Recent Tutoring Session Reviews
"The student and I spent the first part of our session addressing the skills she feels least confident about applying quickly in the mathematics section of the test: specifically, adding or subtracting fractions, finding the prime factorization of numbers, and working problems that require converting different units of measurement. We started by looking at the addition and subtraction of fractions that had the same denominator, ones where one denominator was a multiple of the other, and then ones where the denominators were completely different or where they had a common factor. For each kind of problem, we practiced finding a common denominator and then performing the appropriate operation on the numerator. It helped her a lot to think of the need for a common denominator in concrete terms. The example that seemed to make the most sense was that of having a bunch of grapes, then adding a few plums and apples, and needing to count the total pieces of fruit (as opposed to just the grapes *or* the apples *or* the plums). By the end of the time we spent working on this skill, she was able to add and subtract fractions with a variety of different denominators. She was even able to apply the principles involved to problems in which the fractions featured a variable in either the numerator or denominator. From fractions, we turned our focus to units of measurement. She was familiar with the basic concepts involved in measurement-based problems but didn't have much practice actually working with multiple units of measure in a single problem. We reviewed how many inches were in a foot, feet in a yard, and ounces in a pound using abstract numbers and diagrams and used the meanings of the prefixes deci-, cent-, milli-, and kilo- to review the metric system of measurement. For liquid measures in the imperial system, we were able to fill measuring cups with water to demonstrate the way that two cups make a pint and two pints make a quart. The idea of four quarters adding up to a dollar helped her remember that four quarts make up a gallon. We then applied these conversions to sample problems that required either calculating how many of one unit were in a certain number of larger units or that gave measurements in two different units but asked for operations that would require her to convert everything into the same unit, like finding the area of a 5-inch by 4-foot piece of cloth. Finally, we talked about prime factorization in response to a question that she wanted to be able to answer. Since she was already comfortable with the separate concepts of factors, multiples, and prime numbers, we went over how to combine those ideas in a way that would allow her either to identify or to come up with the list of prime numbers that are factors of a larger number. In the course of this exploration, I also offered her a quick way to determine whether any number is a multiple of three. Since we had some time left in our session after enough practice for her to feel confident that she'd gotten the hang of these math skills, we took a quick look at the verbal section. I showed her what kinds of questions to expect, and we ran through some sample questions of each type. She did an excellent job of classifying words and identifying synonyms and antonyms. We refined her approach to finding the relationship between two words for analogies questions. She only needed guidance in cases where spotting the most specific relationship between the words relied on a student's ability to choose the correct one of multiple possible meanings of one of the words. Likewise, she profited considerably from the incorporation of just one additional practice to her way of approaching verbal logic problems: when she sketched a quick diagram of the information presented in the first two statements, it very much helped her to clarify the information given and to evaluate the third statement based on it. On the whole, she did very well, and continues to show herself to be a bright student and a pleasure to work with."
"Continuing the model from previous sessions, I started this session with a mini-lesson on algebraic concepts and operations. The focus of the lesson was to show visual information and relate it to what happens in an expression/equation. To do this, I used a modern version of a scale, setting items on the scale, some with a known weight, and others without one. The scale would display an overall weight. I asked the student what would happen if a removed differing objects from the scale, and his answers demonstrated a good understanding of the concepts. From there, we proceeded to break down what was happening in different algebraic problems, referring back to the scale when needed. I focused heavily on knowing when to perform operations on both sides, when to simplify, and why each action required an opposite action to simplify/satisfy equations (such as dividing both sides by 8 when you have 8x on one side.) He is getting the concepts down better than before. With help, he can get through some basic Algebraic problems well."
"We moved our focus to math this week. The student has expressed an apprehension of math, so we will be focusing on it for the next few weeks. Fortunately, the student shows great aptitude in math. I believe this could even be his strongest subject. I only had to teach him one new algebra concept, and we spent the rest of the lesson correcting problems from his practice test so that we could identify the sources of his errors and strategize ways to avoid the same patterns. In general, the student performs very well when he slows down and writes out every part of a problem. He often only writes equations for part of a problem when he believes it is easy, but these are frequently the problems that he has a harder time with. I gave him some problems that were more difficult algebra and fraction equations than those on the test, and he had no trouble with them as long as he went through all of the steps in the equation. We will continue to reinforce this habit and finish the quantitative section in our next session."
"Focused on the placement test grammar and vocab sections, as he's done quite well on his math homework of late. Looked back at an older test a bit as well. Good session."
"We finished grammar review and analogies. We also did some mini-sections of the test, timed. The boys both did very well, despite a couple of small mistakes. The boys should have flashcards or a flash card app with words to be studied to help them with their vocabulary. They are going to try to take full tests before I see them again."
"We covered analogy questions pulled from the Internet; Exam PT 5 pp. 469-476 Quant. and Verbal. I emailed the student assignments for 11/10 and 11/13."
"The student and I discussed relationships for words in analogies. In the prep book, she completed exercise 1 with my guidance. She completed a spelling city activity online about analogies, and completed them independently with 100% accuracy. We moved on to reading comprehension and discussed test taking strategies for the placement exam. I had her complete an exercise from the prep book, which she completed with 50% accuracy. We went over the questions she got wrong, and discussed techniques to find the correct answers. I had her complete the language section and reading comprehension sections in a practice placement exam. I asked her to email me her responses so I can look for patterns in errors so I can find areas to help her with in future sessions. After the practice exams, she completed a cloze passage online about pirates in order to try to build vocabulary. She completed this with 50% accuracy, and we went back and looked over the passage together in order to try to come up with "word attack" strategies she could use on the test."
"She took a practice exam in language and reading, then we went over the answers she missed. She has greatly improved in usage and vocabulary, but still struggles with spelling and reading."
"The student continues to improve her confidence. In my opinion, this test is completely about confidence and practice for her. She has gotten very good at reading comprehension. Her math is good and she is confident and attacks the problems. Her verbal is good as well. With a little more practice and confidence, she should excel in every area."
"We worked on a practice test. His vocabulary work is better, and we discussed strategies for narrowing down answers or "thinking about the question in reverse" when he is stuck. We skipped the reading comprehension section as the impression I got from previous work is that his comprehension is fine. We also discussed his tendency to overthink some of the words, going beyond basic definitions to ways they COULD fit. I reminded him that sticking with basic definitions are a must. Math logic is also fairly solid. We worked on rules that will help with the questions (degrees in the angles of a triangle, easiest way to work with fractions and decimals, shortcuts to calculating 10% and multiples thereof, etc.). We went over more of these questions to help solidify the various shortcuts. We ended in the middle of a problem solving section. Here he usually knows how to set up a problem. We will focus was on finding the easiest way."
"In this session we covered vocabulary words and made sentences using the words he defined. In addition, we covered verbal logic, which the student did fairly well on because of our vocabulary coverage. Afterwards, I asked some reading comprehension questions using a movie review article I provided. Then, we covered grammar, including sentence structure, parts of speech, parallelism, and how to fix errors in all of those areas."
"We went over the practice test the student did last week and then focused on math. For next time I assigned a language section."