-
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
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the education system who have a degree
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but are not mathematics teachers and
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that has helped us to a certain extent
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with supporting the lifelong learning of
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teachers in
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mathematics thank you so much look we
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are almost out of time but I'm going to
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do a quick fire around with our panelist
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just before they go and thanks to
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everyone again for sending in your
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questions so yal I think I'll start with
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you um if there was one suggestion for a
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priority action that countries could
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take to make maths more appealing to
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more students if we're talking about
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this culture of mathematics what
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priority action would you recommend to
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make maths more appealing to more
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students
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I think it's probably uh important to uh
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make sure that students have early on
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the right foundation so focus on letting
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what we in D is call number
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comprehension which is the basic Al
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algebra that then too many students miss
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out on that and then that just haunts
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them for the rest of their education
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system so sort of teaching them the most
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important most foundational stuff early
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on and then you know kindling the flame
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and keeping it alive by by not making
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them experience defeat after defeat
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because they missed some basic stuff
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early on would probably be very
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important thank you very much and Linda
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Rams botton totally agree and I suppose
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we have a policy now that our literacy
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numeracy and digital literacy strategy
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if and get all my strategies out here we
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had uh initially was in primary and
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post- primary now we' brought it back to
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the early year settings as well so we've
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included the early year settings with
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numeracy so developing that love and
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that fun and the sense of achievement at
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an early stage and developing it through
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through practical you know real life
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experiences and the continuity
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appropriate continuity and teasing out
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those questions with kids that's what I
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would recommend if I could at all thanks
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ail thanks so much and last but not
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least oec policy analyst Eduardo madish
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uh what do you think uh how do you make
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maths more appealing to students what's
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the one priority action you'd recommend
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well our work is mostly on up per
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secondary education and I I mean and
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yelta and Linda already talked very well
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about the previous the the younger age
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than the primary but I would like to say
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that at least at the per secondary
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education level it would be important to
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adapt to needs of all students uh
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regardless of their previous experiences
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we should build um diverse Pathways to
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make sure they actually can many times
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catch up they can change the perception
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of mathematics and they can build the
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skills they actually they need uh for
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the future and to keep the doors open so
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again I wanted to underline the question
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of option levels also some Bridge
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programs uh I this focus on not leaving
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anyone behind despite uh any negative
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experiences before I think it's the main
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the central point I want to make on how
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to improve the relationship with with
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mathematics thank you so much to Eduardo
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from the oecd of course also to yaa
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malvan from Denmark's children and
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education Ministry and also to Linda
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Rams Borton from Ireland's Department of
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Education that is it for now I'm afraid
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thank you to the production team for all
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their help behind the scenes and thank
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you for tuning in for this o webinar we
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will have plenty more of them in store
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for you right up until Christmas uh
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please do check out the new oecd report
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Maths for life and work which this
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webinar has been based on you'll be able
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to learn much more about what we have
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discussed the link was shared in the
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chat also please do also check out the
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oecd education podcast top class which
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has featured various episodes on
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mathematics including a chat with the US
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teacher of the year who happens to be a
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math teacher herself that's it for now
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hope to see you for another o webinar
-
soon all the best