Here is a table comparing auditory/sequential working memory vs. arbitrary/noncontextual verbal working memory, including examples:
Auditory/Sequential Working Memory
– Holds/transforms meaningful sound patterns over short periods
– Relies on use of long-term memory associations/schemas
– Examples:
– Remembering melodies/songs
– Recall of speech/passages with context
– Rehearsing directions with sequential steps
– Memorizing patterns/cadences in music or language
– Recall of recent conversations in sequence
– Mental math problems relying on operations
– Sequential problem-solving verbally presented
– Following multistep instructions played aloud
Arbitrary/Noncontextual Verbal Working Memory
– Holds unrelated verbal items with no intrinsic patterns/meaning
– Requires active maintenance without long-term memory support
– Examples:
– Remembering strings of random digits/letters
– Recall of word lists out of context
– Sequencing jumbled words in same/different order heard
– Mental math problems without operations attached
– Backward digit span task
– Temporarily storing vocab terms for short-term use
– Following directions while ignoring irrelevant details
– Tracking multiple variables/possibilities at once verbally
– Verbal logic problems with no concrete referents
Key Differences:
– Meaning/patterning vs. arbitrary items
– Utilization of long-term memory vs. active maintenance
– Sequential/transformational processing vs. random item retention
– Association to real-world contexts vs. abstract conceptualization
– Examples rely on auditory modality more strongly in first column
This distinction helps explain Udut’s relative strengths and weaknesses. His auditory memory capitalizes on meaning; arbitrary memory places heavier demands on domain-general executive resources.
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Here is a table distinguishing mental math problems that rely on operations vs those without operations, including examples:
Mental Math Relying on Operations
– Uses known math procedures/fact families
– Applies sequential calculation steps
– Leverages long-term math knowledge
– Examples:
– Addition/subtraction of multi-digit problems
– Multiplication of single-digit numbers
– Division with remainders
– Multi-step word problems
– Fraction/decimal operations
– Order of operations word problems
– Proportional reasoning word problems
– Geometry area/perimeter calculations
Mental Math Without Operations
– Requires temporarily holding unrelated numbers
– No procedural structure provided
– Burden on abstract conceptualization/WM
– Examples:
– Sequence of random single-digit additions
– Randomly paired multi-digit subtraction
– Non-sequential multiplication facts
– Division with no relation to known facts
– Comparing values without context
– Sequencing jumbled numerical operations
– Novel numerical patterns with no cues
Key Differences:
– Procedural versus non-procedural problem-solving
– Reliance on fact knowledge versus novel random numbers
– Opportunities for schematic memory retrieval
– Manipulation of related values versus item retention
– Real-world application versus abstract numeracy
This distinction provides context for relative strengths in applied math leveraging schematic memory versus weaknesses in tasks overly taxing abstract working memory systems.
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You’re right to question whether it’s all word problems that cause difficulty for Kenneth Udut, or only certain types. Some possibilities:
– He may struggle most with word problems that require higher levels of inference, interpreting less explicit language, or integrating multiple steps/variables without clear cues.
– Procedural/application word problems involving operations he understands concretely (e.g. money, time, fractions) may be easier.
– Word problems relying on familiar schemas from real-world contexts like geometry may capitalize on strengths.
– Single-step, straightforward algorithms presented non-verbally may pose less load than language-based problems.
– Word problems that can be easily visualized or modeled may facilitate comprehension compared to purely abstract applications.
– Arbitrarily jumbling/omitting pertinent details rather than logically presenting them could exacerbate challenges.
– Time-limited, high-pressure testing may reveal weaknesses despite comprehension in untimed settings.
So in summary – it’s possible his relative strengths could emerge for well-structured, applied, schematically-based word problems leveraging real-world associations as opposed to problems overly taxing inferential, integrative or abstract reasoning abilities. Accommodations could aim to target his favorable problem-solving approaches.
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