Understanding the Learner
Dalhousie Conference on University Teaching and Learning
Department of Mathematics
What is learning?
In two or three concise sentences, define what learning means to you and describe how you think learning occurs. Write a definition that would make sense to your colleagues and your students.
Learning is …
Introduction to Learning Theories
1. Behaviourist Learning Theory:
Behaviorist learning theorists believe that knowledge exists independently and outside of people. There is a logical sequence of facts and standard skills that have to be learned successively, and you must acquire this in small bits, e.g. via a traditional lecture.
Learning occurs as a result of forming associations between stimuli and responses. Behaviourism focuses on objectively observable changes in behaviour and stems from the work of B.F. Skinner and the concept of operant conditioning.
Here are some examples and applications of behaviourist learning theory:
Drill / Rote Work
Bonus Marks (providing an extrinsic incentive for students)
Participation Marks (providing an incentive for students to participate)
Verbal Reinforcement (saying "well done", "good job", etc.)
Establishing Rules ("no eating in my classroom", "no coming in late")
Frequent Assessment (giving tests and assignments to assess learning)
2. Cognitive Learning Theory:
Cognitive learning theorists believe knowledge arises from the interaction of a particular structure and a person’s own psychological environment. Learning involves the reorganization of experiences, either by attaining new insights or changing old ones. The key idea is to create a meaningful learning environment.
Cognitive theorists place greater interest in knowledge, meaning, creativity, expectations and thoughts as well as cognitive structures and processes such as memory, perception, problem-solving, comprehension, attention, and concept-learning. Cognitive learning theories are credited to Jean Piaget.
Here are some examples and applications of cognitive learning theory:
Repeating Key Ideas
Linking Concepts (associate new content with something that they already know)
Providing Structure (organizing your lecture in efficient and
Real World Examples
3. Constructivist Learning Theory:
Constructivist learning theorists believe that learning occurs when the learner constructs her own knowledge from her current and/or past knowledge. This is a significant contrast to behaviourist theory, which asserts that knowledge is absorbed through observation.
According to constructivists, learning occurs because personal knowledge is constructed by an active learner who resolves conflicts between ideas and reflects on theoretical explanations. Constructivism is based on the idea of discovery learning, where the instructor functions merely as a guide or coach to facilitate exploration, within a given framework.
Here are some examples and applications of constructivist learning theory:
Problems-Based Learning (using carefully-chosen "big" problems to motivate discussion and develop important concepts)
Focus on Learning Process (emphasizing the process, not the product)
Cooperative Group Work (jigsaw method of cooperative learning)
Formative Evaluations (giving students feedback before they hand
in an assignment for evaluation)
Self and Peer Assessment (involving the students in the assessment process)
Large Research Projects (providing for active self-regulated learning)
Summary of Learning Theories:
Type of Learning
Association leads to a change in behaviour
Information processing leads to understanding and retention
Problem-solving and discovery leads to insight
Present and provide for practice and feedback
Plan for cognitive learning strategies
Provide for active, self-regulated, reflective learning
Introduction to Learning Styles
Learning styles refer to the characteristic strengths and preferences in the ways people take in and process information. Due to genetics and upbringing, individuals have different ways of perceiving and processing information. As educators, it is important to recognize these differences to accommodate all of our students.
The Soloman-Felder Index of Learning Styles Test incorporates most of the major approaches to understanding learning styles, and is most appropriate for university students. This test is included in this package.
There are two opposite preferences for each of the four scales recorded by the Index of Learning Styles Test. Everyone uses both of the opposite preferences at different times, but not usually with equal confidence. The scales and preferences are defined below.
The Active-Reflective scale determines how you prefer to process information.
Active learners learn by doing something with information. They prefer to process information by talking about it and trying it out. On the other hand, reflective learners learn by thinking about information. They prefer to think things through and understand things before acting. An active learner would say, "let’s try it!" A reflective learner would say, "let’s think about it first."
The Sensing-Intuitive scale determines how you prefer to take in information.
Sensing learners prefer to take in information that is concrete and practical. They are oriented towards details, facts, and figures, and prefer to use proven procedures. Intuitive learners prefer to take in information that is abstract, original, and oriented towards theory. They look at the big picture and try to grasp overall patterns.
The Visual-Verbal scale determines how you prefer information to be presented.
Visual learners prefer visual presentations of material - e.g. charts, diagrams, graphs, and pictures. Verbal learners prefer explanations with words, both written and spoken.
The Sequential-Global scale determines how you prefer to organize information.
Sequential learners prefer to organize information in a linear, orderly fashion. Global learners prefer to organize information more holistically and in a seemingly random manner.
The National Council of Teachers of Mathematics (NCTM) writes that:
"The best idea yet for developing understanding, is to let mathematics be problematic for students".
In other words, let your students wrestle with an idea,
don’t just show them how to proceed!
The origin of thinking is some perplexity, confusion, or doubt. Thinking is not a case of spontaneous combustion.
- John Dewey, 1910
Kolb’s Model of Learning Preferences
Learning preferences can be viewed on a continuum across two dimensions, based on how people perceive information (concrete vs. abstract) and process information (active vs. reflective).
Four learning stages:
What kinds of instructional activities foster learning at each of these stages?
Concrete ExperienceReflective Observation
Abstract ConceptualizationActive Experimentation
Adult Learning Principles
Malcolm Knowles is associated with the use of the term andragogy, which means "the art and science of helping adults learn".
Andragogy has the following five guiding principles.
Here is a great discussion question:
Especially with our upper level courses, are we teaching our students by incorporating these principles of andragogy? If not, should we?