Wednesday, 1 June 2016

Math - from zero to algebra

I heard many parents are worried about math, and especially algebra, other parents say - why do we need algebra?! While I think... Why not? Numbers rule the Universe - according to Pythagoras.

Here are the steps that we followed... very naturally, without any prior planning. Now Alexandra is 10 y.o. and solving simultaneous linear equations. 
We'll be glad if you find something useful or encouraging here. 

Homeschooling math / Unschooling math / Worldschooling math 

4-6 y.o. 
  • Montessori materials to learn counting 1-10; 10-100 - (only addition, no multiplication)  here 
  • counting on / counting back - (the pictures below) learning and counting with the number lines
  • visiting a playgroup in Thailand and singing there number-songs with kids and counting with the teacher.
  • reading kids' magazines: math puzzles alongside with entertaining labyrinths, drawings etc - math is exciting, it’s not easy - but it’s a challenge - like any other activity.

6 y.o. a very important period when Aleksandra started loving math.
  • column addition
  • skip counting by 3's - we created our very own song 3-6-9…etc, that Aleks was singing all the time. 
  • skip counting by 5 was easy, following the pattern 5 0 5 0 5 0 - One day Aleks challenged herself - Mom, i can skip count till 1000! She was exhausted at around 250…. and said.. and so on.. understanding that there’s a pattern. 
  • various math games with a deck of cards / board math games (from internet) - to understand 1.000s (she was really confused by 1000s.) and to practice addition/subtraction. 
  • applying skip counting skills to understand multiplication. (3 boxes and 5 fluffy kittens in each! - so, she sings her song (kind of counting 5 fingers) - 3-6-9-12-15! So, 15 is the answer!) Her multiplication was not remembering abstract equations 3x5=15 , as I've read - that kids can't go that abstract at such a young age) 
  • singing songs and visualizing multiplication with Right Brain Number WheelsALL THE DETAILS ARE HERE 
By the way.... 
Toddlers love puzzles, labyrinths, challenges, overcoming difficulties, difficult tasks strengthen links between neurons. Math is a puzzle.
Why do many people hate algebra? Many math-problems are just nonsense, fake, artificial, and kids don't like that. And the school-program is a very protracted process. 

In fact the entire 6 years math can be taught in 20 hours.  Daniel Greenberg (Sudbury Valley School) gathered a group of girls and boys 9-12 years old, who have never learned math before, and tought them entire 6 years program in only 20 hours of classes. He describes it in his book “Free at last” (more about it: here)

7-8-9 years old 
  • MATH SALAMANDERS.COM - a well structured website with free printable worksheets - that we used for 2.5 years. (Kindergarten-Grade 5, Algebra and Geometry) I was printing “sets” of as many worksheets as I could… (The back side of the paper was used later for drawings, drafts and notes that we leave “on the fridge”). After solving each set - self-check using the answers.  I think, kids love to be “teachers” and check “students” mistakes or good work. 
  • solving math puzzles like this one: 

  • Creating, solving fun math problems, making jokes on the existing math problems and solving them… (imagining all those characters - who travel from point A to point B, or getting/loosing candies in real life)
  • "Fractions" starting from 8.5 y.o. - reading, understanding, copying a "fractions book" into a notebook. Preparing a colorful photoshoot with fractions, creative activities with math help to work and remember a lot. 

9-10 years old - KUMON books. 
At 8-9 she started doing math and algebra that I sometimes couldn’t remember from my school years… (like dividing decimals by decimals) Kumon books have step-by-step explanations that help students to discover everything themselves. So, I never was like a teacher in a classroom. When something was still unclear - I was always glad to help her to find a youtube video.

Overcoming difficulties: 
  • Watching a few seconds of Tom and Jerry, where little woodpecker calculates something very difficult. 
  • Singing/ quoting Scales and Arpeggios Song  (in youtube) form Aristocats - when something doesn’t work.
If you're faithful to your daily practicing.
You will find your progress is encouraging. 

  • having fun time and good laugh together, while making jokes on math problems.
  • working in a coffee-shops where other freelancers come to work.
  • acknowledging satisfaction - when the hard work is done, and all the papers are full of calculations.
11-12 years old: Khan Academy 
Pre-Algebra, Algebra, Geometry.

PS  (I never suggest her to calculate “imaginary situations” about money. Though books have a lot of examples on money - and she did all the calculations herself, using different money systems - pounds, US dollars, HK dollars, Singapore Dollars, thai baht, depending on the country, where we bought a book or dowloaded a worksheet.)  

9.5 y.o. Kumon
teacher and student - 2 in 1.
10 y.o. Kumon

Isn't it cool - when someone tiny can calculate this! ?
Tom & Jerry