I'd suggest that our American colleague is using examples and non-examples. The difference is that your method is honing in more specifically to the attributes and taking a stepped approach to that noticing and specifically what you want the learners to attend to.
I don't think you can determine which approach makes the learners think more, and the thinking isn't necessarily more visible but is more directed. You're being 'naughty' by asking 4. and 5. but I'll bite. I think the learners would enjoy the American colleague's approach and I would like it too!
2. In the method by the Americans there is more space for students to link back to prior learning
3. I'm not sure thinking is ever visible!!! You can measure everyone's learning of the fact better your way but I think that AFL step added to the Americans way they could have that too.
4. Depends on the class.
5. The Americans way! Sorry, Craig, I respect your work but I can't help but miss teaching these discovery lessons
The reality is the time your instruction takes up within a lesson is critical when you only have 50 minutes/an hour for the subject matter. Therefore I’d argue ‘quicker’ is certainly an important point.
I think given attention spans as well as the importance of independent practice, it's incredibly important to think of 'quicker'. Pace is probably my biggest weakness as a teacher. If the new learning takes too long, all the reinforcement, assessment, problem-solving etc get squeezed out.
I am a huge fan of vocabulary, and I find that students usually like knowing things that other people don't, and they also find it amusing when "normal people" believe something that is wrong (and this gives them a little sense of superiority).
Because of that, I teach them that "poly-" is Greek for "many" and "-gon" is Greek for "angle".
Hence, a "polygon" is a "many angled" 2-dimensional shape.
We can then have a discussion about curved edges, and whether a circle really is a "one-sided" shape, as many teachers seem to teach.
We can also have a conversation about the language... where else do you find "poly" (polystyrene, monopoly often come up) or "gon" (diagonal, even trigonometry comes up sometimes).
It also leads nicely into "-hedron" meaning "bases" for polyhedra, and why they must be 3-dimensional.
I also combine this with a big table of the Greek and Latin prefixes for the numbers, and say, "If anyone can find out why on earth we use Latin for 'quadrilateral', which means 4 sides instead of 4 angles, let me know!" The prefix table has a column of other words that use those prefixes. Having a language lesson in Maths makes a nice change, both for me and the students!
However, I very much like the use of examples and non-examples. I do this occasionally in other topics ("What is an irrational number?") but have never done it for polygons. I like that approach. Thanks.
With the American method there is always the danger that in a weeks/months time the student just remembers their own sorting criteria rather than the correct sorting criteria.
I'd suggest that our American colleague is using examples and non-examples. The difference is that your method is honing in more specifically to the attributes and taking a stepped approach to that noticing and specifically what you want the learners to attend to.
I don't think you can determine which approach makes the learners think more, and the thinking isn't necessarily more visible but is more directed. You're being 'naughty' by asking 4. and 5. but I'll bite. I think the learners would enjoy the American colleague's approach and I would like it too!
1. Your method quicker
2. In the method by the Americans there is more space for students to link back to prior learning
3. I'm not sure thinking is ever visible!!! You can measure everyone's learning of the fact better your way but I think that AFL step added to the Americans way they could have that too.
4. Depends on the class.
5. The Americans way! Sorry, Craig, I respect your work but I can't help but miss teaching these discovery lessons
I would not and do not think you should either consider 'quicker' when secure understanding is the important point.
The reality is the time your instruction takes up within a lesson is critical when you only have 50 minutes/an hour for the subject matter. Therefore I’d argue ‘quicker’ is certainly an important point.
I think given attention spans as well as the importance of independent practice, it's incredibly important to think of 'quicker'. Pace is probably my biggest weakness as a teacher. If the new learning takes too long, all the reinforcement, assessment, problem-solving etc get squeezed out.
I am a huge fan of vocabulary, and I find that students usually like knowing things that other people don't, and they also find it amusing when "normal people" believe something that is wrong (and this gives them a little sense of superiority).
Because of that, I teach them that "poly-" is Greek for "many" and "-gon" is Greek for "angle".
Hence, a "polygon" is a "many angled" 2-dimensional shape.
We can then have a discussion about curved edges, and whether a circle really is a "one-sided" shape, as many teachers seem to teach.
We can also have a conversation about the language... where else do you find "poly" (polystyrene, monopoly often come up) or "gon" (diagonal, even trigonometry comes up sometimes).
It also leads nicely into "-hedron" meaning "bases" for polyhedra, and why they must be 3-dimensional.
I also combine this with a big table of the Greek and Latin prefixes for the numbers, and say, "If anyone can find out why on earth we use Latin for 'quadrilateral', which means 4 sides instead of 4 angles, let me know!" The prefix table has a column of other words that use those prefixes. Having a language lesson in Maths makes a nice change, both for me and the students!
However, I very much like the use of examples and non-examples. I do this occasionally in other topics ("What is an irrational number?") but have never done it for polygons. I like that approach. Thanks.
With the American method there is always the danger that in a weeks/months time the student just remembers their own sorting criteria rather than the correct sorting criteria.
Practice makes permanent.