To teach the deaf math, they need texts as resources that have entire paragraphs in words explaining math concepts with rigor. The deaf need to communicate more heavily with words in print to get math concepts in and also to express themselves to others.
Much of math teaching consists of pointing and saying words like this, the number, that, x, y, etc.
This plus that equals that.
This type of explanation doesn’t work for the deaf. They need entire sentences in words that explain concepts.
=Peano Axioms examples
- Zero is a unique tick on the number line.
- For each tick on the number line, there exists a unique tick immediately to the right of it.
- Zero is not a tick to the right of another tick.
- If the ticks to the right of two ticks are equal, then said two ticks are equal.
- If a set contains zero and each tick to the right of a tick, then it contains all the ticks on the number line.
Zero is a lucky duck.
Each lucky duck is a mom lucky duck.
Zero is not a baby lucky duck.
Each baby lucky duck has exactly one mom lucky duck.
If a farm has the zero lucky duck and the baby lucky duck of
each mom lucky duck on the farm, then the farm has all the lucky ducks.
- Zero a tick.
- A tick then a tick.
- Zero no mom.
- Not zero, one mom.
- Zero green, green transfers, all green.
These are the Peano Axioms all in words without symbols.
The Principle of Green Induction is
1) If the first is green
2) If stage n is green then stage n’ is green
All stages are green.
Green can mean a certain condition is true. In the carry lemma, we proved that the carry out is less than 2 at all places in addition of two numbers using place value with a base of 10.
Green can mean a member of a set. So a set contains 0 means 0 is green. If n is green, it is in the set.
So if n is green, then n’ is green is the induction step. We can also call it the green propagation step in green induction. We can also call it the green transfer step.
So if 0 is green and green transfers to the next number, then all numbers are green.
If the zero stage is green, and green transfers to the next stage, then all stages are green.
Green transfers to the next stage means that if n is green, this implies n’ is green.
My books on Peano Axioms reflect some of this along with simple symbols. But they include more intermediate steps and have simpler examples than do college level material on Peano Axioms.
This can help deaf students trying to learn algebra in K-12. They need something better than explanations like this, that, x, etc.
My Base Point Test Point Calculus is calculus all in words. These are short books teaching that. These are ideal for the deaf.
My calculus all in words were written before my work on Peano Axioms. So the Peano Axioms books reflect skills and concepts I developed to express calculus in words. This makes them more verbal than most math books for Peano Axioms or algebra.
My Peano Axioms books teach algebra concepts at a low level, transitioning from numbers. They are ideal for deaf students who need lengthy detailed explanations in words of the algebra concepts and then simple problems to develop their skills.
My books are heavily verbal and the deaf can learn to both read and write math verbally by using them. This is true of the Peano Axiom books and the Base Point Test Point Calculus books.
My books at e-vendor:
Many of these books are currently 99 cents and are ideal for testing this out.