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