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IB Mathematics Analysis and Approaches (AA) SL Internal Assessment Exemplar: The relation between music and productivity
Finding the correlation between hours spent listening to
music and hours spent being productive per day
The relation between music and productivity
Finding the correlation between hours spent listening to
music and hours spent being productive per day
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3
Official IB Result
8/20
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General feedback
8/20
0
10
20
6.1·Suggestion
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The introductory paragraph lacks context on the target population and scope. Clarify the sample’s demographics and any inclusion criteria to strengthen the rationale.
Criteria A: Presentation
2/4
0
2
4
Criteria Strands
Moderate
Coherence and logical development
Moderate
Organization and structure
Poor
Conciseness and relevance
Criteria Feedback
Clear and concise title that effectively conveys the focus of the exploration.
Use of headings, sub-headings and a table of contents indicates an attempt at logical structure.
Ideas generally follow a cause-and-effect order, allowing the reader to follow the argument.
Long blocks of raw tables interrupt the flow and weaken coherence.
Table of contents is overly nested with inconsistent page numbering.
Excessive inclusion of raw data and step-by-step arithmetic reduces conciseness.
1.1·Strength
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The title is clear and concise, effectively conveying the focus of the exploration and engaging the reader from the start.
1.2·Weakness
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The table of contents is overly nested and lacks consistent page numbering. Simplify headings, ensure accurate page references, and remove duplicated elements for clarity.
1.3·Weakness
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Including the full raw data table interrupts the flow and is excessive. Summarize key statistics and move raw data to an appendix to improve conciseness.
1.4·Suggestion
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Embedding the equation label within the figure caption reduces clarity. Present the mathematical expression separately, with a clear reference label.
1.5·Weakness
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The sum of squares table is exhaustive but could be condensed by calculating totals directly. A summary row with Σ(x−x̄)² and Σ(y−ȳ)² would suffice.
1.6·Weakness
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The conclusion contradicts earlier certainty by expressing doubt about the correlation. Ensure logical coherence by aligning conclusion with interpretation consistently.
1.7·Weakness
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The extensions and learning reflections table is dense and could be broken into distinct sections with clear subheadings for readability.
Criteria B: Mathematical Communication
1/4
0
2
4
Criteria Strands
Moderate
Mathematical language and notation
Moderate
Multiple representations
Poor
Logical structure and clarity
Criteria Feedback
Use of standard symbols (Σ, r, x̄, ȳ) and inclusion of clear figure captions that credit the author.
Computed mean values are highlighted in display math, aiding communication of key results.
Notation is inconsistent (variables mis-typed, decimal commas instead of points).
Tables and graphs lack clear labels and formatting, reducing interpretability.
Logical structure is weak: duplicate mean calculations and compressed derivations hinder clarity.
2.1·Strength
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The figure caption is succinct and credits the author appropriately, supporting clear mathematical communication.
2.2·Weakness
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The summation of deviations is presented in a long inline string. Break the calculation into named steps or use a table to improve readability.
2.3·Weakness
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Tables of deviations are numbered and labeled inconsistently, with missing column headers. Standardize formatting and include titles for each table.
2.4·Strength
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The computed mean value is highlighted in display math, which clearly communicates the result; however, confirm that the numerator is correctly simplified.
2.5·Weakness
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The long inline product series for Σ(x−x̄)(y−ȳ) is difficult to parse. Use a stepped layout or bullet list to separate individual terms.
2.6·Weakness
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Decimal commas are used inconsistently, which can confuse readers. Replace commas with decimal points throughout to adhere to standard mathematical notation.
2.7·Weakness
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The correlation strength categories omit comparison symbols (e.g., ≤0.39). Include inequality symbols to define ranges precisely.
2.8·Weakness
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The significance graph lacks axis labels and units, reducing interpretability. Add clear axis titles and scale annotations to improve communication.
2.9·Strength
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The discussion of anomalies in the scatter plot highlights insight into data behavior, showing thoughtful engagement with outliers.
2.10·Weakness
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The references are mixed in style and punctuation. Adopt a consistent citation format (e.g., MLA or APA) throughout for professional presentation.
Criteria C: Personal Engagement
1/3
0
2
3
Criteria Strands
Poor
Independent thinking
Poor
Personal approach
Poor
Creativity and initiative
Criteria Feedback
The personal rationale clearly connects the student’s own focus habits to the research question.
Reflection on applying two statistical methods shows engagement with real-world application.
Mathematical methods chosen are entirely conventional with no exploration of alternatives.
The overall structure follows a generic template, limiting evidence of true independent thinking.
Creativity and initiative are minimal, confined to standard statistical procedures.
3.1·Strength
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The student’s personal rationale vividly connects their own focus habits to the research question, demonstrating clear evidence of a personal approach.
3.2·Strength
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The author’s reflection on applying two statistical methods demonstrates significant personal engagement and real-world application of course concepts.
Criteria D: Reflection
1/3
0
2
3
Criteria Strands
Poor
Depth of reflection
Poor
Critical analysis
Poor
Evaluation of outcomes
Criteria Feedback
The comparative statement linking Pearson’s and Spearman’s coefficients shows reflective insight.
Reflection on the mathematical process is minimal and primarily descriptive.
Analysis of results is basic, restating thresholds without deeper critique.
Evaluation of outcomes offers only a brief list of limitations and a single extension.
4.1·Suggestion
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The transition from rationale to hypothesis is abrupt. Reflect on how the personal context informed hypothesis formulation to deepen critical analysis.
4.2·Suggestion
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Interpretation correctly recognizes a weak correlation, but discussion of practical implications or limitations at this stage would deepen reflection.
4.3·Strength
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The comparative statement linking both coefficients is well made, demonstrating substantive reflection on agreement between methods.
4.4·Suggestion
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The evaluation table’s second bullet trails off without completion. Expand on how differing definitions of productivity impacted data accuracy.
Criteria E: Use of Mathematics
3/6
0
3
6
Criteria Strands
Moderate
Relevance of mathematics
Moderate
Level appropriateness
Poor
Understanding and accuracy
Criteria Feedback
Appropriate selection and application of Pearson’s r and Spearman’s ρ, both within the SL syllabus.
Mathematics used is fully commensurate with course level and applied correctly in principle.
Final r calculation is presented in clear block equations, demonstrating correct technique.
Arithmetic errors in the summation of squared deviations and duplicate mean computations indicate partial understanding.
No higher-level inference or advanced statistical methods beyond core tools.
Some formula applications (e.g. Spearman’s Σd²) appear to misuse values, reducing accuracy.
5.1·Strength
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The formula for Pearson’s r is correctly stated, showing appropriate choice of relevant mathematics.
5.2·Strength
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The final r calculation is clearly presented in block equations, demonstrating accurate use of mathematics at SL level.
5.3·Weakness
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The Spearman p-value calculation appears to misuse Σd². Verify the total before applying in the formula to ensure accuracy.
Mathematics Analysis and Approaches (AA) IA Exemplar: Music and… | RevisionDojo
