Cognitive load issues in teaching and learning mathematics

UNSW Cognitive load issues in teaching and learning mathematics Slava Kalyuga

Cognitive load issues in teaching and learning mathematics Slava Kalyuga

Outline u Review of CLT principles o Reducing cognitive load in mathematics instruction Learner prior knowledge and instructional guidance o Responding to alternative approaches 口 Implications

❑ Review of CLT principles ❑ Reducing cognitive load in mathematics instruction ❑ Learner prior knowledge and instructional guidance ❑ Responding to alternative approaches ❑ Implications Outline

Working Memory Constructing mental representations of a situation or task Long-Term Memory Knowledge base Sensory Memory: Incoming information

Constructing mental representations of a situation or task Long-Term Memory Knowledge base Working Memory Sensory Memory: Incoming information  

Working memory 385674+938475=? How many windows are in your house?

385674 + 938475 = ? How many windows are in your house? Working memory

Working memory CIABBCABCJVCVCR CIA BBC ABC JVC VCR

CIABBCABCJVCVCR CIA BBC ABC JVC VCR Working memory

WM and ltm Role of knowledge in cognition a Why chess grandmasters always beat weekend players?(De Groot, 1946/1965, Chase simon, 1973) a Knowledge of large numbers of different game configurations held in Ltm dramatically altered the characteristics of WM Similar mechanisms for all high-level cognitive skills(e. g reading) LTM: not a passive store it is actively used in most of cognitive processes (learning, problem solving thinking) O WM is very limited when dealing with novel information, but has no known limits when dea been organized and stored in 出R with information that has as schemas

❑ Why chess grandmasters always beat weekend players? (De Groot, 1946/1965, Chase & Simon, 1973) ❑ Knowledge of large numbers of different game configurations held in LTM dramatically altered the characteristics of WM. Similar mechanisms for all high-level cognitive skills (e.g., reading) ❑ LTM: not a passive store, it is actively used in most of cognitive processes (learning, problem solving, thinking) ❑ WM is very limited when dealing with novel information, but has no known limits when dealing with information that has been organized and stored in LTM as schemas WM and LTM: Role of knowledge in cognition

Why learning could be difficult? O High element interactivity = high intrinsic/relevant cognitive load b is larger than c, a is larger than b. Which is the largest? o Instructional design = high extraneous/ wasteful cognitive load unnecessary search processes redundant information unnecessary inferences when information is not provided explicitly

Why learning could be difficult? ❑ High element interactivity => high intrinsic/relevant cognitive load ▪ b is larger than c, a is larger than b. Which is the largest? ❑ Instructional design => high extraneous/ wasteful cognitive load ▪ unnecessary search processes ▪ redundant information ▪ unnecessary inferences when information is not provided explicitly

Managing intrinsic load O Appropriately segmenting and sequencing tasks from simple to complex a Simplifying tasks by omitting some of the interacting elements initially Getting familiar with separated elements (e. g variables) first pre-training Rote learning O initially presenting complex material as isolated elements allows to process them serially rather than simultaneously(isolated interactive elements effect pollock et al, 2002

Managing intrinsic load ❑ Appropriately segmenting and sequencing tasks from simple to complex ❑ Simplifying tasks by omitting some of the interacting elements initially ▪ Getting familiar with separated elements (e.g., variables) first – pre-training ▪ Rote learning ❑ Initially presenting complex material as isolated elements allows to process them serially, rather than simultaneously (isolated￾interactive elements effect - Pollock et al., 2002)

Imagination effect Cooper, Tindall-Ford, Chandler, and sweller (2001) Instruction on how to use a spreadsheet application Imagining procedures and concepts(mental practice) simple study of procedures

Cooper, Tindall-Ford, Chandler, and Sweller (2001): Instruction on how to use a spreadsheet application Imagining procedures and concepts (mental practice) vs simple study of procedures Imagination effect

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