New ways to look at an old problem

Effective problem-solving consists of two steps: 1. identifying the problem and 2. selecting the appropriate problem-solving strategy (i.e., a plan of action used to find a solution). Humans use four problem-solving strategies:

A revisionist approach to Jean Piaget's theory of cognitive development has brought new insights that challenge and reinterpret his established ideas. Piaget proposed that the formal operational stage, emerging in adolescence, represents the culmination of cognitive maturity. During this stage, individuals are said to develop abstract thinking, engage in systematic problem-solving, and show a form of egocentrism, believing others are as preoccupied with their behavior as they are themselves.

Cognitive learning is based on purposive behavior, incidental learning, and insight learning.
E. C. Tolman's theory of purposive behavior emphasizes that much behavior is goal-directed. He argued that to understand behavior, we must look at the entire sequence of actions leading to a goal. For instance, high school students study hard, not just due to past reinforcement but also to achieve the goal of getting into a good college.
Tolman introduced the idea that behavior is influenced by...

A parallel-plate capacitor with capacitance C, whose plates have area A and separation distance d, is connected to a resistor R and a battery of voltage V. The current starts to flow at t = 0. What is the displacement current between the capacitor plates at time t? From the properties of the capacitor, what is the corresponding real current?
To solve the problem, we can use the equations from the analysis of an RC circuit and Maxwell's version of Ampère's law.
For the first part of the problem,...

In cross-sectional research, a researcher compares multiple segments of the population at the same time. If they were interested in people's dietary habits, the researcher might directly compare different groups of people by age. Instead of following a group of people for 20 years to see how their dietary habits changed from decade to decade, the researcher would study a group of 20-year-old individuals and compare them to a group of 30-year-old individuals and a group of 40-year-old...

Water flow in open channels is often measured using hydraulic structures such as weirs, which allow precise calculation of discharge. In a rectangular channel, flow rates are measured using three types of weirs: rectangular sharp-crested, triangular sharp-crested, and broad-crested. The weir head is set at a fixed height above the channel bottom, simplifying calculations and enabling the relationship between depth and flow rate to be analyzed.For the rectangular sharp-crested weir, the flow...