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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“Rooted in Bloom's "2 sigma problem" [12], which demonstrated the efficacy of one-on-one tutoring, ITS design has been significantly influenced by cognitive architectures, such as Anderson's Adaptive Control of Thought-Rational (ACT-R) theory [13].”
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BackgroundVocaTest : an intelligent tutoring system for vocabulary learning using the "mLearning" approach
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“Studies have found that tutored learners outperform their traditional classroom equivalents by between one and CONTACT Keith W. Brawner keith.w.brawner.civ@mail.mil two letter grades of improvement (Bloom 1984; VanLehn 2011).”
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Integrating motivated goal achievement in maritime simulator training
Hjellvik, S., & Mallam, S. (2023) · WMU Journal of Maritime Affairs (JoMA) · doi:10.1007/s13437-023-00309-2 · Cited by 11
“The social interactions of the education could be considered in the CBS training design to both involve one-on-one instruction (Bloom, 1984) and the benefits of peer instruction (Crouch & Mazur, 2001), and peer comparison (Vesin et al., 2018).”
BackgroundThe Role of Adaptive Personalized Technologies in the Learning Process
Zhilmagambetova, R., Kopeyev, Z., Mubarakov, A., & Alimagambetova, A. (2023) · International Journal of Virtual and Personal Learning Environments · doi:10.4018/ijvple.324079 · Cited by 14
“Bloom (1984) describes a phenomenon known as two sigmas (two curves of the normal distribution of student results), where a student, trained individually, according to an individual program, showed results 98% higher than a control group trained by standard methods.”
BackgroundA Framework for Socio-Developmental Ethics in Educational AI
Tuomi, I. (2023) · Hawaii International Conference on System Sciences (HICSS) · doi:10.24251/hicss.2023.752 · Cited by 19
Adaptive training instructional interventions: A meta-analysis
Fraulini, N. W., Marraffino, M. D., Garibaldi, A. E., Johnson, C. I., & Whitmer, D. E. (2024) · Military Psychology · doi:10.1080/08995605.2024.2377884 · Cited by 18
“It is well-established that individualized tutoring is more effective than one-size-fits-all forms of instruction (Bloom, 1984; Kulik et al., 1990; Vandewaetere et al., 2011).”
AI, Personalized Education, and Challenges
Mimoudi, A. (2024) · Proceedings of the International Conference on AI Research. · doi:10.34190/icair.4.1.3133 · Cited by 14
Adaptive Perceptual Training in a Virtual Environment
Schatz, S. L., Wray, R. E., Folsom-Kovarik, J. T., & Nicholson, D. M. (2012) · Proceedings of the Human Factors and Ergonomics Society Annual Meeting · doi:10.1177/1071181312561503 · Cited by 14
“In his classic study, Benjamin S. Bloom (1984) found that students who received one-on-one tutoring performed two standard deviations superior to students who were taught via the conventional group method.”
BackgroundExploring the effectiveness of a novel feedback mechanism within an intelligent tutoring system
Sullins, J., Craig, S. D., & Hu, X. (2015) · International Journal of Learning Technology · doi:10.1504/ijlt.2015.072358 · Cited by 16
“It has been shown that under the correct circumstances feedback can be an effective means of increasing student learning (Crooks, 1988; Black and Wiliam, 1998) and is a method that all human tutors implement to some degree (Bloom, 1984; McKendree, 1990; Shute, 2008; VanLehn, 2011).”
BackgroundInfluentialFull Packaged Learning Solutions for Studying Mathematics at School
Utemov, V. V., Khusainova, R. M., Sergeeva, M. G., & Shestak, V. A. (2018) · Eurasia Journal of Mathematics Science and Technology Education · doi:10.29333/ejmste/95122 · Cited by 15
“The psychologist Bloom (1984) has described a phenomenon known as two-sigma (two curves of the normal distribution of students’ results), which means that an ordinary student, taught individually under an individual program, shows results 98% higher than a control group taught by standard methods.”
BackgroundResearch Methods for Education With Technology: Four Concerns, Examples, and Recommendations
Wright, D. B. (2019) · Frontiers in Education · doi:10.3389/feduc.2019.00147 · Cited by 17
“” Bloom (1984) discussed how good one-on-one tutoring could improve student performance a large amount: two sigma (two standard deviations) or from the 50th percentile to the 98th percentile.”
BackgroundInfluentialThinwiangthong, S., Eddy, C. M., & Inprasitha, M. (2020) · Malaysian journal of learning & instruction · doi:10.32890/mjli2020.17.1.5 · Cited by 16
“Based on past research evidence, formative assessment has the potential to raise students’ achievements if it is used correctly and consistently (Black et al., 2004; Black & William, 1998; Bloom, 1984; Leahy, Lyon, Thompson, & William, 2005).”
MethodSeun, A., Ajayi, A., Bobga, M. A., Yeboah, T. J., Apelehin, A. A., Ofori, S. D., Elumilade, R. A., & Abutu, D. E. (2023) · International Journal of Scientific Research in Science Engineering and Technology · doi:10.32628/ijsrset232532 · Cited by 29
Broader Bandwidth in Student Modeling: What if ITS Were “Eye”TS?
Gluck, K. A., Anderson, J. R., & Douglass, S. (2000) · Lecture notes in computer science · doi:10.1007/3-540-45108-0_54 · Cited by 14
“Bloom [3] emphasized the striking instructional advantage that one-to-one human tutoring has over traditional classroom instruction.”
Aguiar, E. V. B., Tarouco, L. M. R., & Reategui, E. B. (2014) · Hawaii International Conference on System Sciences (HICSS) · doi:10.1109/hicss.2014.24 · Cited by 14
“In the mid 1980's, Benjamin Bloom [1] demonstrated that one-to-one tutoring could have a significant advantage when compared with more traditional class instruction.”
BackgroundA Robust Multi-Modal Emotion Recognition Framework for Intelligent Tutoring Systems
Liu, X., Zhang, L., Yadegar, J., & Kamat, N. (2011) · IEEE International Conference on Advanced Learning Technologies (ICALT) · doi:10.1109/icalt.2011.26 · Cited by 14
Olney, A. M., Person, N. K., & Graesser, A. C. (2012) · IGI Global eBooks · doi:10.4018/978-1-61350-447-5.ch011 · Cited by 14
“While this progress is significant, Bloom (1984) has reported that accomplished human tutors can produce even greater learning gains than novice human tutors.”
BackgroundThe Importance of Teachers’ Need for Cognition in Their Use of Technology in Mathematics Instruction
Tanaś, Ł., Winkowska-Nowak, K., & Pobiega, K. (2020) · Frontiers in Psychology · doi:10.3389/fpsyg.2020.00259 · Cited by 15
“Active learning methods, such as peer instruction, think-pair-share or minute papers can be introduced without the use of technology (McConnell et al., 2017), but then they rarely answer to the issue raised by Bloom (1984) described as the 2 sigma problem.”
MethodLearning Analytics and Educational Data Mining: An Overview of Recent Techniques
Steiner, C., Kickmeier-Rust, M., & Albert, D. (2014) · PHSG #Proforis (St.Gallen University of Teacher Education) · Cited by 14
Demirci, N. (2013) · Necatibey Eğitim Fakültesi Elektronik Fen ve Matematik Eğitimi Dergisi · doi:10.12973/nefmed.2014.8.1.a10 · Cited by 15
Approximate Natural Language Understanding for an Intelligent Tutor
Hastings, P., Wiemer-Hastings, K., & Graesser, A. C. (1999) · Cited by 14
Large-Scale Deployment of Three Intelligent Web-based Database Tutors
Mitrović, A. (2006) · Journal of Computing and Information Technology · doi:10.2498/cit.2006.04.02 · Cited by 14
“The current state-of-the-art ITSs achieve improvements of one standard deviation compared to traditional classroom teaching, but are not yet as effective as one-on-one human tutoring [1,2,7,8].”
BackgroundEvaluating the Effectiveness of an Affective Tutoring Agent in Specialized Education
Mondragon, A. L., Nkambou, R., & Poirier, P. (2016) · Lecture notes in computer science · doi:10.1007/978-3-319-45153-4_41 · Cited by 15
Adaptive serious game development
Ismailovic, D., Haladjian, J., Köhler, B., Pagano, D., & Brügge, B. (2012) · doi:10.1109/gas.2012.6225922 · Cited by 14
Language teaching in a mixed reality games environment
Powers, D. M. W., Leibbrandt, R., Pfitzner, D., Luerssen, M. H., Lewis, T., Abrahamyan, A., & Stevens, K. (2008) · Petra · doi:10.1145/1389586.1389668 · Cited by 17
“Using this video information, the software system is able to maintain a dynamicallyupdated model of where all objects are located in space.”
MethodIntelligent tutoring system for learning PHP
Weragama, D. (2013) · Cited by 14
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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