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]]>Our issues today seem to be that there are two main very effective ways (based on limited empirical data) of teaching mathematics that have similarities between each other but that neither of these ways has any wide-spread following.

One way is the Jump Math strategy of carefully breaking down each mathematical idea into tiny pieces and having kids practice mathematics as a series of skills, and then discover the connections between different mathematical ideas mostly on their own. There is more to Jump Math than just the practice worksheets but that’s a better topic for a book John Mighton, the inventor of Jump Math, wrote. Jump Math has some examples of the limited empirical evidence they have that their program works on their website.

The other way is even less well known, and in fact most people who hear of it confuse it for ‘discovery learning’. It is what Magdalene Lampert (among others) calls ‘Ambitious Teaching’ wherein students do mathematics as mathematicians would within a mathematical community (again there are other important features of ambitious teaching outside the scope of a comment on a blog). Although there is a recent study out showing that elements of the inquiry-oriented ambitious teaching are correlated with student success on an empirical measure, there is not wide-spread enough use of ambitious teaching to be able to compare it to other forms of teaching.

Note that both of these ways of teaching take Cognitive Load theory (or some variant of it) very seriously but simultaneously are concerned about the internal mental models students develop for understanding mathematics. Jump Math aims to minimize cognitive load, especially extraneous cognitive load. Ambitious Teaching aims to minimize extraneous load but maximize the load (to whatever limit students can handle) for students in which they are thinking about mathematics.

Neither one of these ways is really well described enough in this post to be useful to you yet as a starting teacher, so unfortunately I’ve given you some more reading to do.

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]]>Thanks very much for offering your perspective and experience! I think you’re right in saying that one of the purposes of education is to prepare students for an uncertain future. Uncertain is the key word – that’s why I find it disingenuous when teachers say that simply knowing concept X will make you somehow more prepared in life. This kind of thinking might lead one to think that we should therefore cram as much as possible in (to a unit, a course, a curriculum) to better prepare students for whatever life throws their way – but I propose that we should focus more on thought processes more than the “nuts and bolts”, because strong habits of mind are what will really enable students to deal with difficult problems in their future. (This is not to say that students shouldn’t learn the nuts and bolts along the way.)

I’m wondering if this parallels your views, or if I’m off the mark.

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