he objective behind the creation of the Art of the Problem web series was to produce a learning resource that would show how responses to specific problems have evolved over time, with new approaches building upon old ones to create the complex sets of ideas that enable the modern world to function. Focusing on responses to a single problem over the course of human history can reveal how true it is that modern scientists are “standing on the shoulders of giants“. The lessons that teach people most effectively are the ones that are written with this type of framework in mind. Written lessons should be structured to help students make connections between ideas and understand how each new idea fits into their existing understanding of the world. Lessons that help people to think in this way can help to solve the problem of how to teach someone a lesson.
Learning as a Problem
The task of teaching others is a problem to which numerous responses have been made over the course of human history. Teaching people through written lessons of lectures has never been as simple as just providing a list of facts and assuming that students will be able to grasp their significance unaided. It is not the instinctive mimicry and adoption of language and everyday skills that poses a problem for the developing child, but rather the sort of learning that enables us to build on the work of previous generations of problem solvers. Few people pick up the ability to write in the same manner as they did the ability to talk, and as the solutions to problems like code breaking and written language have increased in complexity, the solutions to teaching people about these ideas have had to follow suit. Throughout history, educators have sought better ways of writing lessons and sharing knowledge, and it is worthwhile considering the solutions that were applied in previous ages when trying to write an effective lesson today.
Solutions to the problem of teaching tend to fall into two types: learning through experience and learning through listening. Learning through individual experience and the questioning of authority was central to education in Ancient Greece, where Plato considered self-reflection to be the key to knowledge, and Aristotle focused on learning through scientific investigation of the external world. The Romans relied more on learning through listening, with a focus on practical training in vocational skills under the guidance of an experienced master. The Roman approach was perpetuated throughout Medieval Europe, with long apprenticeships spent copying the master’s work, and monastic training relying on rote learning and memorization of important manuscripts. The Greek approach to learning was revitalized during the Renaissance, and many Enlightenment figures devised their own ideas about the importance of learning through personal inquiry. John Locke described the child’s mind as a blank slate or tabula rasa, ready to be filled with knowledge, while Jean-Jacques Rousseau insisted on the importance of child-centered education to allow each individual to build their own interpretation of the world from their own experiences.
The divide between these two responses to the problem of education was perpetuated by the psychological theories that arose from the 19th century onward. The Greek perspective can be recognized in the assertions of cognitive psychologists, like Jean Piaget, who see the mind as actively constructing complex theories about the world in response to individual experience. A more Roman attitude is reflected by the work of behaviorists, like B.F. Skinner, who suggest that the mind is simply an advanced machine, capable of learning to remember complex responses to familiar stimuli. Most psychologists recognize the importance of both types of learning in education. Edward Thorndike suggested that students learned through a process of trial and error, incrementally building new mental connections in response to their experiences. Writing an effective lesson is now thought to require a balance between the simple transmission of knowledge and allowing enough scope for students to engage actively with the material and think for themselves. Lessons should be designed to take advantage of what we have learned about the way people learn.
How Do People Learn?
The long history of attempts to develop the perfect educational method, together with psychological research into the process of learning, has produced a complex picture of how people learn. It has also led to many different theories about the best mode of communication to use in teaching. The Greek philosopher Socrates advocated for dialogue between students and teachers, but written lessons were more important to Medieval educators. Reading was also considered one of the key routes for self-education in the Enlightenment, and written lessons continue to be placed at the centre of learning to this day, despite the increase in activity and play based learning inspired by educators like Maria Montessori.
A stimulus rich environment that encourages interaction, whether it is through engaging students as readers or encouraging scientific experimentation, seems to be the best current model for education. In this environment, the student will encouter the new experiences and ideas that will shape their mind. The brain appears to be born ready to acquire knowledge, but its structure changes as a result of its experiences, forming new connections. The physical connections that appear in the brain are matched by the conscious connections that people learn to make between the ideas they encounter. It is this ability to connect new ideas with one another and with existing knowledge that is at the heart of the learning process, and it can be encouraged by the right sort of teaching. Lessons that encourage students to fit ideas into a larger conceptual framework, like the association of apparently unrelated ideas with the single problem they aim to solve, can provide all types of learners with an effective tool for future study.
Difficulties Making Connections
Awareness of the needs of learners is essential if a lesson is going to provide the right balance of support and freedom for students to make their own connections between ideas. People learn in different ways and at different rates, but the right conceptual framework can support all types of learners to make connections. Although such a framework can be useful in a lecture, it is in written lessons that structure is most important. Readers need to be able to navigate through the material by themselves, and they need to see how the parts relate to the whole, without having a teacher to guide them and draw their attention to the most important points. Many people find it easier to learn when they can see how different ideas fit together as part of a story, even when they are troubled by conditions that make it difficult for them to learn through more conventional teaching methods. Focusing on a written lesson that appears as an impenetrable block of text, without an intriguing story or clear framework to draw the student on through the material can turn learning into a chore. Advice regarding ADHD and similar disorders suggests that tasks requiring complex instructions and long periods of concentration on single topics can be problematic. It may be easier for people affected by these types of disorder to think creatively and recognize connections between ideas than it is for them to work with more narrowly focused material. Sensitivity to the needs of different learners can help educators to develop more of these sorts of materials, in order to encourage people to think differently about learning and the world around them. Lessons need to support learners of all styles and abilities to recognize how the pieces fit together, which is exactly what the Art of the Problem project is about.
Three Steps to an Effective Lesson
Teachers need to create an environment that is conducive to learning, and assist students by organizing knowledge in a way that makes it easy to incorporate into their existing understanding of the world. Facts that are connected together are easier to understand and remember. Following the chronological development of a particular problem or theme, and turning it into a story, is an effective means of teaching people to see these connections. It can be achieved in three steps:
1. Do Your Research
Facts are the backbone of a good lesson, but research can be a creative process rather than just a gathering of facts. Using a timeline as a framework for note taking can allow interesting digressions to be explored without losing sight of the overall picture. As notes are added to the timeline, new connections between events and ideas will become apparent. Once the research stage is complete, the material will have been ordered chronologically, and the overarching story linking the events will become clear.
2. Structure the Lesson
The timeline provides the basic chronological structure, which can be shaped into a story in order to create a coherent structure that is focused on one central message or problem. The most successful lessons and lectures engage their audiences by telling stories. The story should begin with the problem, describe all of the different approaches that have been taken to tackle it, and end the most recent, and successful, solution, or the expectation that an improved solution will soon be found. Each step in this story should be a logical progression from the last, so that it is easy for people to see the connections between different elements. In a written lesson, each step can be contained in a separate paragraph, and headings can mark important stages in the progression of the story. Throughout the whole story, a clear focus should be maintained on that one central message that people should understand and remember.
3. Edit Your Script
Editing a lesson or educational script requires more than the usual checks for spelling and grammar. It is important to ensure that the text flows well and is structured logically, particularly when the lesson will be delivered in written form, since the reader will be unable to ask for clarification. A second opinion is often required to recognize any structural flaws, since it is important to consider what the lesson will sound like to a student who is hearing it for the first time.
ْ
________*التــَّـوْقـْـيـعُ*_________
لا أحد يظن أن العظماء تعساء إلا العظماء أنفسهم. إدوارد ينج: شاعر إنجليزي
أمس في 2:16 am من طرف freeman
