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Mathematics Applications & Interpretation (AI) IA Exemplar: Teacher… | RevisionDojo
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IB Mathematics Applications & Interpretation (AI) SL Internal Assessment Example
Is there a difference in free time available between teachers
and students after completing all the school-related duties, and if so, to what
extent?SL
5
Official IB Result
13/20
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13/20
0
10
20
5.1·Weakness
Page 12• Click to view
The student’s variance-to-standard-deviation step contains a calculation/notation slip, which affects mathematical correctness. The square root should be taken of the variance value, not of the variance squared, so the written expression must be corrected.
5.2·Question
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How does assigning the open-ended class >6 hours a midpoint of 7 affect the mean and variance? Considering this would improve the mathematical justification for treating grouped data this way.
5.3·Strength
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The grouped frequency table is an effective use of course-level mathematics because it turns categorical survey responses into a form that can be analysed quantitatively. This makes the later mean and variance calculations meaningful.
5.4·Strength
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The teacher grouped-data table is carefully structured and supports direct calculation of summary statistics. The use of f⋅x and f⋅x2 is appropriate and relevant to the research question.
5.5·Weakness
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The first t-test substitution uses estimated standard deviations, but the way they are inserted into the formula is not fully consistent with the formula shown above. The student should align the written general formula, the substitution, and the calculator result so the method is mathematically sound.
5.6·Suggestion
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It would strengthen the statistical method to state the assumptions behind the two-sample t-test before using it. A short check of independence, approximate normality, and the effect of grouped data would show stronger methodological understanding.
5.7·Strength
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The grouped scale for manageability is a sensible way to reduce many individual ratings into a comparable distribution. This helps the student move from raw survey answers to a mathematically manageable comparison.
5.8·Suggestion
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The inference would be more convincing if the student added a confidence interval or effect size alongside the hypothesis test. That would show not only whether a difference exists, but also how large it may be.
5.9·Question
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If the manageability ratings are ordinal rather than interval, how confidently can a t-test compare their means? Reflecting on this would deepen the mathematical validity of the method.
5.10·Weakness
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The p-value is reported, but the incorrect test setup above means the validity of that p-value is weakened. The student should correct the underlying computation before relying on the inferential conclusion.
5.11·Weakness
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The denominator error in the second t-test is a major problem because it changes the test statistic. If the sample size is 50, then the variance term must be divided consistently by that sample size; otherwise the inferential result is not reliable.
Criteria A: Presentation
3/4
0
2
4
Criteria Strands
A.1Coherence and logical development
Good
A.2Organization and structure
Good
A.3Conciseness and relevance
Moderate
Criteria Feedback
Your exploration has a clear overall structure that moves logically from the research question to data collection, analysis, and conclusion.
You keep the topic relevant throughout and generally avoid major digressions.
Your tables, graphs, and written explanations are placed in a way that helps the reader follow the investigation.
Some sections repeat setup material instead of adding new mathematical insight.
A few transitions between parts of the analysis could be smoother and more explicitly linked.
The work is not always as concise as it could be, which slightly weakens the flow.
1.1·Strength
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A clear title immediately establishes the investigation’s focus on free time and workload, and the research question is well aligned with the later student/teacher comparison. This helps the exploration stay coherent from the start.
1.2·Weakness
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The table of contents is helpful, but the study could be more concise by reducing repeated setup material later in the exploration. Streamlining repeated explanations of the research focus would improve relevance and keep attention on the mathematics.
1.3·Strength
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The introduction sets up the purpose of the investigation and signals the progression from collecting data to comparing groups. That roadmap supports logical development and makes the analysis easier to follow.
1.4·Suggestion
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The action plan gives the exploration a clear structure. The student could strengthen flow further by briefly linking each planned step to the research question, so the reader sees how each stage contributes to the comparison.
1.5·Strength
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The student usefully interprets the grade distribution before moving on to later analysis. Linking the respondent profile to possible bias shows good awareness of how structure affects the investigation.
1.6·Weakness
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This explanation continues the analysis, but it would be stronger if it connected more tightly to the next statistical step. The reader would benefit from a clearer bridge explaining how these observations motivate the grouped-data summaries and t-test.
1.7·Weakness
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The general explanation of what a t-test is is understandable, but it adds length without advancing the argument much. This is a place to be more concise: define only the details needed for the specific two-sample test being used.
1.8·Suggestion
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The second comparison section is well signposted. The student could make the transition even smoother by explicitly reminding the reader why manageability is being analyzed after free time and how it answers the research question.
Criteria B: Mathematical Communication
3/4
0
2
4
Criteria Strands
B.1Mathematical language and notation
Good
B.2Multiple representations
Good
B.3Clarity and consistency
Good
Criteria Feedback
You use appropriate statistical notation such as means, variances, standard deviations, hypotheses, test statistics, and p-values.
You include multiple representations, including frequency tables, graphs, grouped-data tables, and worked formulas.
Your communication is usually clear enough that the reader can follow the calculations and interpretation.
Some notation is inconsistent, especially in the t-test section and the way sample size is shown.
A few formulas are written imprecisely, even when the numerical method is close to correct.
The presentation of some calculations could be more consistent so the mathematics is easier to audit.
2.1·Strength
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The variance formula is communicated appropriately and the substitution is shown step by step. Showing the algebra helps demonstrate mathematical understanding rather than relying only on calculator output.
2.2·Strength
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The grouped-data mean formula is stated clearly and then applied correctly to the students’ table. This supports transparency because the reader can follow exactly how the summary statistic is obtained.
2.3·Weakness
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The standard deviation line contains a notation error: 3.732 is not the correct form here. It should be written as 3.73. The final value is sensible, but the written mathematics must match the computation.
2.4·Strength
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The teachers’ mean is computed and labelled clearly, which keeps the calculation sequence easy to track. This is effective communication because each step is visible and connected to the grouped table.
2.5·Weakness
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The substitution is more coherent than the written formula, but the notation still needs refinement. The student should make the standard error structure explicit so that the reader can see where each sample variance enters the calculation.
2.6·Weakness
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The notation in the definitions is slightly inconsistent: S1 and S2 are described as standard deviations, but the test setup later uses variance-based quantities. The student should keep the symbols aligned with the formula to avoid confusion.
2.7·Weakness
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The displayed t-test formula is not written accurately: the variance terms should combine into one standard error expression rather than being separated as two fractions. The student should rewrite the formula so the notation matches the actual two-sample test being used.
2.8·Strength
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The conclusion uses the p-value in relation to the significance level and states the decision clearly. That direct link between result and inference supports clarity and consistency in the argument.
2.9·Weakness
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The standard deviation calculation is correct numerically, but the presentation would be more precise if the student kept the variance and standard deviation notation consistent throughout the exploration. That would make the mathematics easier to audit.
2.10·Weakness
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The second t-test calculation contains a serious consistency problem: 53.69 appears where the sample size should be reflected in the denominator. This weakens the communication of the result because the test statistic is built from an internally inconsistent expression.
Criteria C: Personal Engagement
2/3
0
2
3
Criteria Strands
C.1Independent thinking
Good
C.2Personal approach
Good
C.3Creativity and initiative
Good
Criteria Feedback
Your topic is clearly personal and meaningful, and it connects to a real-world question you care about.
You show initiative by designing parallel surveys for two different groups and by choosing variables that fit the investigation.
You make thoughtful choices in how to organize and prepare the data for analysis.
The mathematical approach is fairly standard and does not extend very far beyond conventional methods.
There is limited evidence of original modelling or deeper analytical extension.
Your personal interest is clear, but it does not always lead to more ambitious mathematical choices.
3.1·Strength
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The topic is clearly personally meaningful: it is framed around balancing academic duties, free time, and workload. That personal motivation gives the investigation a genuine purpose rather than treating the data as abstract.
3.2·Strength
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The teacher survey is not just a copy of the student survey; it is adapted to the group’s context. That parallel design shows initiative because the student considered how the same research idea needed different questions for different participants.
3.3·Strength
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The student shows independent thinking by justifying each survey question in relation to the investigation. This indicates deliberate design choices rather than simply collecting data without purpose.
3.4·Strength
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Using Google Docs and structuring the survey to make analysis easier shows practical initiative. The student clearly made decisions about data collection with the later mathematics in mind.
3.5·Strength
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The student independently notices that the respondent distribution may affect the results. That kind of self-awareness is a sign of genuine engagement with the investigation rather than simply reporting outcomes.
3.6·Strength
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The interpretation of the manageability ratings shows a personal stake in the question of workload and stress. The student is not only comparing numbers but also relating them to lived experience.
3.7·Strength
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Grouping the rating data into midpoints is a purposeful analytical choice. It shows initiative because the student created a workable representation rather than relying only on the raw frequency list.
3.8·Suggestion
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The reflection is relevant, but it could more strongly show the student’s own thinking by discussing what was surprising or difficult during the data collection and calculation stages. Personal insight into choices and challenges would deepen the engagement.
Criteria D: Reflection
2/3
0
2
3
Criteria Strands
D.1Depth of reflection
Good
D.2Critical analysis
Poor
D.3Connection to understanding
Good
Criteria Feedback
You do reflect on the limitations of your data and acknowledge that the response patterns may affect the conclusions.
You connect some of your findings to practical real-world implications, which shows that you are thinking beyond the numbers.
You include comments that show awareness of how your survey design influenced the investigation.
Your reflection is not sustained throughout the work and sometimes stays at a general level.
The statistical limitations are not examined deeply enough, especially regarding assumptions and grouped-data choices.
Some conclusions would be stronger if you discussed what the data cannot show as well as what it does show.
4.1·Strength
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The student begins to reflect critically by recognising that the grade distribution may have influenced the results. This is a useful starting point because it shows awareness that data collection affects interpretation.
4.2·Weakness
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The student reports a p-value and decision rule, but does not reflect on whether the test assumptions are reasonable. A stronger exploration would question normality, independence, and whether grouped data are suitable for a t-test in this context.
4.3·Weakness
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The conclusion treats failure to reject H0 as if it proves no difference. The student should reflect more carefully on statistical meaning: a non-significant result does not confirm equality, only that the evidence is insufficient to reject the null hypothesis.
4.4·Suggestion
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The suggestions for improving time management are relevant, but the reflection could go further by asking what the data do not show. For example, did the survey capture enough detail to explain why free time differs, or only that it does?
4.5·Weakness
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The student makes an interpretive claim about workload management being similar, but the reflection would be stronger if it discussed practical significance as well as statistical significance. That would help connect the numerical result to real-world meaning.
4.6·Weakness
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This conclusion summarises the findings, but it does not critically evaluate the effect of grouped midpoints, especially the open-ended classes such as >6 hours. Reflecting on how that modelling choice affects precision would deepen the analysis.
4.7·Strength
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The limitations section is a valuable addition because it shows the student considering how the question structure constrained the analysis. That kind of reflection helps move the work beyond simple reporting.
4.8·Question
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What effect might the limited response options and grouped intervals have on the precision of the mean and standard deviation values? Considering this would strengthen the link between limitations and mathematical understanding.
Criteria E: Use of Mathematics
3/6
0
3
6
Criteria Strands
E.1Relevance and level
Good
E.2Accuracy and correctness
Poor
E.3Knowledge and understanding
Moderate
Criteria Feedback
You use relevant mathematics at an appropriate course level, including grouped-data statistics and two-sample t-tests.
You demonstrate procedural understanding by setting up hypotheses and using statistical output to make a decision.
Your descriptive calculations are generally effective and connected to the research question.
There are important accuracy issues in the inferential section, including inconsistent handling of sample size.
Some formulas are written in a way that does not fully match the method being used.
The work shows limited discussion of assumptions, so the mathematical method is not always justified as fully as it could be.
