Friday Presentations
From Kaput Center Wiki
[edit] Notes
[edit] Responses to "Rational Number" Group
- SH: John mentioned in other group—why is this math worth knowing and how can it grow across grades? We focus on rational numbers because it is important knowledge for all grades, k-12+.
- Jere: If you pose the question, what is a over b as a fraction? You’ve already answered ½ of the question in the way that you identify it.
- Rational number- strongest example we have of being foundational because it lays a basis for geometry, algebra, math of change, etc; it crosses so many different areas that makes her think it’s so important.
- It is not historic value in constructing the rational number line; it’s much broader than that.
- She is convinced/ confident about thinking hard and deeply about student resources brought to these topics.
- Need to think more broadly about what we mean of ‘formal’. What is really challenging about the evolution between revolution: we don’t know where authority lies. Motions of transformation.
- Rational number- strongest example we have of being foundational because it lays a basis for geometry, algebra, math of change, etc; it crosses so many different areas that makes her think it’s so important.
- SH: Mathematical integrity.
- Jere: We need to assess it relative to mathematical integrity.
- SH: Are we thinking about math integrity as socially acceptable?
- SH: what if we add infinitesimals to the number line? Then how do we deal with it?
- Walter: need to be careful of doorways we insist on ‘going through’ for certain topics/ issues because they might be the wrong ones.
- Gerry: if the meaning of half of a quarter is meant as take this amt as a quarter and take half that. Learn fraction as part of a whole. Rules are motivated by fractions interpreted as a part of a whole. There is no “really” here. Math education says a rational number is ‘really’ this and math sciences say it is ‘really’ that.
- SH: looking at the child’s perception of number reduces number of trajectories.
- Jere: In the beginning, we are saying that we start where the kid is. Gagne
- Gerry: does’t like Gagne’s approach.
- Gerry doesn’t see a contradiction between taking a perspective centered on child’s way of thinking and taking a perspective on the desire to teach certain concepts. Taking these 2 we are approaching problems of mathematical education.
- Jere: what’s the authority of where you’re trying to go through kids’ learning?
[edit] Responses to "Algebra & Math of Change and Variation" Group
- Walter: layer cake is flawed; gateway classes not a good way to approach mathematics.
- First 2 yrs of undergrad math does not serve mathematics
- Last two years are completely devoted to proof
- Gerry: difficult to assess reasoning; easier to test knowledge
