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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Chou, C., Chan, T.-W., & Lin, C.-J. (2003) · Computers & Education · doi:10.1016/s0360-1315(02)00130-6 · Cited by 270
“In fact, private tutoring has been shown to be four times as effective as classroom teaching, according to a study conducted by Bloom (1984). Unlike a computer treated as a provider of content (mostly text at that time) to students, or as a learning tool or toy, a computer that models a tutor must mimic tutoring inter…”
Anderson, J. R., Boyle, C. F., & Yost, G. R. (1985) · International Joint Conference on Artificial Intelligence · Cited by 270
Generative AI for Customizable Learning Experiences
Pesovski, I., Santos, R., Henriques, R., & Trajkovik, V. (2024) · Sustainability · doi:10.3390/su16073034 · Cited by 274
“While the positive relationship between personalization and student performance is well established [15], its implementation in the classroom has not fully realized this potential.”
BackgroundThe Real Story Behind Story Problems: Effects of Representations on Quantitative Reasoning
Koedinger, K. R., & Nathan, M. J. (2004) · Journal of the Learning Sciences · doi:10.1207/s15327809jls1302_1 · Cited by 431
“Because equation solving is so hard for students to learn and because it is important, a second instructional strategy worth considering is a mastery-based approach (Bloom, 1984) that focuses on equation-solving instruction in isolation.”
BackgroundA Framework for Evaluating the Quality of Multimedia Learning Resources
Leacock, T. L., & Nesbit, J. C. (2007) · Cited by 267
Bodovski, K., & Farkas, G. (2007) · The Elementary School Journal · doi:10.1086/525550 · Cited by 264
“In contrast, our findings contradict studies showing that higher beginning achievement is associated with lower learning rates (Bloom, 1976, 1984; Brown & Saks, 1986; Phillips et al., 2002).”
BackgroundResultWhat Makes Literacy Tutoring Effective?
Juel, C. L. (1996) · Reading Research Quarterly · doi:10.1598/rrq.31.3.3 · Cited by 263
The Effects of Adjunct Questions on Prose Learning
Hamaker, C. (1986) · Review of Educational Research · doi:10.3102/00346543056002212 · Cited by 261
“16 in this review represents a one-sigma effect on Bloom's (1984) scale, and corresponds to an effect size of 1.”
BackgroundChen, H., Park, H. W., & Breazeal, C. (2020) · Computers & Education · doi:10.1016/j.compedu.2020.103836 · Cited by 291
The Ethics of Artificial Intelligence in Education: Practices, Challenges, and Debates
Holmes, W., & Porayska-Pomsta, K. (2022) · doi:10.4324/9780429329067 · Cited by 258
“This approach is deeply ingrained in traditional educational practices focused on school-based subject-domain teaching, which was further boosted by Bloom’s influential “2-sigma effect” studies (Bloom, 1984).”
Kennedy, J., Baxter, P. E., & Belpaeme, T. (2015) · ACM/IEEE International Conference on Human-Robot Interaction (HRI) · doi:10.1145/2696454.2696457 · Cited by 256
“Categories and Subject Descriptors H.1.2 [Models and Principles]: User/Machine Systems Keywords Robot Tutor; Social HRI; Child-Robot Interaction; Social Behaviour”
BackgroundInfluentialApplications of AI in education
Beck, J. E., Stern, M. K., & Haugsjaa, E. (1996) · XRDS Crossroads The ACM Magazine for Students · doi:10.1145/332148.332153 · Cited by 254
Albanese, M. (2000) · Medical Education · doi:10.1046/j.1365-2923.2000.00753.x · Cited by 418
Longitudinal Analysis of Time, Engagement, and Achievement in At-Risk versus Non-Risk Students
Greenwood, C. R. (1991) · Exceptional Children · doi:10.1177/001440299105700606 · Cited by 248
Vandewaetere, M., Desmet, P., & Clarebout, G. (2010) · Computers in Human Behavior · doi:10.1016/j.chb.2010.07.038 · Cited by 274
“One-to-one human tutoring, compared to traditional classroom instruction, makes learning performance to increase with two standard deviations (Bloom, 1984).”
BackgroundThe Research to Practice Gap in Special Education
Greenwood, C. R., & Abbott, M. (2001) · Teacher Education and Special Education The Journal of the Teacher Education Division of the Council for Exceptional Children · doi:10.1177/088840640102400403 · Cited by 250
“Bloom (1984) reported that one-on-one peer tutoring compared to conventional group instruction produced effect sizes as large as 2.0.”
BackgroundInfluentialSlavin, R. E. (1987) · Review of Educational Research · doi:10.3102/00346543057002175 · Cited by 248
Closing Achievement Gaps: Revisiting Benjamin S. Bloom's “Learning for Mastery”
Guskey, T. R. (2007) · Journal of Advanced Academics · doi:10.4219/jaa-2007-704 · Cited by 242
“(Bloom, 1984a, p. 4) Bloom (1984a) referred to this as the “2 Sigma Problem”: The tutoring process demonstrates that most students do have the potential to reach this high level of learning.”
BackgroundCognitive Computer Tutors: Solving the Two-Sigma Problem
Corbett, A. T. (2001) · Lecture notes in computer science · doi:10.1007/3-540-44566-8_14 · Cited by 241
Cur r iculum Resear ch : Tow ar d a Fr amew or k for "Resear ch -based Cur r icula"
Clements, D. H. (2007) · Journal for Research in Mathematics Education · doi:10.2307/30034927 · Cited by 243
Linn, M. C. (1995) · Journal of Science Education and Technology · doi:10.1007/bf02214052 · Cited by 240
“Tutoring, as emphasized in the spatial reasoning environment, has been hailed by many as the most effective way to provide the guidance and explicit problem solving processes necessary for effective learning (Bloom, 1984).”
BackgroundSteenbergen-Hu, S., & Cooper, H. (2013) · Journal of Educational Psychology · doi:10.1037/a0032447 · Cited by 175
“Although not as effective as what Bloom (1984) found, a recent meta-review by VanLehn (2011) found that human tutoring had a positive impact of d 0.79 on students’ learning.”
InfluentialAdaptive Gamification for Learning Environments
Lavoué, É., Monterrat, B., Desmarais, M. C., & George, S. (2018) · IEEE Transactions on Learning Technologies · doi:10.1109/tlt.2018.2823710 · Cited by 236
Corbett, A. T., Koedinger, K. R., & Anderson, J. R. (1997) · Elsevier eBooks · doi:10.1016/b978-044481862-1.50103-5 · Cited by 244
The automated tutoring of introductory computer programming
Anderson, J. R., & Skwarecki, E. J. (1986) · Communications of the ACM · doi:10.1145/6592.6593 · Cited by 225
The End of Techno-Critique: The Naked Truth about 1:1 Laptop Initiatives and Educational Change
Weston, M. E., & Bain, A. (2010) · The Journal of Technology, Learning and Assessment (Boston College) · Cited by 228
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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