Measurement: A rich and ubiquitous context for mathematization in physics Benjamin Zwickl1, Abby Rocha1, Kingston Chen1, Zackary Santos1, Anne Leak1, Kelly N. Martin2 (1) School of Physics and Astronomy (2) School of Communication, Rochester Institute of Technology

Mathematization and Measurement

DGE 1432578 DUE 1359262

Examples of measurement-rich, problem-solving epistemic games

Sample

1. Brahmia, S., Boudreaux, A. & Kanim, S. E. Obstacles to mathematization in introductory physics. arXiv preprint arXiv:1601.01235 (2016). 2. Collins, A. & Ferguson, W. Epistemic forms and Epistemic Games: Structures and Strategies to Guide Inquiry. Educational Psychologist 28, 25–42 (1993). 3. Tuminaro, J. & Redish, E. F. Elements of a cognitive model of physics problem solving: Epistemic games. Physical Review Special Topics - Physics Education Research 3, (2007). 4. Hu, D., Chen, K., Leak, A. & Zwickl, B. Characterizing mathematical problem-solving in physics academic research and industry using epistemic games. Under review 2018

Mathematization – translating between the physical world and the symbolic world in an effort to understand how things work.

Selected References

ben.zwickl@rit.edu www.rit.edu/power

Methods

Measurement – translating between the physical world and numerical quantities to understand how thing work

concepts −𝑚𝑔 sin 𝜃 + 𝜇𝑘𝑚𝑔 = 𝑚𝑎𝑥

0.253 ± 0.001 m

Numbers

Graphs

measurement tools

Knowledge base: STEM skill set (math and

physics), such as differential equations and optics.

Working with data (collection, extraction, analysis).

Programming skill set.

Epistemic forms

Experimental

systems, data,

databases,

software, coding

scripts

Interface with data

acquisition and

databases

Visualize and analyze

data

Interpret data

Make conclusion(s)

that answer the

research question

Entry condition:

A need to make a claim

based on data.

Ending condition:

Presentable results.

Present results to a

larger community

Presentable

documents (e.g.,

PowerPoint,

paper)

Data,

visualization

software, coding

scripts

Answering Research Questions with Data Knowledge base: Professional skills, such as

visualization and interpretation of blueprints, and

programming CNC machine using G-codes;

troubleshooting skills, math skills, and communication

skills.

Epistemic forms

Blueprints with

tolerances Receive blueprints

from engineers

Translate blueprints to

G-code

Make prototypes or

products

Test mechanical and

other properties

Entry condition:

A need to fabricate a product.

Ending condition:

The product and

performance report.

Generate report about

testing results Blueprints,

tables/graphs

Blueprints,

G-code

Blueprints, physical

tools, and numbers

Fabrication Knowledge base: STEM skill set (math and physics),

such as arithmetic and optics; Communication skill set

and coding skill set.

Epistemic forms

Current process Analyze root cause

Design a workflow

simulation or

experiment

Adjust parameters to

optimize the process

Entry condition:

A need to optimize a process.

(e.g. more yield, less time).

Ending condition:

An improved process.

Refine the process New process

Data, software,

coding scripts

Data, symbols,

software, coding

scripts

Improving Processes Mathematization in physics typically refers to a process of connecting the real physical world to the symbolic world using the concepts of physics.1 We argue that measurement should be considered as a related, but distinct, form of mathematization, and one which is highly relevant to a broad range of future science careers and everyday practice.

Tables

• Measurement, data analysis, and visualization is more ubiquitous than symbolic math in nearly all workplaces, both academic and industrial.

• Measurement is relevant across a broader range of career paths, including technical careers at the AS, BS, and PhD level.

Mathematization Measurement

Real-world translates to Symbols Numbers, tables, graphs

Link made by Concepts Measurement tools, sensors, computers

Procedures are Algebraic and calculus manipulations

Statistics, analysis scripts, spreadsheet formulas,

Quantities have Dimensions Units, uncertainty

Entry and ending conditions

Conditions for when to begin and end a game

Epistemic Form

External representations that guide inquiry

Moves

Actions that can be taken at different points in the game

Constraints and other contextual features

Factors that influence actions and decision-making (e.g., rules, tools, and cost)

Knowledge base A collection of knowledge resources associated with the game

Theory: Characteristics of an epistemic game

Data analysis 1. Transcribe interviews 2. Code for discussion of mathematics 3. Identify goal-driven math activities 4. Identify epistemic games as goal-driven activities present across multiple interviews 5. Identify entry and ending conditions, moves), and representational forms typical of

each activity by synthesizing multiple interviews

Semi-structured interview protocol (abbreviated)

1. Could you describe the work you do in your company or research lab?

2. Can you describe a situation where math plays plays a role in your work? What are the goals, tools, representations

being used?

(1) What are some of the epistemic games that describe mathematical problem solving in STEM workplaces?

(2) In what ways does the workplace mathematics diversify what it means to do math in physics

Research Questions

Academic 5 women, 5 men Astro-, optics, materials Computational, experimental, observational

Industry 3 women, 19 men

Engineers, technicians, managers

13 different companies