Author: Eric Parilla, IB Junior
Moving into the months of November and December, a great portion of IB students is in the process of developing their Internal Assessment (IA) for their Standard Level (SL) Mathematics course. The QR codes of surveys pinned into the walls of classroom walls serve as clear reminders that, just like winter, the time of the math IA has arrived. Certainly, for the IB Juniors and some Seniors, the whole concept of an IA is rather foreign, and many fear that they might end up doing the entire IA incorrectly. Nervousness is certainly warranted since doing the math IA incorrectly and getting a poor grade on it can drastically undermine a student’s final grade in the class. The IA makes up 20% of a student’s final grade in the entire SL Mathematics class and it has the possibility of determining the entire final grade in the slight but very real chance that the External Assessment is cancelled, as was the case last year and the year before. As such, it is critical to have the information and tips necessary to take on the math IA with confidence so that the nervousness and anxiety can evaporate.
Remember the mark scheme and the criterions
There are 5 different criterions that an IB math teacher looks for when scoring an IA paper and these are Criterion A: Presentation (up to 4 marks), Criterion B: Mathematical Communication (up to 4 marks), Criterion C: Personal Engagement (up to 3 marks), Criterion D: Reflection (up to 3 marks), and the Use of Mathematics (up to 6 marks). There are 20 marks for the IA, and it is critical to figure out what each criterion is asking for so that the IA can be written in a way that maximizes the marks earned. The number of marks earned determines the number, ranging from 1-7, that the IA receives but the range of marks that correspond to a given grade fluctuates by year. For example, in 2017, an IA that received 18-20 marks would earn a 7 while an IA that received 12-14 marks would earn a 5, but those grade boundaries may not be the same for this school year.
Don’t look at the IA as a research paper, think of it as an exploration
The IA’s purpose is not to make students find a new mathematical or scientific discovery, leave such work for scientists and mathematicians who actually work in academia. The IA’s purpose is to challenge students to apply math concepts learned in class to things that humans see and do in the real world. In the math IB SL handbook, there is no objective that expects students to discover something brand new in math and make conclusions that contribute to the understanding of math or science. When I decided to look into Florida lotteries and the probability of winning them, I asked questions surrounding lotteries such as how much do consumers profit from them? and how much does the state profit from them? Those questions acted as a springboard for my IA and got me to understand more about lotteries and the relevance they had with probability, a topic covered in IB math. When I asked these questions, I had little concern over whether my investigations’ results or conclusions would be massively groundbreaking or interesting because I was aware that the goal isn’t to contribute to mathematical understanding but rather to explore something in the real world and observe what relevance it has with math concepts learned in, and beyond, class. If there isn’t much room to explore a real-world topic in this respect, then it isn’t an ideal IA topic.
It’s about the journey, not the destination (sort of)
The corny subheading above actually reflects how results and conclusions in the IA should be viewed, whatever they come out to be. The results and conclusions that you find may not be as convincing or as interesting as you thought they would have been when you began thinking about your IA but that is alright. The truth is that the data that is provided in regard to whatever specific topic that you are tackling is only meant to help provide insight into its mathematical aspect. If there is sophisticated mathematical work that is being done to explore your topic, the journey, then there is the potential to gain a good number of marks just from that alone. The conclusions and the results themselves may actually amount to a few marks. Ideally though, you would want your data to indicate a particular trend that can lead to a meaningful conclusion, a meaningful destination, but if that proves tricky you can discuss why you weren’t able to reach a clear-cut conclusion and describe its implications. For example, if you were to look into the physics of cheerleading and, after doing all the math, there is no solid or clear conclusion that can be made in regard to what you were originally investigating, you can always explain why no clear conclusions were able to be made and what that means for society, cheerleaders, etc. It’s easier to make the IA’s destination, the results and conclusion, meaningful, than it is the journey, the mathematical exploration, because the bulk of the marks will come from the latter and the use of mathematics isn’t really up for interpretation (it’s either used correctly or not) while there is far more flexibility for you to make the conclusions you wish.
Be concise
Don’t try to explain for over 3 paragraphs why a particular topic was chosen, it won’t add much to the actual IA, and you risk making your IA unclear. Additionally, don’t try to explain for pages upon pages how every single step in your method works. Be concise, because overly long steps can be hard to follow and some marks from Criterion A (Communication) can potentially be taken off if you are not communicating clearly. In some instances, you may not need to explain a step because it is very basic, or it was already implied. Don’t write in overly verbose and flowerily language for the sake of sounding intelligent, there are no marks on the mark scheme that award for that. The clearer and more straightforward you are with explaining, the more marks you are to receive, at least in Criterion A.
Personal engagement can be demonstrated in numerous ways but the best way it can be shown is through effort and initiative
The best way to show that you are personally engaged with your IA is through the work that you do to get your results whether that be compiling long rows of original data (found on the internet or in the real world) on an Excel sheet or finding some innovative ways to answer/discuss the topic in question. Personal engagement does not necessarily mean you have to physically leave your house and do some novel experiment. An IA that includes experiments or physical travel is completely fine and will definitely demonstrate personal engagement, but field work is not required for the IA nor is it possible for some topics. Another thing to keep in mind when you are trying to show personal engagement is that you don’t want to solely rely on personal stories that demonstrate your personal connection to the topic. In reality, anyone can make up a story as to why a given topic is very personal to them, that requires little effort. The data and the innovativeness/creativeness of the approach to your topic, however, is going to demonstrate far more engagement than any personal story can because more effort is involved.
Commensurate math is needed in your IA
According to the Math SL Course description, unless the math that is used to answer or discuss the topic question is more or less the same level in difficulty or complexity as the SL math course, you are unable to gain more than 2 marks for Criterion E. This is very important to keep in mind because solely utilizing math considered “prior learning topics”, topics a student should have learned prior to starting the SL math course, such as Venn diagrams for sorting data, limits the maximum possible marks earned to 16, guaranteeing, at best, a 6. That doesn’t mean, however, that you can’t use math below the SL course level at any point, you certainly can when it is a part of the calculations and analysis you need to do for your exploration. What it does mean is that you cannot base the majority of your math exploration around “prior learning topics” and must instead base it on math concepts that are commensurate or beyond the difficulty level of the SL math course. You can refer to your SL math course’s handbook’s “prior learning topics” section in order to see what math concepts you cannot base your entire math exploration off of.
Remember to place bar charts, tables, and formulas when necessary
Visual representations of your data are vital and are needed to succinctly express what exactly you found in your exploration. You are likely to use bar charts when you want to compare data points over time and tables when you want to clearly demonstrate rows of data. You will also need to type in formulas when you wish to demonstrate and justify how you go about finding the numerical values of your results. Ensure that bar charts, tables and other visuals have text wrapping so that the text is able to flow more easily down the page and therefore allow the reader or grader to understand more clearly what you are writing. Additionally, whether you use Word or Google Docs, ensure that the formulas you put in are done with the help of an equation input tool because it will appear cleaner and more professional that way.
Read finished IAs made by other IB students
Given how confusing the IA process can be at first, there is nothing wrong with reading the works of others on the internet. In fact, reading IAs can give great insight as to how the paper is organized and what is needed in all the required sections. Learning how to properly lay out and organize an IA paper goes a long way towards receiving 20 marks which makes looking at examples of IA papers rather beneficial. Clastify is a website with numerous examples of math IAs that performed very well and not so well. Observing what the superb math IAs do and what the subpart math IAs don’t do may provide the insight needed to score a perfect 7 on it.