Award-Winning Tutors in River Edge, NJ

It was a pleasure meeting and working with the student today. He is an exceptionally polite and good-hearted young man. Thankfully, he is much more frank than most students his age that I've work with. This makes getting a "window into his head and his thought process" easier. I believe we will learn much as a team. The student is more organized with his class materials than I anticipated; his binder and notes system seems to be well-designed (I especially appreciate how everything is three-hole-punched and chronologically arranged). Although he has yet to make note-taking personalized and discernible, he appears to be jotting down for the majority of math classes. It may be that establishing momentum in note-taking and developing a routine has been hard, in part, because the presentation mode in his math class changes frequently: one section will be taught on the whiteboard, the next via video lectures, and another using PowerPoint presentations. He hasn't had the change to establish much of a note-taking rhythm or habit. So, overall his study skills are not terrible, though there is room for improvement. Moving on to the actual pre-algebra content, he attests to having the toughest time with word problems. Without exception, students who struggle with word problems are those who think of math in terms of procedures rather than concepts. Procedural understanding (steps, methods, rote memorization's, etc.) work well during elementary math, but conceptual understanding is required for algebraic thinking. His tendencies for rote procedure came out in many ways. For instance, when I asked him to explain his reasoning behind writing an equation in a certain way, he would say something akin to: "It's either a multiplication or a division problem, and if I write it as multiplication it doesn't get the right answer so it's division." On the next step, he might switch a variable to the other side of the equation to get it to "work out right," without a conceptual reasoning to justify the step. I could list more particulars, but the bottom line is that a conceptual framework for understanding and manufacturing equations hasn't yet been established. So, I took a problem and modeled to him what it looks like to explain, conceptually, why an equation makes sense the way it's written. Then I asked him to apply similar reasoning to a word problem I made up that was similar enough, but distinctly different in its details. He gravitated to the exercise and, in his explanation, showed me (for the first time of our session) a conceptual understanding of what a variable "stood for." He lit up in understanding that an equation merely shows two quantities that represent the same thing (e.g. total cost or "Lana's age") in different ways. He showed in two later problems that he understood this new way of conceptualizing word problems, starting with identifying a variable and what it stands for. It will take much more practice to make second-nature, but today was an excellent start in this direction. He is very quick on the uptake, and he showed me that he was brighter than I was initially giving him credit for (explaining in too much detail or too slowly). (His unconscious posture/eagerness gave it away.) We will work on slowing him down in order A) to understand new concepts more deeply, and B) to avoid errors (e.g. leaving off units). I will have much more to say over the coming weeks, but I believe I got a good "feel" for his current level of understanding, his study habits, and his learning style. I look forward to continue working with him! He's a great kid.

The student has a good sense of when her answers are wrong, which is a good skill to have because it decreases the chance of falling for trap answers. She came across a few problems where she knew what to do, but made algebraic or small conceptual errors that she couldn't fix on her own. She gets most questions right with a few helpful hints. The student is still challenged with answer questions directly, but she is starting to find alternative ways to answer problems, like guess and check and plugging in answers. This can be a very helpful skill to have for multiple choice answers, but I made sure that we went over how to solve more directly, in case she needs to work with similar concepts on parts II, III, or IV.

In addition to analyzing a whole bunch of critical reading passages, the student and I worked on reviewing some more esoteric math concepts. We went over problems that involve the degree of a polynomial, the equation of a circle, imaginary numbers, and the diagonal of a prism. He was able to solve all of the problems once he was reminded of the formula and/or conceptual framework. He showed some improvement on critical reading passages and fill-in-the-blanks. Paired passages are a weak spot for him, but he has adopted solid test-taking techniques that will hopefully allow him to boost his score. At the end of our session, he said that he is going to go into the SAT feeling much more confident than before.

The student reported a 95 on her last test (awesome!) and knew what her small mistakes were. We reviewed math problems in her SAT book covering scatter plots. She did well, and she is very intuitive, but for math tests, she would be well-advised to slow down and make sure she is organized.

The student and I continued our work with the heart, veins and arteries. He said he was struggling a little on deciphering the arteries and veins on the outside of the heart. With a little more help and practice he felt more confident. We went over veins and arteries on a model and I quizzed him on tracing the pathways. Overall, the session went great.

Today, I helped the student with the basics of factoring binomials, trinomials, and harder polynomials. He was calm, polite, attentive, and very responsive. He was very active and willing to learn, and he always asked questions whenever he felt the necessity. I used the easiest strategy to help a person learn about factoring polynomials. I taught him to break down a number or any terms into their lowest, starting with the prime factors. This would help him while using the "factor by GCD" method I taught him about sign convention to help him with the trinomial factoring.