Ann Sitomer Oregon State University ORMATYC

Overview 2 ORMATYC 2015  Why am I hanging out with scientists and engineers?  What am I learning about mathematics in other SEM disciplines?

 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 3 ORMATYC 2015

Implementation Communities of practice Research Organizational change Student outcomes Sustainability Transfer activities to Center For Teaching and Learning Imbed instruments into Institutional Assessment 4 ORMATYC 2015

Anticipated StateCurrent State Cross Disciplinary Disciplinary Implementation: Communities of Practice (Wenger, 1998) 5  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 ORMATYC 2015

Implementation Communities of practice Research Organizational change Student outcomes Sustainability Transfer activities to Center For Teaching and Learning Imbed instruments into Institutional Assessment - Project Design 6 ORMATYC 2015

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 7 ORMATYC 2015

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 8 ORMATYC 2015

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 9 ORMATYC 2015

Proportional reasoning in physics 10 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

Proportional reasoning in physics 11 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

Proportional reasoning in physics 12 ORMATYC 2015 The figure shows a binary star system. The mass of star 2 is twice the mass of star 1. Compared to F 21 (the force on star 2 from star 1), the magnitude of the force F 12 (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.

Exponential growth in biology 13 ORMATYC 2015 An excerpt from a lecture on population ecology

In-Class Activity TimePop. APop. BPop. C 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 2015 Biology

ORMATYC 2015 Biology

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 2015 Biology

TimePop. APop. BPop. C ORMATYC 2015 Biology

At time 10: A > B > C ORMATYC 2015 Biology

TimePop. APop. BPop. C 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 2015 Biology

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. ORMATYC 2015 Biology

N t + 1 = N t + [ N t proportional change ] A: N t + 1 = N t + [ N t (1.0)] B: N t + 1 = N t + [ N t (0.5)] C: N t + 1 = N t + [ N t (0.1)] ORMATYC 2015 Biology

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 2015 Biology

Non-linear systems in engineering 23 ORMATYC 2015

Non-linear systems in engineering 24 ORMATYC 2015 Mass Balance Mass 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)

Geometrical imagination in chemistry 25 ORMATYC 2015

Geometrical imagination in chemistry 26 ORMATYC 2015

Geometrical imagination in chemistry 27 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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