Interesting Exponential Equation

Solve for x.

 

.....
will be true only if

x=1/2

.....true

or, simple write right side of given equation as
(sqrt(2))^(-sqrt(2))

since sqrt(2)=2^(1/2)

=(2^(1/2))^(-2^(1/2))

=(2^(1/2))^(1/(2^(1/2)))

=(1/2)^(1/2)^(1/2) ...........then

x^x^x=(1/2)^(1/2)^(1/2) => x=1/2

 

You are currently helping me with trigonometric equations. How do you remember the earlier chapters and sections?

 

I remember the earlier chapters and sections very well.

 

I know that you remember the early chapters and sections very. You also remember Calculus 3. I want to know what is the secret. How do you remember all this stuff?

 

what is the secret? there is no secret, it's memory

The secret of a good memory is attention, and attention to a subject depends upon our interest in it. We rarely forget that which has made a deep impression on our minds.

 

I agree. I also would like to say that understanding the concept, knowing the WHY and HOW something is done, is more important than answering tons of questions. This is what is lacking in the schools.

Students are being taught to be robotic and mechanical in terms of answering questions. This is ok but no one is learning. A week or two after taking final exams, students cannot pass the same test taken just a few days before.

Parents are not aware that this is precisely what is going on in the public schools in NYC. I can't speak for other states. By the way, I consider myself a victim of the NYC corrupt public school system. Students know how to solve, for example, 2x + 5 = 50 but they have no idea that this is a linear equation or what makes a linear equation. You say?

 

US public school system (public and private) missing most important ingrediency to be successful-oral or verbal exam
I'm familiar with the US education system, but I use to work in a country where, from the elementary school to the university, verbal tests and oral exams are mandatory, and I've administered oral exams for about 17 years.

Here is what an US teacher thinks about oral exam:
“An oral exam takes me about 30 minutes (including preparation and discussion afterwards). I have about 110 students in my class. Doing an oral exam for that class would take me about 55 hours. This is not the only class I teach. I teach about 5 classes per semester. In order to avoid some of the subjectivity my department requires that an additional staff member is present. So implementing this for my courses would take about 55*5*2=550 person hours. That is just not practical (not to mention that my colleagues won't thank me for the additional work I give them as they have to sit in for these exams).”

I know how long an oral exam takes because I did use it, as my colleagues as well. We did two oral and one written exam per semester. Why? Because you want to see how the student understand material when "put on the spot", so an oral exam is the best way to see it. The oral exam allows you to show that you understand your research, the literature and the subject as a whole. It provides you with an opportunity to demonstrate that you can talk about your work in a professional manner.

 

Define oral exam.

 

The oral exam (also oral test or viva voce; Rigorosum in German-speaking nations) is a practice in many schools and disciplines in which an examiner poses questions to the student in spoken form. The student has to answer the question in such a way as to demonstrate sufficient knowledge of the subject to pass the exam.

 

What makes you think this approach will work in NYC public schools? Students in NYC public schools get confused in terms of answering simple, say, job interview questions much less explaining what a limit is orally. Students in the NYC public schools are trained to answer THE SAME standardized test questions they will faced in the classroom when taking exams.

For example, Jerry has two boxes of 25 marbles. How many marbles does he have in all? Students are trained to answer this question and then tested on THE SAME question with the exception that the numbers used on the actual test are different. In this example, there are 25 marbles in each box. On the test question, there 15 marbles in each box.

Students remember the process in terms of working out the 25 marbles question in class and then they apply THE SAME method to the 15 marbles question and get it right. However, does it mean that they understand how to solve this problem? What if the problem uses variables in place of numbers? For example, Jerry has two boxes of x marbles. How many marbles does he have in all? Do you think they can answer this question if the teacher decides to orally ask in class? You say?

 

this approach works in all schools around the globe, why should not work here too

The oral exam is all about using questions to stimulate the recall of prior knowledge, promote comprehension, and build critical-thinking skills. It is an age-old practice and has been a cornerstone of education for centuries.

Teachers ask questions to help students uncover what has been learned, to comprehensively explore the subject matter, and to generate discussion and peer-to-peer interaction.
Student-initiated questions increase higher-order learning by requiring them to analyze information, connect seemingly disparate concepts, and articulate their thoughts.

Indeed, questions are ubiquitous, but are the right kinds of questions – ones that promote learning, not recall – asked at the appropriate time?
Poor questions can stifle learning by creating confusion, intimidating students, and limiting creative thinking.
Effective questions asked in a psychologically safe learning environment support student learning by probing for understanding, encouraging creativity, stimulating critical thinking, and enhancing confidence.

 

We should continue this discussion some other day. I want to take advantage of my days off to continue my precalculus review. Thank you for your input.