Theories of learning C&I 393 Mathematics Methods I

Learning Theory Q: How do people learn? A: Nobody really knows. But here are a few theories: Behaviorism Cognitivism Sociocultural Theory Social Constructivism Multiple Intelligences

What is Learning? A process that brings together cognitive, emotional, and environmental influences and experiences for acquiring, enhancing, or making changes in one's knowledge, skills, values, and world views ( Illeris, 2004 ). The way in which information is absorbed, processed, and retained. Ileris, K (April 2001). "Transformative Learning in the Perspective of a Comprehensive Learning Theory". Journal of Transformative Education (2): 79–89.

Behaviorism Confined to observable and measurable behavior  Classical Conditioning - Pavlov  Operant Conditioning – Skinner

Paris, N.A. Kennesaw State University- M.Ed in Ad Ed program5 Assumptions of Behaviorism All species of animals learn in similar (equal ways with the same guiding principles To understand learning processes, focus on stimulus and responses Internal process should be excluded from the study of learning. Learning is evidenced by a behavior change

Paris, N.A. Kennesaw State University- M.Ed in Ad Ed program6 Assumptions of Behaviorism (cont.) Organisms are blank slates at birth Learning is a result of environmental events

Behaviorism  Classical Conditioning – Pavlov S R A stimulus is presented in order to get a response:

Behaviorism  Classical Conditioning - Pavlov S US UR CS US CR

Behaviorism  Operant Conditioning - Skinner The response is made first, then reinforcement follows.

Behaviorism in the Classroom Rewards and punishments Responsibility for student learning rests squarely with the teacher Lecture-based, highly structured

Benny (Erlwanger, 2004) Stimulus Response

Paris, N.A. Kennesaw State University- M.Ed in Ad Ed program12 Your turn! With a partner, list two examples of operant conditioning that you have used or that you see regularly in your classroom or school. Try to think of a “behavioral” example and an “instructional or academic” example.

Critiques of Behaviorism Does not account for processes taking place in the mind that cannot be observed Advocates for passive student learning in a teacher-centric environment One size fits all Knowledge itself is given and absolute Programmed instruction & teacher-proofing

Learning Theory Cognitive Learning Theory

Cognitivism Grew in response to Behaviorism Knowledge is stored cognitively as symbols Learning is the process of connecting symbols in a meaningful & memorable way Studies focused on the mental processes that facilitate symbol connection

Cognitive Learning Theory  Discovery Learning - Jerome Bruner  Meaningful Verbal Learning - David Ausubel

Cognitive Learning Theory  Discovery Learning 1. Bruner said anybody can learn anything at any age, provided it is stated in terms they can understand.

Cognitive Learning Theory  Discovery Learning 2. Powerful Concepts (not isolated facts) a. Transfer to many different situations b. Only possible through Discovery Learning c. Confront the learner with problems and help them find solutions. Do not present sequenced materials.

Examples My 10 th grade Chemistry class Identify this green powder:

Cognitive Learning Theory  Meaningful Verbal Learning Advance Organizers: New material is presented in a systematic way, and is connected to existing cognitive structures in a meaningful way.

 Meaningful Verbal Learning Cognitive Learning Theory When learners have difficulty with new material, go back to the concrete anchors (Advance Organizers). Provide a Discovery approach, and they’ll learn.

Cognitivism in the Classroom Inquiry-oriented projects Opportunities for the testing of hypotheses Curiosity encouraged Staged scaffolding

Critiques of Cognitivism Like Behaviorism, knowledge itself is given and absolute Input – Process – Output model is mechanistic and deterministic Does not account enough for individuality Little emphasis on affective characteristics

Learning Theory  Situative Cognition

What is Situative Cognition? Also known as Situated, Sociohistoric or Sociocultural. Learning is tied to the context or situation, students’ culture shapes their cognitive development All learning is highly social, rather than individual.

A Little on Learning Two main elements of learning in situated cognition: 1. All learning is social and happens within a community through participation. 2. Learning is tied to its situation or context.

…and more on Learning Collins (1988) defines situated learning as “the notion of learning knowledge and skills in contexts that reflect the way the knowledge will be useful in real life” Examples of situated learning: Brazilian street kids’ math when making sales on the street

Transfer According to situated cognition, knowledge does not transfer between tasks. Teaching through abstraction is of little use since real learning occurs in authentic situations only Ex: New police academy grads being told by experienced cops “now forget everything you learned”.

More on Transfer If learning is being able to participate in a community of practice, the issue of transfer can be problematic. Does transfer apply to new practices within a community (e.g. new math problems) or to practices outside the community (e.g. work) ? Many resources and supports in one community don’t carry over to a different community.

Situative Cognition in Education Knowing how to participate in social practices has a large role in schools. Classroom activities are often organized as social groups and children participate in these groups with varying degrees of success. Much of students’ identities are formed by the groups they participate in at school, e.g. sports, chess, journalism, A.P. classes...

Situative Cognition in Education A push for “authentic learning” where students learn content matter that is situated in a real world context (ex: Resnick article) Students are encouraged to think and work like scientists, historians, mathematicians, etc. Authentic does not necessarily mean “real world” but rather tasks that are “true” to the domain Encouraging classrooms to create a community of learning that promotes inquiry and development of identities.

Critiques of Situative Cognition While the theory takes into account the social, the individual tends to be ignored. Transfer is problematic since knowledge doesn’t transfer between tasks. The theory can’t account for learning through abstraction or generalization (most school learning)

Learning Theory  Social Constructivism

Social Constructivism Grew out of and in response to Cognitivism, framed around metacognition Knowledge is actively constructed Learning is… A search for meaning by the learner Contextualized An inherently social activity Dialogic and recursive The responsibility of the learner Lev Vygotsky Social Learning Zone of Proximal Development

Lev Vygotsky (1896 –1933) A Russian psychologist, Vygotsky worked in the post-revolutionary Soviet Union to rebuild psychology along Marxist lines. He worked to apply psychology to the problems confronting the new state, especially in the field of ed psych. Vygotsky’s writings were banned in the Soviet Union in 1936 and only became available in the west in the 1960’s at which point they became highly influential.

Vygotsky Continued Cognitive development depends on interactions with people and tools. Tools are real: pens, paper, computers; or symbols: language, math systems, signs

...and more Vygotsky Vygotsky developed the theory of the Zone of proximal development (ZPD) The ZPD is the distance between where a learner is at developmentally on their own and where a learner could be with the help of a more knowledgeable other. A more knowledgeable other can be an adult or a peer, helping a learner in this way is to scaffold their learning.

Social Constructivism in the Classroom Journaling Experiential activities Personal focus Collaborative & cooperative learning

Critiques of Social Constructivism Suggests that knowledge is neither given nor absolute Often seen as less rigorous than traditional approaches to instruction Does not fit well with traditional age grouping and rigid terms/semesters

Learning Theory  Multiple Intelligences

Multiple Intelligences (MI) Grew out of Constructivism, framed around metacognition (H. Gardner 1983 to present) All people are born with eight intelligences: Enables students to leverage their strengths and purposefully target and develop their weaknesses 1. Verbal-Linguistic5. Musical 2. Visual-Spatial6. Naturalist 3. Logical-Mathematical7. Interpersonal 4. Kinesthetic8. Intrapersonal

MI in the Classroom Delivery of instruction via multiple mediums Student-centered classroom Authentic Assessment Self-directed learning

Critiques of MI Lack of quantifiable evidence that MI exist Lack of evidence that use of MI as a curricular and methodological approach has any discernable impact on learning Suggestive of a departure from core curricula and standards