Richard R. Skemp

  1. What is inflicted on all too many children and older students is the manipulation of symbols with little or no meaning attached, according to a number or rote-memorized rules.
    (The psychology of learning mathematics, p.29 Penguin Books)
     
  2. [...] topics still regarded as elementary are found on analysis to involve ideas which even those teaching the topic have for the most part never heard of. In this category I include the manipulation of fractionnal numbers.
    (The psychology of learning mathematics, p.32 Penguin Books)
     
  3. [...] an answer has more meaning to someone who has first asked a question.
    (The psychology of learning mathematics, p.33 Penguin Books)
     
  4. One obstacle to the further increase of understanding is the belief that one already understands fully.
    (The psychology of learning mathematics, p.44 Penguin Books)
     
  5. Being sure of something is one thing; knowing why one is sure is another.
    (The psychology of learning mathematics, p.51 Penguin Books)
     
  6. The final contribution of the excellent teacher is gradually to reduce the learner's dependance.
    (The psychology of learning mathematics, p.63 Penguin Books)
     
  7. The best teachers are those who are still active learners.
    (The psychology of learning mathematics, p.63 Penguin Books)
     
  8. [...] a good teacher can, by initialy asking questions that the student can answer, reduce anxiety and build up confidence, and thereby improve the performance; a bad teacher can reduce an averagely intelligent pupil to tongue-tied incompetence.
    (The psychology of learning mathematics, p.121 Penguin Books)
     
  9. The major strides which have been made, in mathematics as in the sciences have resulted from the quest for knowledge for its own sake.
    (The psychology of learning mathematics, p.126 Penguin Books)