IA (HL) Math HL IA - An Exploration of the Exploration

[Rahul]

---Author's Note---

This is the third draft of a concise guide I'm working on in regards to the new mathematical exploration IA; this started as an HL guide but has now been generalized to include the SL curriculum as well. Please do let me know if there are any improvements you can suggest, or any questions you have after reading through this. I plan to keep this updated and add to it as I work though my own IA. Thanks for taking the time to read through!

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Table of Contents

1. Preface and Introduction to the Exploration
2. The Process (to be added)
3. Formatting (to be added)
4. Acceptable Topics (SL)
5. Acceptable Topics (HL)
6. Grading and Evaluation​​​​​
   1. Criterion A - Communication (to be added)
   2. Criterion B - Mathematical Presentation (to be added)
   3. Criterion C - Personal Engagement (to be added)
   4. Criterion D - Reflection (to be added)
   5. Criterion E - Use of Mathematics (SL Only) (to be added)
   6. Criterion E - Use of Mathematics (HL Only) (to be added)
7. Sample Papers
8. Postface and Notes

Preface and Introduction to the Exploration

The Mathematics SL/HL Exploration internal assesment. It is certainly a difficult assignment - a paper on math isn't the easiest thing to write. I've written this guide up to clarify a few questions and hopefully help out with your work. However, please don't just trust what I say do some of your own research as well because I cant hope to claim everything I say is entirely accurate. I hope this helps!

In essence, this is an exploration of a topic in mathematics that has a real-world connection, done in a rigorous manner that connects back to the material we have covered and will cover in class. 6-12 pages in length should be appropriate enough to concisely explore your chosen topic with the depth required and complete the necessary parts of evaluation as shown in the rubric.

You want to write at a level and regarding mathematics that is accessible to other students. For HL students, this generally means anything within the HL core curriculum and any option is fair game. Just be certain to provide requisite explanation for any material beyond those two areas and for options not covered in class, to the extent that your classmates can understand the work you've done with some thought.

The Process

<to be added>

Formatting

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Acceptable Topics (SL)

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Acceptable Topics (HL)

I've been asked a lot of questions about acceptable topics for the IA's mathematical focus. These acceptable topics are mainly focused towards fulfilling the part of Criterion E that requests "sophisticated mathematics commensurate with the level of the course" - more detail regarding the other aspects of this criterion can be found in the Grading and Evaluation section slightly later on.

One guideline I've heard from a few sources is to choose something beyond the SL syllabus: a summary of those topics can be found slightly later in this section. Keep in mind you do not have to restrict yourself to these topics, and anything beyond is fine. Also, that a topic in the SL syllabus can be beneficial if done well - it's rather easy to do comparatively and can still net you a 7 on the IA. See the Florence Nightingale Sample IA. Finally, I'm not certain if all of these topics have sufficient levels of difficulty, or if there are any in the SL syllabus that would be acceptable this is simply based on the SL and HL syllabi.

What follows is a list of the topics which are in the HL syllabus, but not the SL, to provide a guideline of all acceptable topics within the syllabus:

Topic 1: Algebra
1.4: Proof by induction.
1.5: Complex numbers, the Cartesian form of a complex number.
1.6: Modulus-argument of polar form of an imaginary number and the complex plane.
1.7: Powers of complex numbers, nth roots of complex numbers, and de Moivre's theorem.
1.8: conjugate roots of polynomial equations with real coefficients.
1.9: Solutions of systems of linear equations.

Topic 2: Functions and Equations
2.1: ONLY domain restriction for inverse functions as well as self-inverse functions.
2.2: The graphs of y=|f(x)| and y=f(|x|), the graph of y=(1/f(x)) given the graph of y=f(x).
2.5: Polynomial functions and their graphs, the factor and remainder theorems, the fundamental theorem of algebra.
2.6: Viete's theorem, or the sum and product of the roots of algebraic equations.
2.7: Solutions of g(x)>=f(x) by graphical or algebraic methods for polynomials up to degree 3.

Topic 3: Circular Functions and Trigonometry
3.2: Definition of the reciprocal trigonometric functions sec(x), csc(x), and cot(x). The tangent-secant and cotangent-cosecant forms of the Pythagorean identity.
3.3: The tangent double angle identities, compound angle identities.
3.5: The inverse functions y=arcsin(x), y=arccos(x), y=arctan(x), and their domains, ranges, and graphs.

Topic 4: Vectors
4.2: The properties of the scalar product of vectors.
4.4: Specifically intersecting and skew lines in distinguishing between coincident, parallel, intersecting, and skew lines.
4.5: Definition of the vector product of two vectors, properties of the vector product, and the geometric interpretation of the magnitude of the vector product.
4.6: Vector equation of a plane, use of normal vector to obtain a particular solution form, Cartesian equation of a plane.
4.7: Intersections of: a line with a plane, two planes, three planes. Angle between: a line and a plane, two planes.

Topic 5: Statistics and Probability
5.4: Use of Bayes' theorem for a maximum of 3 events.
5.6: Poisson distribution.

Topic 6: Calculus
6.2: Related rates of change, implicit differentiation, and the derivatives of the inverse trigonometric functions, the reciprocal trigonometric functions, the exponential function, and the logarithmic function
6.7: Integration by substitution, integration by parts.

All material in all option topics.

Grading and Evaluation

You can find the grading scheme for this IA here: http://bit.ly/1iOdQl7. There are 5 criteriae: communication, mathematical presentation, personal engagement, reflection, and use of mathematics.

To clarify a few terms used: Personal engagement refers to the intent of the investigation to develop your interest in the area, and its evaluated based on the visibility of your personal engagement in the area and your own individual expression of those ideas. Precise and correct are differentiated by the need of precise mathematics to include proper notation and completely accurate work whereas correct mathematics can contain some errors as long as these errors don't lead to egregious incorrectness. The criterions themselves are defined here in the markscheme.

Criterion A - Communication
<to be added>

Criterion B - Mathematical Presentation
<to be added>

Criterion C - Personal Engagement
<to be added>

Criterion D - Reflection
<to be added>

Criterion E - Use of Mathematics [sL]

<to be added>

Criterion E - Use of Mathematics [HL]
<to be added>

Sample Papers

Its difficult to understand and conceptualize what is expected without exploring some examples of strong work. So here are a couple example papers, to show you what other students have done in the past, how theyve been evaluated and annotations, the mark they received and grader comments, as well as a couple small notes of my own.

Sectors, Arcs, Descriptive Statistics, and Florence Nightingale (Mark Achieved: 20/20 at SL, 17/20 at HL)

Paper: http://bit.ly/18KcK5q
Paper with Comments: http://bit.ly/1fFkYe2
Marks: http://bit.ly/1dBrz7z

This one is a perfect example of the kind of work you want to be doing in your math IA - however, the level of mathematics isn't at a high enough level given that all mathematics used is within the Math SL curriculum.


Differential Equations and Modeling Rain. (Mark Achieved: 16/20 at SL, 15/20 at HL)

Paper: http://bit.ly/1c491Oi
Paper With Comments: http://bit.ly/19KUPKw
Marks: http://bit.ly/1d6PSMD

This paper has many errors in notation, it is not concise in form, the reflection is not critical, examples are not quite sufficient, and the mathematics is not precise. However, the mathematics is certainly at the level required. Very strong work in general, just missing that final layer of polish.

Postface and Notes

I hope I've been able to help out with this guide. Please let me know if you find any issues or inaccuracies or if you still have questions after reading through this. Good luck with your IA!

Sourcing Notes:

• A good deal of these links and some of the information was retrieved from M. Chao's blog, which can be found here: http://bit.ly/K12vhF. It was quite useful to me in doing my own research.
• The IB Mathematics IA website was very useful to me: it can be found here: http://bit.ly/JbK1e4.
• The SL and HL Mathematics IB Course Guides were useful to me, especially in the analysis of acceptable topics and criterion E. They can be found at http://bit.ly/1eJQ08k and http://bit.ly/19oDBik, respectively.

Revision History:

• December 24, 2013: Guide first posted.
• December 25, 2013: Differences between SL and HL syllabus (Acceptable Topics) added. Formatting improved
• December 27, 2013: Added skeleton for remainder of guide. Added table of contents. WIP: Grading and Evaluation section for all criterions. Reorganized guide.
• January 3, 2014: Proofread and edit.
• January 07, 2014: Generalized guide to include the SL exploration as well.

To Do List:

• Improve formatting further.
• Flesh out postface.
• Examine criterions in depth.
• Discuss formatting of IA and how best to write it.
• Add mistakes section.
• Add SL criteriae.
• "SL-ize" the guide.
• Discuss the draft submission and teacher feedback process as well as the extent to which your teacher can help.

Edited March 15, 2014 by Rahul

[ChocolateDrop]

I would just like to add you can do the exploration on any topic that is similar to or covered in the options, not just limited to Calculus.

[Rahul]

Thanks for catching that, ChocolateDrop! This was originally written for my classmates, as we're studying the Calculus option - I'll correct that right away. I also intend to get done the in-depth exploration of each criterion today.

Edit: Stuff came up as it has been for the past week, life hasn't been kind to me recently. I'll make time for it very soon.

Edited January 4, 2014 by Rahul

[CWQ]

This is really helpful! Thanks for sharing!!

[John Hoose]

Thanks this is really helpful

I was wondering if the IA can be to explore some type of paradox ... or does it have to be an 'investigation' in the classical sense and lead to a definitive answer.

John

[Rahul]

Thanks this is really helpful

I was wondering if the IA can be to explore some type of paradox ... or does it have to be an 'investigation' in the classical sense and lead to a definitive answer.

John

I would think an exploration, as long as it fits the criterions, should be fine!

[nina101]

hey guys,

I have to choose a topic for my exploration now and I am a bit confused. I wanted to do it on Newton Rhapson method because I do really like this graphical way of finding the roots of a function. Unfortunately, exploration with such topic has been already posted here: https://drive.google.com/viewerng/viewer?a=v&pid=sites&srcid=Zy5jb3BwZWxsaXNkLmNvbXxjb3BwZWxsLWliLW1hdGh8Z3g6M2QwODhlNWEwNDg3NGIwOQ  

Do you think that if I did my very own exploration on Newton method it would be considered as a plagiarism because such a work has already been done?

[Vioh]

hey guys,

I have to choose a topic for my exploration now and I am a bit confused. I wanted to do it on Newton Rhapson method because I do really like this graphical way of finding the roots of a function. Unfortunately, exploration with such topic has been already posted here: https://drive.google.com/viewerng/viewer?a=v&pid=sites&srcid=Zy5jb3BwZWxsaXNkLmNvbXxjb3BwZWxsLWliLW1hdGh8Z3g6M2QwODhlNWEwNDg3NGIwOQ

Do you think that if I did my very own exploration on Newton method it would be considered as a plagiarism because such a work has already been done?

 

Plagiarism or not depends on how much influence that student's work has on your own IA. If you plan to have the same structure or even similar structure as that IA sample, then i'm afraid that could be considered as plagiarism. However, if you are sure that you can find a completely different approach towards this problem/topic, then go ahead. But make sure that you have different structure, different arguments, different derivations, different graphs, & everything else. Note that this student's work is on IB's webpage, thus it would be very easy for the IB to check your work against this particular work.

 

Anyhow, I would advise you to not do this topic, but not due to the reason of plagiarism. This topic has been chosen as the sample, so it's very likely that all examiners, teachers, and possibly even students have known about it and studied it by heart. Hence, the examiners/teachers would be harsher when marking your IA. It's like you would have a greater advantage compared to other students. For that reason, don't do it! Perhaps, think a bit harder to come up with a new topic?

[nina101]

 

hey guys,

I have to choose a topic for my exploration now and I am a bit confused. I wanted to do it on Newton Rhapson method because I do really like this graphical way of finding the roots of a function. Unfortunately, exploration with such topic has been already posted here: https://drive.google.com/viewerng/viewer?a=v&pid=sites&srcid=Zy5jb3BwZWxsaXNkLmNvbXxjb3BwZWxsLWliLW1hdGh8Z3g6M2QwODhlNWEwNDg3NGIwOQ

Do you think that if I did my very own exploration on Newton method it would be considered as a plagiarism because such a work has already been done?

 

Plagiarism or not depends on how much influence that student's work has on your own IA. If you plan to have the same structure or even similar structure as that IA sample, then i'm afraid that could be considered as plagiarism. However, if you are sure that you can find a completely different approach towards this problem/topic, then go ahead. But make sure that you have different structure, different arguments, different derivations, different graphs, & everything else. Note that this student's work is on IB's webpage, thus it would be very easy for the IB to check your work against this particular work.

 

Anyhow, I would advise you to not do this topic, but not due to the reason of plagiarism. This topic has been chosen as the sample, so it's very likely that all examiners, teachers, and possibly even students have known about it and studied it by heart. Hence, the examiners/teachers would be harsher when marking your IA. It's like you would have a greater advantage compared to other students. For that reason, don't do it! Perhaps, think a bit harder to come up with a new topic?

 

I guess you are right with the examiners' approach towards such a piece of work. I am thinking hard about some mathematical method used in economics. Perhaps something like Lorenz curve and Gini coefficient which are used to evaluate the inequality in an economy... Economics is my favorite IB subject and that's why I rieally wish to do something Econ-related. Maybe any one of you have some ideas/suggestions?

[TheLonelyDog]

I have a question about the page number.

 

Is it 12 pages without the title, references, and other stuff? My IA currently has 12 pages of work itself + 3 other pages. Is it a problem? Do I have to cut a lot of things out?

[choyiny]

The newest teacher support material is updated and contains 20 sample Math Explorations:

https://ibpublishing.ibo.org/live-exist/rest/app/tsm.xql?doc=d_5_matsl_tsm_1205_1_e∂=2&chapter=2

 

[smay97]

Hello, I found this very helpful for the exploration (I was quite confused with it haha)!

 

I just have one question. Do you think conic sections (specifically, ellipses) are an appropriate topic to get a level 7 in maths HL?

 

Thank you!

[BioMed]

Could someone that has gotten a good grade on their IA share it with me please