Thursday, March 22, 2012
- How well you do know square roots? What would you tell someone if you were trying to describe a square root?
- Why do we call it a square ROOT? Side length of a square equals the square root of the area of the square.
- Does SQRT(16)= +/-4, or just 4? 4 is correct. SQRT(16) is a number on a number line, it is 4. x^2=16 gives the answers +/-4 as solutions to the algorithm, but just looking at SQRT(16) it's 4. Really, the answer to SQRT(x^2)=Absolute value of x. SQRT isn't a command to do something. It's meant to represent the positive value of the number under the SQRT.
- Question from student: So, we have this definition of SQRT. What does absolute value of x mean? x=x when x is greater than or equal to 0. x=-x when x is less than or equal to 0. So SQRT((-7)^2)=7. The radical sign is asking, what is the positive value of the SQRT of the number inside. For any positive number there are two different numbers you can square to get that number. the +/- tries to explain that phenomenon.
- Question from student: so -x=SQRT(25) has one answer, but (-x)^2=25 has two answers, +/-5 will both solve the equation.
- If you add in the SQRT then it's +/-, but if the SQRT is already there, then it's positive.
- x^2=16. We have to add the SQRT, so there are 2 answers
- x=SQRT(25). The SQRT is already there, so there is only the positive answer.
- It's possible to understand SQRTs without needed to be able to calculate it
- Leatham gave us 32212 told us to find SQRT. couldn't. Gave us 2. Couldn't find SQRT
- carrying out an algorithm isn't the same as understanding the underlying idea
- Students are constantly in the situation where you are presenting an algorithm to them, and they have no idea what is going on.
- Leatham showed us example of bad teaching. Taught us square root algorithm.