Friday, October 9, 2020

Blockchain 101

 

The Basics

News/Media

 

 

 

Grades Vs. Efforts

 Yesterday,  I received my son's final assessment report for Grade 2. He did get good grades (mostly A+, a few A's and one B+). I chuckled at the overall assessment because I wasn't sure what I could make out of it. Being the skeptic I am on any non-independent assessment in this rampant grade inflated era, I wasn't sure if the report is actually helping me or my son. While he tried explaining to me why he got a B, I told him that wasn't my concern at all and that I am indeed happy because there is scope for improvement. I told him that I was concerned about the A+s and As.  He didn't quite understand. I thought about how I could explain this to a 2nd grader. Then I drew a version of the picture below and told him that the most preferred place to be is #1 and least preferred is #4. And I told him that I don't have enough information whether he is placed  #1 or #4 as the assessment is not outside his school and more importantly difficulty is not known. . Since he had previously written Math Kangaroo, I managed to use that as an example for independent assessment.


I don’t know if he actually understood what I told him, but he sure understood that just getting a A+ or A will not impress me

Ubuntu 18.04 and Unison

 I have been using Unison for several to sync files and I recently upgraded to 18.04 LTS.

Unision will no longer synch between the upgrade machine and my local machine. When a file is copied from my local machine to the upgraded machine, it copied well but the otherway around got an error
unison loadlocale.c _nl_intern_locale_data: Assertion `cnt < (sizeof (_nl_value_type_LC_TIME) / sizeof (_nl_value_type_LC_TIME[0]))' failed

After some trial and error the following workaround helped

1. Rename the unison executable. You can find it under (/usr/bin/unison-x.xx (to for e.g. /usr/bin/unison-x.xx.exe)
2. Rename the unison symbolic link /usr/bin/unison (to for e.g. /usr/bin/unison.exe) and  make it point to the new renamed executable in Step 1.
3. Create the following shell scripts and save it under the 2 original names
#!/bin/bash
LANG=C unison.exe "$@"

Worked like a charm. I know I will have issues when upgrading unison but I am hoping the bug in loadlocale.c is fixed before that.
Notes

a) You will have to be logged in as root for steps 1-3
b) Step 1 is necessary because when synching from a Windows machine through ssh, it searches and invokes unison
c) Step 2 is necessary because when synching from a Mac machine through ssh, it searches and invokes unison-x.xx
d) This workaround could've been made simpler for e.g. creating only one script, etc. but I wanted to retain the original deployment structure. When the issue is fixed all I have to do is to delete the scripts and do a rename.

Learning from Top Students




The video is about research findings across thousands of high school students in Australia, UK and the US.
Key observations

  1. IQ does not matter for success in schools
  2. Hard work is necessary but not sufficient.
  3. Behavioural traits of top students include - self motivation, self discipline and resiliency (i.e. keeping at it even when marks go down in a test).
  4. Memorizing doesn't help - Tests are about how you use what you remember, not what you remember.

What Top students do that you can do

  1. Do more practice exams.
  2. Create a study timetable with first putting all the times you will not study (where you do other things), and then fill in with the times you will study.

Some notes Feynman Technique for learning anything


Summarized from Genius: The Life and Science of Richard Feynman.

  1. Write up all you know or want to explain about the topic. This is will be a work in progress and the material will increase when your knowledge increases. In the electronic medium you want to want to write up a blog page for that or a separate One Note page.
  2. Pretend to teach it to a classroom - or to self.
  3. Identify areas you are shaky, stuck or not confident - Go back to sources and review.
  4. Identify any technical jargons in your explanations, simplify them using analogies/metaphors.


Some Notes from Five Principles of extraordinary math teaching

  1. Start with the question.
  2. Students need time to struggle. Dont provide solutions/answers. Some math problems should take hours or days to solve.
  3. You are not the answer key. Dont provide answers, instead ask why it is true.
  4. Say yes to ideas - even wrong ideas - don't dismiss them. Rather explore them.
  5. Math is not about following rules - but playing
https://youtu.be/ytVneQUA5-c
 

AMC 8

 What is it?

  • American Mathematical Contest is a middle school math contest conducted by Mathematical Association of America (MAA)
  • Anyone Grade 8 or lower can participate
  • First of the AMC tests - Others being AMC 10 (covers first 2 years of high school) and AMC 12(covers all 4 years of high school except calculus)
  • Around 200,000 kids write the exam (~2016 stats)

Contest Format and Duration

  • 25 Questions - 40 Minutes - Arranged in increasing order of difficulty
    • Questions 1-10 are considered easy - If you can't solve these, seek help for school math. It is extremely unlikely you will do well in high school. 
    • Questions 11-20 are considered moderately difficult. If you can solve these, you can consider yourself average in math.
    • Questions 21-25 are considered difficult. If you can solve these, then you are proficient in Math
  • No Penalty for wrong answers
  • All multiple choice

Topics Covered

  • Number Sense (16%) 
  • Number Theory (32%) 
    • Odd and Even Parities
    • Divisibility Rules
  • Counting (8%)
    • Double Counting
    • Complimentary Counting
    • Casework
  • Measurement and Probability (12%)
  • Algebra (16%)
  • Geometry (16%)
    • Exterior Angle Theorem

Why should I write AMC 8

  • Most of the math problems in many textbooks are close to being useless. You cannot learn useful math. Solving them is tantamount to copying a large book by hand with the objective of learning literature.
  • An objective assessment of your math skills. Math contests in the erstwhile USSR and most of Asia is for mathematically talented kids. The beginning level of the problems is pretty high. Not being able to solve them doesn't necessarily mean you lack math skills.  But Math contests in North America is for the masses. There will be problems that students every level can solve. Doing well in these mean you are good at math and not being able to do any or only able to do 1 or 2 problems mean that you are bad at math even at a basic level. You need help at school if you perform at the bottom. So contests like AMC 8 and CEMC are good diagnostic tools.
  • Opportunity to practice problem solving. There is no material advantage of writing AMC 8 (unlike AMC 10 and 12). You don't get special admission or recognition anywhere based on your AMC 8. The reward is itself. 
  • How contest writing helps

Strategies & Tips

Preparing for AMC

  • Take Old Practice Exams in a simulated test environment
  • Keep a record of every practice test - marking 1 for correct, 1! for correct guess, 0 for wrong, 0! for incorrect guesses,  0? for attempted (but no answer) and blank for skipped
  • Questions 1-10 are all about using tricks for school math. If you don't use the tricks or shortcuts you may still solve it but will spend time that you can't use for other problems.
  • In geometry problems draw additional lines or grids to see if the problem gets simplified
  • Learn the basics - divisibility tests, 

On Exam Day

  • Have a test kit ready - Pencil, Paper, Graph paper, rulers, protractors, erasers
  • Organize your scratch paper so you can check your work faster
    • Divide paper to grid
    • Box answer, draw clear diagram.
    • Put a circle on unsure answers (put on problem numbers)
    • No eraser on scratch paper
    • Even write down mental math answers (don't skip writing down answers)
    • Don't solve more than what is required.
    • Even if guessing answers write choices down e.g A or B (dont forget to circle the question)
  • Leave last 3-5 minutes to check answer (starting with the ones you circle)

Problem Solving Tips


  • A great tactic to start most geometry problems is to just figure out all information you can to get started and then mark them on the diagram.
  • If something is too complex try to break it up into smaller pieces that are easier to handle
  • Dont panic if you don't understand a problem. Take a deep breath!!
  • When computing areas of complex/irregular figures try to start computing areas of simple figures (triangles, rectangles, circles) and then adding or subtracting the smaller areas to get the area of the complex figure.
  • In counting problems, check for boundary items. It is easy to make one-off errors and undercount or overcount.
  • It is important to be systematic when solving a counting problem. When it's easy to get lost, it's even more important.
  • In counting problems, it can be helpful to come up with a different way of getting the answer, so you can check if your answer is correct.





Awards

  • Certificate of distinction - Score of 22-25 (Top 2%)
  • Honor Roll - Top 5% - 18-21
  • Certificate of Merit - 6th Grades or lower - Top 15% (Score >=15)

Resources

Thursday, October 8, 2020

James Tanton Problem Solving Strategies

 

James Tanton - Problem Solving Strategies - Curriculum Inspirations from MAA

https://www.maa.org/math-competitions/teachers/curriculum-inspirations



Strategy 1 - Successful Flailing. 

Have no idea how to answer the question? - Try successful flailing

Write everything you know related to the question and hope things will fall into place and make some sense.

e.g. if it is about divisibility, try something (or everything) you know about divisibility
if it is about averages, try something (or everything) you know about averages.

draw picture or do something related to the problem


Strategy #1 - Engage in successful flailing



Grade 8


A Tricky Length


Non-Congruent Triangles


Area in a Polygon - TBD - Doesn’t belong here? - Repeated in Strategy #2 as well.


A Sneaky Area


Additional License Plates


Overlapping Triangles


Counting Jelly Beans



Abstract Sums


Unicorns at Play


Counting Coins


Divisible by 13


Trapezoidal Perimeter


Mixed Colors



Grade 10


Logarthim and Exponents


Painted Cube


Sum of Powers of Ten


Hypotenuse Please


Gothic Windows



Selecting Committes



Counting Multiples


An Integer Sequence


Changing Mean


Mowing Lawns


All Read Beads



Grade 12


Hundreds Digit of a Power


Point of a Contact Triangle


Maximum Ratio




Focus and Directrix


Two Digit Means



A Trigonometric Length



Filling a Grid



Logs of Divisors



A Lopsided Pyramid


Strategy #2 - Do Something

https://www.maa.org/node/129113/

https://www.maa.org/sites/default/files/pdf/CurriculumInspirations/essay2.pdf


Grade 8


Area in a Polygon


Units Digit



Counting Wins


An Array of Sums


A Length in a Square


Probably a multiple of Three



A Weird Calculator


Three Special Factors


A Trapezoid Area


Circle Gaps


Grade 10


Stacking Coins


Logarithms and Exponents



Distributive Rules


Walking the Track



Chords in a circle



Length in a Trapezoid



Units of Big Powers



A Tricky Length


Repeated Visits


Successive Triangles



Arranging Mean, Median and Mode


Some Algebra


Multi-Base Three Digit Numbers


Arithmetic Algebra



Lots of Chimes




Grade 12


Quadaratic Values


Frog Leaping



A Third of an input



A Ratio of Areas


A Complex Minimum



Dividing by 100


Strategy #3 - Engage in wishful thinking

https://www.maa.org/math-competitions/teachers/curriculum-inspirations/Essay3

https://www.maa.org/sites/default/files/pdf/CurriculumInspirations/essay3.pdf


Grade 8


Three Digit Reversal


One Versus Two Coin Tosses


A Triangle Area


Grade 10


Eliminating Roots



Grade 12


The Biggest Circle


Quadaratic Values


Elite Players and Logarithms



Strategy #4 - Draw a picture

https://www.maa.org/math-competitions/teachers/curriculum-inspirations/Essay4

https://www.maa.org/sites/default/files/pdf/CurriculumInspirations/essay4.pdf


Grade 8


Two Trees


Dealing with Averages


Grade 10

Intersecting Tetrahedra


Areas of Nested Squares


Chords in a circle


Skipped counts



Two Counterfeit Coins




Rectangular Region


Counting Two Sets


Cut the Cube


Biking Towards Each other


Selecting Donuts


A Ferris Wheel Ride


Grade 12


Focus and Directrix


Frog Leaping


Parking Probability


Bug Walking



Strategy #5 - Solve a smaller version of the same problem

https://www.maa.org/math-competitions/teachers/curriculum-inspirations/Essay5

https://www.maa.org/sites/default/files/pdf/CurriculumInspirations/essay5.pdf



Grade 8


Units Digit

http://youtu.be/161SYIL4sR0

https://www.maa.org/sites/default/files/pdf/CurriculumInspirations/CB015_Units-Digit.pdf



Stair Climbing

http://youtu.be/nAP2npokFok

https://www.maa.org/sites/default/files/pdf/CurriculumInspirations/CB028_Stair-Climbing.pdf


A Big last Digit 

http://youtu.be/gjfJSNAoqjU

https://www.maa.org/sites/default/files/pdf/CurriculumInspirations/CB043_A-Big-Last-Digit.pdf



Rows and Columns Sums

http://youtu.be/DTl4QAgJK0s

https://www.maa.org/sites/default/files/pdf/CurriculumInspirations/CB076_Row-and-Column-Sums.pdf


Overlapping Squares

http://youtu.be/MMwnQN7RaAw

https://www.maa.org/sites/default/files/pdf/CurriculumInspirations/CB115_Overlapping-Squares.pdf



Grade 10


A Cross Section Area

http://youtu.be/pNmWiynmaPc

https://www.maa.org/sites/default/files/pdf/CurriculumInspirations/CB069_A-Cross-Section-Area.pdf



Circle Area

http://youtu.be/5t9M5TwJgw4

https://www.maa.org/sites/default/files/pdf/CurriculumInspirations/CB007_Circle-Area.pdf


Grade 12


No Grade 12 Problems.



Strategy #6 - Eliminate the incorrect choices

https://www.maa.org/math-competitions/teachers/curriculum-inspirations/Essay6

https://www.maa.org/sites/default/files/pdf/CurriculumInspirations/essay6.pdf


Grade 8


Consecutive Squares


Matching Cards


A Sailing Ship



Grade 10 


Stacking Coins



A Curved Area


Largest Common Divisor


Avid Reading




Grade 12


Differences of Four Numbers


Mean, Median and Mode



Strategy #7 - Perseverance is Key

https://www.maa.org/math-competitions/teachers/curriculum-inspirations/Essay7

https://www.maa.org/sites/default/files/pdf/CurriculumInspirations/essay7.pdf


Grade 8

At least as many heads


Angles in a Star


Counting Non-Congruent Triangles


A Dart Probability


Best Value


Sitting and Standing


Circles in Squares


A Complicated Area




Grade 10

Probably Above a Parabola


Coloring a Pentagon


Sum of the Ends


Counting Events


A Random Sequence


Selecting Digits


Removing Square Tiles


Ending with 23


Rounded Roots



Grade 12

Focus and Directrix


Arthimetic Logs


Iterated Function Domain


Strategy #8 - Second Guess the author



Grade 8

Hidden Primes


Grade 10

Pencil Prices


Town Population



Given a Bye


Melted Icre Cream


A Reflected Triangle


Grade 12

Whats the Domain


Bug Walking



Strategy #9 - Avoid Hard Work

Grade 8


Units Digit


Shaded Triangles


Pinwheel Area


A curious surface area


Oneless Numbers


Percent Shaded



Running Lemming


Overlapping Circle and Square


Remainders of Two


Circle Moves


Hands of a clock


One Zero


99 Digit Products



Grade 10

Intersecting Tetrahedra



Red and White Chips


Grade 12


Renumbered Dice


A Compound Complex Function



Strategy #10 - Go To Extremes

https://www.maa.org/math-competitions/teachers/curriculum-inspirations/Essay10

https://www.maa.org/sites/default/files/pdf/CurriculumInspirations/essay10.pdf



Grade 8


Hats and Gloves


Different Darts


False Relation


Grade 10


A Line through Lattice Points


Differences of Four Numbers


Union of Two Sets


How Many Twos?


A Magic Square


Very Eight-Centered


Perfect Square Fraction


Grade 12


No Grade 12 problems



Math Curriculums and Recommendations

This page is an attempt to list my list of math curriculums, books, programs that covers K-12 Basic Math knowledge - Basic Literacy  I have ...