brycewang-stanford/learning-science-guide

Learning Science Guide

A comprehensive skill for applying evidence-based learning science principles to educational research, instructional design, and teaching practice. Grounded in cognitive psychology and educational neuroscience.

Foundational Learning Theories

Cognitive Load Theory (Sweller, 1988)

Working memory has limited capacity. Effective instruction manages three types of cognitive load:

| Load Type | Definition | Design Strategy | |-----------|-----------|-----------------| | Intrinsic | Complexity inherent to the material | Sequence from simple to complex; chunk information | | Extraneous | Load from poor instructional design | Eliminate redundancy; use spatial contiguity | | Germane | Load from schema construction | Use worked examples; encourage self-explanation |

# Estimate cognitive load using element interactivity
def estimate_intrinsic_load(elements: list, interactions: list) -> str:
    """
    elements: list of knowledge components
    interactions: list of (element_i, element_j) tuples that must be
                  processed simultaneously
    """
    interactivity = len(interactions) / max(len(elements), 1)
    if interactivity < 0.3:
        return "low intrinsic load - suitable for independent study"
    elif interactivity < 0.7:
        return "moderate intrinsic load - scaffold with worked examples"
    else:
        return "high intrinsic load - use fading strategy and segmenting"

# Example: teaching statistical regression
elements = ['variable', 'coefficient', 'intercept', 'residual', 'R-squared']
interactions = [('coefficient', 'variable'), ('intercept', 'residual'),
                ('coefficient', 'R-squared'), ('residual', 'R-squared')]
print(estimate_intrinsic_load(elements, interactions))

Constructivism and Active Learning

Constructivist approaches emphasize that learners build knowledge through experience. Key active learning strategies with measured effect sizes (Freeman et al., 2014, PNAS):

• Think-Pair-Share: d = 0.41
• Problem-Based Learning (PBL): d = 0.68
• Peer Instruction (Mazur): d = 0.74
• Inquiry-Based Labs: d = 0.52

Evidence-Based Study Methods

Retrieval Practice

Testing is not just assessment -- it is a powerful learning tool (Roediger & Karpicke, 2006). Implement the testing effect:

Study Session Structure:
  1. Initial encoding (read/watch)          - 15 min
  2. Free recall (close materials, write)   - 10 min
  3. Check accuracy and fill gaps           -  5 min
  4. Spaced retrieval after 1 day           - 10 min
  5. Spaced retrieval after 7 days          - 10 min
  6. Spaced retrieval after 30 days         - 10 min

Spaced Repetition Algorithms

Implement optimal review scheduling:

def next_review_interval(repetition: int, ease_factor: float = 2.5,
                          quality: int = 4) -> float:
    """
    SM-2 inspired algorithm.
    repetition: number of successful reviews
    ease_factor: item difficulty (>= 1.3)
    quality: response quality 0-5
    """
    if quality < 3:
        return 1  # reset to 1 day
    if repetition == 0:
        return 1
    elif repetition == 1:
        return 6
    else:
        interval = 6 * (ease_factor ** (repetition - 1))
        # Adjust ease factor
        new_ef = ease_factor + (0.1 - (5 - quality) * (0.08 + (5 - quality) * 0.02))
        return round(interval, 1)

# Schedule for a moderately difficult concept
for rep in range(6):
    days = next_review_interval(rep)
    print(f"Review {rep + 1}: after {days} days")

Interleaving and Desirable Difficulties

Research shows interleaved practice (mixing problem types) outperforms blocked practice for long-term retention (Rohrer & Taylor, 2007):

• Blocked: AAABBBCCC -> short-term gains, long-term forgetting
• Interleaved: ABCBACACB -> harder during practice, better retention

Assessment Design

Bloom's Taxonomy Alignment

Map learning objectives to assessment items across cognitive levels:

remember:
  verbs: [define, list, recall, identify]
  assessment: "Multiple choice, matching"
understand:
  verbs: [explain, summarize, compare, classify]
  assessment: "Short answer, concept maps"
apply:
  verbs: [solve, demonstrate, use, implement]
  assessment: "Problem sets, simulations"
analyze:
  verbs: [differentiate, organize, attribute, deconstruct]
  assessment: "Case studies, data interpretation"
evaluate:
  verbs: [judge, critique, justify, appraise]
  assessment: "Peer review, rubric-based essays"
create:
  verbs: [design, construct, produce, formulate]
  assessment: "Research projects, portfolios"

Item Analysis

After administering assessments, compute item difficulty (p-value) and discrimination index to validate question quality. Target p-values between 0.30 and 0.70 and discrimination indices above 0.30 for optimal measurement.

References

• Sweller, J. (1988). Cognitive load during problem solving. Cognitive Science, 12(2), 257-285.
• Freeman, S., et al. (2014). Active learning increases student performance in science. PNAS, 111(23), 8410-8415.
• Roediger, H. L., & Karpicke, J. D. (2006). Test-enhanced learning. Psychological Science, 17(3), 249-255.