Since first teaching logic in middle school, I have used the following working definition of reasoning and have found it quite helpful. “Using knowledge one has to discover new, previously unknown knowledge.” It comes from Martin Cothran’s Traditional Logic I. Some progressive pedagogies place a heavy emphasis on understanding before memorization and sometimes to the exclusion of it. I disagree with this emphasis, for understanding is the fruit of reason, and reason cannot be conducted if there is not pre-existing knowledge in the mind. One must have memorized facts to reason to thorough understanding.
There is a difference between reading an argument on a page or experiencing it as an experiment and owning it in one’s mind. Comprehend might be a better word—grasp a truth with the mind. So long as we do not require our students to memorize the basics, we prevent them from truly owning understanding, for all their facts are “borrowed.” I see this in the children of poverty with whom I have worked. They are required to memorize very little, so in the learning process, they must do more than the child who has memorized facts. They must reason and hold information in working memory, recalling it from a page or an experience instead of from their own long term memory. This requires intensive effort—the very kind of effort that socio-economically disadvantaged students struggle to give.
One of the greatest academic challenges for children in poverty is a deficiency of words. It is really hard to teach without words and even harder to understand without them. When I think about the importance of words and teaching socioeconomically disadvantaged children, Frederick Douglass almost always comes to my mind. In particular, I recall a wonderful article entitled “Freedom through Education” (Pages 14-15) in The College, the magazine of St. John’s College.
“The speeches he found in his first book, The Columbian Orator, gave him the means to articulate his own thoughts. ‘The more I [Douglass] read them, the better I understood them. The reading of these speeches added much to my limited stock of language, and enabled me to give tongue to many interesting thoughts, which had frequently flashed through my soul, and died away for want of utterance.’ He had discovered the power of naming.”
Many socioeconomically disadvantaged children have a deficiency of words. You need words to teach math. You need words to think (the naming Douglass refers to), and you need to think in order to understand. These children do not have anyone speaking to them intelligently at home. They do not have the required reading of good books at home. So when I talk to them about probability, it is like trying to hang a coat on a wall where there are no coat-hooks. All my words fall to the floor and very few stick. So few stick, that no sense can be made of what does. It feels like my words do not grab hold of any concept in their head. “Use manipulatives!” you say. I do. I lined up a row of markers when I encountered a student who did not know what “before” or “after” meant. He still could not tell me which marker came before another. You can play with counting chips all day, but if the vocabulary/concept for what is happening physically is not in the brain, then the concept stays on the table, for the default way of life for these kids is a word-deprived one. Every chip experiment is a brand new world as long as their “thoughts die away for lack of utterance.”