Sunday, October 08, 2023

Handle the Stupid Stuff

No amount of test prep tutoring, practice, careful review, or lost Saturdays and Sundays can make up for lack of sleep the night before test day. 

Put simply, sleep deprivation is death to test scores.  Without sufficient sleep, all that effort and personal sacrifice go right out the door.

It’s vital that students give themselves the best possible chance of success on test day. “Stupid stuff” can sink math scores like nothing else, and must be assiduously avoided.

Don’t ruin you score over stupid stuff!

To perform at your best, you should:

1. Get eight to nine hours of sleep on each of the three nights immediately preceding test day.

2. Drink extra water on each of the three days immediately preceding test day.

3. Go to bed 30 minutes early, and get up in the morning 15 minutes early, on each of the three days immediately preceding test day, using the extra waking minutes to study your most important test prep notes.

4. “Night before, stuff at the door.” Before going to sleep on the night before the test, put all the things you’ll need at the front door, so you won’t forget anything (admission ticket, pens/pencils, snack, calculator, laptop, etc.)

5. Eat a normal breakfast on test day, with protein for extended energy. But don’t get too full (digestion can drain energy). Drink a glass of water, use the bathroom, and bring a small snack (e.g. a power bar) to eat during breaks.

6. Don’t sit during breaks! Get up and stretch, walk around, relax, and think about other things (to recharge your body and mind).

7. Leave in time to arrive at the test sight at least 15 minutes early.

8. To provide extra motivation and “Winning Focus,” write the name of your dream college atop your test page or scratch paper. Glance at this note when fatigued, and dive back into the test with renewed vigor.

9. If you’re preoccupied with anything upsetting, procrastinate dealing with it till after the test. Put the negative experience entirely out of your mind. You can deal with it later.

10. If you find yourself stressing out during the test, break the pattern of anxiety by taking three deep, slow, “belly breaths” and/or subtracting by sevens from 100; then re-focus on the test question right in front of you. 

-----


Copyright © 2006-present: Christopher R. Borland. All rights reserved.

Sunday, October 01, 2023

dSAT Math Topics

After trying and failing to find a comprehensive online resource that thoroughly detailed math content covered on the dSAT, I finally decided to put together my own. I've also written a companion piece on dSAT Reading and Writing Topics.

Questions in the Math section of the dSAT cover four broad topic areas: Algebra, Advanced Math, Problem Solving and Data Analysis, and Geometry/Trigonometry.

The entire Math section is 70 minutes long with 44 multiple-choice questions.

-

Modules

Two math modules:

Each module is 35 minutes long, with 22 questions (1:35 per question)

75% multiple choice (33 questions), 25% student produced response (11 questions)

30% in-context word problems (≤ 50 words)

Progressive difficulty (easiest first, hardest last)

Calculators are allowed – but don't use a handheld – learn to use Desmos, instead

Questions from each topic area appear in each module
-

Algebra

35%: 13-15 questions total

Linear equations in one variable (analyze, solve, create)

Linear equations in two variables (analyze, test, solve, graph, create)

Linear inequalities in one variable (analyze, solve, create)

Linear inequalities in two variables (analyze, test, solve, graph, create)

Linear functions (create, analyze, interpret, graph)

Linear systems of equations and inequalities (create, analyze, solve)

-

Advanced Math

35%: 13-15 questions total

Equivalent expressions (including algebraic fractions)

Non-linear equations (solve): absolute value, quadratic, polynomial, exponential

Non-linear functions (create, analyze, interpret, graph): absolute value, quadratic, polynomial, exponential

Non-linear systems (solve)

-

Problem Solving and Data Analysis

15%: 5-7 questions total

Ratios, rates, proportions, units

Percentages

Analyze and interpret one-variable data: distributions and measures of center and spread (mean, median, mode, range, standard deviation)

Analyze and interpret two-variable data: models and scatter plots

Simple probability

Conditional probability (from a data table)

Inference from sample stats and margin of error

Evaluating statistical claims: observational studies and experiments

-

Geometry and Trigonometry

15%: 5-7 questions total

Perimeter, area, volume

Lines, angles, triangles

Right triangles

Trigonometry (SOH CAH TOA)

Circles

-----


Copyright © 2006-present: Christopher R. Borland. All rights reserved.

Friday, September 08, 2023

The Backward-Forward Method

Unfortunately, little or no time is spent in most math classrooms discussing "heuristics," the art of problem solving. 

This often leaves students grasping at straws, struggling even to know where to begin when staring down an unfriendly, unfamiliar math question.

George Pólya's How to Solve It is a classic on this subject, required reading for all serious math students.

In another classic, How to Read and Do Proofs, author Daniel Solow advances a powerful problem solving approach he calls the “Forward-Backward Method.” 

I’ve found it helpful in my own teaching and mathematical work to reverse the method, first thinking backward from the ultimate goal to various subgoals which, if achieved, would enable direct progress to the original objective.

Whether writing complex proofs or tackling simple algebra problems, this “Backward-Forward” process provides students with a simple yet powerful structure for solving problems.

Just as an archer would prefer to move the target closer, so can a math student make a problem easier by finding a nearer target to shoot at. The next step would be to think further backward, to find another even closer target tied directly to the first, and so on. These subgoals are set by repeatedly asking the same question: “What would I need to know to find that?” And then “What would I need to know to find that?” Subgoals should be written down, to keep the trail clear.

After looking backward as far as possible, it’s time to reason forward from each given fact, with the last subgoal in mind. A different question governs the forward process: “What can I imply from that fact?” And then “What could I imply from that?”

Eventually, forward progress enables us to hit the target. All that’s left is to follow the string of subgoals up the ladder to the desired result.

-----


Copyright © 2006-present: Christopher R. Borland. All rights reserved.

Friday, September 01, 2023

Bring a Mouse to the SAT

Most people find use of a mouse to be a time saver, especially if you’re accustomed to employing one.

On the digital SAT, every second counts, and use of a computer mouse can save time on this important assessment. 

The College Board allows use of a "USB A" mouse (wired or wireless) with mouse pad on the digital SAT. Practice taking digital SATs at home using your favorite mouse. Then bring the same mouse with you on test day, plug it in, and go. Don't forget to bring a small mouse pad, as well.

This seems like a minor detail, but there’s almost no such thing when it comes to high-stakes testing.

-----


Copyright © 2006-present: Christopher R. Borland. All rights reserved.

Tuesday, August 08, 2023

How to Handle Super-Hard Questions

For high scorers, only the hardest problems near the end really matter. That’s where top math students get lost, waste time, feel stress, and lose points.

How to avoid freaking out over crazy-hard questions?

Three concrete suggestions follow.  

1. Handle intimidation

It’s normal to feel intimidated by a long, wordy, or complex problem. Most of the time, however, you’ll be able to answer the question correctly in a reasonable amount of time, if you give yourself a chance. Always approach such a problem with the mentality that you can solve it. Boil down the question. Reread and make sure you understand each sentence, part by part. You probably can, in fact, do this. If you slow down a bit, read carefully, take notes, and focus intently, you’ll be successful most of the time.

2. Dodge nightmare questions

Instead of getting hung up on an unsolvable problem, it’s better to surrender, as quickly as possible, and live to fight another day. Prevent the wasted time, loss of energy, frustration, and stress caused by battling impossibly difficult “nightmare questions.” The fight isn’t worth it. Avoid the bottomless pit. Earn points somewhere else. Once you realize a question is over your head, just guess and move on. Do not come back later, even if you have time.

3. Employ Skip-Guessing

Naturally, top students want top scores, and often assume they’ll have to work hard to crack every single question. But this is not true. Students can generally afford to skip-guess lots questions without worry (to confirm this, study the scoring tool for any official practice test). When faced with an uncomfortably difficult question, don't get stuck, whatever you do. Quickly make your best guess, skip the question for now, flag it for later review, and move merrily along. 

What matters is making the utmost of what you’re able to do on test day. To optimize your score, spend your limited time where it can be maximally effective, not on crazy-difficult problems you’ll just get wrong, anyway.

-----


Copyright © 2006-present: Christopher R. Borland. All rights reserved.