Just finished reading an interesting paper on how different scenes in a mathematics classroom and students’ heterogeneity in it are related.

The paper concludes that mathematics classrooms must gear up for independent learning through multiple ways. Unfortunately, the factors underlying heterogeneity can rarely be found in different paces of work and in individual mathematical deficits that dominate everyday teaching. Those factors can be found in many aspects by which learners surprise us everyday.

An important condition for finding resources, the paper argues, is to break away from deficit-oriented consideration of students’ abilities (Who is still not able to do??) in favour of competence-oriented considerations (What are they able to do??). If such a change of perspectives can extend our understanding of what counts as performance in mathematics classrooms, we can get good conditions for a productive way of addressing diversity.

PUZZLE 1: Eight players participated in the recent Cucumberland chess tournament; each participant played against all of the others exactly once.

The winner of a game received 1 point and a loser 0; draws were allowed, giving each player 1/2 point. Now, it turned out that everyone received a different number of points. Furthermore, Molly, who came in second, earned as many points as the four bottom finishers put together. What was the result of the game between Waldo, who came in third, and Basil, who came in seventh?

PUZZLE 2: Divide Rs113 (in whole rupee increments) into a number of bags so that I can ask for any amount between Re1 and Rs113, and you can give me the proper amount by giving me a certain number of these bags without opening them. What is the minimum number of bags you will require?

Solutions on December 19

CORRECT ENTRIES

November 28

Trisha Biswas, Calcutta-40; Ramit Sarkar, Ichapur; Madhab Datta, Purulia; Debratna Nag; Sreechandra Banerjee, Calcutta-19; Mukulika Jana, Hooghly; Debasis Ganguly, Alumnus Software; Shayak Bhattacharjee; Manish Bakshi, Calcutta-28; Arnab Kr Sadhukahn, Jadavpur University; Jnanendra Nath Ray, Calcutta-48; Ravi Raja, Calcutta-20; Ashish Dattani, Calcutta-25; Dhrubajyoti Daityari, Santoshpur; S. Krishnaiyer, Calcutta-8; Subrato Ranjan Das, KITS, Bhubaneswar; Bithi Sengupta, Dum Dum Park; Arundhati Das, Barrackpore; Sunidhi Sharma, Jamshedpur

CORRECT ENTRIES

November 21

Debasish Ganguly, Alumnus Software ; S.K. Choudhary, Durgapur; Snehal Doshi, Calcutta-25; Subha Ghosh, Jamshedpur; P.K. Majumdar, Calcutta-39; Saikat Datta, Bandel; Indrajit Paul, Bokaro Steel City; T. K. Sengupta; Subhadip Chatterjee, Asansol; Samir Ghosh, Contai; P.K. Choudhary, Durgapur; T.P. Chattopadhyay, Ballygunje; Sukumar Sharma, Jamshedpur

PUZZLE CRACKED

The response this week was lukewarm. How do you feel about the Waldo series? Please let me know.

Solution 1: It’s clear that Mortimer had to have been born in the 1900s, and his grandfather in the 1800s. If Mortimer was born in 1900+x and his grandfather in 1800+y, then 1900+2x=1800+2y (the year this happened), and so y=x+50. Now any odd prime number plus an odd number must be greater than 2 and even and so not a prime; hence Mortimer must have been 20-something. But 25 and 27 are not prime, so Mortimer must have been 23, and so his grandfather was 73 (which is indeed also a prime). It follows from this that the year was 1900+2x23=1946.

Solution 2: It could be either 879-9912 or 989-9901, so perhaps Waldo isn’t that absentminded after all.

The puzzles appeared on November 28.