I have to come up with three topics for my Math Studies Internal Assessment as summer work but I am completely lost. My teacher didn't really explain how we form these topics. Can someone sort of explain this to me and give me examples of topics for Math Studies Internal Assessment?
Thanks in advance!
I've heard of an Italian group that just published a paper, in which it was claimed that the frequency of world records in all sports follow an s-curve, and that we now are on the upper part of it - fewer new world records are being set. You could choose a sport of your interest, look at the history of world records, and by applying some model to it, extrapolate from the data and suggest if the competitors have reached the peak performance or when thay will reach it. You could give the investigation a slight twist by including yet another sport and analysing it similarly. In that case, you would be able to compare the potential for new world records being broken, etc.
The most important thing you shouold think of when choosing a topic is that you are certain that a lot and different math can be applied.
I think I could help you! I did math studies, got a 19/20 on my IA. The title and the RQ were:Investigation of the biological relationship between body length and shoe size in a group of women
RQ: Does a relationship between the two variables body length and shoe size in a group of women exist, or do they vary independently of each other?
I collected data from 386 women, it's a lot better to have an abundance of data than small samples of data. However my method was not random, as I explain and motivate in the section called Evaluation of methods used:
"Notice how the word “group” was included in the RQ;
Does a relationship between the two variables body length and shoe size in a group of women exist, or do they vary independently of each other?
This fact effectively conveys the message that it is not this investigation’s intention to discuss whether or not the results of this investigation can be applicable on the whole Swedish female population; the focus is primarily the group of 386 women in the group. Additionally, without the inclusion of the word “group” the method of the investigation would have had to be simple random sampling, a method which was consciously rejected as the method of sampling due to the amount of time that had to be spent in that case, due to the procedures of generating random numbers, assigning them to the subjects etcetera."
I did the following calculations:
2. Correlation analysis including Pearson's product-moment correlation coefficient and the sample coefficient of determination
3. Regression analysis including least square regression line and the standard error of estimate
These calculations was then critically discussed (such as the fact that Pearson's tend to generate an incorrect picture of the strength of the relationship whilst the sample coefficient of determination doesn't).
I was much aided by the book Hamburg, Morris. Basic Statistics: A Modern Approach (Third Edition). I used my GDC and the Minitab statistical package (free trial).
Hope that gave you an idea
Maths Studies IA Exploration Topics:
This is the British International School Phuket’s IB maths exploration page. This list is primarily for Maths Studies students – though may also be of use to SL and HL students interested in statistics and probability. If you are doing a Maths SL, HL exploration then go to this page instead.
Make sure you read the Maths Studies guidance from the IB prior to starting your IA maths exploration – this linked site gives the full list of assessment criteria you will be judged against and also gives 9 full examples of investigations students have done.
Given the assessment criteria it’s probably easiest to conduct a data analysis investigation, though you can choose to explore other parts of the syllabus instead. To get good marks make sure you carefully follow the marking criteria points given by the IB and try and personalise your investigation as much as possible. Be innovative, choose something you are interested in and enjoy it!
Primary or Secondary data?
The main benefit of primary data is that you can really personalise your investigation. It allows you scope to investigate something that perhaps no-one else has ever done. It also allows you the ability to generate data that you might not be able to find online. The main drawback is that collecting good quality data in sufficient quantity to analyze can be time consuming. You should aim for an absolute minimum of 50 pieces of data – and ideally 60-100 to give yourself a good amount of data to look at.
The benefits of secondary data are that you can gain access to good quality raw data on topics that you wouldn’t be able to collect data on personally – and it’s also much quicker to get the data. Potential drawbacks are not being able to find the raw data that fits what you want to investigate – or sometimes having too much data to wade through.
Secondary data sources:
1) The Census at School website is a fantastic source of secondary data to use. If you go to the random data generator you can download up to 200 questionnaire results from school children around the world on a number of topics (each year’s questionnaire has up to 20 different questions).
2) If you’re interested in sports statistics then the Olympic Database is a great resource. It contains an enormous amount of data on winning times and distances in all events in all Olympics. Follow links at the top of the page to similar databases on basketball, golf, baseball and American football.
3) If you prefer football you can also find a lot of football stats on the Who Scored website. This gives you data on things like individual players’ shots per game, pass completion rate etc.
4) The World Bank has a huge data bank – which you can search by country or by specific topic. You can compare life-expectancy rates, GDP, access to secondary education, spending on military, social inequality, how many cars per 1000 people and much much more.
5) Gapminder is another great resource for comparing development indicators – you can plot 2 variables on a graph (for example urbanisation against unemployment, or murder rates against urbanisation) and then run them over a number of years. You can also download Excel speadsheets of the associated data.
6) Wolfram Alpha is one of the most powerful maths and statistics tools available – it has a staggering amount of information that you can use. If you go to the examples link above, then you can choose from data on everything from astronomy, the human body, geography, food nutrition, sports, socioeconomics, education and shopping.
7) Plotly is a great visual graphic site – you can create visually interesting infographics and analyse data from hundreds of other sources.
8) TSM – the Technology for Secondary Mathematics is something of an internet dinosaur – but has a great deal of downloadable data files on everything from belly-button ratios to lottery number analysis and baby weights.
9) Google Public Data – an enormous source for public data, which is displayed graphically and can be searched.
10) Nationmaster – another huge site with pretty much any statistic and data comparing countries. Currently they have 19 million data points – so you’re likely to find something useful!
11) Google word usage analysis – a great tool which allows you to track the usage of words over the centuries.
Example Maths Studies IA Investigations:
Some of these ideas taken from the excellent Oxford IB Maths Studies textbook.
1) Is there a correlation between hours of sleep and exam grades?
Studies have shown that a good night’s sleep raises academic attainment.
2) Is there a correlation between height and weight?
The NHS use a chart to decide what someone should weigh depending on their height. Does this mean that height is a good indicator of weight?
3) Is there a correlation between arm span and foot height?
This is also a potential opportunity to discuss the Golden Ratio in nature.
4) Is there a correlation between the digit ratio and maths ability?
Studies show there is a correlation between digit ratio and everything from academic ability, aggression and even sexuality.
5) Is there a correlation between smoking and lung capacity?
6) Is there a correlation between GDP and life expectancy?
Run the Gapminder graph to show the changing relationship between GDP and life expectancy over the past few decades.
7) Is there a correlation between numbers of yellow cards a game and league position?
Use the Guardian Stats data to find out if teams which commit the most fouls also do the best in the league.
8) Is there a correlation between Olympic 100m sprint times and Olympic 15000m times?
Use the Olympic database to find out if the 1500m times have go faster in the same way the 100m times have got quicker over the past few decades.
9) Is there a correlation between sacking a football manager and improved results?
A recent study suggests that sacking a manager has no benefit and the perceived improvement in results is just regression to the mean.
10) Is there a correlation between time taken getting to school and the distance a student lives from school?
11) Does eating breakfast affect your grades?
12) Is there a correlation between stock prices of different companies?
Use Google Finance to collect data on company share prices.
13) Does teenage drinking affect grades?
A recent study suggests that higher alcohol consumption amongst teenagers leads to greater social stress and poorer grades.
14) Is there a correlation between unemployment rates and crime?
If there are less work opportunities, do more people turn to crime?
15) Is there a correlation between female participation in politics and wider access to further education?
16) Is there a correlation between blood alcohol laws and traffic accidents?
17) Is there a correlation between height and basketball ability?
18) Is there a correlation between stress and blood pressure?
19) Is there a correlation between Premier League wages and league positions?
1) Are a sample of student heights normally distributed?
We know that adult population heights are normally distributed – what about student heights?
2) Are a sample of flower heights normally distributed?
3) Are a sample of student weights normally distributed?
4) Are a sample of student reaction times normally distributed?
Conduct this BBC reaction time test to find out.
5) Are a sample of student digit ratios normally distributed?
6) Are the IB maths test scores normally distributed?
IB test scores are designed to fit a bell curve. Investigate how the scores from different IB subjects compare.
7) Are the weights of “1kg” bags of sugar normally distributed?
Other statistical investigations
1) Does gender affect hours playing sport?
A UK study showed that primary school girls play much less sport than boys.
2) Investigation into the distribution of word lengths in different languages.
The English language has an average word length of 5.1 words. How does that compare with other languages?
3) Do bilingual students have a greater memory recall than non-bilingual students?
Studies have shown that bilingual students have better “working memory” – does this include memory recall?
4) Investigation about the distribution of sweets in packets of Smarties. A chance to buy lots of sweets! Also you could link this with some optimisation investigation.
5) 22) Using Chi Squared to crack codes – Chi squared can be used to crack Vigenere codes which for hundreds of years were thought to be unbreakable. Unleash your inner spy!
6) Which times tables do students find most difficult to learn? – Are some calculations like 7×8 harder than others? Why?
Modelling using calculus
1) How can you optimise the area of a farmer’s field for a given length of fence?
A chance to use some real life maths to find out the fence sides that maximise area.
2) Optimisation in product packaging.
Product design needs optimisation techniques to find out the best packaging dimensions.
Probability and statistics
1) The probability behind poker games
2) Finding expected values for games of chance in a casino.
3) Birthday paradox:
The birthday paradox shows how intuitive ideas on probability can often be wrong. How many people need to be in a room for it to be at least 50% likely that two people will share the same birthday? Find out!
4) Which times tables do students find most difficult?
A good example of how to conduct a statistical investigation in mathematics.
5) Handshake problem
With n people in a room, how many handshakes are required so that everyone shakes hands with everyone else?
If you want to do an investigation with a bit more mathematical content then have a look at this page for over 100 ideas for Maths SL and HL students.