The Empirical Basis for the Value of One-on-One Tutoring:

How Mindspire was Inspired


            In 1984, Benjamin Bloom, an educational psychologist at the University of Chicago, published a paper entitled ‘The 2 Sigma Problem’. This paper has since become a seminal work in the fields of education and educational psychology because of what it so convincingly demonstrated. In this piece, I’d like to talk about the study’s findings and how that influences Mindspire’s modus operandi. To begin, I’ll give some context followed by the ‘long-story-short’ version for those who don’t want to read a somewhat science-y article.


The Context

Two of Bloom’s brightest graduate students had written their dissertations on comparisons of students learning under one of three types of instruction: conventional, mastery learning, and tutoring. Bloom describes each of these conditions of instruction in the following ways:

1. Conventional. Students learn the subject matter in a class with about 30 students per teacher. Test are given periodically for marking students.

  1. 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.
  2. 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.

(Bloom, 1984)

            Do these descriptions sound familiar? The conventional model is the classroom model that the vast majority of schools, both private and public, operate under. Under conventional learning, when some students receive inadequate marks on a test, the entire class moves on anyway and it is up to the individual students to ‘catch up’. On the mastery learning model, students who fail are instead given feedback, corrected, and then tested again until they master the material. This type of individualized care is not at all typical of a standard middle school or high school classroom. The tutoring model is essentially the same as mastery learning but it greatly lowers the teacher-student ratio, allowing for increased individualized care.


To Make a Long Story Short…

It may not surprise you to hear that the conventional students exhibited the lowest achievement at the end of the instructional period, with mastery learning students showing better achievement and tutored students showing the best achievement. After all, the more individualized a learning process is, the better it can meet a student’s needs, right? But what is particularly striking is that tutored students, on average, scored higher than 98% of conventional students who spent the same amount of time learning the same subjects with the same tests. What’s more is that the relationship between a student’s aptitude at the beginning and their achievement at the end was quite strong for conventional students. For tutored students, however, the correlation between aptitude and achievement was shown to be quite weak. The study showed, in other words, that most students can achieve high degrees of learning with the right instruction, regardless of where they start. (To skip the rest of the article and go directly to how this influences Mindspire, click here.)


The Full Story

In the ‘experiments’, students with similar aptitudes, achievements, scores, etc. were randomly placed into one of the three groups. In other words, the students all began in almost the same position regarding their intellectual capacity and development up to that point. The three groups also received the same amount of time for instruction. This procedure was replicated for students in grades four, five, and eight and with two different subjects: probability and cartography.

The differences in final achievement were more than striking. The average student under mastery learning was one standard deviation above the average conventional student. The average student under tutoring was approximately two standard deviations above the average student under conventional instruction. (Standard deviation is notated by the Greek letter sigma [σ], which is where the study got its name.) In plain terms, the mastery learning student was, on average, above 84% of the conventional learning students. The tutored students was, on average, above a staggering 98% of conventional learning students. While this alone is an enormous difference, the list goes on.

At the end of the instruction period, 70% of mastery learning students and 90% of tutored students attained a level of cumulative achievement reached by only the top 20% of conventional students. Significant differences were also noted for variables such as students’ time on ask, attitude, and interest.

Importantly, there were serious reductions in the strength of the relationship between students’ initial aptitude and achievement and their summative achievements. Under conventional instruction, the relationship between aptitude and achievement was +0.6 – a strong correlation. Under mastery learning the correlation fell to +0.35 and under tutoring the correlation fell to +0.25 – both weak correlations. What this suggests is that most students have the potential to achieve a high level of learning, their initial aptitudes notwithstanding.



Though it looks quite plain, this figure represents the study’s most important conclusion.

Up to this point, the data presented was gathered and analyzed largely by Bloom’s graduate students. His primary contribution to the 2 Sigma Problem came in the form of an analysis of significant variables and their effects on the learning process. With the newfound insight concerning just how much more growth could be achieved by tutoring or mastery learning than by conventional learning, Bloom and his graduate students sought to identify variables that could have a 0.5 σ effect or greater. They are shown in the figure below.


Quite noticeably, four of the five top variables affecting student achievement concern the teacher as the object of change, not the student. Of the 12 variables listed, six are teacher-centered, four are student-centered, and two are home-environment-centered. The implication is that, at the level Bloom and his students deemed statistically significant, at least half of the variables affecting student achievement are based on the teacher. At the highest level, that number jumps to 80%.


How Mindspire was Inspired:
Bloom’s work illuminates a number of key points about the way children learn. Firstly, it demonstrates the measurable difference that personalized instruction has on a student’s learning. Secondly, it demonstrates that most students can achieve at a high level regardless of their initial aptitude. Lastly, it shows that among the most influential variables in a student’s learning environment, the majority are teacher-centric, not student-centric.

Mindspire’s approach to tutoring and test prep is driven by a philosophy informed by Bloom’s contributions to education. Mindspire used to offer group classes but does not anymore because the evidence simply does not support the efficacy of group classes when compared to one-on-one. When a student is paired with a tutor, there is no attempt to fit the student to a mold or to run through a cookie-cutter curriculum. Frankly, there is no one-size-fits-all tutoring or test prep strategy. The strategies that Mindspire tutors use are strategies that directly reflect what has been scientifically shown to work best – engaging material, moving at the student’s pace, targeted work, timely and consistent feedback, deliberate practice, heuristics and mnemonics, and a genuine investment in the student.