1. REASONING AND PROBLEM SOLVING
1.1. AGE TRENDS IN REASONG AND PROBLEM SOLVING
1.1.1. INFANCY AND TODDLERHOOD (BITH TO 2 YEARS) (p. 158)
1.1.2. EARLY CHILDHOOD (3 TO 5 YEARS) (p. 158)
1.1.3. MIDDLE CHILDHOOD (6 TO 12 YEARS) (p. 159)
1.1.4. ADOLESCENCE (13 TO 19 YEARS) (p. 160)
1.2. INDIVIDUAL DIVERSITY IN REASONING AND PROBLEM SOLVING
1.2.1. What do INDIVIDUAL DIFFERENCES in REASONING PREDICTS?
1.2.2. What PREDICTS INDIVIDUAL DIFFERENCES in REASONING?
1.2.2.1. FEEDBACK
1.2.2.2. MODELLING
1.2.2.3. PRIOR KNOWLEDGE
1.3. LEARNING AND TEACHING IMPLICATIONS OF REASONING AND PROBLEM SOLVING
1.3.1. REQUIRE EXPLANATIONS (p. 162)
1.3.2. TEACH EFFECTIVE STRATEGIES (p. 162)
1.3.2.1. 1. USE FEEDBACK AND MODELLING 2. ASK STUDENTS TO REFLECT ON THE PROBLEM AND ASK THEMSELVES 'What strategies could be use to solve this problem' 3. ASK STUDENTS TO SHARE AND COMPARE STRATEGIES
1.3.3. FOSTER ARGUMENT (p. 163)
1.3.4. USE INQUIRY-BASED LESSONS (p. 163)
1.3.5. DIRECTLY TRAIN REASONING (p. 163)
2. PUTTING THE THEORIES TO WORK: THE CASE OF MATHEMATICS
2.1. AGE TRENDS IN MATHEMATICS
2.1.1. INFORMAL MATHEMATICS (p. 165)
2.1.1.1. What can you do to help? 1. Use mathematical talk with toddlers and preschoolers 2. Play number-oriented board games 3. Directly teach mathematics
2.1.2. SCHOOL-AGE MATHEMATICS (p. 166)
2.2. IMPLICATIONS FOR TRACHERS FROM. DIFFERENT THEORIES
2.2.1. BEHAVIOURISM AND MATHEMATICS (p. 167)
2.2.1.1. From this perspective, learning (or conditioning) begins with simple stimulus-response connections and then progresses to the complex level of abstract reasoning. Students cannot solve advanced problems if they do not have the prerequisite low-level skills mastered.
2.2.1.2. * Behavioural objectives are used to structure lessons and are organised hierarchically, with basic skills mastered before attempting advanced skills. * Direct instruction with drill and practice to create strong basic connections ( -> can be play-like, does not have to be rigid and boring) * According to behaviourists perspective, some aspects of learning should not be substantially more difficult than others, yet they are * Existing knowledge structure can interfere with new learning
2.2.2. PIAGET'S THEORY OF COGNITIVE DEVELOPMENT AND MATHEMATICS (p. 168)
2.2.2.1. Children reinvent number concepts on their own, based on experience. Constructivism is a popular strategy adopted by mathematical teacher (it is embedded in the Australian Curriculum.. * Hands-on tools to illuminate concepts -> direct manipulation of materials relevant to the mathematics whenever possible. * Learners assimilate new experiences with what they already know, creating strategies that teachers may not have intended. * From a constructivist perspective errors are intelligent and a natural part of knowledge construction. * Research suggests that accurate pictures, like diagrams or graphs, may promote mathematics more than manipulating of self-constructions. * Students tend to perform better following direct instruction *Asking children to explain their strategies is important. Explainers learned more regardless of instructional approach * Direct instruction does not preclude invention, but helps prevent invention if incorrect strategies.
2.2.3. VYGOTSKY'S SOCIOCULTURAL THEORY AND MATHEMATICS (p, 169)
2.2.3.1. * The full development of mathematical ability requires social interaction- opportunities to use and observe strategies, and receive scaffolding from adults. * In school children should talk about how they solved. a problem because they learn by reasoning about a problem and explaining to others why is right * Cooperative learning
2.2.4. INFORMATION PROCESSING MODEL AND MATHEMATICS (PP. 169-171)
2.2.4.1. This model fits either perspectives. Information processing researches demonstrated that children learn by direct instruction, skill-and-drill practice or rehearsal, modelling from more skilled others and constructing their own knowledge through insight and metacognition as they receive feedback about the success of their strategies
3. INFORMATION PROCESSING
3.1. COMPONENTS OF THE INFORMATION PROCESSING MODEL (p. 137)
3.1.1. SENSORY REGISTER
3.1.2. LONG-TERM MEMORY
3.1.3. WORKING MEMORY
3.1.3.1. Adult working memory capacity is about one to four chunks of information and can be retained only for a few seconds. Chunking helps you remember other types of information as well.
3.1.3.2. MEMORY SPAN
3.1.4. EXEXCUTIVES FUNCTIONS
3.1.4.1. INIHBITORY CONTROL (p. 139)
3.1.4.2. ATTENTION SHIFTING (p. 139)
3.1.4.3. METACOGNITION (p. 139)
3.1.4.3.1. Metacomprehension
3.1.4.3.2. Metamemory
3.2. AGE TREND IN INFORMATION PROCESSING
3.2.1. INFANCY AND TODDLERHOOD (BIRTH TO 2 YEARS) (p. 140)
3.2.1.1. Processing speed is relatively slow because myelination, knowledge, and language are limited.
3.2.1.2. Language affects processing speed because it organises the storage and retrieval of inforamation. Processing speed, in turn, limits working memory. As each of these factors improve, working memory improves
3.2.2. EARLY CHILDHOOD (3 TO 5 YEARS) (p. 140)
3.2.2.1. Processing speed continues to improve. Executive functions improve dramatically
3.2.3. MIDDLE CHILDHOOD (6 TO 12 YEARS) (p. 141)
3.2.3.1. Working memory improve substantially, party because; ~Attention shifting improves steadily (= better control of attention) ~Processing speed continues to improve (although the rate of change eventually slow down)
3.2.4. ADOLESCENCE (13 TO 19 YEARS) (p. 141-142)
3.2.4.1. Processing speed increases into adolescence, levels off, and begins to get slower after 18. Performance on complex working memory tasks (strategy task, including new info, and monitoring process) also peaks. Executive functions improve too (adolescents are better art controlling their thinking)
3.3. INDIVIDUAL DIVERSITY IN INFORMATION PROCESSING (p. 143)
3.3.1. Individual differences are apparent as early as 9 months but larger in adolescence than early childhood
3.3.2. Information processing abilities are also linked to emotional and social skills at school
3.3.3. Students must ignore distractions when given a task that require concentration, and they must suppress irrelevant information. This is know as SELECTIVE ATTENTION
3.3.4. Inhability to control attention is a defining feature of ATTENTION DEFICIT HYOERACTIVITY DISORDER (ADHD). However, mind wandering is common, and the larger your working memory capacity, the more you mind wanders during undemanding tasks.
3.3.5. What might predict differences in information processing?
3.3.5.1. GENES
3.3.5.2. HOME ENVIRONMENT
3.3.5.2.1. Parents who are sensitive and provide activities that stimulate their children's cognitive and language development tend to have children who have better memory and control over their attention
3.4. LEARNING AND TEACHING IMPLICATIONS OF INFORMATION PROCESSING
3.4.1. REDUCE WORKING MEMORY AND EXECUTIVE LOAD (p. 146)
3.4.1.1. 1. Limit your talking 2. Reduce distractions 3. Increase your learners' expertise 4. Provide external storage 5. Carve problems into smaller subtasks that can be performed sequentially
3.4.2. FOCUS ATTENTION (p. 147)
3.4.2.1. Make learning goals explicit and remind learners of the goal help them control their attention
3.4.3. STRENGHTEN EXECUTIVE FUNCTIONS (p. 147)
3.4.3.1. How to strengthen your students' executive functions? 1. Promote healthy habits (sleep, good nutrition, exercise). Executive functions requires large amount of glucose which are replenished during sleep or after eating 2. Help learners practice through mundane, daily activities (sitting up straight or persisting in activities) 3. Help children to improve their verbal abilities, as these are linked to executive functions
4. MEMORY
4.1. Remember? Maybe, maybe not
4.1.1. MEMORY ERRORS (p. 148)
4.1.1.1. VERBATIM traces (detailed accurate memories) vs FUZZY traces (a distilled gist of an experience rather than a memory)
4.1.1.2. FORGETTING INFORMATION
4.1.1.2.1. 3 REASONS learners FORGET things: 1. Decay (memory decays over time) 2. Retrieval failure 3. Interference
4.1.1.3. FALSE MEMORIES
4.1.1.3.1. Adults can be more prone to fate memories compared to children. Imagining doing something or watching someone else do it, can create false memories that you actually did it
4.1.1.3.2. One type of false memory is the SOURCE MONITORING error, or a false memory of the source of their information
4.1.2. CONTEXT and MEMORY (p. 149)
4.1.2.1. Physical context can influence memory. Eg. NOISE (this can cause divided attention because learner is attending Tei things at one)
4.1.2.2. Encoding specificity (when info is encoded in memory, the context in which the info was stored is stored along = children more likely to recall specific subject in the same class they learnt it)
4.1.3. MEMORY STRATEGIES (p. 149-50)
4.1.3.1. ENCODING strategies
4.1.3.1.1. 1. Rehearsal
4.1.3.1.2. 2. Organisation
4.1.3.1.3. 3. Elaboration
4.2. AGE TRENDS IN MEMORY
4.2.1. INFANCY AND TODDLERHOOD (PRENATAL TO 2 YEARS) (p. 150)
4.2.1.1. CHILDHOOD AMNESIA
4.2.2. EARLY CHILDHOOD (3 TO 5 YEARS) (p. 151)
4.2.3. MIDDLE CHILDHOOD (6 TO 12 YEARS) (p. 151)
4.2.4. ADOLESCENCE (13 TO 19 YEARS) (p. 152)
4.3. INDIVIDUAL DIVERSITY IN MEMORY (p. 152-53)
4.3.1. What do INDIVIDUAL DIFFERENCES in MEMORY PRECIDCTS?
4.3.2. What PREDICTS INDIVIDUAL DIFFERENCES in MEMORY?
4.3.2.1. PRIOR KNOWLEDGE
4.3.2.1.1. It has a powerful influence on memory because knowledge is organised in long-term memory as webs of networks or related information. These networks of knowledge are called SCHEMAS. Much education is an attempt to build accurate schemas for specific topics. One type of schema is a script
4.3.2.2. CONVERSATION
4.4. LEARNING AND TEACHING IMPLICATIONS OF MEMORY
4.4.1. CONNECT KNOWLEDGE (p. 153)
4.4.1.1. KWL approach (Know, What, Learn) KWHL (adding How)
4.4.2. FACILITATE MEMORY STRATEGIES (p. 154)
4.4.2.1. MNEMONICS can also be taught to help students memorise
4.4.2.1.1. ACRONYM
4.4.2.1.2. KEYWORD METHOD
4.4.3. INCREASE EXPOSURE TO MATERIAL TO NE LEARNED (p. 155)
4.4.4. PROVIDE SPACED PRACTICE (p. 155)
4.4.5. TEST STUDENTS (p. 156)
4.4.5.1. 1. Teach your students about the benefits of testing 2. Test frequency 3. Use recall rather than recognition tests 4. Use cumulative tests (integrate new material to old) 5. Provide feedback soon after