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I used the student's past precalculus tests to prepare a set of problems targeting the types of questions that had previously challenged him. Specifically, we reviewed algebraic solutions to equations involving exponential and logarithmic transformations, as well as subtle domain restrictions (e.g., given f(x) = x^2 and g(x) = sqrt(x), f(g(x)) = x, but x must still be greater than or equal to 0 due to the restriction imposed by g(x)). We also derived the proof of the rotation transformation in 2-dimensions, in order to better understand how a hyperbola might be rotated around the origin. Given a rotated coordinate system XY and the "natural"ù coordinate system xy, this involves representing an XY function in terms of xy through algebraic substitution. We also used his current chapter in AP Biology as a springboard for a discussion of memory and learning. I specifically asked him about his understanding of memory, and how he attempts to learn and remember the new material he reads. He said that he simply reads it and tries to remember what he read. I explained that there is a common misconception in our culture that memory is automatic or genetic or just sort of happens on its own, when memory is actually a skill that can be practiced and improved like any other. I then elaborated on ways to improve memory. First, I mentioned the importance of appreciating hierarchy when trying to learn and remember new information. I explained this by pointing out that we will never make it through the simplest of short stories if we insist on understanding every detail of the mechanics of the car the main character drives, and the coffee he drinks, and the newspaper article he reads on page two. In other words, we are constantly attempting to understand big pictures without having enough time to understand the details of all the little pictures that form the big ones. Given this reality, we must learn general processes, i.e., the skeleton of a story, before we can really start to see how all of the little processes come together, even though we don't necessarily know exactly what the little processes are. This means that we must always come to understand complex material by passing over it many times, first taking in the most general relationships, and then slowly expanding our understanding of the details that connect those general relationships. Then we slowly expand our understanding of the details that connect the first set of details... etc... and it is through this process that we come to understand the deeper connections of dense material over time. To put this concept a little differently: our general understanding of any relationship is always a necessary foundation for our detailed understanding of that relationship. In short, we must accept that reading the same material multiple times is often a necessary component of learning that material deeply. Only very simple subject matter can be comprehensively understood at first glance. We also discussed the power of associative memory techniques. I mentioned that when learning new information, it is helpful to think of that information in many different ways, even using different senses. In other words, the linguistic, visual, aural, practical, and emotive nature of new information should always be given attention. This practice will create additional pathways to the same memory, thereby increasing the likelihood that we can find a way to recall that memory. Relating new information to our sense of personal identity is also one of the strongest ways to improve storage and recall. I concluded by briefly mentioning Joshua Foer and his research on memory competitions. Foer interviewed many "memory athletes"ù and asked them how they perform such incredible feats of memory. He discovered that most of them do so through ancient memorization techniques which intentionally incorporate our spatial memory in the storage and retrieval of data. They almost universally claimed that they were not uniquely gifted and that they are utilizing a well-practiced skill in order to remember information as well as they do. Skeptical and eager to test the limits of these techniques, Joshua practiced aggressively for a year. After learning the technique, he returned to one such competition as a competitor instead of a journalist, and in 2006, he won the United States Memory Championship. I encouraged the student to look into Joshua Foer's story and the "memory palace"ù learning strategy.

This was my first session, and we pretty much went straight to work. The student had a worksheet for homework that was over simplifying variables with exponents. The sheet was double-sided and progressed in difficulty. He slowly worked through the sheet, but finished with about 20 minutes left. I did give him a short break in the middle so he wouldn't be burned out. I made one last problem to do, which combined everything we had practiced. He got through the whole problem. Concept-wise, he got everything correct. He is taking three math courses currently to catch up with other classmates and be on the same grade-level. I talked to him about what subjects he does enjoy and some hobbies he has. Math used to be his favorite subject, but now due to difficulty, is his least, while literature switched from difficult to favorite. I told him I'd try to bring problems next time that were more relatable to the real world and hopefully more exciting.

This evening, the student and I worked on a couple of word problems he procured from his classwork. It was a slow go in the beginning, as we took some time to figure out the best methods to answer each problem visually. He seemed a bit rushed and hasty in the beginning of the session. But once we tackled those problems and moved onto his homework, I noticed a pattern. He seemed to be getting tripped up on dealing with fractions. Namely, converting numerators after identifying the lowest common denominator. But with some practice exercises I wrote up for him and introducing a few drills to convert mixed numbers, he seemed to really take on an understanding of the processes. It was nice to see. He's a quick study, once he opens up about what his weaknesses are.

The student got a 49/50 on her most recent algebra test on conics - phenomenal work on that! - and things are going well in the current subjects (exponentials/logarithms). She had some confusion on the current chemistry content, so we spent most of the class discussing that - light waves, light energy, the Bohr model of the atom/energy levels, spectra, electron configuration, etc. We went through all of her worksheets and by the end she was doing an excellent job of describing excited state configurations, and listing the ground configurations of elements from the periodic table. She asked some great deeper-learning questions about how electron configurations relate to valence shells and the "full valence desire" that atoms have.

We reviewed an assigned review packet and reviewed a previous quiz to examine where the student lost points. He understands material, but tends to lose points due to little mistakes. We discussed slowing down and ways to double check in the middle of the problem.

I really enjoyed working with the student! We went over what to expect with the PSAT and how it has changed over the last year. We also discussed strategies for the Reading and Writing/Language section of the PSAT. I have asked her to employ the strategies we discussed as she completes the Writing Section and the Reading Section of the Sample PSAT. We will go over the answers and discuss missed questions next time we meet (on Wednesday). I will also be sending her several resources to review (grammar resources and reading comprehension resources). Next week we will discuss strategies for the Mathematics section.