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Learning Theories must be selectively applied merited by content, learners, and context to yield the most efficient learning experience.  

Name of Learning TheoryDescription of Theory and How Learning is PromotedHow this Theory Can be Used in the Classroom

Knowledge exists separately outside the mind & must be imprinted on it, or  ACQUIRED. Pavlov: Achieve learning by designing stimulus to evoke a desired response. Positive  Feedback reinforces behavior. Negative feedback discourages it. Design environment to facilitate transfer. External world must be mapped onto the learner. Passive transfer of acts & routines.  ID designs stimulus to evoke response. Assess learner to determine beginning & best consequences. Chunking. 

 Students are visually taught to analyze math work for types of errors and error patterns, vs. checking for correct answers. Students are taught to identify dyscalculic errors and patterns. 
Cognitivism Learning is a mental activity, active processing. Meaning is acquired by connecting new information with existing info. Feedback guides mental connections. Use efficient  processing strategies. Memory is knowledge-base: rules, concepts, discriminations. Learner mental activities: planning, goals, organization, attention, rehearsal, coding, storage & retrieval, attitudes, feelings, thoughts. Active involvement of learner. Task analysis, sequencing & organizing, making connections with known.  Practice with feedback. Know learner previous experiences
before organizing lesson. Framing, outlining, advance organizers, concept mapping. Chunking. 

 Students are provided with dyscalculic and nonMLD math assessments and are asked to score them. Then students are asked to analyze the  scores and formulate conclusions justified by the evidence. Students are  asked to postulate  reasons for poor performance.  
Constructivism Learner CONSTRUCTS his own knowledge through a filter of experieces.  Learning / understanding / knowledge  is a function of how one creates meaning from or interprets their own experiences,  must be relevant. Piaget. Mind filters info to create its own reality. Meaning is created. Flexible use of pre-existing knowledge to real world applications. Lasting learning through activity / practice, concept knowledge, cultural context. Authentic tasks, meaningful contexts. Higher-level thinking, applications.  Relate content to personal experience. Create tools to use effectively. Lessons in meaningful context, 
learner controls manipulation, modality variety, assessment of applied problem solving. Group learning. Apprenticeships.
Goals stated in terms of growth made toward working independently and cooperatively. 

Teacher facilitator, guide, collaborator as students construct own knowledge through exploration. 
 Tech: problem solving, multimedia production, web

Group projects, exploration, product development (portfolio via rubric).  

Different content and criteria by case. 

Students are asked to study MLD error patterns to compare to solid math performance. Students must create a multimedia presentation illustrating each, offering strategies for bridging the performance gap between the 2 sets. 

Students take turns sharing an experience with a real MLD student and tell of what happened. Group acts as advisors armed with new knowledge & offers advice on what to do. 
Directed Instruction 

espoused by Objectivists & Constructivists.

Results in inert knowledge that can't be used to solve probs.
DM is grounded in Behaviorist Theory and is the information-processing branch of Cognitivist Theory. Goals of Mastery learning, & behavioral competence benchmarks.Teacher expert directs  concept & skill development with structured experiences.  Knowledge hierarchies, sequenced instruction, same content and  standards for all. Written tests & product development to set objectives, all students measured on same criteria & assessments. 

Programmed / systematically designed instruction for self-study. Courseware. Games for drill, practice, simulations.
Tech: drills, practice, tutorials.
Lecture, demonstration, practice, discussion, seatwork, testing. 

Teacher defines MLD, normal, and ideal math performers & provides examples. Students  given examples and asked to analyze and assign to categories. Written  exam calls for analysis and ID of samples with rationale. 

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