Date: Jun 29, 2012 3:04 AM
Author: Jonathan J. Crabtree
Subject: Re: How would YOU simplify arithmetic?
Thank you all for sharing your thoughts.
BOB you ask a good question, "How does making school more simple help?" and later suggested my topic was a contradiction rather than a question.
In Australia four million adults out of 7 million of working age do not have sufficient numeracy skills to function in society. Every day thousands join the unemployment queue as manufacturing and retail jobs disappear. We are leaving the agricultural and manufacturing era and entering the information age.
STEM will increasingly be important if we are to solve problems that matter. The more children we help get though K-6 the more likely STEM subjects will be studied at tertiary level. However at the moment, there is a shortage of math(s) teachers in Australia. It is a downward spiral.
My two sons, now at uni studying science, scored 99. If they wanted to become K-6 teachers they would only have needed a score of 59.
ACER research shows correlation between teacher pay and student performance. Maybe teacher university entrance scores more reveal causality of PISA scores. the Asian countries generally require more academic performance before people can become teachers.
So "How does making school more simple help?"
Making arithmetic simpler may reduce the number of children failing math at school. It may increase the number of students studying math as the foundation of STEM subjects. Making arithmetic simpler will also make it easier for teachers to understand math.
Making arithmetic easier will also reduce the number of people who feel failures for the rest of their life and increase the number of people earning higher incomes and/or increase the number of people who lead happier lives.
India participated in PISA 2009+ and appeared second last to Kyrgyzstan out of 74 countries. So forget documentaries like 2 million minutes that portray India as a math superpower. This year India will not participate in PISA testing. As India created modern arithmetic (zero as a number) my goal is to help fix the problem of arithmetic in India first.
Anyway, why not make arithmetic simpler? Everything else gets updated and becomes new and improved! My agenda is not that of a department, union or mafia. It's just to see if a simpler arithmetic can be accepted.
I understand arithmetic differently and seek to explain it more simply then previously. As per my post, any changes I may suggest are natural and not pedagogical.
HAIM, perhaps you jumped to a false conclusion. I do not claim a linguistic blend of eleven, twelve, thirteen with an Asian approach of two-one, ten-two, ten three alone warrants a math revolution. That approach is only a part of the solution.
For example Finland is the current fashionable flavour for math, yet their language is truly atrocious for counting. The number 18 is kahdeksantoista meaning 8 of the second, which is perhaps sillier than our dyslexic eighteen. Ninety-eight is yhdeksänkymmentäkahdeksan.
I do agree with your statement Haim, "You should make things as simple as possible, but no simpler." which as you know is Einstein's Razor morphed into ASAPANS (As Simple As Possible And No Simpler). As for not holding your breath for an arithmetic simplifier, it took me 25 years to arrive at just one good idea.
CLYDE you presented two great papers which my youngest son explained to me. What I am creating is like Peano logic yet operating at the integer level. If somebody has rewritten Grassman's work to include axioms, please share the link. Grassman proved the rule of signs (negative times negative is positive) inductively. I'm told Grassman defined multiplication inductively by:
"Any number m times 0 is defined as 0. If n is a positive number then m times n is defined as (m times the number preceding n) plus m.
If n is a negative number then m times n is defined as (m times the number following n) minus m.
Then Grassman proved proved the rule of signs inductively from that."
As some may know, I start from an integer set and explain arithmetic via bumps and holes. What I hope my next post my prompt, is formal 'math speak' that either proves or disproves the value of my approach. I am not optimistic any arithmetic simplifiers found will catch on in the USA as it, Liberia and Myanmar refuse to embrace base ten.
PAUL thank you for your post on fractions provided in response to a post by Wayne. I appreciated your thoughts as downunder in Oz, four out of three kids get mixed up over fractions. <joke>
DOMENICA my dad was the only teacher in a one room school in Bylands Victoria Australia in the 1960s. He was one of the first to use Cuisennaire rods. I believe much more of math can be taught in parallel than serial alone. Why wait until you are 13 to understand something a six year old can understand? My big sister hung around my Dad's school and learnt so much from the older kids. (She in turn taught me pythagoras in a tent on a camping holiday.) Kid to kid transmission can work, yet not when a system is involved. (Maybe I should ask more children how THEY would simplify arithmetic?)
JOE I hope to be able to share some research on PISA scores vs language to address the Gladwell theory. I define simplicity via ASAPANS (As Simple As Possible And No Simpler)
GS CHANDY provided useful tools to help solve problems and Cool Jessica provided a useful definition.
I see my contribution as an editor, seeking the minimal set of ideas that will deliver an outcome. My motivation is that I failed math at school, smashed my spine, was told I may never walk again, made a promise to fix math if I could walk, walked and have been trying to keep a hospital bed prayer/promise since 1983. I wield no power or status.
As a naive (amateur) explorer, I believe I have made basic math simpler and along the way have received positive comments from students in 70+ countries, several of whom are math teachers.
My next post will outline my framework for making arithmetic simpler. Then I hope subsequent ideas will be seen in context.