Notes on a presentation by Mark Olson
On teaching math fundamentals while teaching calculus (etc.)
A transplanted Canadian who teaches in Sweden.
Sat. April 14 at 2pm on Math 2.0
Mark Olson’s website: http://eightfalls.com
Olson is a Canadian high school math teacher who has been teaching (in English) in Sweden for a number of years.
Interesting fact: In Sweden, students need to be able to explain and prove their answers to pass math, it’s not sufficient to merely get the right answer.
The substance of this talk developed out of an effort to find the missing dependencies of math students skill-wise.
Olson Developed a workflow analysis for number systems and order of operations, which he calls a mathflo.
A claim of Olson’s is that it takes 10 years for students to understand order of operations in an abstract sense.
Olson found that Swedish students were not intimidated by complicated sounding English words for representing concepts. For instance, in the abstract terminology of an operation, the first operand is the Augend, and the second is the Addend (BTW, neither word is recognized by the wordpress spellchecker).
He has created a nifty chart showing the relationship of math operators and entities that many seminar participants wanted copies of.
Simplify mathflo – Is a system he created for simplifying algebraic expression in 11 steps. You always proceed through the steps in the same order, though you may not need to do them all.
This method seemed very laborious and to draw things out, but was very predictable. However, once students get used to it (and it probably does not take that long), it gives them a very strong framework for understanding what they are doing. His students have embraced the technique (as laborious as it may seem).
It seems like a good method to keep in the toolbox, since it is so often skipping steps that causes difficulties for students.
He introduces this system with simple linear algebra expressions, and continues to use it with his students all the way through precalculus. Here are the steps in order from first to last.
1. DOS Definition of subtraction (turn subtraction into plus a negative number)
2. Dlim Delimiters (identify parenthesis)?
3. DP Distributive property (distribute terms with parenthesis)
4. Jux-Cdot Introduce cdot notation for multiplication in place of juxtaposition
5. CPM Use Commutative property for multiplication inside the different terms
6. OOE Operation of exponentiation (exponentiate)
7. OOM Operation of multiplication (multiply)
8. Cdot-Jux Translate back from cdot to juxtaposition
9. CPA Use Commutative property for addition
10. OOA Operation of addition
11. DOS Definition of subtraction (revert back to subtraction operations)
Olson “Good system for students who are asking the question ‘Why am I doing this? (about the order of operations)'”
The technique can be revolved to use for solving equations in 5 steps:
1. simplify mathflo 2. additive inverse
3. simplify mathflo 4. multiplicative inverse 5. simplify mathflo