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Hanging out with scientists and engineers

What I am learning about mathematics…

Ann Sitomer

Oregon State University

ORMATYC 2015

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Overview

ORMATYC 2015

Why am I hanging out with scientists and engineers?

What am I learning about mathematics in other SEM disciplines?

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ESTEME@OSU Project goal: Catalyze broad institutional

change with respect to the use of Evidence-Based Instructional Practices (EBIPs) in the classroom

Focus: Introductory (gateway) courses in Biology, Physics, Chemistry, Mathematics, and Engineering

ORMATYC 2015

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Implementation

Communities of practice

Research

Organizational change

Student outcomes

Sustainability

Transfer activities to Center For

Teaching and Learning

Imbed instruments

into Institutional Assessment

ESTEME@OSU

ORMATYC 2015

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Anticipated StateCurrent State

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Implementation: Communities of Practice (Wenger, 1998)

General features Members have a shared interest or goal There is a community in which people interact and

engage in shared activities The members are practitioners who develop a shared

repertoire of resources for learning together

Communities of practice involve negotiation and social construction of ideas

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Implementation

Communities of practice

Research

Organizational change

Student outcomes

Sustainability

Transfer activities to Center For

Teaching and Learning

Imbed instruments

into Institutional Assessment

ESTEME@OSU - Project Design

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Preliminary Findings Organizational change

Undergraduate Learning Assistants (LAs) training and use of LAs in course design

Events Identification of a problem of practice Potential solution development

Workshop attendance Community of practice meetings

Cross-pollination Sensemaking

Research on impact of LAs on learning

Next Step: Feedback of analyzed data to guide future events

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Why am I hanging out with scientists and engineers? Role as a participant-observer in SEM

classrooms and the Communities of Practice in which SEM faculty participate Algebra-based physics sequence and the Physics

Teaching Seminar Introductory biology and an inter-disciplinary

Community of Practice, called a Teaching Triad Material Balance and Stoichiometry and role as a

researcher studying organizational change Introductory chemistry and the community of first-

year chemistry GTAs

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What am I learning about mathematics in other SEM disciplines? Proportional reasoning in physics

Exponential growth in biology

Non-linear systems of equations in engineering

Geometrical imagination in chemistry

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Proportional reasoning in physics

ORMATYC 2015

A woodworker has made four small airplanes and one large airplane. All airplanes are exactly the same shape, and all are made from the same kind of wood. The larger plane is twice as large in every dimension as one of the smaller planes. The planes are to be painted and then shipped as gifts. The amount of paint required to paint the planes is directly proportional to the surface area. Will the amount of paint required for the single plane in Case A be _____ the total amount of paint required for all four planes in Case B?.  A. greater than B. equal to C. less than

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Proportional reasoning in physics

ORMATYC 2015

A woodworker has made four small airplanes and one large airplane. All airplanes are exactly the same shape, and all are made from the same kind of wood. The larger plane is twice as large in every dimension as one of the smaller planes. The planes are to be painted and then shipped as gifts. The shipping cost for the planes is proportional to the weight which is related directly to the volume. Will the weight of the single plane in Case A be _____ the total weight of all four planes in Case B?  A. greater than B. less than C. equal to

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Proportional reasoning in physics

ORMATYC 2015

The figure shows a binary star system. The mass of star 2 is twice the mass of star 1. Compared to F21 (the force on star 2 from star 1), the magnitude of the force F12 (the force on star 1 from star 2) is _____.  A. one quarter as large. B. half as large. C. the same magnitude. D. twice as large. E. four times as large.

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Exponential growth in biology

ORMATYC 2015

An excerpt from a lecture on population ecology

In-Class Activity

Time Pop. A Pop. B Pop. C1 1 10 1002 2 15 1103 4 23 1214 8 35 1335 16 53 146

Below is population density data for three populations (A, B, C) all taken during the same time intervals.

1. Graph DENSITY VS. TIME on one set of axes.2. Calculate which population is growing the fastest. Brainstorm

how you might quantify population growth rate.3. Discuss among your groups how you determined your answer.

ORMATYC 2015Biology

ORMATYC 2015Biology

Based on what you just calculated, the graph below, and assuming the growth rate remains constant, rank the estimated population size at time 10.

A. A>B>C

B. C>B>A

C. B>A>C

D. None of the above.

E. There is not enough information to determine the answer.

ORMATYC 2015Biology

Time Pop. A Pop. B Pop. C

1 1 10 100

2 2 15 110

3 4 23 121

4 8 35 133

5 16 53 146

6 32 80 160

7 64 120 176

8 128 180 193

9 256 270 212

10 512 405 233

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At time 10: A > B > C

0 2 4 6 8 10 120

100

200

300

400

500

600

ABC

Time

Num

ber

ORMATYC 2015Biology

Time Pop. A Pop. B Pop. C1 1 10 1002 2 15 1103 4 23 1214 8 35 1335 16 53 146

Calculate the proportional increase in population size in a given time interval? Is it constant?

Below is population density data for three populations (A, B, C) all taken during the same time intervals.

ORMATYC 2015Biology

A > B > C

Population A is growing by 100% (or doubling) in each time interval.Population B is growing by 50% in each time interval.Population C is growing by 10% in each time interval.

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Nt + 1 = Nt + [Nt• proportional change]

A: Nt + 1 = Nt + [Nt• (1.0)]

B: Nt + 1 = Nt + [Nt• (0.5)]C: Nt + 1 = Nt + [Nt• (0.1)]

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Population growth in these examples are…

A. additive in all cases

B. multiplicative in all cases.

C. may be additive or multiplicative but varies by population.

ORMATYC 2015Biology

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Non-linear systems in engineering

ORMATYC 2015

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Non-linear systems in engineering

ORMATYC 2015

Mass BalanceMass balance evaluates materials crossing a system boundary. The subscripts denote different materials streams entering and leaving the system. The conservation of mass tells us that the total mass of the materials entering the system must equal the total mass of the materials leaving the system, independent of reaction or a material phase change within the system boundary.

m = mass (in kg)x = mass fraction (kg material/kg)y = vapor fraction (kg material/kg)

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Geometrical imagination in chemistry

ORMATYC 2015

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Geometrical imagination in chemistry

ORMATYC 2015

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Geometrical imagination in chemistry

ORMATYC 2015

Let’s Think—A Linear Molecule?* • Imagine for a second that the water molecule was linear and not bent.

• How would this change the strength of the different contributions (i.e., dispersion, dipoledipole, and H-bonding) to the IMFs [intermolecular forces] between water molecules?

• What would be the impact of this change on (a) the physical properties of water, (b) Earth’s climate, and (c) life in our planet?

• Share and discuss your ideas with a classmate.

* From Reaching Students: What Research Says about Effective Instruction in Undergraduate Engineering, National Academies Press.

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Thank You

Email: ann.sitomer@oregonstate.edu