Data Scientist and Machine Learning (Understanding Student Responses to Math Questions)

I am building a website/application in education. The website/application will ask students a series of mathematical questions which they answer. As they progress through these questions we want to develop a 'profile' of these students to determine their ability. However, we want to track more than just right or wrong answers to develop this profile, we want to develop something that takes in as many factors as possible to produce a single number that reflects each students ability as accurately as possible. Examples of factors that should be taken into account are: 1. Right or wrong answer 2. Time taken to answer the question 3. Number of wrong attempts before getting that question right 4. If the student asks for a hint/tip on a question All this and more will be taken in to account to produce a single number that reflects their ability. We need this score to be extremely accurate so Teachers can rely on it and also it will allow us to serve questions to each student that reflects their ability. Beyond that, we have a range of question styles (some harder than others) and questions of varying difficulty. That said, we want a system setup so that we can effectively present students with this questions in an iterative (progressive/sequential) manner for their learning benefit. The idea is that this platform would adapt to the students ability and present questions that are appropriate for that student. This is just an example I have come up with, I would like someone with knowledge in machine learning, data science, education (preferable) and someone who can come up with creative ways to track vital information beyond just right and wrong answers to determine a students ability. We are also open to looking at other insights that you may feel are useful for a teacher looking to assess the students learning profile and ability.