Thursday, September 10, 2009

Math Concepts for kids and teens

Summarizing some key math concepts that I teach my kids.

  • A correct value system is the most important foundation (the goal to excel, the willingness to help)
  • How to make decisions ? (differentiate emotional decision and strategic decision)
  • How to do planning ?
  • How to do reasoning, analyzing and drawing conclusion ?
  • How to be open minded, humble but not blindly follow conventional wisdom ? (why human walk with 2 legs, why do we have supermarkets, how do we decide where to put a bus station, why an apple is more expensive than an orange)
  • How to be patient and control emotions ?
  • Develop a good sense of numbers and able to read different charts and graphs, observing relationship between variables and their trends.
  • Appreciation of doing things in a smart way

Basic Math Concepts
  • Numbers, counting (Integer) and quantities (Real)
  • Cause and effect
  • Set (belongs, union, intersect, subset)
  • Function (dependent and independent variable, continuous vs discrete). Various graphing (histogram, line graph, plot), 2D curve and 3D plane
  • Linear equations, degree of freedoms, relationship between number of variables and number of equations.
  • Calculus (differentiation and integration), multi-variables and partial differentiation
  • Logic (if/then, necessary/sufficient conditions, equivalence) and Proof establishments
  • Debate and Logic fallacies
  • Geometry and Vector (think 3D instead of 2D)
  • Probabilities (Draw a tree of all outcomes and counting)
  • Probability distribution function and expected gains
  • Permutations and Combinations (how to find out "all possibilities")
  • Mathematical induction, recursion in proofs.
  • Digits with different bases (and their relationship with Polynomials)
  • Making predictions: False positives, False negatives and how trade-off decisions should be made

Math Models
  • Decision tree (decision and outcome alternations, min/max strategy). Expected gain and optimization
  • Game theory (Nash equilibrium). Outcome prediction within a social group. Win/win and win/lose and lose/lose situations.
  • Finding solution using Search tree, exhaustive search in all possibilities in a systematic way (tree traversal, breath-first vs depth-first vs heuristic)
  • Linear programming for constraint satisfaction and optimization
  • Deterministic vs Stochastic process (Markov chains), Queuing theory
  • Control system (equilibrium, stability and feedback loop)
  • Graph model (nodes and arcs, path finding, shortest path, minimal spanning tree)
  • Finite State Machines (everything happens in a cycle)


coderguy said...

This is quite a list. How do you teach your kids these lessons? Do you homeschool? How much time a day do you spend working with them on math? Any books recommend?

PS I found your blog via your "CouchDB Implementation" post. It is a great read. Clear and concise. The charts and graphs really help.

Ricky Ho said...

I am not home schooling them. I teach them opportunistically, most of the time when driving them to school. We'll look at the street for things like why the road is black, why do we need the signal light, why we are driving on the right ... etc.

I usually teach my kids a totally new math concept (other than what they learn from school) about every 3 months. I also teach them on an as-needed basis when their school teacher doesn't explain the concepts well enough.

I also get them appreciate the power of Math as well as abstract thinking. Math model can help them to see through things and recognize that many different things (like species classification, company structure, family history, government structure ... etc) are all based on a "tree" concept. Once they understand the properties of a trees, everything looks familiar.

I mean just the knowledge is not that important. The important skills is to be able to notice differences and similarities among different things and be able to build a few models around them.

I haven't used any specific book but I also have another blog that talks about some good sites.

Anonymous said...

Mostly kids and teens don’t like the math as a subject and I want to say that kindly post some more advices for this purpose because many teachers faces this kind of problem!
Math advice

tomcat6 said...

teaches math concepts pretty nicely

tomcat6 said...

teaches math concepts pretty nicely