Student understood certain ideas quite clearly. i.e how the intersection of possible outcomes A and B corresponds to the probability of A and B occurring, and used a double table well in figuring out problems.

Some issues regarding remembering probability rules, however, more problems appear to be in how student was taught. i.e. student's teacher apparently had not yet taught the class that P(A and B) = P(A) * P(B) in the case of independent events, despite already being well into conditional probability. Otherwise, student had difficulty seeing how P(A) + P(not A) = 1 could be rearranged and used to determine probabilities, likely stemming from the known weakness with algebraic manipulation.

Was able to improve student's understanding of probability after working through problem of rolling doubles with two dice.

Student lacked intution with basic probablity. e.g. when asked how many possible outcomes there were when rolling two dice, answered 12. Student also seemed distracted and paid less attention than usual.

Student demonstrated quick recognition of most network theory concepts, such as isomorphism between networks and planarity of networks.

Student needed some prompting on vertex degree. Student also had significant difficulty mentally rearranging Euler's formula to make the number of vertices, edges or faces the subject, stemming from a lack of algebraic skill overall.

Student was very quickly able to mentally calculate mentally paths through weighted graphs and determine total length. After going through multiple examples of algebra problems, student also seemed to recognise the mistake that's plagued their working in the past and tried to adjust for it.

Student still displays limited ability to work with fractions, with an inability to add them together before being shown. Shows a lack of confidence and intuition in understanding what a fraction is actually representing, and seems to treat it as merely a symbol on the page.