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Started by sending email.

Talked about article:

    • "Knowing in avance the difficules that students may experience can be helpful"
      • like the ti inspire, pre tests can be helpful.
        • ti inspire just taught what students missed
      • this teacher actually taught about all the math, and just made sure to highlight the things that students
        • she could have just warned her students
      • it depends on what you do with that knowledge- makes a difference of how valuable the mathematics actually is for the students
      • with experience you'll learn what mistakes people usually make, so it could be tempting to just warn students about that. It's better to let students bump up against it.
      • the author noticed what people usually miss and created a task so that all the students had the chance to make the mistake and learn from it
    • translations using vectors
      • we were taught to just slide the figure. we didn't think about the underlying properties of the slide.
      • she points out that there are two things to pay attention to: direction and how far
    • the transformations transform the entire plane, not just the figure.
      • students have misconceptions about what is actually moved
        • they might think it's only the things that are labeld that get moved.
      • a transformation is a function domain- preimage is a subset of the domain, whole domain is the entire plane. range- image is a subset of the range
        • domain can be defined as two things
          • everything that is possible
          • everything that you want it to be
        • we want everywhere on the plane to be fair game, so everything has to be in the range.
      • transformation maps everything from the entire plane back on to the entire plane.
      • in GSP you can move the image that is made, that was a choice that the creators made
    • She calls the line of reflection, center of dilation or rotation, translating vector as parameters. why?
      • Leatham called it a function, not a parameter.
    • Why do we work hard to make things familiar for students?
      • paradow of learning: inorder to learn something you have to build on something else.
      • how do you get something new if you don't have anything to build on?
      • the instant that you make an association with something you know about it's easy to make a one to one correlation, but that relationship could be wrong.
      • we start off by over generalizing, then we eventually narrow our conseption/ make distinctions
      • learning is the process of refining generalizations
      • the word similar in geometry is a little bit different that similar in every day language. in geometry things have to be alike in specific ways
        • when we teach our students similar we have to remember that our students have already come to class with ideas about the word similar.
      • the word slide that is used for traslate- we thing about how far we're moving the figure, not the direction. we need to make sure to teach them about moving a vector, direction and magnitude.
    • location of the vector doesn't matter. it's defining a direction and a magnitude.
    • Relating geometry to algebra:
      • top of page 209
      • preimage independent, image dependent
    • mathematics common core.
      • congruence
        • we memorized theorems and properties
        • now they are learnin them as the properties of these transformations
    • how do teachers access research that has been done on certain topics?
      • articles like this one
        • comes from a mathematics journal
      • dilema: researchers are encouraged to share researhh with others who are doing research, but not really the people who could use the research
      • nctm.org -> ? -> online resources -> research clips and briefs
      • workshops, journals.... oportunities for professional development are available if you look
      • try to do professional development that is specific to mathematics
    • What's one piece about students misconceptions that we got from this article?
      • define things well, sometimes paper and pencil can be the best/ most effective
      • the tool determines a lot of the work that you're going to do
        • GSP you have to define a center of rotation, paper and pencil not so much
      • perpendicularity in reflections
        • line connecting reflected points is perpendicular to mirror
      • creating connections is just as important as learning new material
        • students have to build on what they already know, so it's good to find out what they know and build on that.
        • how do you view it? lets build on that
          • don't make it an authority thing. "here's what you know that's wrong, let me replace it with things that i know that are right"
    • just visual doesn't work, students do also need the properties

Now talked about parabola paradise:

    • strategies that you used to come up with that locus for a
      • a=-b/2x
      • plug the value of a in the ax2+bx+c
      • plug the value of a in the y value of the vertex