This course is for students wanting to improve their analytical and problem solving ability. The course is particularly recommended for Chinese students who would like to study at a Western university.
In the course, students learn to solve problems in the Right Way -- not just get the right answer. Students are introduced to advanced problem-solving strategies and heuristics normally not taught until the undergraduate or PhD level.
Right Way Thinking is particularly useful to Chinese students because it can help them avoid academic failure at the university level. Studies show that Chinese university students begin their studies about three years ahead of their western classmates, but that westerners quickly catch up. In this course, we discuss the causes for this, and how to prevent it from happening.
Thinking in the Right Way
For an example of Right Way thinking, take the following problem:
Ball and Bat
A baseball bat and a baseball together cost $1.10. The bat costs $1.00 more than the ball. How much does the ball cost?
There are three main solutions to this problem:
1. The fast intuitive answer: 10 cents
The initial answer for many people (regardless of education) is ten cents, or $1.10 - $1.00. In this course we discuss why both western and eastern people fall into this trap, and how best to avoid it.
2. The algebraic answer: 5 cents
The problem can easily be solved using algebra. Using cents as units:
Bat = Ball + 100
Ball + Bat = 110
Ball + (Ball + 100) = 110
2Ball + 100 = 110
2Ball = 10
Ball = 5
This algebraic approach is typically taught in middle school and high school, and is what Stanford students call "plug and chug." Like using a calculator, this method of symbol manipulation can arrive at a correct answer without real understanding. And although this method may be fast for simple problems, it becomes tedious, time-consuming and error-prone as problems become more complicated.
3. The Right Way answer: 5 cents
This Right Way method begins with two insights.
Insight 1: the dollar can be removed
Insight 2: The price of the ball and bat in the new problem are equal.
Now the solution can easily be calculated:
2Price = 10
Price = 5
In this "right way," the problem is simplified first, before the calculation is begun. This simplification step is vital as problems become more complex.
Right Way thinking is already taught in Singapore, where is is known simply as "Reasoning," and forms the foundation of Singapore Math. In Japan, Right Way thinking is called "Sui Ron" (Thinking), to distinguish it from the lower level "Kai San" (algebraic calculation). In our course we present an advanced version of these topics.
Avoiding university-level academic failure (or "plateau")
Chinese high school students, for cultural reasons, are far better than western high school students in algebra. This Chinese excellence, however, becomes an ironic detriment at the university level. While western students are forced to learn simplifying heuristics (the core of Right Way Thinking) in order to meet the demands of the university curriculum, Chinese students persist with their powerful algebraic techniques. This only works for so long, however, and as problems continue to increase in difficulty, the Chinese advantage evaporates.
Early exposure to Right Way thinking, including ways to balance it with a straightforward algebraic approach, is therefore crucial for any student who would like to avoid this common university-level downward spiral so many Chinese students face.