IB Mathematics Applications & Interpretation (AI) SL Internal Assessment Example

The introduction still leaves an unresolved precision issue: the investigation refers to examining patterns in 19 pieces, but the later dataset contains 15. This inconsistency weakens the logical development because the reader cannot tell what sample the conclusions are based on.

The correlation formula is still incomplete because $r=\sqrt{R^2}$ loses the sign of the relationship. The student should write $r=\pm \sqrt{R^2}$ and then match the sign to the slope, otherwise a negative association could be reported as positive.

The student uses standard regression notation appropriately here, including $Y={\beta }_0+{\beta }_{1}X+ϵ$. Using formal symbols helps establish a mathematical framework for the investigation and makes the later slope/intercept discussions easier to follow.

The analysis mentions frequency tables and other variables, but some of these do not later influence the mathematics in a meaningful way. The student should either use those variables in the regression work or omit them so the personal investigation feels more deliberate and less scattered.

The student’s own piano-learning experience clearly drives the data collection, which gives the exploration a genuine personal basis. This makes the investigation more than a generic statistics exercise because the data and question come from the student’s real practice context.

What would change in the investigation if the student treated learning quality, not just learning time, as part of the outcome? Considering this could lead to a more personally meaningful model and might explain why some seemingly “complex” pieces are still learned quickly.

The personal design would be stronger if the student briefly justified why these particular musical variables were chosen over others. Explaining that choice would show more independent decision-making and help the reader see how the student shaped the investigation.

The investigation would show more independent thinking if it tried to model learning time directly rather than treating several musical features separately in parallel. A more original design would be to justify one combined model or explain why separate simple regressions were the best choice.

The closing personal comment about wanting to improve performance shows initiative and a clear real-world motivation for the study. This helps the investigation feel purposeful because the mathematical results are linked back to the student’s own musical goals.

The student correctly uses the weak fit to qualify the conclusion instead of claiming the predictor is strongly useful. This shows growing reflective judgment because the interpretation is not oversold beyond what the statistics support.

The reflection shows genuine awareness of limitations by identifying the narrow sample, missing variables, and limited explanatory power. This is valuable because it moves beyond simply repeating the results and starts to evaluate how trustworthy the model really is.

The reflection is still fairly general here: it praises regression and correlation without explaining what the results actually imply for this dataset. The student should refer directly to the weak relationships found for pedal marks, duration, and accidentals to show more critical synthesis.

When proposing future work, the student should rank the next steps by importance and explain why each would improve the model. For example, increasing sample size, adding practice difficulty ratings, or using multiple regression would each address a different weakness in the current design.

The impact section still contains a contradiction by claiming duration showed a negative correlation, even though earlier results give a positive $r$ and positive slope. The student should revise this so the final implications are consistent with the calculated statistics.

The student has improved the investigative focus by naming the variables to be tested and linking them to learning time. This makes the modelling purpose much clearer than a purely descriptive project and gives the reader a concrete sense of what the regression is meant to examine.

The dependent variable is defined as learning time “in hours,” but the later table and regression interpretations use minutes. The student should keep one unit system throughout, or explicitly convert all values, because mixed units make slopes and intercepts hard to interpret correctly.

The metre/time-signature variable is not justified as a useful explanatory variable because the investigation later shows it is constant at 4/4. A variable with no variation cannot explain differences in learning time, so it should be removed from the model or replaced with a measurable rhythmic feature.

The duration coefficient is still reported as a bare decimal without clearly linking it to the units of the axes. The student should state the slope in context, for example as minutes of learning time per unit of duration, so the meaning of $0.0121$ is mathematically and practically clear.

Including p-values alongside the regression output strengthens the mathematical use because it goes beyond describing correlation and asks whether the relationships are statistically persuasive. That is a sound extension of the modelling process at SL level.

The p-value section would be stronger if the student stated the null and alternative hypotheses explicitly for each regression. That would make the significance test easier to follow and would show a fuller understanding of why the p-value matters.

The p-value interpretation is correct in direction, but the reasoning stops at significance and does not connect back to the small effect sizes already shown by the low $R^2$ values. The student should explain that statistical non-significance and weak explanatory power together make these predictors poor for prediction.

The intercept interpretation is still not properly grounded in the model units. If the regression uses duration measured in seconds or minutes, the baseline estimate must be interpreted in the same unit system; otherwise the claim that it is “about 37.6 minutes” is not justified.