Morning Round table Discussion

From Kaput Center Wiki

We started off the morning summarizing discussions from the previous day for those participants who could not join us. SH broke up the two days categorizing Thursday as the "what" day (identify foundational issues) and Friday as a "how" day (how do we address these issues).

SH: This symposium can be the first in a series of symposiums. Identify what is truly a foundational issue/ concern. Can do this by focusing in 3 areas:

1. synthesis of now (not so much as a historical account; something that helps us understand the issues in the field we might not have known about)
2. conversation in 50 yrs (is the discussion we’re having truly looking forward/ relevant/ important in our future?)
3. intentional design vs. redesign

The break out groups for Thursday were: Participation, Design and Implementation, Learning Trajectories.

SH: Want to close today with an answer to the question 'What have we done here?' and some conclusion of plans for the future.

Smartboard Image

Notes

Potential topics for break out groups:

• concerns about things that might be lost with new technologies and Luis’ notion of mathematical integrity; what does it mean to blend mathematics and technology. Do mathematicians and math educators need to part ways to accomplish goals?
• Corey: before splitting out into smaller groups, identify problems and potential actions. (loss/gain of math integrity, fear of technology)
• Jim: technology has a lot of potential for increasing autonomies. Adaptive. We have choices on where to go that might be more progressive or more adaptive and more efficient but less “free”.

Autonomy:

• divergence of self outside of school and divergence of math from relevance
• Agency and participation
• making ideology visible
• choice in curriculums or choice/ decisions about what comes next. Ability to choose wisely a part of knowledge?
• Role of policy makers: is this a ‘technical’ question?

• Social Engineering: curriculum, classroom structure. What are the pragmatics of what we do? –how do we bring students in to this? Making a value statement: It’s the right thing to do from a political standpoint.

• Walter: use Peirce's notion of science

Smartboard Image

Making Social Science Matter: Three organizing principles

1. Where are we going?
2. Is it desirable
3. Who gains and loses power?

• We do not challenge university mathematics.
• Nancy: to truly look into the future we need to focus more on what we desire instead of what is happening now.

• Jere: naïve use of political; only use political if it is not what we want. How do you get out of that dichotomy?
  • Argument in Social Science Matters—if you see yourself as trying to increase informed decision making, then how can you do this?
    • helpful when we’re trying to see how we can help people at the policy level.
    • Luis: anything at social level, there is an intentionality. It’s not just changing the system. It is a process of continuing transformation. (Higher use of technology in education system. Content of mathematics. Integrity)
    • Jim: goal of maintenance is at odds to transforming the educational system

• Walter: People see algebra as something that is purely a stepping stone to calculus. If you want students doing calc as freshman at universities, they need to be doing algebra by 8th grade—no one ever thought about what algebra really means or defined. Backwards moving?

• SH: the mathematics is missing from our conversation. What is the math of today and the future? In 50 yrs, what do we want to see? Looking through the eyes of mathematics/ our mathematics. What do we value in terms of mathematical ideas and knowledge?

Smartboard Image

Notes

• Tereasa on the education system in Mexico:
  • universal curriculum. What topics were decided to be included? Decided to keep curriculum the same and just add technology.
    • Teachers must teach traditional algebra.
    • Emphasis on manipulative algebra.
    • Using calculators more to do manipulations.
    • Teachers cannot conceive the algebra as just modeling without the transformation. Teach traditionally; simplify expressions.
    • Children are assimilating two knowledge domains unless the teacher deliberately tries to close the gap between the two.
  • Students remain in the same room for all classes and teachers move. They work with paper and pencil. Go to lab once a week to work with innovative models.
    • Assessment plays an important role; they asses the traditional work. Children are developing new competencies, new abilities that are not being taken in to account.
    • Using calculators and spreadsheets for exploration on how to solve problems.
    • Refining self-expression on how to solve a problem.
    • They fail when they get back to the traditional classroom. Refining the way they talk about things. Not seen in traditional classrooms. Students do not make connections. The teacher values what kids are doing in the classroom differently.
    • Same activities in both environments, and students behave differently in each different environment.
  • Luis: Difference between content and design. Curricular design keeps them separate. Problem of permanence and change.
  • Alan: Teachers in traditional classes cannot be separate from the technology or the issues of the students in the classroom. In the US this would be considered as a structural design flaw. They need to be merged in such a way that the teacher and students are working together; deliberate professional development. Cannot say the assessment system by itself maintains the bridge between the two.
  • Jere: in the US we may be physically blending them but how does the student perceive this? Calculators: students don’t reason anything about the functions, they just look at the graphs. Graphs on a calculator are just images with no mathematical meaning – students cannot reason about the graph before seeing it – cannot think/reason across representations. Jere is tired of what the calculator has done to education. Computers are much better.
  • We do not have a lot of evidence that students reason in stats, that they like it. Computers are much better environments for statistics than calculators. Stats are least abstract.
  • SH: Theoretical mathematicians separate themselves from applied mathematicians. New forms of environments – dynamic mathematics
  • Walter: need to stop thinking about a device made by a specific company but really need to take the functionality into consideration. The functionality is in kids hands - it doesn't matter where it lives (calculator or computer)

Proposals for Content Topics for Break Out Groups:

Smartboard Image

Notes

1. Algebra for all. What is algebra?
2. technology
3. science and engineering
4. math education vs. mathematical sciences (Jim: this assumes that they are different)
5. mathematics vs. social sciences
6. math education in social context/ conditions we’re in
7. political ramification; we should focus on what we understand and what we can develop

Smartboard Image

Smartboard Image

Math topics for break out groups:

1. Statistics and data analysis
2. algebra and geometry
3. rational numbers

WE are thinking in very traditional, restrictive ideas of what math is with these topics.

Final Decision on Break Out Groups Topics:

1. Rational Number
2. Math of Change and Variation

Working Groups - link to the working groups for Friday

Smartboard Image