Inherent problems of classroom schooling
This text is part of: "I would never send my kids to school" by Piotr Wozniak (2017)
Classroom learning
Schools enforce strict segregation by age and capability. This is to prevent stratification of skills deepened by the age-related rates of growth. Stratification of skills results in suppression of giftedness (e.g. by harmful effects of boredom). It also results in the regression of weaker students (e.g. by stress, loss of self-esteem, toxic memory, learned helplessness, and more).
Natural unrestricted development results in dendritic growth and diversification of interests and capabilities. For that reason, schools are increasingly strict in meeting standards, penalizing laggards and bad teachers, passing testing benchmarks, etc.
Using a simple model of diversification of push zones, we can show how classroom learning is suppressive for development and for intelligence.
Modeling reality
Modeling based on abstract knowledge underlies intelligence. It makes it possible to see things that we cannot see with the use of common sense reasoning. Most of teachers can see the problem of applying the same standard to a classroom of different abilities and of different interests. Teachers can see that an increase in teacher freedoms would increase the ability to adapt to a particular class or to a particular student. They see that a gifted student will often waste a great deal of time in the classroom, and that a weaker student would need a great deal of extra effort to bring him to the required standard. In the end, it is pretty obvious that freedom and space to learn is what most kids need to develop better. However, the Prussian system would collapse if we introduced more freedoms. If kids could come late to class, they usually would, and there is no good school start hour that would accommodate that freedom. The kids are not lazy, they can just see the benefits of getting good sleep, or spending some extra time learning on YouTube. If kids were free to leave the school during a break, they would, and they would probably not return on that day. If kids could talk freely during the class, they nearly always would. Freedom for students and teachers means better learning, but it threatens the plan of the Prussian system, which is roughly circumscribed in the curriculum and verified with testing.
If most people see the value of incremental increase in freedoms, why are we culturally trapped in the belief in the value of compulsory schooling? It seems that everyone's good understanding of a fraction of classroom reality does not add to a good global model of the harm of classroom schooling.
Classroom model
There are many obstacles on the way to classroom progress, but a few can help us quickly illustrate the problem:
- differences in ability make it hard for the teacher to choose the right level of difficulty
- push zone graphs show that only a small degree of coercive forces in education may have a beneficial impact on development (in declarative learning that area may be defined by the optimum semantic distance that can be travelled by a student in interaction with a particular teacher aiming at particular goals)
Growth of knowledge in free learning is dendritic and irregular. However, a healthy learn drive provides an exponential progression in the size of the growth platform (the more leaves in the tree, the more attachment points we have). In reality, exponential progress is stifled by factors such as social limits, stressors, ill health, learning setbacks, toxic memories, etc. This means that in theory the progression of knowledge should show stagnation and be S-shaped, but for the present analysis we can tolerate a simplification in which growth is roughly exponential with the exponent determined by the circumstances of the environment (i.e. conditions for learning, family settings, access to knowledge, etc.).
If we apply the push zone formula using different semantic distances, on a classroom group with a different levels of competence, we will see that for a group of gifted students, classroom may inhibit their development. However, the gifted will still dazzle with their performance, and the credit for their success will often be taken by the school, despite the actual harm inflicted on the very same students. For a small fraction of middle-level students, coercive schooling may appear beneficial if it hits the optimum push zone. For the largest group, whose size will be determined by the teacher's target knowledge level and the teacher's ability to customize approach to students, coercive schooling will push kids into the regress zone, with an inherent increase in the hate of learning.
We can then divide classrooms into the gifted, into the beneficiaries, and the casualties. We do not need to worry about the gifted, we should let them grow free. The beneficiaries are a group for who school makes sense. Naturally, beneficiaries in Subject A may differ from beneficiaries in Subject B. This increases the total size of the group of casualties even if those are "only" partial casualties. Sadly, benefits in one area do not compensate for the loses in other areas. We may not be able to compute the details, but if nearly all teens hate school, we know that the balance of forces is skewed towards penalization and injury.
Capability convergence
We can use a simple model in which the semantic distance between the target and the prior knowledge determines the degree of progress as determined by the optimum push zone. If we use this model to study growth dynamics, we will quickly notice the convergence of the capabilities of the beneficiaries with the target knowledge level set by the teacher. This will reduce the gap to the gifted who will slow down to reduce diversification. However, we have only two approaches to the casualties of the regress zone: reduce the target level of knowledge, or retain the casualties at the their current target for another year (i.e. grade retention).
To minimize grade retention we tend to tolerate excessive semantic distances and push students through to another grade using asemantic learning (e.g. via cramming). Because asemantic knowledge gets quickly forgotten, we develop a system in which capabilities converge, overall level of growth is inhibited, and knowledge is lost at staggering rates that few seem to measure or appreciate. We inhibit the gifted, induce intellectual regression in a large group of students, and occasionally lift some students with the assistance of gifted teachers who can differentiate their methodology by adapting to student needs.
The pictures below show a conceptual and a simulated illustration of the skill convergence in classroom learning:
Figure: Skill convergence in classroom learning is intended as well as inevitable. Skill development (vertical) is shown over time (horizonal) for students of different skill level (colors). Restrictions on freedom suppress overall progress as compared with free learning. Curriculum targets are met. Testing results are satisfactory. However, overall development slows down as expressed by quality of knowledge, creativity, and intelligence. For students in regress zone, school is particularly harmful as it results in decline, esp. as expressed in the loss of the love of learning and gradual descent into learned helplessness. Bad apples that disrupt the convergence are sifted out by grade retention. The relatively small height of the regress zone in the picture indicates a small range of capabilities, not a small range of affected students. This zone, in some classrooms, may encompass all students, i.e. 100% (even in a class peppered with gifted minds)
Figure: Tentative simulation of skill convergence in classroom learning. Left: Students experience free learning and are stratified at skill levels from 0 to 10. Their development is exponential and the exponent correlates mildly with the starting skill level. The growth exponent might be inaccurately called "talent". The most "talented" group reach the skill level of 90, and all students average 42 at the end of the learning period (thick blue average growth line). Right: The same group of students with the same stratification of skills is subjected to classroom learning. If we assume constant push zone function, and derive growth exponent from the hypothetical semantic distance from the required target skill level, we can see a slowdown in overall growth. Gifted students experience slowed development (red regress zone), average students may benefit if lecturing meets their semantic distance optimum (blue acceleration zone). The weakest students enter the most harmful brown regress zone in which they can become "rejects" of the system. The growth exponents have generously not been made negative on the assumption that in a good classroom we can hope of not experiencing an actual regress. The skill levels tend to converge, esp. at upper skill echelons. The overall growth is suppressed and reaches 31 at the end of the learning period (thick red average growth line)
Strategies
If an ambitious teacher lifts up the target, he quickly increases the casualty zone without making much dent into the gifted zone. Casualties can be reduced by letting them all off the hook, and this was the good thing of the days I was a student. However, today, this approach is usually not tolerated well by the system, and teachers are penalized by poor test results (e.g. No Child Left Behind).
With an increase in targets, the size of the beneficiary zone depends on the distribution of ability, but is likely to shrink due to the scarcity of giftedness. If a compassionate teacher attempts to reduce the target, she may add to the level of boredom, and still be brought to hill by the system due to poor tests scores.
The formula for success in the system is to produce maximum uniformization of levels by strict adherence to standards, benchmarks, attendance, discipline, i.e. all the factors that are most limiting to freedom, and have the greatest contribution to the hate of learning. Gifted will be suppressed, weaker students will be sifted out by grade retention, and the core mass of the product of schooling will converge to a resultant mediocre level of actual knowledge (as opposed to knowledge certified with testing, which provides the illusion of reasonable progress). That uniformity is increasingly hard to retain with passing years, and leads to increasing frustration on the part of students and teachers. There is only one solution to the problem: freedom of learning.
Illusion of progress
Teachers and principals experience the same illusion of progress. They take gifted as a shiny example, and beneficiaries as a measure of progress, and keep hoping that the casualties can just clean up their act and get to work. Principals boast of gold medals in knowledge olympics. So do teachers. They all boast of good test scores for the school. They never seem to ponder why kids uniformly hate school by the time of high school graduation.
As a result, schools form a self-perpetuating illusion that the system works and generates net educational benefits. See: Glorification of schooling
Summary
- diversification of knowledge leads to the diversification of net effects of push zones in a classroom
- in a typical classroom, gifted slow down, some kids benefits, and a large group of students enter the regress zone
- to minimize the negative effect of diversification schools increasingly tighten the standard benchmarks to homogenize progress
- discipline of progress compounds the universal hate of schooling among teen students
- schools take credit for the gifted, and blame poor outcomes on insufficient efforts of those who score less in tests
- by focusing on the success of the gifted, schools fail to appreciate the degree of failure in the system
See also