# Session Documents

Math and Making Open Conference Notes

8. Research Questions & Priorities

Facilitator: Erica Halverson

THE IMPORTANCE OF ITERATION

What are the opportunities for trying things over and over again with representational tools?

How do I improve this product vs. how do I improve my thinking?

What happens when I get to do stuff over and over again?

How is my use of representations changing through each iteration?

What’s the relationship between action (building) and thinking (reflection)? In a way that’s natural that supports future action

TIME

What’s the learning horizon that you’re imagining for yourself (e.g. 6 weeks vs. 15 minutes)?

- Design experiments in 8 weeks vs. 1 year

- Really long term seems to be uncomfortable so kids tend toward shorter projects often in service of their longer project

- When they get stuck they find something else to do

How does the forward production of ideas proceed?

WHAT IS DIFFERENT ABOUT MAKING WITH MATHEMATICS WHEN :

a) the solution is already known

b) the solution is unknown

c) the solution solves an actual problem

d) all of its permutations?

What is the relationship between developing intuitions and mathematical instruments?

- Making is a powerful context for exploring this relationship

- Can we bring a distributed cognitive lens to this approach/work

WHAT DO WE ALREADY KNOW?

- How much was in the #Mathmaking lit review?

- What about the professional literature? (math-at-work)

- Ethnomathematics

- Making models of mathematical ideas

- Embodied cognition perspective on through the making you’re learning the mathematics – there’s less of this than the former. Almost all of it is about geometry

- Computational thinking (visual, embodied, and scaffold understanding abstract relationships)

- Across all the different making contexts – welding, 3D printing

ARE THERE META-THEMES TO HOW MATH FITS IN?

HOW ARE THE FEATURES OF MAKING ACTIVITIES WAYS INTO/AFFORDANCES THINKING ABOUT THE RANGE OF MATH PRACTICES?

WHAT ABOUT PRIOR MATH KNOWLEDGE?

- People who understand a lot about math experience making much differently from people who don’t have the vocabulary for it.

- Do they do the work differently? The task?

- Do they say different things mathematically

- This could be a low-hanging fruit?

WHEN DO YOU SAY – “THIS IS MATH!”

- Seems empirically testable

- How is this related to what makers’ goals are?

- How is this related to what designers’ goals are?

- How does that differ when you have short-term and long-term goals?

How can we trouble the directionality of the relationship between mathematical symbol systems and math as “basic to the operation of our understanding”?

HOW CAN WE RECONCEPTUALIZE MATHEMATICAL LANGUAGE AS EMBODIED?

What’s the line between “math language” and “lived math”?

“Math was basic to the operation of her understanding”

Symbol-systems as communicative tools. Are there other ways to communicate?

Insight into the distribution of what the possibilities are of mathematical ontologies? How are they connected? How can we make them non-hierarchical?

- Where is the practitioner?

How do we understand the way participants use the language of math for their own purposes?

- How do they shape their interests and identities using that language?

How do we create a culture in which we feel we are addressing the same issues?

- New ways of thinking that are unknown to everyone

How do we get policy makers involved in research/practice partnerships?

LEARNING THEORY

How do we challenge theories of learning through making?

- we have a lot of theories of learning and we don’t know how they’re related to one another – how are our characterizations of learning related to what we make in design?

- How do we define the role that bodies have in learning?

- What are the different affordances of different perspectives on learning for the same kinds of making activities?

- What’s your analytic frame?
- What’s your task frame (math, timescale, etc.)?
- What about the relationship between theoretical framing and mentoring/instruction?

BROAD ISSUES

- Bring practitioners

- Make equity explicit –

- getting with communities first; where do you want to effect the world
- social experiment design NOT design-based research [see special issue of C&I with Bang]