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Each point is on 7 lines, and there are 35 lines in all. The lines of PG(3,2) are identified by their Plücker coordinates in PG(5,2) with 63 points, 35 of which represent lines of PG(3,2). These 35 points form the surface S known as the Klein quadric. For each of the 28 points off S there are 6 lines through it which do not intersect S. [27]: 67
Ashby (1960, section 11/5) offers three simple strategies for dealing with the same basic exercise-problem, which have very different efficiencies. Suppose a collection of 1000 on/off switches have to be set to a particular combination by random-based testing, where each test is expected to take one second.
Problem solving is the process of achieving a goal by overcoming obstacles, a frequent part of most activities. Problems in need of solutions range from simple personal tasks (e.g. how to turn on an appliance) to complex issues in business and technical fields.
Traditional assessment would identify the last child as solving the problem correctly, while the children with mistakes or no answers would receive no credit. A dynamic assessment would place the children in three different categories: those who cannot solve the problem, those who can with help, and those who can independently.
Problem-based learning (PBL) is a teaching method in which students learn about a subject through the experience of solving an open-ended problem found in trigger material. The PBL process does not focus on problem solving with a defined solution, but it allows for the development of other desirable skills and attributes.
First, you have to understand the problem. [2] After understanding, make a plan. [3] Carry out the plan. [4] Look back on your work. [5] How could it be better? If this technique fails, Pólya advises: [6] "If you cannot solve the proposed problem, try to solve first some related problem. Could you imagine a more accessible related problem?"
Many students work in groups to solve them and help get a better understanding of the material, [6] [7] but most professors require each student to hand in their own individual problem set. Some professors explicitly encourage collaboration, [5] [6] some allow it, and some explicitly disallow it [3] or consider it cheating.
Each team is given a score out of 350 points: 200 from Long-term, 100 from Spontaneous, and 50 from Style. Style is scored from 1–10 in each of the five categories, and the Long-term and Spontaneous problems are scored according to each problem's individual rules.