 weebecka: The axiomatic aspects of mathematics could indeed be organised in this way, with students taking tests as and when they are ready. If they fail they can retake them at an appropriate juncture and if they are struggling with the test the teacher can override the testing system and deem them to have passed. For each level they can be rated - working towards, pass or mastery.
Yes, that is a possibility - I admittedly haven't try to work out the logistics of such a system in any kind of detail. I would envisage that any given level, there would be a range of topics to cover (arithmetic, algebra, geometry, etc.), so that if a student is struggling with a particular topic then (s)he can always return to it later. If they need to focused one-to-one help to understand a topic, that could be provided. If the topic is not essential for further progress, then yes, a temporary waiver might be reasonable. But if it is essential, then perhaps alternative approaches should be tried to see if they are useful - or simply throw in the towel for a while and consider alternative subjects/activities until a greater level of maturity has been attained. weebecka: It could be organised in the way you have suggested although this is not always going to be practical to mix year groups, especially in a secondary school timetable - the larger number of sets make gradation with a year group more effective anyway.
Yes, I agree that timetabling could be a bit of nightmare in such a scenario. An alternative might be to have individualised teaching within each class. I am reminded of English classes in my primary school in Glasgow, where there was a box of colour coded cards, each with a comprehension passage, increasing in difficulty (a bit like Oxford reading tree, or similar). I can imagine Mathematics being taught in a similar way, where part of the time is given up to a mixture of "low road" and "high road" (sic) teaching covering the basics as well as extension topics, and the remainder of the time to students progressing through these worksheets at their own pace - they should be allowed to choose whichever subtopics they want based upon the prerequisites that they have mastered - though it should be ensured that all topics at level 3 (say) have been mastered before moving on to level 4. During this time, the students will beaver away quitely like angels and the teacher(s) will provide assistance and guidance whenever a student gets stuck. Ideally the worksheets will be in the style of Durell's textbooks from the 1930s. :) weebecka: I would add, Sabbir that there are aspects of a mathematics education which are best not taught and assessed in this way. Students' interactions with complex real life situations and their work with long, connected problems are best assessed by teachers rather than by tests. There is no need to strictly set the students according to attainment during this aspect of their mathematics education and indeed there are many benefits of mixing students with different prior exposures as doing so greatly enriches the conversation and cross teaching which takes place.
I see no harm in having a wide range of different problems and tasks set on the colour-coded cards - some could be quick drills, while others could be more project-like requiring significant exploration over two or more lessons (though these should not necessarily be made compulsory for all students). Anyway, this certainly seems doable - we could even make each worksheet a pdf file that children can print out from the computer which will kept out of sight in another lest that anyone mistakenly get the impression that it is some kind of teaching aid. (The advantage of this would be that the computer can keep track of which student has done what in the syllabus hierarchy). The students could even potentially do them from home. weebecka:
Wa `alaikum as-salam(!), - Sabbir.
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