Participation
From Kaput Center Wiki
Participants: Gerry, Stephen, John & Arden
Contents |
[edit] Synthesis of Now
Disparity between research and motivation in students
Problems measuring motivation
Literature on affect, identity and self-efficacy Intrinsically interesting activity might not be attractive Why are you doing this activity: for someone else or for yourself? How does this change? Social norms are very stable from outside, so how do impact student's propensity to want to do a mathematical problem?
Mathematical Intimacy:
Group work
Small group
1-1
Division of space, respect, comfort in sharing ideas related to risk (embarrassment)
Extrinsic motivation such as rewards can have an undermining effect and decrease intrinsic motivation.
Intrinsic motivation reflects the propensity for humans to engage in activities that interest them.
Key factors for participation have been orthogonal to the field of inquiry to the development and instruction of content.
Motivational strategies have been in the form of incentivizing students because it is fun.
[edit] Conversation in 50 years
[edit] History
Recall Cambridge Group in 1963
- Abstract Algebra as a High School topic - Unifying mathematics - 2 sequences branching at Middle School: Academic track (towards differential geometry), less academic track (towards abstract algebra)
Supported by Bruner's methods of how to teach anything!
100 years ago 3% of population learned Algebra, today it is "algebra for all"
Are there analogues to our projections?
[edit] Future
How do we want to look back? Are our research programs today cutting-edge enough to predict implementations at scale in 50 years?
[edit] Intentional Design vs Re-Design
[edit] Intentional design
Constructivism vs Traditionalism
Defined problem that has to be completed in the traditional world vs a problem can be completed in a vareity of ways
Constructivism: Not wrong but viable. Frustration is missing. Frustration develops affect.
[edit] Re-Design
Don't have goals in Mathematics Education: Affective Appreciation, Sense of Enjoyment Sense of self-efficacy Persistence Frustration as a motivator
Could we re-design the Standards with these in mind?
Example: Games - design of games with progress-time models with bounds of boredom and frustration Specific affect models used in design/saleability of games.
Need to attend to rewards (in the social sense)
Frustration needs to lead to meta-affect
[edit] Limits/Issues of Participation
- Assessment
- Filtering process: making decisions/pathways in programs
- Democratizing - allowing access
- Affect side: How students interact with others? Underrepresented groups
[edit] Notes:
- Role of proof in graduate school
- Importance of assessment-can limit participation. (Example: success determined on student ability to prove theorems. Does assessment of this make sense?)
- Assessment of Program
- form of feedback
- intention of standardized tests
- Assessment of Program
- Gerry: two definitions of participation
- Entering environment of where math is learned-getting them there in the first place.
- students are filtered out (either on their own or not); academic tracks-fewer expectations
- broad political concerns of democratizing access. Certain math all students should learn. How?
- in future, hope is that access is more democratized or society has shifted and accepted that math is only for a subset of a group.
- Extent of engagement in mathematical environment.
- Where we are right now: broad agreement of democratizing access but have done little to achieve this. No way of assessing this.
- There is a gap between what research has been done and what people know.
- People tend to think what influences adults influences children
- Mathematics needs to become more friendly or adapt to its environment?
- Focus: not changing norms of system but changing activity structure within classroom
- Is the goal to make students fall in love with math or be less anxious to do it?
- If kids can do math, does this change their view of math or themselves? Self efficacy
- Powerful social dimension--affect of doing mathematics
- Mathematical Intimacy:
- Large group: students are given a math problem to work on. Low risk-feelings of inadequacy are not exposed and not resolved
- Smaller groups (of 4, for example): students cannot escape exposure. There is more vulnerability but also opportunity to do something (depends a lot on the group itself)
- 1-1: Most vulnerable. No comparisons are being made
- Intimacy involves risk; established position.
- in certain situations, a mistake is beneficial-suggests a correction to someone else
- Teacher limitations-student ability
- Teachers award the courage of students who offer ideas/ answers even if they are incorrect
- Advanced mathematics-social courage
