Jonathan’s confidence has improved and he grasped the explanations of the content covered in his test quicker this time around.

At this stage, Jonathan needs to improve retaining his understanding and applying it outside of these sessions.

Reuben showed clear understanding of where the “neat” values come from and how they relate to angles, how to count forward and backward around the unit circle for multiples of “neat” angles, and how to use the quadrant symmetries to find the sign of the sin and cos values at different angles.

At this stage, Reuben needs to practice using the techniques and concepts discussed with trig equations of varying complexity to get more comfortable with the processes and concepts involved, as well as reinforcing the fundamentals and getting used to applying them to more advanced contexts.

Reuben has retained a solid understanding of the content, consistently able to work through simple questions without help, and mostly able to approach more advanced questions and attempt them.

At this stage, Reuben needs to focus on retaining the mental models and intuition connecting trig concepts together as most of his problem solving comes from isolated knowledge of the relevant concept and struggles when multiple concepts are combined. He should also work on his algebra, as this limits his skill at rearranging equations and applying operations correctly.

Reuben is doing well at grasping the general concepts and doing most questions correctly once he knows how to approach them. He can use the period to calculate the frequency most of the time using the velocity analogy and has been able to connect some of his physics content to the concepts we’ve been covering.

At this stage, Reuben struggles with algebraic steps involving complex fractions, and tends to get confused about determining the frequency as it is a multi-step calculation and he often forgets or mixes up the intermediate step. To improve on this, he should do practice problems involving finding the frequency and practice writing out the steps including the velocity analogy to strengthen that mental model, as well as practicing more problems in general to get more familiar with how trig functions transform.