to traditional classroom-based approaches (e.g., Bausell, Moody & Walzl, 1972; Bloom, 1984).”
MethodFatima, S. S., Sheikh, N. A., & Osama, A. (2024) · Postgraduate Medical Journal · doi:10.1093/postmj/qgae088 · Cited by 52
Chou, C., Huang, B.-H., & Lin, C.-J. (2011) · Computers & Education · doi:10.1016/j.compedu.2011.06.005 · Cited by 49
“One-to-one human tutoring is an effective teachingmethod, which enables high achievement for most students (Bloom,1984).”
BackgroundHeffernan, N. T., Koedinger, K. R., & Razzaq, L. M. (2008) · International Journal of Artificial Intelligence in Education · doi:10.3233/irg-2008-18(2)04 · Cited by 48
“However, dialog systems are not new; Carbonell (1970) built one of the early dialog-based computer tutors over 30 years ago.”
BackgroundThe Role of the Lecturer as Tutor: Doing What Effective Tutors Do in a Large Lecture Class
Wood, W. B., & Tanner, K. D. (2012) · CBE—Life Sciences Education · doi:10.1187/cbe.11-12-0110 · Cited by 61
“Bloom’s taxonomy, Benjamin Bloom also contributed significantly to insights on the effectiveness of tutoring (Bloom et al., 1956; Bloom, 1984).”
InfluentialMeta-Cognitive Strategy Instruction in Intelligent Tutoring Systems: How, When, and Why
Chi, M., & VanLehn, K. A. (2010) · Cited by 48
A Web-Based Intelligent Tutoring System for Computer Programming
Butz, C. J., Hua, S., & Maguire, R. B. (2005) · IEEE/WIC/ACM International Conference on Web Intelligence · doi:10.1109/wi.2004.10104 · Cited by 48
On opportunities and challenges of large multimodal foundation models in education
Küchemann, S., Avila, K. E., Dinc, Y., Hortmann, C., Revenga, N., Ruf, V., Stausberg, N., Steinert, S., Fischer, F., Fischer, M., et al. (2025) · npj Science of Learning · doi:10.1038/s41539-025-00301-w · Cited by 47
Modeling students’ behavioral engagement through different in-class behavior styles
Gomes, S., Costa, L. F. C., Martinho, C., Dias, J., Xexeo, G. B., & Santos, A. M. (2023) · International Journal of STEM Education · doi:10.1186/s40594-023-00407-w · Cited by 64
“In fact, although research has defended that collective instruction may bring more challenges than one-to-one tutoring (Bloom 1984), recent work regarding the use of technology in education is considering to model learners at a group/ team level as a path to aid collective learning (Bonner et al.”
BackgroundEffect of Chat GPT on the digitized learning process of university students
Castillo, A. G. R., Silva, G. J. S., Arocutipa, J. P. F., Berríos, H. Q., Rodríguez, M. A. M., Reyes, G. Y., Lopez, H. R. P., Teves, R. M. V., Rivera, H. V. H., & Arias‐Gonzáles, J. L. (2023) · Journal of Namibian Studies History Politics Culture · doi:10.59670/jns.v33i.411 · Cited by 61
“There is a two-standard-deviation improvement in performance between students who receive private tutoring and those who use more conventional teaching methods, as reported by Bloom (1984).”
MethodGusukuma, L., Bart, A. C., Kafura, D. G., & Ernst, J. V. (2018) · ACM Conference on International Computing Education Research (ICER) · doi:10.1145/3230977.3231002 · Cited by 47
“While direct feedback from experts is the “gold standard” [5], it has two pragmatic drawbacks.”
BackgroundThe Foundations and Architecture of Autotutor
Tutoring Research Group, Hastings, P., Graesser, A. C., & Harter, D. (1998) · Lecture notes in computer science · doi:10.1007/3-540-68716-5_39 · Cited by 47
“3 standard deviation units compared to classroom teaching and other suitable controls [2].”
BackgroundFacilitating Student Learning With a Chatbot in an Online Math Learning Platform
Cheng, L., Croteau, E., Baral, S., Heffernan, C., & Heffernan, N. (2024) · Journal of Educational Computing Research · doi:10.1177/07356331241226592 · Cited by 49
“In the realm of education, providing effective support to students is crucial for improving their learning experiences and outcomes (Bloom, 1984).”
BackgroundPeer tutoring with the aid of the Internet
Evans, M. J., & Moore, J. S. (2012) · British Journal of Educational Technology · doi:10.1111/j.1467-8535.2011.01280.x · Cited by 53
The Impact of a Peer-Learning Agent Based on Pair Programming in a Programming Course
Han, K., Lee, E., & Lee, Y. (2009) · IEEE Transactions on Education · doi:10.1109/te.2009.2019121 · Cited by 46
“Bloom [23] has suggested that one-on-one tutoring is the most effective strategy, as it is generally known to lead to better performance compared to traditional instruction.”
BackgroundNegotiation based adaptive learning sequences: Combining adaptivity and adaptability
Chou, C., Lai, K.-H. R., Chao, P.-Y., Lan, C. H., & Chen, T.-H. (2015) · Computers & Education · doi:10.1016/j.compedu.2015.05.007 · Cited by 46
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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