As we learn, brain cells make connections with each other that build into networks, enabling thinking and memory. The discoverer of these connections, Santiago Ramón y Cajal (Nobel Prize, 1906) described them as seeming to reach out to each other to do so, though in reality we are dealing with a series of electro-chemical processes whose most recent descriptions are in the work of Stanislas Dehaene and Eric Kandel (Nobel Prize, 2000). Whatever builds these connections contributes to learning, and can be described as teaching. Whatever hinders them, or fails to take account of their development, is mis-teaching.
As I write, in 2016, school systems across the world contain a mixture of teaching and mis-teaching, usually because the elements in teaching that hinder children's progress are either not understood, because teachers are not aware of the key texts, or are ignored, because they do not fit with the educational principles of people who still have charge of teacher training. The clearest statement of these principles lies in Professor Geoff Whitty's address to the British Educational Research Association in 2005. Professor Whitty sees the goal of education as the promotion of social equality, a point of view that sees education as a primarily political process, rather than one of intellectual development.
Teaching takes place when:
Children's knowledge is carefully developed. This knowledge includes:
mathematical facts, ranging from number combinations and multiplication tables to principles of Euclidian proof
spelling patterns in English, their relation to sound and to other features of language, including historical developments
vocabulary and usage in formal English, including grammar
key facts about the world, its history, geography, and place in the universe
the operation of technology
Children apply their knowledge in the course of the whole of their work. This prevents them from having to start from scratch, for example, in reading new texts, solving mathematical problems, and writing.
Mis-teaching takes place when:
Networks are given more new material than they can cope with at a time.
Teaching moves on too quickly to allow material to be consolidated, so that connections are not properly established.
Pupils are not given accurate information, for example about the relationship between letters and sounds in English, which is not exclusively phonic.
Pupils copy, thus jerking their attention back and forth between the original and their own version. This hinders or prevents connections from being made, unless the pupil already knows the material.
Pupils are taught concepts that depend on others that they have not understood.
Pupils are expected to solve problems or carry out operations without being given the knowledge they need in order to do so.
Languages. Presenting spoken language at a pace that is too fast for the learner to understand. Giving long lists of unconnected vocabulary to learn without application. Having pupils complete exercises without understanding. Not teaching the grammatical structures that enable them to construct sentences in their new language, or teaching these in ways that present too much complexity at a time, a particular historical fault with German.
Reading, including dyslexia. Failing to teach the connections between letters and the sounds they represent (phonics). Presenting a misleadingly simple account of these connections. Not seeking to explain words in which letters do not represent the sounds they most often do. Not taking account of the use and development of memory in teaching, so that children are forced to work out words from scratch that they have previously learned to read. This is a particular problem where children are assessed as dyslexic, and find this ab initio processing difficult.
Maths. Teaching counting in multiples rather than multiplication tables. Not ensuring that tables are mastered, so that pupils can use them in calculation. Not teaching the principles of geometric proof, so that pupils are left with ineffective ad hoc reasoning. Not ensuring that number facts, addition and subtraction, are mastered to the extent that their accurate use becomes automatic.
There could be many further examples. In some cases, such as copying notes, misteaching is sustained by force of habit. In others, it is the unintended consequence of basing teaching on social rather than intellectual principles. Wherever misteaching occurs, children learn less effectively than they should. We need to understand what it is, and to replace it with teaching.