Recent Tutoring Session Reviews
"The student seemed to really get the hang of division by 2's today, so we moved on to division by 3's. This paid off tons in her ability to reduce fractions, and though it still takes her a few minutes to reduce high-numbered fractions, she does it correctly, which is the most important thing. We worked on division and fractions during our math part of our session. We did our usual reading passage for our reading portion, and she flew through it, as always, and is now beginning to understand more difficult questions regarding tough concepts, such as "author's purpose.""
"Today we highlighted some areas of quantitative reasoning problems where the student can show improvement One thing we emphasized is the importance of isolating steps in word problems and breaking down a problem into "basic math" steps. One type of problem we worked on was rate-type problems and related unit conversion (i.e. how long it would take to make 5 dozen donuts if it takes x minutes to make one). We also talked about understanding simple arithmetic problems disguised with tricky diagrams. She seems to be especially responsive when sample problems connect to her; we had a lot of success today using examples like visiting her friend, driving to the city, and even having her move around to get more involved by counting how many steps it takes her to cross a room and then applying that rate to a bigger distance. For homework next time, I thought it would be a good opportunity to look at some of the vocab exercises in the Lower Level ISEE book; start with lesson one (p 42) and lesson 2 (48), but she should feel free to do more if they go quickly."
"Writing review: I reviewed the student's essay with him. I complimented his correct construction of compound sentences with coordinating conjunctions. Reading assignment review: He answered the multiple choice questions I prepared based on the two Bigfoot articles we exchanged, and I answered the questions he prepared. He followed all the requisite question forms we discussed in the previous lesson. First, we reviewed his answers to my questions. He answered 3/5 questions correctly without my help. He answered the question based on the factual content of the articles correctly. He also answered the true/false question and the "What does the word in this sentence mean?" question correctly. During our next lesson, I will ask him if he reread the article before the lesson. If he did reread the article after Friday, on Sunday morning, for example, then we need to do further work on retention and active questioning techniques. In future lessons, I will encourage him to read the articles closer to the lesson. Future lessons will also allow him to look back at the article. Skills for efficient look-backs will be taught as well. He is capable of achieving a high score on the reading comprehension section, and I want to be sure he does. We decided to exchange articles on another topic of his choosing-he chose another topic from cryptozoology: the yeti. Note: In future lessons, to incorporate writing practice and look-back strategies, he will write a summary of his chosen article. I would have asked him to write a summary for the next lesson, but I want to review the active vs. the passive voice in the next lesson, then ask him to monitor his writing style accordingly when writing a summary. In addition, I will also have him practice mapping-writing a restatement of the main idea of a paragraph in the margins-to practice verb-based active writing and to quicken his pace during look-backs. Math I made an assessment math activity for him based on our previous lesson. He was asked to solve two long division problems and then identify the dividend, divisor, and quotient in each problem. He was also asked to simplify 2 fractions (75/165, 120/1,200) showing all the factors for both the numerator and the denominator, to "simplest terms." He prefers mental computation to manual calculation (manual meaning "written with a pen or pencil" as his mental computation is usually accompanied by manual movement of his fingers to represent numbers). When asked to divide, he prefers to skip count; when asked to divided 120 by 14, he wrote 14 x 8 and then 14 x 9; he then wrote out the multiples of 8, up to 14, with my encouragement to "write out his thought process"; without such encouragement, he would have continued counting mentally, occasionally looking at his fingers. His mental calculations are often accurate but very time consuming, especially when he is counting to a three-digit number: he will sometimes skip count to a number higher than the dividend and is slower when counting in reverse than counting forward, as is only natural. I showed him manual long division as an alternative; he conceptually understood it but forgot steps in the sequence when he was completing the first problem. The second time he did manual long division, he still required verbal scaffolding of the third and fourth steps (divide, multiply, subtract, bring down). He was able to solve the problem successfully. This method of manual long division will be practiced in future lessons. He understands the concept of division, but his experience with alternate methods outside of skip counting appears to be limited based on his performance. He will be slower with manual division at first, but the acquired speed over time will make him a more efficient calculator and should also strengthen his mental skip counting skills. He did better when simplifying fractions, but he again required my prompting to write out the factors of each numerator and denominator when searching for the greatest common factor. I will teach him to write "factor diagrams" in the next lesson; hopefully, these will be visually appealing to him. He simplified the two fractions correctly, but it became obvious to me that he did not know "The Ten Rule" when he attempted to simplify 120/1.200. The ten rule states that "add a zero to the ones place of any number when multiplying it by ten, and the result is your answer." We made a vocab card for this concept and added it to his pile. It also became obvious to me that he was not yet fluent with "The Zero Rule," which states "any number multiplied or divided by zero is always zero," when we were solving a long division problem. After subtracting two numbers and getting a difference of zero, he thought the remainder in the division problem was zero, when zero actually needed to be divided by the divisor and was consequently part of the quotient. We made a vocab card for the zero rule and added that to his vocab card pile. He correctly identified the dividend, divisor, and quotient for each division problem. We also reviewed his vocab cards in a quick drill and practice activity. He correctly identified each term demonstrated by a visual example and gave a verbal definition of each term. I decided to begin review of ratios and proportions now. It is a popular topic on the exam, and it is closely related to division and simplifying fractions; that is, to identify a correct ratio that compares two numbers, a person often has to write the ratio as a fraction and simplify it. This overlap of skill practice with fractions makes the topic of ratios and proportions a natural next step in a math sequence. We read through examples that defined the terms ratio and proportion. He completed two problems. One asked him to write the relationship between two numbers as a ratio. The other asked him to find an unknown quantity in a proportion. He solved both problems correctly. He made a vocab card for ratio and another for proportion and added them to his math vocab pile. Ratios and proportions were introduced in this lesson. He grasps the concept of each well. I emailed him a ratio and proportion packet, which included definitions of each term, illustrative examples, and a math challenge question involving a proportion. The types of ratio and proportion questions asked on the exam will all be included in future practice math sessions. I decided against including any long division practice on the homework, given the amount of verbal and visual support he needs to learn the new method. I will review the steps with him frequently in the next lesson then ask him to do some problems independently once I feel he is capable of following all the long division steps without prompting."