Imagine you are going to advise a K-8 school on a new math curriculum that focuses on problem solving. Take what you know from the readings to advise the school. What should be their learning objects? What should they look for in new curricular materials to help achieve those objectives?
Something that really struck a cord for me in the the reading (Gredler, p. 232) was the study discussed third to fifth grade student error detection in "more than" & "less than" mathematical word problems. Gredler makes a brilliant yet possible over-looked concept once one gets to involve in the academic analysis of learners (I believe at every level - not simply young ones):
"One reason for the lack of identification of unsolvable problems is that children develop a "WORD PROBLEM" SCHEMA in which WORD PROBLEMS are DIVORCED from REAL-WORLD problems (emphasis added by me).
I believe this is one of the core reasons (not to mention student-owned cliches) learning simple doesn't happen.
I've studied the teaching methods of Maria Montessori (Links to an external site.) in order to better understand the young men I taught in Rabigh, KSA. It was a vocational school in a remote village. Much of the teaching was done by text book or making wonderful, high-end Lenovo tablets into shiny e-readers or pretty platforms for engineering Philippino professor's pirated PowerPoints. They had wonderful equipment - conduits, pumps, operations boards & instrumentation panels - but the students were asked to solve word problems on paper for the majority of their two year program.
With that said, I've never been able to understand why anyone would study or learn math - except for those few who enjoy it. I know it does appeal to some - and that's absolutely fabulous.
From my experience of learning math in high school &/or hacking it or completely avoiding it wherever else possible, I would advise that a new curriculum be made virtual . . . though not necessarily virtual reality.
Montessori believed that students learned best by real world doing, touching, smelling & listening. The schools that are her namesake produce some of the finest young minds today - including Larry Page & Sergey Brin, the founders of Google. I believe metacognition - thinking about thinking - happens when the learner is thinking about she is doing. The need to remember becomes more "real" when the learner is in the act of doing something very real, & possibly failing at it.
I think math curricula should include much more touchy-feely stuff, like a Montessori (Links to an external site.) school or a vocational school. If there's a problem with how many buses would be needed for so many soldiers - rather than giving young learners an option of a remainder - materials in a virtual world (possibly something in the WolframAlpha (Links to an external site.) persuasion) could be manipulated by the students to understand the real world relation that is so vital for true learning & the long-term retaining of knowledge.
Montessori Method
Want to give the students a problem about cookies? Use real cookies - or Skittles.
I certainly realize that my approach has real-world financial limitations. It could be expensive. In the best of all possible schools, I would make those suggestions.
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