A first draft at assessing problem-solving with Further Mathematicians.
- Find a problem, written in 1950 for university applicants to Stanford University
- Work on it with Tom, and then work on it a bit more alone.
- Distil the question to its bare bones
- Students work, at first alone, and then in front of 30 visiting teachers, on the problem.
- After noticing how hard the students found the task of generating questions from the prompts, I asked PHD students to do it too…
- Students analyse all questions that were asked, and start to analyse what makes a good question. Could you guess which were written by professionals and which by students?
We came up with the following rules for question generation:
Examples of good questions:
- What are the conditions required to create a 45 degree angle from the lines going through a square’s vertices? What would the collection of possible “45 degree points” look like?
- Suppose the squares have side length 1 – what is the largest possible perimeter for the triangles formed from the straight lines and the square (with the 90 degree angle still assumed)
Examples of poor questions:
- Is it drawn to scale?
- How can I link this to trigonometry?
- Are those squares?
7. After all of this warm-up, when the students saw the original question they were remarkably quick at finding the answer (once they had parsed the word-heavy question). Great recall of circle theorems. I made a toy on Geogebra to illustrate the problem