Hardy's Math Tips

12/25/2018 Newton Develops the Power Rule for Derivatives.  Using Algebra and his "Leap of Faith" Newton moves from the average velocity to velocity.  This becomes his only rule for derivatives and you shall see in future lectures. https://www.youtube.com/watch?v=V_Np9yuCOgM

12/25/2018 Newton does some Algebra.  Newton uses the data gathered by Galileo to discover a relationship between distance and velocity. https://youtu.be/yrMrl3h0OMc

12/24/2018 Newton #2  In this lecture Newton shows a process on how to use his series to approximate radicals. https://youtu.be/O8f03N20l0w

12/24/2018  Newton #1  In this first lecture the author talks about the impact that Newton made on math and calculus.  He discovers the General binomial Theorem. https://youtu.be/z-SjsDQbTHc

In this talk I try connect problems noting that sometimes our own methodologies hinder doing so. https://studio.youtube.com/video/sE5Aih3Db6U/edit

I offer suggestions when working with students individually.  I try to find out what they know and then try to have them connect later problems to problems that they have done successfully. https://studio.youtube.com/video/TrgR96YrhgU/edit

Algebra I and above  This is a history lesson.  Students would ask why we were rationalizing the denominator.  First I answered that it was considered better form.  But I was dissatisfied by my own response.  I started asking my fellow teachers and they knew of no other reason.  I started to reflect my experience and realized that the answer came when approximated expressions involving irrational numbers.  I am old to remember doing this by hand.  The answer became obvious, the computations were easier with the radical in the numerator. https://studio.youtube.com/video/YEayhFfZ2Bk/edit