Originally Posted by zebra15
Sadly he was teaching about the 'number line' yesterday.Oye!
This is the sort of tutoring I would find so satisfying!
He should pick up a book called "The Myth of Ability" by John Mighton. It's about a math tutoring charity that Mighton started. The approach he uses is based on the belief that most of the time when students are failing at math it's because they just missed one or two of the early concepts and the curriculum kept moving forward. When they were being taught stuff that built on those missing concepts they developed intellectual workarounds and emotional defenses that worked for a while, but eventually the coping skills weren't enough. Their natural intuitive ability to draw connections and infer concepts was severely hampered by their anxiety about the senselessness of math ... but if you help them go way back to the basic aspects of number sense that they do
understand, and help them feel successful and confident using what they know and moving forward in -- at first -- microscopically small increments that they simply cannot fail to master, the anxiety and defeatism can be overcome. Often with great joy.
Mighton himself nearly failed first-year calculus and dropped math for almost a decade, figuring he just wasn't a math person. He became a playwright and film actor. But in his late 20s he rediscovered an interest in math, waded back in with a sense of joy, and went on to earn a PhD in Mathematics.
Your number-line reference reminded me of this, because often in tutoring the tendency is to take students back to the point at which mastery dropped below the C level, when in fact the crucial piece of the puzzle went missing years earlier. It was only because they were so smart that they managed to cope -- to a point -- for several years after that. The trick is to help the student fill in the understanding they missed way back in second grade or whatever while helping them feel like they're not being put back in
second grade, and giving them the sense that they are making progress towards their goal of mastering (and thoroughly understanding, and fully enjoying) high school level material.
Anyway, the book is a great read as a testimonial to human potential. But the techniques Mighton describes that help his students unlock a feeling of success are pretty cool. He founded the JUMP Math non-profit and curriculum, and trained many volunteer tutors who have been able to replicate his success, so it's not just a spurious bit of magic he was able to generate. It's also, in my opinion, a great book for homeschooling parents who have math anxiety themselves, or are dealing with kids who are beginning to develop such issues.