Webinar: Understanding international differences in maths

Γεια σας και καλωσήρθατε σε αυτό το OECD σεμινάριο

με εμένα τον Duncan Crawford

Σας ευχαριστώ πολύ που συμμετέχετε

Σήμερα συζητώντας θα συζητήσουμε αν οι μαθητές σε μερικές

χώρες απολαμβάνουν τα μαθηματικά περισσότερο από άλλες.

υφίσταται μια λεγόμενη κουλτούρα των μαθηματικών

έχει σημαντική επίδραση στην επιτυχία των μαθητών

Τα δεδομένα του OECD δείχνουν ότι

καμία χώρα δεν έχει ιδιαίτερη αγάπη για τα μαθηματικά

αλλά είναι οι πολιτές της οι οποίες είναι σημαντικές

και υπάρχουν δράσεις που κάνουν οι χώρες

ώστε να ενδιαφέρονται οι μαθητές για το θέμα.

Θα έχουμε

μία συζήτηση πάνω σε αυτό το θέμα σε πολύ λίγο

Αλλά μιλώντας για ενδιαφέρον

Αν σας ενδιαφέρει αυτό το θέμα και θέλετε να

μάθετε περισσότερα από από αυτά που θα

συζητήσουμε σε αυτό το σεμινάριο

Μόλις κυκλοφόρησε μια ολοκαίνουργια έκθεση του ΟΟΣΑ με τίτλο

Μαθηματικά για τη ζωή και την εργασία, που περιγράφει

τους διάφορους τρόπους με τους οποίους τα μαθηματικά

παρέχονται στη δευτεροβάθμια εκπαίδευση

εκπαίδευση· είναι κυριολεκτικά ολοκαίνουργιο

μόλις κυκλοφόρησε σήμερα, οπότε θα μπορέσετε να

το δείτε τώρα — όμως ας δούμε μερικά

λεπτομέρειες από τον πολιτικό αναλυτή του ΟΟΣΑ,

Εδουάρδο Μαγάλ από τις μεταβάσεις στη δευτεροβάθμια

εκπαίδευση, από την ομάδα της δευτεροβάθμιας

εκπαίδευσης και δεξιοτήτων, σωστά

εδώ στον ΟΟΣΑ,

ο λόγος σε εσάς Εδουάρδο,

γεια σου Λαν, ευχαριστώ πάρα πολύ

για την ευγενική εισαγωγή — είναι χαρά μου

είναι πραγματικά χαρά μου που είμαι εδώ

όπως είπε και ο Ντενάν πριν ξεκινήσουμε

με τη συζήτησή μας, θα προσπαθήσω

να σας κάνω μια — θα προσπαθήσω να είναι σύντομη

μια σύντομη παρουσίαση και

θα μοιραστώ τώρα την οθόνη μου μαζί σας

(αναμονή)

μπορείς να μου επιβεβαιώσεις Ντάνκαν ότι

βλέπεις την παρουσίαση; ναι, τη βλέπουμε, εντάξει

όλα καλά, ας ξεκινήσουμε λοιπόν τη

σύντομη παρουσίαση για αυτό το σεμινάριο

κατανοώντας τις διεθνείς διαφορές

στα μαθηματικά, οπότε απλώς λίγα πράγματα

ένα σύντομο πλαίσιο πριν από αυτές τις αναφορές

που ανέφερε ο Ντάνκαν, οι οποίες αρχικά

ανατέθηκαν από το Υπουργείο Παιδείας

στο Ηνωμένο Βασίλειο

το 2023 υπό την πρώην συντηρητική κυβέρνηση

του Ρίσι Σούνακ, ως μέρος μιας

πολιτική που στόχευε στην αύξηση της

συμμετοχής στα μαθηματικά μέχρι την ηλικία των 18 χρονών

— αποτέλεσμα, ο πρώην πρωθυπουργός

ανησυχούσε για τη

σχετικά χαμηλή συμμετοχή στα μαθηματικά στο

Ηνωμένο Βασίλειο σε σύγκριση με άλλες ανεπτυγμένες χώρες,

και ανέφερε ότι η Αγγλία

αντιμετώπιζε μια συγκεκριμένη αρνητική στάση προς τα μαθηματικά

-

που έπρεπε να καταπολεμηθεί κάνοντάς τα

υποχρεωτικά μέχρι την ηλικία των 18, οπότε

στην έκθεσή μας που ανέφερα προηγουμένως

εξετάζουμε τον τομέα των μαθηματικών

στη δευτεροβάθμια εκπαίδευση στην Αγγλία και σε έξι

άλλα συγκρίσιμα εκπαιδευτικά συστήματα — αυτά είναι απλώς

πληροφοριακά: Αυστρία, Βρετανική Κολομβία στον Καναδά

Δανία, Ιρλανδία,

Νέα Ζηλανδία και επίσης Σιγκαπούρη, οπότε

είναι σημαντικό να πούμε, φυσικά, πως

από τότε άλλαξε η κυβέρνηση στο Ηνωμένο Βασίλειο

και αυτή η πολιτική για την υποχρεωτική διδασκαλία των μαθηματικών

μέχρι τα 18 δεν ισχύει πλέον

όμως, παρ’ όλα αυτά,

η ανάλυση που περιέχει αυτή η έκθεση έχει πολύ

ενδιαφέρουσες παρατηρήσεις, που εγώ πιστεύω — και πιστεύουμε

— ότι είναι πολύ χρήσιμες όχι μόνο

για την Αγγλία αλλά και για πολλά εκπαιδευτικά συστήματα

σε όλο τον ΟΟΣΑ και τον κόσμο, οπότε

ας ξεκινήσουμε με αυτές τις μεγάλες έννοιες

που σχετίζονται με την πολιτισμική αντίληψη των μαθηματικών

υπάρχουν πολλές απεικονίσεις και

συνδηλώσεις των μαθηματικών στη δημοφιλή κουλτούρα,

που μπορούν να προσφέρουν

κάποιες ιδέες για το πώς οι άνθρωποι βλέπουν και

μιλούν για τα μαθηματικά και πώς τα παιδιά

και τα νέα παιδιά στην πραγματικότητα το ακούν

και διαμορφώνουν τις δικές τους αντιλήψεις, οπότε

το πρώτο παράδειγμα είναι από μια έκθεση στην Αγγλία,

που μιλάει για τις αντιλήψεις γύρω από

τα μαθηματικά, συγκεκριμένα για τους γονείς και

είναι μια φράση από γονιό προς παιδί

η οποία αναφερόταν ως μια συνηθισμένη στάση

και αυτό — πιστεύω ότι αυτό, με ακρίβεια,

εκφράζει αυτό που είπε ο πρώην πρωθυπουργός

ο Ρίσι Σούνακ όταν μίλησε

για μια «αντι-μαθηματική» νοοτροπία — ένα άλλο παράδειγμα

και αυτό το βρήκα ιδιαίτερα αστείο

αλλά και με τον δραματικό τόνο ενός

από έναν 16χρονο

άρθρου από το King's College London σχετικά με

τους λόγους που, κατά δήλωσή τους, οι 16χρονοι

δίνουν για να μην συνεχίσουν να σπουδάζουν μαθηματικά

ένα ακόμη παράδειγμα έρχεται από τις ΗΠΑ

το 1992, νομίζω, σχετικά με την κούκλα Barbie

η οποία έλεγε τη φράση «τα μαθηματικά είναι δύσκολα»

και εννοείται πως

σήμερα θεωρούμε αυτή τη φράση ιδιαίτερα προβληματική

προφανώς και λόγω

των έμφυλων στερεοτύπων που αναπαράγει, αλλά

πιστεύω ότι λέει πολλά για το τι

θεωρούνταν φυσιολογικό — τουλάχιστον εκείνη την εποχή

σε ό,τι αφορά τις αντιλήψεις για την

πειθαρχία, και το τελευταίο παράδειγμα είναι ένα πιο

αντίθετο παράδειγμα από την Ιαπωνία, το

2002, όπου υπήρξε

μια παρεξήγηση στο πλαίσιο

ορισμένων μεταρρυθμίσεων πολιτικής — το Π

διδασκόταν στο σχολείο ως τρία — αυτό

προκάλεσε τεράστια αναστάτωση στην ιαπωνική κοινωνία,

κάτι που είναι επίσης ένα ενδιαφέρον

αντίθετο παράδειγμα σε σχέση με

τα προηγούμενα που είδαμε, οπότε υπάρχουν

τρία βασικά μηνύματα που θέλω να τονίσω

από εδώ και πέρα, πριν μπούμε στην

ανάλυση την ίδια — πρώτα απ’ όλα, είναι σαν

πολιτισμικές αντιλήψεις για οτιδήποτε, αλλά στα

μαθηματικά ειδικότερα, είναι εξαιρετικά δύσκολο

να τις προσδιορίσεις — δεύτερο σημείο: προφανώς

ο καθένας έχει τη δική του άποψη για τα μαθηματικά,

και αυτές επηρεάζονται από

πολλούς και διαφορετικούς παράγοντες, αλλά

οι απεικονίσεις που δημιουργούμε γύρω από

τα μαθηματικά — και τώρα μιλάμε σε επίπεδο κοινωνίας

— είναι εξαιρετικά επιδραστικές

στο πώς οι νέοι άνθρωποι στην πραγματικότητα

αντιλαμβάνονται και αντιμετωπίζουν την επιστήμη των μαθηματικών

στο μέλλον τους — λοιπόν, προχωράμε στην

έκθεση «Μαθηματικά για τη Ζωή και την Εργασία»

η οποία κυκλοφόρησε σήμερα το πρωί

και σας προτείνω όλους να ρίξετε μια ματιά

εξετάσαμε μερικά πράγματα — είδαμε

τα μαθησιακά αποτελέσματα στα μαθηματικά μέσα σε

δευτεροβάθμια συστήματα — τις απαιτήσεις για

τα μαθηματικά σε όλα τα εκπαιδευτικά συστήματα —

πώς αυτά τα διαφορετικά συστήματα ανταποκρίνονται

στις διαφορετικές ανάγκες των μαθητών και των ικανοτήτων τους,

μέσω διαφορετικών προγραμμάτων

παρέχοντας διαφορετικά επίπεδα επιλογών

επίσης, συζητήσαμε τις πολιτισμικές

αντιλήψεις και στάσεις απέναντι στην

επιστήμη των μαθηματικών — και τέλος, την επιρροή

που έχουν οι μαθητές, οι γονείς και η αγορά εργασίας

με βάση τις οπτικές τους για τα μαθηματικά — ένα

σημαντικό συμπέρασμα από αυτή την έκθεση είναι

ότι πρέπει να εξετάζουμε φυσικά τις πολιτικές

και πώς αυτές διαμορφώνουν τον τρόπο με τον οποίο

οι μαθητές αλληλεπιδρούν με το γνωστικό αντικείμενο και ότι

πολλά από όσα φαίνονται στην αρχή

ως πολιτισμικές αντιλήψεις, στην πραγματικότητα είναι

όπως ανέφερε και ο Ντάναν στην εισαγωγή, σχετικές με

δημόσιες πολιτικές — λοιπόν, προχωρώντας σε αυτό

το κομμάτι των δεδομένων — στην πραγματικότητα, το σημαντικό

εύρημα είναι ότι δεν υπάρχει κάποια συγκεκριμένη χώρα

ή ελάχιστες συγκεκριμένες χώρες

που να έχουν αυτό που αποκαλούμε «κουλτούρα των»

μαθηματικών — εδώ έχουμε κάποια δεδομένα, κοιτάμε

την απόλαυση των μαθηματικών από 15χρονους, από την

έρευνα PISA και από το δημοτικό σχολείο, από

την έρευνα TIMSS — καθώς και έναν δείκτη

αυτοαποτελεσματικότητας και συμμετοχής

για να δώσουμε ένα πλαίσιο, τι είναι αυτός ο δείκτης;

είναι ένας δείκτης που δημιουργήθηκε

στο πλαίσιο του PISA και

βασικά, πρόκειται για την αυτοαντίληψη του μαθητή

σχετικά με την ικανότητά του να

επιλύει προβλήματα — προβλήματα καθαρών ή εφαρμοσμένων

μαθηματικών — θα δώσω ένα παράδειγμα, ώστε

ο κόσμος να κατανοήσει καλύτερα, για παράδειγμα,

σε σχέση με την άλγεβρα, αν οι μαθητές κοιτάξουν

ένα πρόγραμμα δρομολογίων τρένων, μπορούν

να καταλάβουν, για παράδειγμα, τι ώρα

θα φτάσει το τρένο σε συγκεκριμένους σταθμούς;

αυτό που βλέπουμε εδώ είναι ότι όταν κοιτάμε

την Αγγλία, στην πραγματικότητα είναι πάνω από τον μέσο όρο του ΟΟΣΑ

και των περισσότερων συγκρίσιμων χωρών

ως προς την απόλαυση και την αυτο–

ο δείκτης, αλλά η συμμετοχή παραμένει

αρκετά χαμηλή — και αυτό το σημείο, λοιπόν, είναι ένα

σημαντικό ερώτημα για εμάς, να

κατανοήσουμε — αλλά αυτό δεν αφορά μόνο

την αυτοαντίληψη

η αυτοαντίληψη σχετικά με τις στάσεις είναι επίσης

ορατή στα αποτελέσματα, όταν βλέπετε τα δεδομένα από

τους μέσους όρους των μαθηματικών

στην PISA 2022 — βλέπουμε ότι η Αγγλία είναι

στα δεξιά — με μωβ χρώμα, παρεμπιπτόντως

το μωβ φυσικά είναι η Αγγλία και οι συγκρίσιμες

χώρες που ανέφερα νωρίτερα — βλέπουμε ότι

τα πάνε αρκετά καλά, οπότε είναι

ενδιαφέρον να δούμε ότι στην πραγματικότητα

-

όχι μόνο έχουν θετικές στάσεις,

αλλά τα πάνε και καλά, και παρ’ όλα αυτά

υπάρχει ένα αρκετά — αρκετά χαμηλό ποσοστό συμμετοχής

ποσοστό συμμετοχής — ένα

ένα επιπλέον στοιχείο εδώ είναι το διάγραμμα

που εξετάζει τα μαθηματικά και τις αριθμητικές

δεξιότητες μεταξύ 15χρονων και

24χρονων στο Πακιστάν, για να δώσουμε

ένα πλαίσιο — βασικά, αυτό είναι ένα

μια άσκηση που έγινε σε μια έκθεση του ΟΟΣΑ

που εναρμόνισε τα δεδομένα μιας ομάδας

η οποία συμμετείχε στην PISA το 2003 — και μετά πώς

οι δεξιότητες αυτές αξιολογήθηκαν αργότερα, όταν

στο Πακιστάν, το 2012

— και φυσικά αυτό είναι μια

εναρμόνιση δεδομένων, αλλά δεν είναι

μια μακροχρόνια μελέτη — όμως παραμένει

χρήσιμη και έχει σημαντικά συμπεράσματα — και το βασικό

μήνυμα εδώ είναι ότι η επίδοση στην ηλικία των 15

αν και είναι σημαντική, δεν είναι το τέλος

της πορείας — και ό,τι συμβαίνει μετά τα 15

στην ανώτερη δευτεροβάθμια εκπαίδευση και στην

οι πρώιμες επαφές με την αγορά εργασίας είναι

εξαιρετικά σημαντικές για την ανάπτυξη

νοητικών δεξιοτήτων όπως ο αλφαβητισμός στους μαθητές

— και βλέπουμε εδώ ότι

στον ΟΟΣΑ, αυτή η ομάδα κέρδισε 31 μονάδες

κατά μέσο όρο σε αυτή την περίοδο, κάτι που είναι

πολύ σημαντικό εύρημα — και παρεμπιπτόντως

τα νέα δεδομένα της PISA από το Πακιστάν

αν και αυτά εδώ είναι παλιά, θα κυκλοφορήσουν

τον επόμενο μήνα, τον Δεκέμβριο — οπότε να είστε σε επιφυλακή

-

οπότε, αν η κουλτούρα δεν μας λέει

την απάντηση, τότε κοιτάμε

τις πολιτικές, και προσπαθούμε να εξηγήσουμε

ίσως γιατί η Αγγλία έχει τόσο χαμηλή

συμμετοχή — και φυσικά εδώ

μιλάμε για τις επιλογές και τα επίπεδα

και για μια ποικιλία επιλογών στα μαθηματικά

στην ανώτερη δευτεροβάθμια εκπαίδευση, κάτι που είναι

πολύ σημαντικό ώστε να καλύπτονται οι μαθητές με

διαφορετικές φιλοδοξίες και διαφορετική δυναμική

— και βλέπουμε ότι αυτές είναι

πολύ συχνές στρατηγικές, όπως στη British Colombia

Δανία, Ιρλανδία και λοιπά — το δεύτερο

σημείο ή δεύτερος παράγοντας είναι η

επαγγελματική εκπαίδευση — είτε ως

ξεχωριστό αντικείμενο είτε ενσωματωμένο

σε άλλα μαθήματα — είναι μια κρίσιμη

στρατηγική για πολλά εκπαιδευτικά συστήματα ώστε να διασφαλίσουν

ότι όλοι οι μαθητές αποκτούν

τις μαθηματικές δεξιότητες που χρειάζονται — και

η Αυστρία και η Δανία είναι πολύ

επιτυχημένα παραδείγματα αυτής της προσέγγισης — το τρίτο

σημείο είναι, προφανώς, να γίνονται υποχρεωτικά,

κάτι που δεν ισχύει

στο Ηνωμένο Βασίλειο μετά τα 16 — αλλά ισχύει, για παράδειγμα,

στην Αυστρία ως βασικό μάθημα του

προγράμματος σπουδών — αλλά είναι σημαντικό

να πούμε ότι, παρόλο που το να τα κάνεις υποχρεωτικά

θα μπορούσε να βοηθήσει, δεν είναι απαραίτητα

η λύση — και βλέπουμε

συστήματα που, παρόλο που δεν τα έχουν υποχρεωτικά,

έχουν σχεδόν καθολική

συμμετοχή — όπως συμβαίνει

στην Ιρλανδία, στη Σιγκαπούρη, κάτι που μας οδηγεί

στο επόμενο σημείο σχετικά με την ανώτατη εκπαίδευση

και τις απαιτήσεις εισαγωγής που μπορούν να λειτουργήσουν

ως επίπεδο σύγκρισης — για παράδειγμα, εσύ

μπορεί να μην είναι υποχρεωτικό, αλλά αν

όλα τα πανεπιστήμια και η ανώτατη εκπαίδευση

απαιτούν να το έχεις,

στην πράξη οι άνθρωποι θα πρέπει να το παρακολουθήσουν

και αυτό μπορεί να είναι ένας σημαντικός παράγοντας

— και τώρα προχωρώντας προς το τέλος

της παρουσίασης, ήθελα να επιστρέψω

στο πρώτο μου σημείο, αυτό της διαφορετικότητας, που

είναι πραγματικά σημαντικό — όπως μπορείτε να δείτε

εδώ, όλα τα συστήματα παρέχουν σχεδόν

διαφορετικά μαθηματικά επίπεδα

και επιλογές — και βλέπουμε

στον άξονα Χ — πρόσβαση, δηλαδή, στον αριθμό των

επιλογών που προσφέρουν τα συστήματα της δευτεροβάθμιας

και στον άξονα Υ, ο αριθμός των επιπέδων

και εδώ βλέπουμε ότι η Αγγλία, για παράδειγμα,

τονίζεται για το ότι έχει

ιδιαίτερα χαμηλή ποικιλομορφία — ναι, προσφέρουν

τα Μαθηματικά Πυρήνα (Core Mathematics)

ως εναλλακτική στα A Levels, αλλά

προφανώς υπάρχουν κάποια προβλήματα — και

η συμμετοχή ήταν πολύ χαμηλή — ένα από τα

ζητήματα που αναφέρθηκαν στην έκθεση, και

ένα από τα εμπόδια ήταν στην πραγματικότητα

κάτι που αναφέραμε νωρίτερα, ότι

τα εκπαιδευτικά ιδρύματα δεν εκτιμούσαν

αυτό το γνωστικό πεδίο — αλλά βασικά,

ποιες είναι οι συνέπειες αυτού; Αυτό είναι

που θέλουμε να συζητήσουμε — και ένα από τα θέματα

της έλλειψης ποικιλομορφίας είναι ο κίνδυνος ότι

τα προγράμματα της ανώτερης δευτεροβάθμιας εκπαίδευσης

δεν θα καλύπτουν τις ανάγκες όλων των

μαθητών — κάτι που με φέρνει στο τελευταίο μου σημείο,

το οποίο αφορά, βασικά, τα επίπεδα

στα μαθηματικά — απλώς για λίγο πλαίσιο,

στην Αγγλία, η υποχρεωτική εκπαίδευση

χωρίζεται σε στάδια από τα 14 έως τα 16

και μετά έχουμε αυτό που αποκαλούν GCSE

δίνουν αυτές τις εξετάσεις

και μετά τα 16 μπορούν να επιλέξουν τρία

τρία A-levels για να συνεχίσουν μέχρι τα 18

τα μαθηματικά δεν είναι υποχρεωτικά μετά τα 16

αυτή η μετάβαση στην ηλικία των 16 ετών και εδώ

εξηγούμε απλά αυτό το γράφημα

στον άξονα x βλέπουμε ποιοι είναι οι βαθμοί

δίνουν αυτή την εξέταση στα 16

το GCSE, όπου το 9 είναι ο υψηλότερος βαθμός

και στον αριστερό άξονα

στον άξονα y βλέπουμε τα ποσοστά μετάβασης

από το στάδιο του GCSE στο επίπεδο A Levels

σύμφωνα με τις διάφορες

ειδικότητες για τις οποίες μιλάμε, και αν

κοιτάξετε αυτό το γράφημα, μπορείτε να δείτε ότι

τα μαθηματικά που εμφανίζονται εδώ σε αυτή την ομάδα

με αυτό το γαλαζοπράσινο χρώμα, βλέπουμε ότι

η γραμμή είναι πολύ επίπεδη στα χαμηλότερα

επίπεδα και μετά γίνεται εξαιρετικά απότομη

που σημαίνει ότι μόνο οι

υψηλής απόδοσης μαθητές στα μαθηματικά

είναι αυτοί που τελικά εγγράφονται στα A levels

στα μαθηματικά, για να σας δώσουμε

λίγες πληροφορίες για το τι σημαίνει ένας βαθμός

από επτά έως εννιά είναι ισοδύναμος με

ένα Α ή Α* στην Αγγλία, που σημαίνει

ότι αυτό είναι ουσιαστικά το αποτέλεσμα

μόνο παιδιά με πολύ πολύ υψηλές επιδόσεις

το κάνουν αυτό, αν δεν έχουν επιλογή

δεν θα το επιλέξουν, οπότε

υπάρχει έλλειψη επιλογών κυρίως για

μαθητές υψηλών επιδόσεων, όχι κορυφαίων

μαθητές που θα μπορούσαν να κάνουν μαθηματικά

αλλά δεν έχουν τη δυνατότητα

που να τους ταιριάζει, απλώς ως συμπληρωματική επιλογή

αυτό φαίνεται επίσης στη κατανομή των βαθμών

όταν βλέπουμε την Αγγλία, βλέπουμε

ότι όταν βλέπουμε τα A Levels

βαθμολογίες από διαφορετικά γνωστικά αντικείμενα

στα μαθηματικά είναι μόνο η κατανομή

που δείχνει ότι οι περισσότεροι έχουν υψηλές

βαθμολογίες, κάτι που αντικατοπτρίζει προφανώς

τη μεροληψία επιλογής όσων εισέρχονται

σε αυτόν τον κλάδο, και αυτό έρχεται σε αντίθεση με

άλλα συστήματα που έχουν περισσότερες επιλογές

περισσότερα επίπεδα, και όπου η κατανομή

είναι πιο επίπεδη και πιο ισομερής, κάτι που

είναι η περίπτωση της Ιρλανδίας, αν η Linda θέλει

να επανέλθει σε αυτό το σημείο αργότερα

με αυτό ολοκληρώνω και ζητώ συγγνώμη για

την μικρή υπέρβαση χρόνου

ευχαριστούμε πολύ Έντουαρντο για τον χρόνο

ήταν πραγματικά πολύ ενδιαφέρον και

επίσης ενδιαφέρον να δούμε τη μείωση

των μαθητών που αγαπούν τα μαθηματικά όταν είναι στο δημοτικό,

αλλά πόσο μειώνεται μέχρι

την ηλικία των 15 ετών – υπάρχει

μια ερώτηση από την Kyi Mamoto που ρωτάει

για τον πρώην πρωθυπουργό Ρίσι Σούνακ

και τη δέσμευσή του να μάθουν όλα τα παιδιά

μαθηματικά μέχρι την ηλικία των 18 – ρωτάει αν αυτό ισχύει για το Ηνωμένο Βασίλειο

ή μόνο για την Αγγλία, και τελικά είναι μόνο

για την Αγγλία, επειδή η εκπαίδευση είναι

αποκεντρωμένη στο Ηνωμένο Βασίλειο, και φυσικά τώρα

η συντηρητική κυβέρνηση του Σούνακ δεν είναι

πια εκεί – έχασαν τις εκλογές, οπότε

Kώρα υπάρχει μια κυβέρνηση των Εργατικών στο Ηνωμένο Βασίλειο

--

ευχαριστούμε για αυτή την ερώτηση και παρακαλώ

σε όλους τους υπόλοιπους, γράψτε τις ερωτήσεις σας

και θα προσπαθήσουμε να απαντήσουμε

όσες περισσότερες μπορούμε, αν και νομίζω

ότι είναι μάλλον καλή στιγμή να παρουσιάσουμε

την ομάδα μας χωρίς άλλη καθυστέρηση, οπότε

ο Μιλάνγκ θα μας συνοδεύσει, είναι ανώτερος σύμβουλος

στον Εθνικό Οργανισμό Εκπαίδευσης

και την ποιότητα στα παιδιά και την

Υπουργείο Παιδείας της Δανίας, και η Linda Ramsbottom

συμμετέχει επίσης – είναι ανώτερο στέλεχος

επιθεωρήτρια πρωτοβάθμιας εκπαίδευσης από

ο Υπουργείο Παιδείας της Ιρλανδίας – σας ευχαριστούμε και τις δύο

πολύ που είστε μαζί μας, θα ήθελα να ξεκινήσω

μιλώντας για ηλικίες και τα Μαθηματικά

επειδή τα μαθηματικά και η αριθμητική είναι

ξεκάθαρα ένα σημαντικό κομμάτι της εκπαίδευσης

αλλά μέχρι ποια ηλικία πρέπει τα παιδιά να τα μαθαίνουν

τα μαθηματικά – προφανώς, ο πρώην Βρετανός

πρωθυπουργός είπε την ηλικία των 18 ετών

Yola Milang, εσύ τι πιστεύεις;

Νομίζω πως η σύντομη και «πολιτική» απάντηση

θα ήταν: «ε εξαρτάται», και

δηλαδή, προφανώς τα μαθηματικά είναι

σημαντικά για τους περισσότερους, σωστά; είναι

εξαιρετικά σημαντικά για πολλά επαγγέλματα

είναι απαραίτητα για την περαιτέρω

εκπαίδευση, αλλά είναι επίσης κάτι που είναι

χρήσιμο στην καθημερινή ζωή – όλοι χρειαζόμαστε

να μπορούμε να κάνουμε τον προϋπολογισμό μας

να καταλαβαίνουμε γιατί είναι κακή ιδέα

να δανειζόμαστε με πολύ υψηλό επιτόκιο.

Οπότε, προφανώς, δεν θα έπρεπε κανείς

the exact right age would be I think is

a difficult question I think empirically

looking at Denmark we can see that we've

had a change over the past decades from

a system where the mathematics education

that we would do in our academic upper

secondary track would be geared H

towards mathematics as

um as a science disciplined to watch

more of a view that well really mathemat

and then those that chose not to do and

then you know that level could be really

high because it was a smaller group but

then with the with the for like 20 years

ago 15 20 years ago there was definitely

changes in how we we did our academic

track in Upper upper secondary so that

much more students like a greater number

of students now probably study

mathematics but then perhaps for some at

least at a lower level because the types

of student that used to not study

mathematics now study it but and that

reflects also I think a change in

mathematics is important for everyone so

one shouldn't end mathematics education

too early but it's definitely impossible

to say whether 16 17 18 19 14 would be

the right

age just a quick followup for you if you

don't mind so you said now there's more

children who are studying it to a later

age do you get push back from certain

young people you say you know why should

I be studying mathematics I'm not

interested in it I know you're telling

me it's important but it's not something

which I think I want to pursue in the

future or is necessary for whatever

career I want to do so luckily I don't

think the young people are aware of what

how they're impacted by reforms done 15

years ago so we don't definitely don't

get the push

back

in that

way um but uh what we definitely do get

is that you know the more varied student

population you have in a in a in a given

math problem the harder it is to teach

right it would it's easier to sit down

with five PhD students in mathematics

and discuss something that it is to

introduce a class of 25 people with with

different entry levels in mathematics so

uh you know there it is definitely the

case

that people's prior experience with

mathematics and how and motivation for

being in class would would definitely

have an impact that's something we hear

from from from teachers for sure okay I

see thanks so much for that Linda R

bottom from Ireland's Department of

Education let me bring you into the

conversation what is the situation in

Ireland actually do all students study

maths up until the age of 18 good

morning everybody um thank you yes in

Ireland we have compulsory mathematics

up to the age of 16 so that's lower

secondary um education in Ireland and

then after that we have a couple of

different ways students can access

mathematics well it's not compulsory it

is technically compulsory because the

majority of students will take um

mathematics to gain entry into further

education so into third level or they

may also want their mathematics to enter

the workforce or a trade so after our

Junior cycle which we call the first

three years we then have a track which

we call the leaving start applied about

3,000 students out of um a small

proportion of our students take that

that option which would be an

mathematical applications they call it

it's very practical it's not geared

towards getting you into University

although you can eventually move into

University or third level education it's

more practical course this students

would follow for two years the

traditional leaving start we would call

it is broken up then into three

different levels so students can access

a level that appropriate their needs and

abilities so technically while it's not

compulsory we have retention in Ireland

uh for for students from first year

lower secondary all the way to their

final upper secondary is over 90% so the

vast majority 98% of students would

follow some level of mathematics in in

Ireland

and if you having so many students do

that some 90% does that have an impact

which is quantifiable on the economy um

do you see it have a positive impact on

jobs or is that not is there not data to

show that yes we we do have some data to

show that um about

120,000 um Irish people would be

involved in stem educa stem um careers

and about a quarter of them are females

and we also have have statistic to show

that over the highest level of stem

graduates per capital we would have

between the 20 year years of age and 29

years of age in in comparison to Europe

so we would have a kind of um I suppose

a population who would be highly

qualified in the area of mathematics we

have a lot of industries that come into

Ireland um in the pharmaceutical

Industries and other that likes those

kind of industries that would require

mathematics in

Ireland thank you for that Eduardo let

me bring you back in to discuss some

more about the international data is

there any data that shows it's important

to teach more complex mathematics until

the age of

18 yeah definitely I think I think there

is a strongly evidence to support that

is important to to teach mathematics

during the during the upper secondary

and has implications not only for

individuals but also for society one of

the first things I wanted to to mention

here very briefly is that uh it's not

only not only about mathematics but also

numeracy while mathematics deals with

things as geometry algebra Etc numeracy

refers to the Practical ability to

understand these Concepts and apply them

on real life situations and these things

are

interconnected um many times people

would wonder oh why do I need this

certain content from the mathematics

program to to my daily life uh but but

the problem is is not only necessarily

by this content per se but about the

skills that this this gives to the to

the students and how they can apply them

then in their lives and this goes to a

goes from things to financial decisions

to health decision Etc and particular I

wanted to say about the the role of a

per secondary it's very often the last

stage of formal education people are uh

in contact with and it's just before

transitions to the transition to

adulthood where students many when

people many times will have to uh will

need these skills these numerously

related skills uh to make decisions in

very very complex decisions in the real

the real world setting but in more in

terms of data because because you

mentioned that there's some financial

data um we know from many studies and

studies in the UK particularly that uh

low numy skills are related to poor

financial decisions and there was one

stud in particular that says the annual

cost of around 460 pounds per year uh on

individuals that have low low numeracy

uh skills but also like in employment

and earnings we have some data from DOD

from from the P survey of adult skills

that I I mentioned uh early uh earlier

uh that St people with high numeracy

skills are more likely to to be employed

and earn per hour up to 133% more than

the their peers with lower numeracy

skills and not only that but we actually

see that this this impact on employment

and earnings is more is higher uh in

when we compare the numerous the

difference in numerous skills than

actually the differences in in literacy

skills so it's actually very important

but also the so societal level I want to

to make a last point it does affect

productivity national income social

wellbeing there was another state in the

UK that mentioned more than 20 billion

pounds per year of losses coming from uh

uh low numeracy skills uh that a lot of

people uh that lot a lot of percentage

of young people had in society and this

is equivalent to 1.3% of the GDP at the

time um and this also brings a question

of equity and distribution of skills um

a lot of times people that come from

more privileged backgrounds um actually

are the ones that are caught on this

Perpetual cycles of disadvantages and

having lower numeracy skills not

reaching the opportunities not reaching

the well the best paying jobs and

actually cannot break the this this

cycle so it's really important to

increase the the social Mobility to

restore the social elevator but also to

respond to a diverse and high skill

demands of today's economy so just uh

just to tell you like where where like

for example we see in pza level two it's

what we call the minimum proficiency uh

in mathematics is important uh we need

more and this is what the data from Pak

that I show earlier wanted meant is

meant to to tell you is precisely it

matters what happens after 15 it matters

what happens at the age of uh a per

secondary education and even perhaps

further so it's it's extremely important

that yes students to take this

discipline and uh acquire the numeracy

skills they need to lead successful

lives thank you so much for that Eduardo

and thank you to everyone who is in

sending in comments and questions uh hi

to Rachel from Bristol saying hello

greetings from Australia from Kina uh

Mel in Denmark saying hello and there's

a question from which has just jumped

off my screen from Ivon Elliot so I'll

I'll uh pose this question I think to

who's who's probably best yal at Malang

I think is probably best this question

ion Elliot asks yter do you think

mathematics is taught in a manner that

allows students to appreciate the need

to learn

mathematics I'm not sure but I'm

also I was thinking about whether we

whether it should be like that whether

we want you know students to learn

mathematics or indeed learn anything at

least if we talking about primary school

children because they feel the need to

do it I mean when when children enter

school at uh at six or five or seven

they're sort of little learning machines

right they want to learn they're really

really curious about the world and they

want to learn about reading they want to

learn about numbers they want to learn

about the world and then for whatever

reason uh we managed to make them less

interested in in learning I think 's

report showed this really well that when

you have those International assessments

that can uh that that have a measuring

Point both at fourth grade and e8th

grade you see that the children are

generally less or the young people are

less enthusiastic about learning

mathematics and other subjects when

they're older uh which I think is one of

the major problems we have with with

education in general and perhaps

mathematics

in in uh mathematics specifically so I

don't know whether it's the way we teach

uh La misses out because we don't manage

to communicate to students why

mathematics is important or whether it's

we fail for making it as engaging or

interesting as it should be but I'm I I

would certainly agree that there is

something about the way schooling is set

out and the way that mathematic is

taught where we seem to be losing people

losing children along the way and that's

certainly not good and we can see this

also moving you know beyond lower

secondary into all the different tracks

that all our countries have in Upper

secondary that the experiences that the

students the young people have had with

mathematics previously certainly have an

impact uh let's say the more vulnerable

student group we work with our national

education system I have I have talked to

teachers saying you know we really need

to before we can even get into teaching

mathematics we need to you know remove

from them all the bad experiences

they've had with uh being taught

mathematics previously uh and I mean

that's certainly important and I mean

most of those exper experiences are

experienced in in primary school so

there is something about how mathematics

is taught whether it's mathematics

specifically or whether it's something

in general with our schooling model I

don't know but we certainly have

challenges on on on retaining motivation

as as children grow older whereas very

few people have a problem with you know

maintaining the motivation to learn of

six years old and seven year olds right

me that's just just not a problem but it

it it increases as as they get

older thank you so much for that and

just a quick followup for you if you

don't mind because what kind of mats are

we talking about when you're teaching

older students um in Denmark is it is it

understanding how to do more complex

equations for example or is it giving

young people um information on how to

understand things like mortgages in car

loans what's sort of math are we talking

about well it depends I mean so for the

end of uh of a lower secondary right so

the last stages in which everyone

basically follows the same track you

know what which you do until you are 15

or 16 I mean there are more formal math

than there is when they're younger but

there is also an emphasis on uh on

applied math I think you know the idea

of mathematical competencies which is

basically that you should have some

skills and you should apply them to the

real world I think that's very strong in

in the Danish uh curriculum for uh for

lower secondary then moving into upper

secondary it it depends even more

because you know there are there are

different tracks right I mean there are

the general academic upper secondary

what we call gimnasium in Denmark

following sort of a German tradition and

even within that there are

different uh tracks that you can choose

from and some of them go more towards

mer education something more towards

technical education and something is

just more General academic and in all

these three you know they're supposed to

mathematics is supposed to be different

but of course once you you you finish

what we call a level or mathematics I

mean it becomes especially the general

academic it becomes quite theoretical

academic but of course always with an

emphasis on you know it should be used

for something it shouldn't just be for

its own sake but then you have a

completely different track in Upper

secondary which is vocation Education

and Training where you essentially train

to do a specific profession right you

train to become a carpenter or you train

to become a

um um something else right A technician

of some sort and I mean most

of the majority uh of sort of the the

technically minded profession

professions will have some requirements

for math there and there the curriculum

for the math studies you do will always

be geared towards the profession right

so so to the greatest extent possible

the teaching should be done with

examples that are relevant for the work

that's also because students in in the

vet track are often in the ret track

because they wanted to study a

profession not because they wanted to

study mathematics per se so it's

important to keep motivation and

engagement that also math class seem

relevant thank you so much for that one

of the key questions that OC report was

looking at was if there's a predominant

culture towards maass in different

countries that can influence the success

of policies uh Linda Ramsbottom from

Ireland's education department you're an

inspector so you're probably going in

and out of schools meeting teachers and

students and so on even maybe parents is

there sometimes an anti-mass mindset

among those who you meet in Ireland yes

I suppose um my role as an inspector

we're part of the division of the

Department of Education and we have a

dual role as such we have an evaluation

of we started early year so from about

three four years of age all the way

through to 18 19 years of age so we've

inspectorates for each of the different

sectors and we would regularly undertake

a variety of inspection models and we

have announced and unannounced

inspections and during the announced

inspections we would often um have focus

groups meetings with parents uh during

our whole school evaluations and we'd

often have then during the regular

inspections subject inspections in

particular mathematics or program

evaluations with have a number of

programs that we offer in in post

primary we would have a number of

meetings with the focus groups of

students we don't we don't like to call

our those anti-ms what we call their

perception of their ability and it was

interesting when Eduardo put up there

about the the little you know what the

child said about their own understanding

of mathematics I was never good at it

you'd often hear parents saying I was

never good so I don't expect my child to

be good at them or the child themselves

would say my brother or sister was

always better than I was at mathematics

and sometimes there's a gender

difference there as well more recently

in the last couple of weeks we've

started a project where we are looking

at the transfer from the upper upper uh

post Primary School into the first year

second year in post primary and looking

with the with a specific focus on

mathematics and we call these um an on

they're announced inspections for

incidental so it happens in in

incidental model and we're talking to

children and it's really interesting

listening to their voices and the kind

of the motivation that they have and

already they're having preconceived

ideas so that mindset is set nearly

before they even enter the post primary

lower post primary and then that'll

manifest itself as they go through I

think kind of come back to what you were

talking about a few minutes ago well

well we don't call it anti-at we think

it's kind of a perception about their

abilities um and I suppose looking at it

you know as they're how they're

motivated to learn and in Ireland I

suppose we can see as they move in to

the at the teaching practice that they

engage with they'd often say to you in

sixth class mind when I go into first

year the lower secondary it's going to

repeat of sixth class when I get into

second year there's a jump in my

education it's very different and then

we're ready for our first um high stakes

exam in the third year in lower

secondary and that determines sometimes

the approaches the methodologies that

are engaged with during the classes so

it can be once you get to high stakes we

find sometimes at the inspectorate we

would see the teachers per teachers um

pedagogies change um maybe sometimes

maybe it's not as engaging it's more you

know take it down from the board let's

make a note of this let's do the next

one do the next example do the next

question so I think pedagogi does have

an important influence on what happens

also coming back to something Edwardo

said there in Ireland in the last we've

had significant change in our curriculum

and I suppose in 2009 we had literacy

numeracy strategy but coming back to

numeracy in our new curriculum for

junior cycle the first three years of

lower secondary we' now have key skills

and we're looking at moving from a kind

of a comp a Content based curriculum to

a more skills based and one of the key

skills we have at Junior cycle would be

being numerous and what that entails and

moving into our post senior end our

upper secondary we're now looking at

revising our curriculum for upper

secondary and we're talking about key

competencies and we wrap around key

competencies we've ate key competencies

um but the real the main focus ones are

literacy anderes again and in each of

the curriculum specifications that are

being designed those key competencies

must factor into how the curriculum is

designed we've done it at Junior cycle

lower end but now we're moving it so

numeracy is quite a strong feature in

our mathematics and ensuring that

everybody has the ability and the skill

set um to implement it in Beyond

mathematics in other curriculum areas as

well so it's quite an interesting um

link that Eduardo has made as well

between mathematics and numeracy and

what we've done in Ireland so we're

still under a pathway of change

significant change our primary

curriculum is changing our early years

curriculum and framework that we use at

Asher is changing

also thank you for that Linda if I can

bring yelta back in on the question of

an anti-mass mindset is that much of an

issue in Denmark or

not I think I would say much the same

things Linda said right indeed building

on what I said before

that in many way mathematics might be an

Unforgiven subject right I mean at least

it's perceived as such uh that just

to say it really really really simply

and probably too simplistic but you know

an equation is either right or wrong and

making quite a few students scared of

mathematics right it's harder to just

Venture a guess or indeed having a a

discussion about let's think about this

problem mathematically because many

students think that mathematics is not

something you discuss right it's not

something where you reason together it's

something where you have you calculate

and then you have a right or a wrong

answer and that's not you know what

we're looking for in our curriculum

because we actually want students to be

able to see well we have this real life

problem let's translate it into

mathematics and then let's do some

calculations take the Cal the the

results of the calculations and

translate them back into real life

um and that's not often understood you

know it's more the Precision of

mathematics is often what people take

away from it so I wouldn't say anti in

the way that people have a coherent you

know opinion where they don't like math

it's more that I think the the quote

that Edo had on his slide you know

mathematics is just not for me or I've

had bad experience with mathematics in

the past is is is deeply ingrained in in

some student

who might also have had you know parents

saying exactly as was also on that slide

you know mathematics we were never good

at mathematics in this family um and I

think you know these kind of reactions

you can get that with students that have

had bad learning experiences in the past

you can get them in in any subject right

it's it's also really really really

prominent when you try to uh do dyslexia

teaching for adults that have just like

where reading is almost a traumatic

experience but I do think even though

you can get it across the Bo of subject

it's just it's prominent in mathematics

so it's not an anti I wouldn't call it a

culture in that you know it's not like

the the quotation from runak where there

are something in our culture where we

dislike math it's more that you know the

particular the more micro level

engagement that people that students

have had earlier on in their learning

careers uh with mathematics have made

them you

know like like that subject less and

then you know that's something you need

to work on a quick followup for you is a

question from Quan who's talking about

the rise of AI and other technologies

that can easily solve math problems is's

talking about and in a world of AI where

you can ask a computer to work out

almost anything specifically everyday

math questions um how is that impacting

the teaching of math and does math need

to

adapt so as I understand it uh AI is a

language model so it's actually much

worse I think the OCD did a project

where they tried to make uh artificial

intelligent work on on different uh

things and and you know in general they

they are less good at math than at

wordss your traditional computers are

good at words the sort of langu large

language models they're good at words

not numbers which is why they're

interesting anyway so of course you know

the society we live in uh impacts how we

should do I mean if for no other reason

as education systems we need to engage

with AI because it challenged our

examination model uh perhaps less so in

mathematics than in other subjects but

in Denmark we have sort of like long

form written assignments is quite quite

typical of how we assess and I mean

that's obviously the most AI vulnerable

way to assess so we need to we need to

take account of the fact that students

will probably use AI whether we want

them to or not so in that way we should

adapt but I mean at least personally I

haven't I don't think it's it's at least

currently I don't think there is any

need to revolutionize how we teach or

that there are any of the skills and

competences that we think are important

there none of those competen have become

less important with AI I don't think so

thank you so much for that again and I'd

like to for a moment if we all agree or

if most people agree watching this that

it is important for young people to

learn maths to a later age to 18 for

example uh as suggested at the start of

this webinar um how do you go about

doing that in practice particularly for

other countries where it might not be

the same approach uh Linda uh what

approach does Island

take yeah we have um at at the upper

senior cycle we have um we call it

senior cycle uh after our three-year

compulsory education up to the age of 16

or there about students can have the

option then of what we call a one-year

transition program so there's a one year

where students it's an optional program

and they can act up opt in or opt out of

the program if the school offers it in

their in their school in their school

area and and that would actually allow

them to follow on continue on with their

maths education in some format it

doesn't have to be formally it could

follow some aspects of the curriculum

for senior cycle but it shouldn't always

be in the full curriculum and then after

that year you have the two or three

further options we have what we call the

leaving certif leaving certificate

established and that offers three

different options to the students three

different levels of mathematics are

offered in that um leaving start

established we have a foundation level

which really cases for students

abilities who may want mathematics for

everyday life and may not want to go on

to further studies but may need it as an

access point to maybe a trade or an

apprenticeship we then have we call the

next level up will be ordinary level and

in the ordinary level then that will be

Geared for students who who are dealing

with kind of abstract they're starting

to begin with abstract IDE ideas um and

they would access the third level

education at a different level to what

their needs would be but the higher

level then is the top level we would

have in our twoyear final two years of

examination and that is geared towards

students who want to progress the

further studies of mathematics or other

disciplines associated with mathematics

and that would be developing um I

suppose the powers of abstraction and

generalization so there are the kind of

traditional established leaving

certificate the leaving certificate

applied then is a standalone two-year

program however more recently that has

um we've allowed the students to to who

are taking the leaving certify program

to access the leaving certif leaving

certificate established mathematics so

they can opt to do their leaving C

Applied Mathematics and and or follow

the ordinary level or higher level or

Foundation level depending on the school

so we have a range of options available

to students so we don't just after the

junior cycle that's it you don't have

options there are three more levels that

they can continue on with um and I

suppose after that we would um um we

also offer for students who take the

higher level program the higher level

option we've brought in um a bonus point

we call it that's purely for students

who want to go on to third level so they

get an extra 25 bonus points we call it

all of our students who sit their

leaving certif leaving certificate um

receive based on what award they receive

a H1 or whatever it is they receive

points and an additional point is added

on for higher level math matics not for

ordinary level not for foundation just

for higher level so I suppose they're

the kind of ways the the curriculum ways

that we can support

students sorry thank you very much I

need to unmute myself um a quick

followup for you actually because

there's a it's a statement from elizabe

Pastor on the chat who says my

experience is that people think that

being good at mathematics is a question

of talent and not of hard work this is a

serious problem if teachers reinforce

this impression what what experience do

you have uh in irland related to that

kind of issue yeah I suppose from my

perspective being in and out of

classrooms we can see that that there

are some teachers who would perceive

that a student if they're talented

they're excellent they'll be very good

at mathematics it's not always the case

you always have to you will see students

who would try their best and work hard

and will be quite good mathematically I

think sometimes it's how they it's their

motivation I suppose their exposure from

an early stage of as as we've already

spoken about I suppose you know that

need to kind of tease out questions talk

through the possibilities not just one

answer is the only answer and maybe yes

there are talented kids who are quite

good they will get to An Answer without

even thinking about or writing anything

down but some students have to work

through a process and I suppose it's the

ability of a teacher to understand that

some students have the ability to an

innate ability to understand and

different way and that not one approach

is the only approach and I find

sometimes in my inspection work we can

see that that it has to be the teacher's

way to do the question and not allowing

for the creativity amongst the students

and understanding and teasing out why

did you say that is there a

misconception here and using that

misconception to develop a students

understanding what's happening in the

Math's classroom so I think you are

right I think Talent is always

misunderstood as being very good at

mathematics it can be hard work that you

need to think about it work through and

see different problems in in different

ways and in different

contexts thank you so much I want to

bring Eduardo back in to get his

Reflections on some of the past few

comments also there's loads of stuff

going on in the chat apologies right now

it's moving so quickly I'm actually

struggling to read it but yeah AO if I

can bring you back in what are General

approaches that the oecd is taking oecd

countries I should say are taking to

encourage people to to stay in Ms yeah

so um building up uh on what building on

what Lindo was was talking about is very

important to understand that in

mathematics and particularly in F

fundamental disciplines like like

mathematics there is a individual

individual development rates and not uh

every not every student does develop it

like at the at the same Pace uh so I

mean while while for instance some some

students might have a great great skills

uh at 15 many many do need like after

after after 15 16 to solidify solidify

this FAL so I think the main the main

conclusion we take by looking at the

different o systems is the importance of

flexibility a lot of times when there is

no flexibility on how we provide

mathematics how we teach mathematics we

we might uh get students stuck in

certain milestones and then experience

problems of cycles of repetition of dis

motivation of this sense of failure and

um these more on the on the on the

policy side of the provision of

mathematics and um the assessments

actually there was a comment from I

believe Elizabeth that mentioned the

Reed in gcsc and this is actually a

great example to to to bring during this

discussion because in England for

instance when we saw at 16 when students

take the the match CSS and they don't

achieve grade four um when they don't

achieve at least this grade four they

need to take these resits meaning they

need to after 16 continue to do to try

to pass and a lot of times uh they just

get stuck on this cycle of repetition of

doing the same thing over and over again

which might imprint this sense of

failure this the motivation and also

create this fear of mathematics this

horrible thing they cannot get rid of um

so it's an important policy question if

uh the one fit size fits all policy is

actually the most effective approach and

uh in indeed it is not we need like a

diverse range of solutions um the the

the what Linda described as the like the

the Irish case with the different levels

or even we know also from d Mark there's

there is diversity are definitely a are

very important strategies to to do this

and to to make sure that we have a Tor

offer of students on how according to

their strengths and interests uh but the

main point here I I will I will say

again because it's really important to

to to say this is the diversity and um

there are also other ways for instance I

want to bring in the example from

Austria which is one of the peer

countries although for instance Austria

uh only have one maatic option in each

program that is mandatory uh there is a

variety of programs as offers many

programs and in particular in the

vocational uh sector uh it's extreme is

a extreme reach sector in which they

have mathematics taught in different

forms in many cases applies as well as

in different subjects ma imprinted on

the way they they they teach some trades

and some some other subjects and this is

extremely important because it provides

uh diverse range of Pathways uh and it

guarantees at least that students uh can

can can deal with Matas in different

ways and not and not only in one which

is important for their success and for

for their engagement um so yeah I would

say I would say definitely this is one

of the main messages uh we wanted to

bring is to uh one size fitall policies

normally don't work that well and uh try

to be open to to cater from the French

students thank you very much Eduardo and

thanks for all the messages coming in on

the chat as well I'll quickly run

through a few of them uh vmir writes

excellence in maths is a gift from God

which demands hard work but Maths for

every day is a result of hard work only

um in contrast I'm trying to ZIP down

here uh Vester writes mathematics is not

only talent but also hard work and it's

needed to develop logical thinking in

solving problems and there are loads

more comments as well but we really

don't have time to go through all of

them Y at Malang from Denmark's children

and education Ministry if I can bring

you back in because I want to talk to

you about student perceptions which we

did touch on earlier on Denmark does

comparatively well in math to those who

don't know uh internationally uh but

when you look at student perceptions

there is quite a big drop off between

primary and secondary schools and the

decline is pretty big in Denmark we see

this trend in lots of countries but the

decline is pretty steep in Denmark so

why do you think that is and is anything

being done to try and combat

that so I think I I I spoke to that uh

earlier right that there is there seems

to be a general uh problem with uh

children being more motivated to learn

than younger uh than um than older CH

older children and then you know old

older children becoming less motivated

as they go older so I mean we don't I

don't think we have any particular

policy on sort of like say the the stage

where you move from upper secondary to

lower secondary on but it's definitely a

part of our general let's say problem

description uh a couple of years ago we

had an expert group on mathematics

across uh both uh basic education and

upper second theory and all the the

tracks within the upper second that's

tried to uh look at at a a holistic

picture of mathematics teaching in

Denmark and you know this this issue

that you're talking about with the

students being disengaged is definitely

a part of that problem especially

because it means that it's um I think I

I'm repeating something I said earlier

but uh it's harder to teach a class

where you have not only

a uh not only variation in skill but

also a variation in motivation and a

motivation in self efficacy so uh

especially for uh um our vet tracks and

also our tracks for those that didn't

find an easy path path through education

uh there are quite a few students there

that that really have this uh

mathematics was not for me mindset and

you know that's definitely something

that you need to to address and I think

that's probably addressed best

uh by using different strategies in the

different tracks of Education because

you have different students so in the

sort of more practically oriented uh vet

track I think it's one one good way of

addressing motivation of students is to

show how mathematics is relevant to the

profession that they are there to learn

I mean they're motivated to train that

profession that they elected into and we

then think that it's probably good for

them to have some general mathematics as

well but that General mathematics should

be taught so that it's always clear to

the students that it's relevant then if

you go to academic up a secondary where

students or at least some of them are

are should be prep prepared for study in

The Sciences physics mathematics

chemistry where you kind of need

abstract Advanced mathematical skills um

in that way it's probably okay to focus

more on mathematics in its own in its

own sense so I mean I think it's uh just

as most countries in the world have more

differentiated education systems after

the age of 15 16 right and I think the

the solutions for this for how to cheat

math best is probably to build on

whatever was built into your system and

then tailor the teaching of math to uh

whatever track the students are in thank

you very much Linda if I can bring you

back in on the subject of lifelong

learning um we spoke we focus a lot on

you know students and then you know um

Yalta there was just explaining you know

differences between primary age and the

age of 15y old but what about adults how

do you engage or re-engage adults in in

math so that they're better equipped to

deal with societies which are becoming

more complex with more complex data and

more complex

Technologies Now in Ireland we have a

dedicated support service we call it

it's it's like teacher it's an Irish

word for um teacher um it's a

culmination of a number of support

services that we've had over a number of

years they traditionally they would have

had um an opportunity to engage with

teachers through um you know a variety

of different supports and now it's

emerged into this one dedicated um

support service and I suppose in terms

of mathematics we have um it provides a

support service in terms of one day um

release from school so teachers of

mathematics when a new curriculum is

established they have a number of days

one usually one or two per year and the

teachers would access that in addition

then the support services also have uh

worked on initiatives what we call um

numeracy Deep dive where the mathematics

teacher would collaborate with an we

call it um a carrier subject so would

say maybe geography or something like

that would have a level of mathematics

in it and it kind of promote numeracy in

the classroom and promote good

mathematical skills and competencies

throughout the system so you have a peer

working with you so your colleague would

be working with you to develop your

numeracy skills but also to support the

consistency in approaches and and

language that was used in the

mathematics class into other discipline

areas we would also have um out of field

report so teachers who want to come back

in and re-engage as a mathematics

teacher um the department has funded

since 2012 we've had two versions 2012

to about 2018 and 2019 then it started a

second um uh phase of this um support

the department will fund um upskilling

of teachers who want to come back into

the education system who have a degree

but are not mathematics teachers and

that has helped us to a certain extent

with supporting the lifelong learning of

teachers in

mathematics thank you so much look we

are almost out of time but I'm going to

do a quick fire around with our panelist

just before they go and thanks to

everyone again for sending in your

questions so yal I think I'll start with

you um if there was one suggestion for a

priority action that countries could

take to make maths more appealing to

more students if we're talking about

this culture of mathematics what

priority action would you recommend to

make maths more appealing to more

students

I think it's probably uh important to uh

make sure that students have early on

the right foundation so focus on letting

what we in D is call number

comprehension which is the basic Al

algebra that then too many students miss

out on that and then that just haunts

them for the rest of their education

system so sort of teaching them the most

important most foundational stuff early

on and then you know kindling the flame

and keeping it alive by by not making

them experience defeat after defeat

because they missed some basic stuff

early on would probably be very

important thank you very much and Linda

Rams botton totally agree and I suppose

we have a policy now that our literacy

numeracy and digital literacy strategy

if and get all my strategies out here we

had uh initially was in primary and

post- primary now we' brought it back to

the early year settings as well so we've

included the early year settings with

numeracy so developing that love and

that fun and the sense of achievement at

an early stage and developing it through

through practical you know real life

experiences and the continuity

appropriate continuity and teasing out

those questions with kids that's what I

would recommend if I could at all thanks

ail thanks so much and last but not

least oec policy analyst Eduardo madish

uh what do you think uh how do you make

maths more appealing to students what's

the one priority action you'd recommend

well our work is mostly on up per

secondary education and I I mean and

yelta and Linda already talked very well

about the previous the the younger age

than the primary but I would like to say

that at least at the per secondary

education level it would be important to

adapt to needs of all students uh

regardless of their previous experiences

we should build um diverse Pathways to

make sure they actually can many times

catch up they can change the perception

of mathematics and they can build the

skills they actually they need uh for

the future and to keep the doors open so

again I wanted to underline the question

of option levels also some Bridge

programs uh I this focus on not leaving

anyone behind despite uh any negative

experiences before I think it's the main

the central point I want to make on how

to improve the relationship with with

mathematics thank you so much to Eduardo

from the oecd of course also to yaa

malvan from Denmark's children and

education Ministry and also to Linda

Rams Borton from Ireland's Department of

Education that is it for now I'm afraid

thank you to the production team for all

their help behind the scenes and thank

you for tuning in for this o webinar we

will have plenty more of them in store

for you right up until Christmas uh

please do check out the new oecd report

Maths for life and work which this

webinar has been based on you'll be able

to learn much more about what we have

discussed the link was shared in the

chat also please do also check out the

oecd education podcast top class which

has featured various episodes on

mathematics including a chat with the US

teacher of the year who happens to be a

math teacher herself that's it for now

hope to see you for another o webinar

soon all the best