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Having tutored dozens of students in ACT and SAT Math and evaluating their scores before and after taking the test, I think it may be helpful to a.) quantify the effectiveness of tutoring for these tests and b.) summarize the differences between the tests.

There are four parts to the ACT exam, *Math*, Reading, English, and Science. There are three parts to the SAT exam, *Math*, Reading, and Writing and Language. Both the ACT and SAT have optional *Essay *exams.

**ACT Math: **The ACT *Math* segment consists of 60 problems with a 60 minute time limit. It is my observation that very few students are seriously hindered from lack of time as most finish with many minutes to spare. The problems, themselves, regard arithmetic, coordinate and plane geometry, intermediate algebra, and trigonometry. There is now no penalty for wrong answers so this has artificially elevated the scores from what they were several years ago.

A calculator is not *required* to answer any of the problems. On some problems, using a calculator is slower than not using one. Nevertheless, a *permitted calculator (ACT) *may be used throughout the test. I have found calculators to be so vital to today’s students that their presence is virtual Lorazepam.

The ACT Math scores are scaled from 1 to 36 using roughly a linear mapping.

**SAT Math: **The SAT *Math* segment is divided into two tests: *No-calculator* and *Calculator*. The No-calculator test is 20 questions (15 multiple choice) for which the student has 25 minutes. It is my experience that most students do *not* have sufficient time because they are embarrassingly inept at even the simplest calculations and have not the remotest ability to even add correctly without a calculator. (The platitude that this generation is the “brightest and smartest ever to grace the planet,” like so many other saws in modern education, is nonsense).

The *Calculator *segment is 38 questions (30 multiple choice) in 55 minutes. The non-multiple-choice questions on both tests require a computation and filling in a grid with the correct numerical answer. A *permitted calculator (SAT)* may be used on the Calculator test.

As with the ACT, there is no penalty for wrong answers. The SAT scores are mapped from 200 to 800, said mapping seems to be adjusted by the graders each year to allow for “complexity differences year to year” (read grade inflation).

*Who owns and creates these tests?* The ACT test is owned by a nonprofit company of the same name founded in Iowa City, Iowa in 1959. The SAT test is owned by the College Board, a nonprofit company (not a college) whose first test started in 1926.

*Who takes these tests?* For the most part the tests are taken during students’ junior year when the students are applying to colleges. ACT claims that 64% of the 2016 High School graduating class took their exam at least once. SAT numbers indicate that 47% of High School graduates took the SAT exam at least once. The percentages do not add to 100% because they are not related. Students can and do take either or both exams. Colleges specify which exam they utilize for evaluations, but students typically apply to several colleges. In addition, students can take either of the exams more than once and only the highest grade scored will be sent to the colleges (yes, again, read grade inflation).

*What about tutoring? *My experience (and data from students taking the test) is that tutoring typically can add 8 – 10% to the Math portion of the overall test. Taking the test multiple times also helps so that by taking the test multiple times, getting tutoring, and practicing, the final math score can be as much as 15% higher than the original score. These are my numbers based on students who attended college-preparatory High Schools.

*Which is more difficult, SAT Math or ACT Math?* While the ACT and College Board companies claim a similar level of difficulty, my students who have taken both tests are almost unanimous in ranking the SAT the more difficult math test. One reason for this is, of course, the No-calculator test, which sends them retching from this planet and reeling toward another.

What about the calculator portion of each test? How do they compare? I believe the SAT problems are still deemed the more difficult by students because they require the translation from logic into formula, whereas the ACT problems are more clearly worded and no “translation” is needed. There is no doubt what the ACT question is asking but you are sometimes left scratching your head as to what the SAT problem means. I do *not *think this has so much to do with English-as-a-second-language as I think it goes back to the fact that today’s students are not trained to *think*. (Keep in mind that I do teach High School physics, chemistry, and mathematics). By and large, students are accustomed to Study Guides whereby they memorize answers or “similar problems” to the test and echo them back as needed for a grade. They practice techniques in math without really understanding the underlying concepts. Actual *thinking* and *reasoning* about *concepts* is more complex than arithmetic manipulation alone. Here are example SAT/ACT problems related to the same subject that illustrate my point:

*SAT: Acceleration is the rate of change of velocity of an object with respect to the time interval of that change. The average acceleration of an object can be found by the formula shown here *

* a = (v_{f} – v_{i})/(t_{f }– t_{i}) *

*where the average acceleration is directly proportional to the change in velocity and inversely proportional to the interval of time. Which of the following represents the final velocity as a function of the other variables …*

*ACT: A train travels at the rate of 90 miles an hour for 2 hours and then travels at the rate of 60 miles an hour for 3 hours. Which of the following expressions represents the average velocity of the train …*

Need I say more?