Feb 22

Can math education professors and the K-8 teachers they train answer these two Grade 5 level questions? (Exp. 15 March 2022)

You'd expect it would be pretty easy for mathematics education professors and the K-8 level teachers they train to explain simple addition, subtraction, multiplication and division of integers. The integers you'll recall are the positive and negative whole numbers on either side of zero on a number line.

One thing all the books below have in common is explanations of the four basic operations: addition, subtraction, multiplication and division.

1522 The art of calculation in four books

In 1522 The art of calculation in four books became the first mathematics book printed in England. It's Latin title was De arte supputandi libri quattuor and its author was an English Catholic bishop called Cuthbert Tunstall. Cuthbert got his ideas from the Italian Luca Pacioli's 1494 Summa de arithmetica, geometria, proportioni et proportionalità. Luca got his ideas from Piero della Francesca's, Trattato d'abaco (c. 1465). Piero got his ideas from Leonardo Pisano's book Liber Abaci from 1202. Leonardo, also known as Fibonacci, got his ideas from North African traders who followed the arithmetic of the Persian al-Khwarizmi written in Arabic around 825 CE. The Latin title of al-Khwārizmī's book was Algoritmi de numero Indorum (Al-Khwārizmī Concerning the Hindu Art of Reckoning). He in turn, got his ideas on arithmetic from the Indian, Brahmagupta, who documented the four basic operations with rules of negatives, positives and zero in 628 CE.


Without resorting to abstract laws or rules, show how you use classroom manipulatives to explain:

So a Grade 5 child can understand and explain why, for example –1 × –1 = +1
So a Grade 5 child can understand and explain why, for example +12 ÷ –4 = –3

To enter, simply upload a video to YouTube before midnight 15 March 2022 AEST with #QuincentenaryQuiz in the title and as a hashtag AND email research@jonathancrabtree.com

The first entry
uploaded to YouTube from a current mathematics education professor or K-8 level teacher IN AUSTRALIA as adjudicated by mathematics historian Jonathan Crabtree to have explained and/or defined multiplication and division correctly and demonstrated simple visual solutions using classroom type manipulatives (i.e. successful solutions cannot be reliant on written instantiations) will be awarded the AUS$500 prize to be paid in full by 31 March 2022 via PayPal or VISA Debit Card at the winner's discretion. Both questions need to be answered. Should two correct entries be uploaded the same day, the winner will be whoever lodged their entry via email first. Entrants must provide their definitions on multiplication and division they CURRENTLY USE WITH CHILDREN OR STUDENT TEACHERS and answer the questions directly, without changing the question. E.g. changing the division task into a discussing of multiplication is avoiding the question. All entrants must provide evidence of prior knowledge and existence of their proposed solutions. If there is a set of correct solutions provided, all entrants will have the suggested solutions of the winning entrant emailed to them by 15 April 2022. All entries become public domain and permission is granted by the entrant for sharing in any form. If there are no successful entries, the QUIZ WILL JACKPOT TO AUS$1000 in a future challenge with the same two questions and be open to mathematics education professionals both within and outside Australia. It is understood such questions may not be formally addressed in your institution's curriculum for Grade 5, yet that would not stop a teacher from answering these questions from a Grade 5 level child. Total prize pool AUS$500. Friends and family members of the promoter Jonathan Crabtree cannot enter. For any clarification and/or question, please email Jonathan Crabtree via research@jonathancrabtree.com Judges decision is final.