Het Canadese Discovery-Based Math experiment

*Uitspraken-blogs*

______________________________

Discovery-based learning wordt ook wel genoemd: ‘problem-based-‘,  ‘inquiry-based-‘, ‘experiential-based-‘, of ‘constructivist-learning’.

Aan het einde van de jaren 90 hebben de overheden van een aantal Canadese provincies besloten om het reken-wiskunde-onderwijs te baseren op ‘discovery-based learning’.  Want reken-deskundigen hebben gewaarschuwd: door ‘drill-and-practise’ (‘drill-and-kill’) verliezen leerlingen hun motivatie, hun creatieve vermogens en hun probleem-oplossende vaardigheden. Ze wezen op de gevaren van het van buiten leren van de vermenigvuldigingstafels. Wiskunde gaat over redeneren; de mechanistische standaardprocedures staan begrip en inzicht in de weg. Ook moet er rekening gehouden worden met de verschillende leerstijlen van de leerlingen en moeten ze meerdere strategieën kunnen bedenken, die ze dan aan klasgenoten uitleggen. Door leerlingen zelf de wiskunde te laten ontdekken onthouden ze het beter, begrijpen ze het beter, verkijgen ze een dieper inzicht,  is er meer transfer, ontwikkelen ze betere ‘problem-solving skills’,  ‘kritisch denkvermogen’ en creatieve vermogens. Voortaan is niet de uitkomst belangrijk maar de weg daarheen. Het motto nu: ‘You do the math’.

De discovery-math deskundigen laten zich o.a. leiden door een rapport uit 1998 van de onderwijskundigen Constance Kamii en Ann Dominick:‘The Harmful Effects of Algorithms in Grades 1-4’:

“Algorithms not only are not helpful in learning arithmetic, but also hinder children’s development of numerical reasoning. We have two reasons for saying that algorithms are harmful: (1) They encourage children to give up their own thinking, and (2) they unteach place value, thereby preventing children from developing number sense. The persisting difficulty with standard algorithms lay in the column-by-column, single-digit approach that prevents children from thinking about multidigit numbers. Children in the primary grades should be able to invent their own arithmetic without the instruction they are now receiving from textbooks and workbooks.“

De invloed van dit artikel: “Textbook curricula which were inspired by the NCTM standards fully carry out the recommendation of not only omitting instruction of traditional computation methods, but instructing teachers in the teacher guides to not permit students to use such methods as e.g. multiplying length by width by height to compute volume, even if learned outside the class from home.”

Er is ook kritiek op dit rapport:  *The Bogus Research in Kamii and Dominick’s Harmful Effects of Algoritms Papers*.

________________________________

Laten we eens kijken hoe dit in de praktijk allemaal uitpakt:

[You do the math. Because our kids cant]  [New math doesn’t add up for Calgary parents]  [Why is it your job to teach your kid math?] [This new math is stealing their confidence and their dreams] [The Great Canadian Math Debate]

Samenvatting:

Leraren durven zich niet uit te spreken. Velen hebben hun baan opgegeven. Kinderen komen  huilend thuis. Ze worden neurotisch bij het horen van het woord ‘math’. De eenvoudigste berekeningen lukken niet. Zelfs kinderen die goed zijn in wiskunde haten nu de wiskundelessen. Ouders spenderen overmatig veel uren aan bijles aan hun kinderen, of betalen voor bijlessen, dit alles gestimuleerd door de scholen met de opmerking dat ze niet de standaardalgoritmen mogen gebruiken. Ook ouders in tranen. Ze begrijpen niets van de schoolboeken. De standaardalgoritmen leren mag niet, want blokkade voor begrip. De tafels leren mag niet, want betekenisloos. Wiskunde op de middelbare school lukt deze kinderen helemaal niet meer, ze raken hopeloos in de knoei met algebra. Breuken optellen, staartdelen, is ook aan universiteiten te hoog gegrepen.

Scholen hebben de keuze uit meerdere rekenboekjes: allemaal discovery-based en niet geschreven door reken-experts maar meestal door ‘educational professors’; de boeken bevatten nogal wat (grote) fouten en onduidelijkheden.

Er is hoogconjuctuur bij onderwijsadviesbureau’s: allemaal preken ze het belang van leerstijlen en discovery-based-learning. Royal Oak School maakte zoveel gebruik van hun diensten dat ook aan de ouders een bijdrage gevraagd werd van $20.000. De ouders reageerden furieus; ze wilden juist af van dit type reken-onderwijs.

In een poging het tij te keren hebben een aantal wiskunde hoogleraren *WISE* (Western Initiative for Strengthening Education in Math) opgericht.

In 2015 publiceerde het Howe Instituut een kritisch rapport over het Canadese wiskundeonderwijs:   *What to do about Canada’s Declining Math Scores?*.

_____________________________________________________

Voorstanders van Discovery Math

“The standard algorithms pose a serious threat to the retention of insight” (Math Education professor).

“In  the current mathematics program of studies, students are expected to know and master number facts as they develop number sense”. (team leider wiskunde van het ministerie van onderwijs)

“Students can learn through memorization, but it’s not enough. They need to learn through inquiry and discovery and learn a number of different ways to approach problems”  (Onderwijsadviseur).

“By decreasing emphasis on rote calculation, drill and practice, and the size of numbers used in paper and pencil calculations, more time is available for concept development”. (team leider wiskunde van het ministerie van onderwijs)

“It’s no longer sufficient to just pass information from teacher to student”. (Onderwijsadviseur)

_______________________________________________________

Tegenstanders van Discovery Math

“This math curriculum looks like it was written by an elementary Language Arts professor”. (Universitair docent)

“As a retired secondary math teacher, I am astounded at the imbecility of the new math curriculum”.

“There are a fair number of consultants who do not think it’s important for kids to be fluent with calculations”.  (Hoogleraar)

“The notion that practice of basic skills interferes with understanding of math concepts is illogical and misguided and denigrating terms like “drill and kill” do not serve students or teachers well. Indeed, understanding and practice of basic skills go hand-in-hand”. (hoogleraren wiskunde)

“How can the memorization of times tables harm understanding of numbers?” (Ouder)

” ‘Mindless algorithms’ are powerful tools that allow us to operate at a higher level. The genius of algebra and calculus is that they allow us to perform complex calculations in a mechanical way without having to do much thinking. One of the most important roles of a mathematics teacher is to help students develop the flexibility to move back and forth between the abstract and the mechanical. Students need to realize that, even though part of what they are doing is mechanical, much of mathematics is challenging and requires reasoning and thought”. (Hoogleraar)

“Strategies and tricks are interesting for the brightest students, but the average student (including future professionals) will be better served by learning the time-tested algorithms for arithmetic computation that we learned as children and continue to use in our daily lives”. (Hoogleraar)

“Multiple strategies and discovering their own strategies confuses most students. This is not to say that you don’t accept different ways of solving problems,  but the ones who can do this are the same ones who master and memorize their basic facts, who master fundamental algorithms. You can show them why algorithms work, but they want the simplicity and ease of established algorithms – this has been proven to me time and again by students”.  (Docent)

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

Ze is Award Winner ‘National Teaching Fellows’ 2021:

“Dr. Anna Stokke is a mathematician and an ambassador for math education. Her passion for improving the way students at all levels learn math has inspired curriculum improvements provincially and nationally and led to higher university standards. Anna is determined to dispel the myth that some people are good at math while others are not.”

Anna Stokke geeft uit noodzaak bijles aan haar 2 kinderen en een aantal van hun vriendjes. Toen ze de schoolboekjes bekeek schrok ze:

• Instead of teaching the standard methods of arithmetic, the emphasis had shifted to a wide range of alternative methods, such as using grids, blocks, or strips of paper to multiply. Even as a professor of math, I found the methods confusing. It was shocking. We’re talking about adding, subtracting, multiplying and dividing. It shouldn’t be so overly complicated that even parents can’t understand it. It’s absolutely ridiculous.
• You see a lot of convoluted methods for doing simple problems that end up being really confusing for kids. Overly complicated teaching techniques using blocks to solve arithmetic problems instead of doing it with pencil and paper are making it tough for kids to learn basic math. If you’re doing 36 plus 78, you shouldn’t be using blocks to figure that out, you should be able to do it quickly using pencil and paper of in your head.
• Relying on ad hoc strategies to calculate the number facts involved puts the student at an extreme disadvantage relative to one who can quickly recall a fact such as 7 × 8 = 56, since working memory becomes overburdened with the strategies involved to compute basic number facts.
• You know what’s the worst kind of instruction? The kind of instruction that makes kids feel stupid. And that’s what a lot of that discovery stuff does; their working memory gets overloaded, they’re confused.
• Giving people addition or subtraction or multiplication questions and then giving hem a calculator to do them is not testing them on the basics. It’s testing them on whether or not they can use a calculator.
• I have already seen a number of deficits in the math skills of my own university-aged students centred around basic learning, including the use of fractions. Since the introduction of discovery-based math, students are being overwhelmed with trying to figure out basic skills, like multiplication, which should simply be memorized. And when they go on to more complex problem-solving they struggle, they feel defeated and then quickly give up.
• Provincial governments use meaningless buzzwords like ‘problem solving’and ‘critical thinking’ when teaching math.
• You don’t acquire problem-solving skills by being thrown into a classroom with a bunch of blocks and given no help from a teacher.
• You acquire good problem-solving skills by being given a good foundation by a teacher and given the tools to actually solve those problems.
• There is no valid research that supports teaching multiple strategies to novice learners or that supports the elimination of standard algorithms, etc.  At least, no one has been able to provide me with any reasonable studies and I’ve been asking for the past 2.5 years.  Every time someone makes a “research shows” claim, I ask for articles.  I haven’t received any yet.
• Where there any math experts (not math education profs) involved in the writing of the textbooks?  As far as I know, there weren’t any involved and those texts contains some major mathematical errors.

Vladimir Troitsky (Hoogleraar Wiskunde aan de Universiteit van Alberta)

• Students show up in my university classroom unable to perform basis arithmetic without a calculator and are unable to add fractions.
• Knowledge is necessary for discovery.
• You cannot Google your way through mathematics.

“Today’s math isn’t about numbers, it’s about words and theories, as if the curriculum was written by folks who hate the clear logic of pure mathematics.”
David Staples, Edmonton Journal