Middle school math student

Jules displayed significant improvement this week in the math unit we have been working on together. She worked carefully and confidently, remembering not only the new content she has learned but also the test-taking techniques (such as ballparking, process of elimination, drawing and labeling figures, and underlining/ annotating word problems) we have been discussing. They should serve her well in her upcoming assessment.

Jules remembered how to calculate perimeter, area, and volume. She also felt more confident completing multi-step problems, such as solving for a side length and then the area of a figure, or solving for the width and then a perimeter. Triangles were also easier for Jules this week: she better understood the difference between an isosceles and equilateral triangle, grasped that triangles contain 180 degrees, and easily solved for the third angle when given two angles in a problem. We also reviewed how to calculate the area of a triangle and, using the whiteboard feature, Jules and I were able to explore together why it's 1/2 base times height, since the (right) triangle is essentially ½ a rectangle .

Jules said she felt a bit confused by the coordinate geometry introduced in math class today, so we reviewed the basics of the x-y axis. We then moved on to independent probability, which Jules quite enjoyed. We discussed how to calculate the probability of choosing a yellow or a red marble out of a bag of colored marbles, then completed our content review doing problems using charts and graphs. Early in the session, Jules said she was still struggling with these sorts of problems in class, but once she read through the text accompanying the charts and the data itself, underlining and annotating key data and making her own diagrams when needed, Jules was able to answer all of these questions correctly. I reminded Jules that she is a far more capable math student than she sometimes believes and asked her to continue to try revising this self-concept.

Jules and I also practiced word problems and reminded ourselves that word problems are also reading comprehension problems. Often the math itself in these problems is not difficult – the challenge is figuring out what the question is asking and which operations to employ in answering it. For example, when working on the first word problem of the day, Jules initially struggled to understand what the problem was asking her to do. Her first impulse was to multiply, but as we talked through the problem and looked closely at language, she noticed that the rate would be in “packages per day” and that she thus needed to divide. Otherwise, Jules did a good job reading carefully and annotating key bits of information. Jules made a few calculation errors that we identified and corrected in real time; the errors were mostly related to flagging concentration. We discussed monitoring focus and concentration and techniques for re-focusing when needed.

Jules and I ended the session talking about the progress she had made this semester and revisiting, once again, how helpful it will be for Jules to continue to challenge the notion that she is “not good” at math and allow herself to stay open to the possibility that she is, in fact, quite good at math. We discussed that fact that just because we believe something about ourselves does not always make it true. Jules is starting to see this. It is always exciting when students begin to glimpse that they are capable of so much more than they previously realized.

Middle school test-prep student

Tim is doing a wonderful job augmenting his vocabulary. He's retained all of his a-words, b-words, c-words, and now we are on d-words. His four words for today are “demolition,” “discern,” “docile,” and “endorse.” Tim had a working definition for more words today than on any of our previous days, correctly defining the words “descendant,” “devious,” “devout,” and “disuse.”

Tim is still having trouble determining a word’s part of speech, but we are practicing this each time we meet. Today, we did a deep dive into nouns. Tim understands a noun as the kinds of things he “can find in his room” but is still working to understand that ideas can also be nouns and also that certain verbs can be transformed into nouns called gerunds. When Tim first attempted to classify the word “swimming,” he said it was a verb, which allowed us to talk about the way in which grammar is about much more than isolated words and memorized definitions; rather, it is about the way different parts of a sentence relate to each other and the job each part of the sentence is performing. Once we discussed this, Tim could see that in the question at hand, “swimming” was functioning as a thing, whereas the word “enjoy” was the verb in the sentence. We also touched on how good grammar can clarify messaging, and bad grammar can obscure what we are trying to share, which seemed to resonate with Tim and deepen his interest.

We then switched to math, taking a look at fractions, reviewing how to multiply and divide them. Tim completed all of the problems on Practice Drill 10 correctly, a very nice improvement from just a couple weeks ago. Next, we moved on to decimals, reviewing how to add, subtract, multiply, and divide them. He did very well on Practice Drill 11. His few small mistakes were due to rushing, both in reading the questions and in his calculations. We discussed this, as well as how to employ his new skill of metacognitive awareness to track whether he is working carefully or losing accuracy because of feeling anxious or rushed. We also worked on ways to refocus and relax when he senses he has become distracted.

High school test prep student

Marie did terrific work today! We spent today’s session working on the essay section of the ACT. As you know, we have been using the essay section as an opportunity to develop and strengthen Marie’s academic writing skills: how to articulate a compelling argument, how to gather and present evidence, how to write a thesis statement and topic sentences, and how to ensure the essay presents a unified, and compelling argument. We have also been working on strengthening Marie’s writing on the sentence level, looking at such things as grammar, word choice, and style.

Our time today was devoted to helping Marie read multiple prompts, then brainstorm, develop an argument, list possible evidence, and then write a thesis statement and accompanying topic sentences. This is the road map of an academic essay, and many students never reach a point where they can reliably produce one, which leaves them wandering through the essay. Marie is gaining confidence in her ability to both come up with an argument and articulate it clearly. We revised one of her thesis statements multiple times to ensure that the language was clear, precise, and grammatically correct, and to ensure that it contained the whole of what she will be arguing. These multiple revisions of a single thesis sentence also helped Marie to begin to see the power of revision, and how writing can improve dramatically simply through working and reworking it. On a timed test such as the ACT, she will not have the opportunity to revise in this way. But she will grow as a writer and gain an understanding and a mastery of the writing process through incorporating rigorous revision into her test prep. For next week, I have asked her to write and revise 3 thesis statements from today’s session and to bring her revisions to our next appointment. I have also asked her to write the introductory paragraph for one of them, as we will begin working on introductions next week.

Marie and I spent the last few minutes of the session discussing some of her initial ideas for the Personal Statement. I reminded Marie that what she writes about is less important than what she reveals about herself through her chosen topic. The topic itself does not have to be dramatic or grand. Students have written profound essays using ordinary experiences as the vehicle. For next week, I have asked her to spend some time thinking about what essential quality about herself she wants to use the essay to communicate. This will guide our next brainstorming session.

High school economics student

John and I had a wonderful session this afternoon. I wish him all the luck on his next econ quiz, though it don’t believe he’ll need it!

We started the session off by discussing his current textbook chapter “The Costs of Production.” John had a terrific grasp of total revenue, total cost, and profit. Second, we examined the various ways of thinking about cost, including explicit costs, implicit costs, opportunity costs, and the cost of capital. John was able to articulate the ways in which distinguishing between implicit and explicit costs is what leads to different concepts of profit: economists include all opportunity costs when analyzing a firm, whereas an accountant only cares about explicit costs. This inevitably leads to economic profit always being lower than accounting profit.

Discussing these various types of costs also led us to better understand a firm’s production function, which is the relationship between the quantity of inputs used to make a good and the quantity of output of that good. John gave a fabulous example in relating the story of Caroline’s Cookie Factory! As John prepares for tomorrow’s quiz, I recommend he review our Whiteboard notes on a firm’s production function and its total-cost curve.

We ended the session by taking a look at two practice short-answer essays John wrote in advance of the session. The first defined a competitive market and how it impacts the revenue of a competitive firm and included a good discussion of the relationship between total revenue, total cost, profit, marginal revenue, marginal cost, and the change in profit (MR – MC). His second piece covered the difference between a firm shutting down in the short run and exiting the market in the long run and concepts such as fixed costs, fixed and variable costs, short-run supply curve, and marginal-cost curve. John’s ability to communicate his ideas through clear, correct writing continues to improve. His short essays were organized and laid out his answers in a convincing fashion. He continues to struggle a bit with run-on sentences, comma usage, and pronoun-antecedent agreement. We discussed the errors he made and he was able to correct each of the sentences and explain why the revisions were correct.

Doctoral writing student

Congratulations on a very productive session! You were an outlining champion. You got a solid outline down for your paper, one that includes a strong thesis and very specific topic sentences, as well as a plan for integrating your research, and you are now ready to start writing your first draft.

You also highlighted the places in your outline where you need to do more research. Make sure you stick to doing additional research only on the topics you highlighted and not getting sidetracked, and remember that the goal of research is to find answers to the specific questions you have identified as essential to your argument. You are working towards a complete first draft prior to our next session. And remember: it doesn’t have to be perfect. It just has to be done. You can, and will, revise it multiples times – but you can't revise what is not yet written.

You were also able to articulate a successful process for producing outlines for timed essays on your upcoming exams. As you communicated that to me, your process will be to 1) read the question twice to make sure you understand what it is asking; 2) brainstorm answers to the question as you read through your notes; 3) choose the best of the answers; 4) mind map that answer; 5) use the mind map to develop an outline. You did all of this and produced an outline for Question 2 in 20 minutes in session today, which was exactly your goal. It wasn’t an accident. It was an outcome of your process. You can do this!

We will continue working with this as you head toward your finals. As I said at the end of our session, students sometimes focus exclusively on content when preparing for essay exams, thinking that if they have mastery over course content, successful essays will naturally follow. This is not necessarily the case. It is as important to prepare and practice a process for taking the test as it is to master the concepts the test will address.