Eerst begrip, dan ‘trucjes’ ?

Het Freudenthal Instituut waarschuwt telkens weer tegen het van buiten leren van 'betekenisloze' trucjes en procedures, welke gedachteloos toegepast worden.  Wiskunde gaat over redeneren en problemen oplossen. Vandaar de invoering dit schooljaar van de wiskundige denkactiviteiten (WDA).

In de openingsrede van Kees Hoogland op de Panamaconferentie 2016 wijst Kees op de toekomst van het wiskunde-onderwijs: we moeten van een 'Answer-getting mindset' naar een 'Problem-solving mindset'.

Uit '[Rekenen-wiskunde-over denken]':   "Het gericht zijn op goede antwoorden is een effect van de bestaande inrichting van het onderwijs, dat volgens Hoogland oppervlakkige resultaten oplevert." 

 

Andere geluiden:

Bron: [The building blocks of understanding are memorization and repetition (Barbara Oakley)]

Barbara Oakley is hoogleraar ‘Engineering’ aan de Oakland University in Michigan. Ze is schrijfster van het boek  ‘A Mind for Numbers: How to Excel at Math and Science’.

Barbara Oakley:

  • Students have been reared in elementary school and high school to believe that understanding math through active discussion is the talisman of learning. If you can explain what you’ve learned to others, perhaps drawing them a picture, the thinking goes, you must understand it.
  • In the current educational climate, memorization and repetition in the STEM disciplines [Opsomming van alle studies in 'Science', 'Technology', 'Engineering' en 'Mathematics']  are often seen as demeaning and a waste of time for students and teachers alike. Many teachers have long been taught that conceptual understanding in STEM trumps everything else.
  • The problem with focusing relentlessly on understanding is that math and science students can often grasp essentials of an important idea, but this understanding can quickly slip away without consolidation through practice and repetition. Worse, students often believe they understand something when, in fact, they don’t. 
  • As one (failing) engineering student recently told me: “I just don’t see how I could have done so poorly. I understood it when you taught it in class.” My student may have thought he’d understood it at the time, and perhaps he did, but he’d never practiced using the concept to truly internalize it. He had not developed any kind of procedural fluency or ability to apply what he thought he understood.
  • In the same way, once you understand why you do something in math and science, you don’t have to keep re-explaining the how to yourself every time you do it. You memorize the idea that you simply add exponents when multiplying numbers that have the same base. If you use the procedure a lot, by doing many different types of problems, you will find that you understand both the why and the how behind the procedure very well indeed. The greater understanding results from the fact that your mind constructed the patterns of meaning. Continually focusing on understanding itself actually gets in the way.

 

De sectie wiskunde van het Stedelijk Gymnasium Leiden:

"Vaker dan we zouden willen komt begrip pas na en door heel veel oefenen."

 

Anna Stokke  (Associate Professor at the Department of Mathematics and Statistics, University of Winnipeg):

"You acquire good problem-solving skills by being given a good foundation by a teacher and given the tools to actually solve those problems."

"Students need basic facts and techniques in long-term memory, developed through hours of practice, in order to become strong problem-solvers."

 

Jo Boaler (Hoogleraar Maths Education aan de Stanford Universiteit), hier :

"The PISA-tests (OECD) show that the lowest achieving kids in the world are those that are memorizers."

Robert Craigen (Hoogleraar wiskunde):

"To support the statement 'Memorizers are the lowest achievers' Boaler references a single source: an article on the OECD site. In that article I found nothing pertaining to her claim, I searched the word 'memorization' the substring 'memor'. This does not occur anywhere in the very large document. I am guessing hat this idea was pulled out of Boaler's…eh…. active imagination, and the OECD document was voluminous enough to be a credible place to bury a reference and expect to maintain plausible deniability."

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