Criterion A: The work is divided into sections: introduction, body, and conclusion.

Comment: Although there s a clear indication of the introduction, the conclusion seems to be the subsection while the indication of where the body begins is nonexistent. The student should indicate clearly that the body of the exploration begins before the data description and include all the sections up to the matrix factorization in the body. The student should indicate a separate section with a conclusion. This would ensure that the correct division of text is carried out

Criterion A: The body of the work is further subdivided so that phases of the exploration are clearly indicated.

Comment: The student further subdivides the phases of the exploration, although they are advised to narrow down the number of subdivisions as the body of the exploration is not indicated

Criterion A: The body of the work is further subdivided so that phases of the exploration are clearly indicated.

Comment: The student further subdivides the phases of the exploration, although they are advised to narrow down the number of subdivisions as the body of the exploration is not indicated

Criterion A: The work is divided into sections: introduction, body, and conclusion.

Comment: It would be best for the student to narrow down the number of subdivisions as it might complicate the division of the body. The student should omit the 3.1.1, 3.1.2, 4.1.1, 4.1.2, 4.1.3 as so drastic divisions are unnecessary in the exploration

Criterion A: The body of the work is further subdivided so that phases of the exploration are clearly indicated.

Comment: The student further subdivides the phases of the exploration, although they are advised to narrow down the number of subdivisions as the body of the exploration is not indicated

Criterion A: The work is divided into sections: introduction, body, and conclusion.

Comment: Although there s a clear indication of the introduction, the conclusion seems to be the subsection while the indication of where the body begins is nonexistent. The student should indicate clearly that the body of the exploration begins before the data description and include all the sections up to the matrix factorization in the body. The student should indicate a separate section with a conclusion. This would ensure that the correct division of text is carried out

Criterion A: The body of the work is further subdivided so that phases of the exploration are clearly indicated.

Comment: The student further subdivides the phases of the exploration, although they are advised to narrow down the number of subdivisions as the body of the exploration is not indicated

Criterion A: The work is divided into sections: introduction, body, and conclusion.

Comment: Although there s a clear indication of the introduction, the conclusion seems to be the subsection while the indication of where the body begins is nonexistent. The student should indicate clearly that the body of the exploration begins before the data description and include all the sections up to the matrix factorization in the body. The student should indicate a separate section with a conclusion. This would ensure that the correct division of text is carried out

Criterion E:

Criterion A: The topic of the Internal assessment is stated clearly and explained in the introduction

Comment: The student explains the collaborative filtering systems in '1.2. Background' section of the exploration in which they explain two different forms of the system and the aim of the use of it

Criterion A: The introduction includes a general description of the student's approach to the topic and what area of the math curriculum the exploration focuses on

Comment: The student should additionally state the mathematics used in the exploration and explain it, i.e. the matrices used in the exploration should be indicated in the introduction as well as explained. The student should move some of the information placed in the 'Data description section to the introduction

Criterion A: The conclusion is a summary of the outcomes and a response to the aim of the exploration stated in the introduction

Comment: The student includes a response to the aim of the investigation. They state that the stochastic gradient descent was the closest value to the original matrix which is the response to the aim of the investigation. The student also includes a summary of the outcomes of the stages of the investigation

Criterion A: The conclusion is a summary of the outcomes and a response to the aim of the exploration stated in the introduction

Comment: The student includes a response to the aim of the investigation. They state that the stochastic gradient descent was the closest value to the original matrix which is the response to the aim of the investigation. The student also includes a summary of the outcomes of the stages of the investigation

Criterion A: The exploration is clear and understandable throughout - no rereading of sections is necessary

Comment: The student includes strange crossing out of the value from the table which should not be present in the exploration as it should be clear whether the student has included a thought-out table with the values or inserted random data. The student should remove the crossed-out value

Criterion A: The exploration is clear and understandable throughout - no rereading of sections is necessary

Comment: Once again, the same issue with the crossed-out value in the investigation. The student is advised to remove it

Criterion A: The exploration is clear and understandable throughout - no rereading of sections is necessary

Comment: This table is confusing to the reader ad the student should provide additional explanations or a separate table with the cosine similarity and Pearson's correlation

Criterion A: The exploration is clear and understandable throughout - no rereading of sections is necessary

Comment: The student should include additional descriptions of the table as it is confusing at first glance. The student could improve the clarity of the investigation

Criterion A: The exploration is clear and understandable throughout - no rereading of sections is necessary

Comment: Why are some values present in frames? The student is advised to describe such a choice of highlight and link it to the exploration's purpose

Criterion A: The exploration is clear and understandable throughout - no rereading of sections is necessary

Comment: The appendices section should be present on another page as it is beyond the scope of the exploration. The student should also first include the bibliography as it indicates the end of the exploration

Criterion A: The consequent parts of the work are linked logically - one is the follow-up of the other

Comment: The student uses linking words such as 'as I stated above' or 'after doing the calculations above' which point to the logical order of the exploration

Criterion A: The consequent parts of the work are linked logically - one is the follow-up of the other

Comment: The student uses linking words such as 'as I stated above' or 'after doing the calculations above' which point to the logical order of the exploration

Criterion A: The consequent parts of the work are linked logically - one is the follow-up of the other

Comment: The student uses linking words such as 'as I stated above' or 'after doing the calculations above' which point to the logical order of the exploration

Criterion A: The use of technology, when applied, is clearly indicated and explained

Comment: The student does not indicate the use of the software that graphed the angle. The student should include a description of the purpose and a link to the software in the bibliography

Criterion A: The use of technology, when applied, is clearly indicated and explained

Comment: The student should indicate the use of software in which the graph was made as well as include a description of a purpose of the software

Criterion A: If analytical software is used, its purpose is described and the link to it is provided

Comment: The student describes the use of Python in the investigation as well as indicates the link in the text to the code. Although, the student should include a link to the software used to create the code in the bibliography as well as in-text

Criterion A: The graphs, tables, and diagrams are present in appropriate places (in the body paragraphs, after their descriptive introduction)

Comment: The table does not include a description before insertion. The student should include a brief statement before insertion in which the student would explain that the table shows possible products of the matrix additionally to the labeling of the table

Criterion B: Multiple forms of mathematical representation: formulae, diagrams, tables, charts, graphs, and models are present but used only if appropriate

Comment: The student includes tables, formulae, and figures that represent the steps of the investigation, for example, the Python code is necessary to understand the investigation

Criterion A: The graphs, tables, and diagrams are present in appropriate places (in the body paragraphs, after their descriptive introduction)

Comment: The student should state that the description refers to Figure 3 to ensure that there is a description that links the tables to the exploration

Criterion A: All information outside of the syllabus scope is referenced <i style='font-size: 11px'>(using footnotes or in-text citations)</i>

Comment: The student includes necessary sources in the investigation. The student includes sources for concepts such as the Latent factors, their affinity, and the sparse matrix

Criterion A: All information outside of the syllabus scope is referenced <i style='font-size: 11px'>(using footnotes or in-text citations)</i>

Comment: The student includes necessary sources in the investigation. The student includes sources for concepts such as the Latent factors, their affinity, and the sparse matrix

Criterion A: All information outside of the syllabus scope is referenced <i style='font-size: 11px'>(using footnotes or in-text citations)</i>

Comment: The student includes necessary sources in the investigation. The student includes sources for concepts such as the Latent factors, their affinity, and the sparse matrix

Criterion A: All mathematical formulae, equations, and other calculations are centered

Comment: The matrices should be centered throughout the investigation as they also are equations/formulae

Criterion A: All mathematical formulae, equations, and other calculations are centered

Comment: All the equations throughout the exploration should be centered. The student does not center the highlighted equation but is advised to do so and apply the centering to all other equations present in the investigation

Criterion A: There are no unnecessary or repetitive calculations/graphs/descriptions

Comment: There are two same figures that are labeled the same: this one and the one on page 8. The student should remove one of them as it is unnecessary to include the same figure twice

Criterion B: Correct mathematical notation, symbols, and terminology are used consistently and correctly

Comment: The student does not include a true equation of Pearson's correlation. The student should show the correct equation and further explain how they obtained the equation present in the investigation and refer to Pearson's correlation as r instead of 'sim(a,b)' as it is a correct symbol for the correlation

Criterion B: Correct mathematical notation, symbols, and terminology are used consistently and correctly

Comment: The symbol for the mean is x with a bar on top or y with a bar on top, not r. The r refers to the correlation coefficient calculated by the student. They are advised to correct the symbols to show the universal ones used in the International Baccalaureate syllabus

Criterion B: Correct mathematical notation, symbols, and terminology are used consistently and correctly

Comment: It is unclear why the student has used the same symbol for the mean and the predicted rating. The two concepts should have different symbols as they are two separate calculation processes related only to the variable level

Criterion B: Computer notation is present only if software-generated (clear indication necessary)

Comment: The student includes a Python-generated code on page 12 in the form of a picture that is clearly software-generated

Criterion B: Multiple forms of mathematical representation: formulae, diagrams, tables, charts, graphs, and models are present but used only if appropriate

Comment: The student includes tables, formulae, and figures that represent the steps of the investigation, for example, the Python code is necessary to understand the investigation

Criterion E:

Criterion B: Key terms/variables are defined and explained when first introduced

Comment: The student includes a clear distinction of the variables in each of the equations as well as an explanation of the U and I present in the data description section

Criterion B: Key terms/variables are defined and explained when first introduced

Comment: The student includes a clear distinction of the variables in each of the equations as well as an explanation of the U and I present in the data description section

Criterion B: The main concepts are described in the introduction

Comment: Although the student describes the concepts outside the syllabus, they do not include descriptions of the mathematical concepts included. The student should explain the matrices, Pearson's coefficient as well as cosine similarity. This would ensure that the student covered the mathematical background of the investigation as well as understood it

Criterion B: Additional terms are defined in detail in appropriate places (dependent on the development of the exploration)

Comment: The student describes the additional terms and how they relate to the exploration, e.g. the student states that the cosine similarity will be used in user-based CF. However, the student does not explain Pearson's correlation. They should state what the measure is used for as well as what it relates to in the investigation and why it is beneficial to study in this case. The student should also state the characteristics of Pearson's coefficient as the student mentions the best-fit line but does not explain it. The concept of positive, negative, and neutral correlation is also omitted. The student is advised to improve the explanation of Pearson's coefficient

Criterion B: Additional terms are defined in detail in appropriate places (dependent on the development of the exploration)

Comment: The student has mentioned the use of latent features in matrix factorization, however, they did not mention how matrices are built and what the figure represents as it is unclear why m times n would be 4. The student is advised to include the necessary descriptions listed previously to improve the criterion

Criterion B: Multiple forms of mathematical representation: formulae, diagrams, tables, charts, graphs, and models are present but used only if appropriate

Comment: The student includes tables, formulae, and figures that represent the steps of the investigation, for example, the Python code is necessary to understand the investigation

Criterion B: Computer notation is present only if software-generated (clear indication necessary)

Comment: The student includes a Python-generated code on page 12 in the form of a picture that is clearly software-generated

Criterion B: Multiple forms of mathematical representation: formulae, diagrams, tables, charts, graphs, and models are present but used only if appropriate

Comment: The student includes tables, formulae, and figures that represent the steps of the investigation, for example, the Python code is necessary to understand the investigation

Criterion A: The graphs, tables, and diagrams are present in appropriate places (in the body paragraphs, after their descriptive introduction)

Comment: The table does not include a description before insertion. The student should include a brief statement before insertion in which the student would explain that the table shows possible products of the matrix additionally to the labeling of the table

Criterion B: All mathematical calculations are explained and any data presentation is described

Comment: The student does not describe the thinking process behind the figure and it is unclear to the reader what it represents

Criterion B: All mathematical calculations are explained and any data presentation is described

Comment: The student does not state what each of the variables indicates and only includes an indication of the estimated rating being calculated. The student is advised to include a description of the equation

Criterion B: All mathematical calculations are explained and any data presentation is described

Comment: What do the values present in cells different than those that indicate the variable mean? How are they calculated? The student should include a description of the tables before insertion as the process of the calculations is unclear and what the values indicate is also unclear. Usually, the cells represent the multiplication of the variables, however for clarity, the student is advised to indicate it clearly

Criterion B: The degree of accuracy is stated for any rounded values

Comment: It is unclear in the investigation whether the student is rounding the figures to any of the significant figures. To ensure that there is clarity when it comes to rounding, they are advised to include an indication of the rounding in the brackets in all the calculations, e.g. here the appropriate comment would be that the values are unrounded or an inclusion of the bracket: (8 d.p.)

Criterion B: Results are rounded only at the end of the calculations thread

Comment: It is unclear whether the results are rounded at the end of the calculations. To ensure that the student applied correct rounding at the end of the calculations, they should display them, perhaps in appendices

Criterion B: The student used a deductive method and set out logical proofs where appropriate

Comment: The student shows logical thinking in interpreting the results in the conclusion as well as in the text in some parts in which they explain the reasoning of the investigation

Criterion B: The student used a deductive method and set out logical proofs where appropriate

Comment: The student shows logical thinking in interpreting the results in the conclusion as well as in the text in some parts in which they explain the reasoning of the investigation

Criterion B: The graphs, tables, and diagrams are labeled (titled and numbered) at the bottom

Comment: The figure is not labeled at all. The student is advised to include labeling at the bottom

Criterion B: The graphs, tables, and diagrams are labeled (titled and numbered) at the bottom

Comment: The student does not label the tables. The inclusion of the labeling at the bottom would improve the criterion. As all previous labels are correctly done in terms of correctly identifying what each of the figures shows, the student could take inspiration from them

Criterion B: The graphs, tables, and diagrams are labeled (titled and numbered) at the bottom

Comment: The student includes two of Figure 3s, which they should avoid. The student should include a labeling of all figures at the bottom as well as include a correct numbering that is continuous

Criterion C:

Criterion C:

Criterion C:

Criterion C:

Criterion C:

Criterion C:

Criterion D:

Criterion D:

Criterion D:

Criterion D:

Criterion D:

Criterion D:

Criterion D:

Criterion D:

Criterion D:

Criterion D:

Criterion E:

Criterion B: Computer notation is present only if software-generated (clear indication necessary)

Comment: The student includes a Python-generated code on page 12 in the form of a picture that is clearly software-generated

Criterion E:

Criterion E:

Criterion E:

Criterion E:

Criterion E:

Criterion E:

Criterion A: The work is divided into sections: introduction, body, and conclusion.

Comment: Although there s a clear indication of the introduction, the conclusion seems to be the subsection while the indication of where the body begins is nonexistent. The student should indicate clearly that the body of the exploration begins before the data description and include all the sections up to the matrix factorization in the body. The student should indicate a separate section with a conclusion. This would ensure that the correct division of text is carried out

Criterion A: The body of the work is further subdivided so that phases of the exploration are clearly indicated.

Comment: The student further subdivides the phases of the exploration, although they are advised to narrow down the number of subdivisions as the body of the exploration is not indicated

Criterion E:

Criterion A: The work is divided into sections: introduction, body, and conclusion.

Comment: Although there s a clear indication of the introduction, the conclusion seems to be the subsection while the indication of where the body begins is nonexistent. The student should indicate clearly that the body of the exploration begins before the data description and include all the sections up to the matrix factorization in the body. The student should indicate a separate section with a conclusion. This would ensure that the correct division of text is carried out

Criterion E: