12 research outputs found

### A framework for the natures of negativity in introductory physics

Mathematical reasoning skills are a desired outcome of many introductory
physics courses, particularly calculus-based physics courses. Positive and
negative quantities are ubiquitous in physics, and the sign carries important
and varied meanings. Novices can struggle to understand the many roles signed
numbers play in physics contexts, and recent evidence shows that unresolved
struggle can carry over to subsequent physics courses. The mathematics
education research literature documents the cognitive challenge of
conceptualizing negative numbers as mathematical objects--both for experts,
historically, and for novices as they learn. We contribute to the small but
growing body of research in physics contexts that examines student reasoning
about signed quantities and reasoning about the use and interpretation of signs
in mathematical models. In this paper we present a framework for categorizing
various meanings and interpretations of the negative sign in physics contexts,
inspired by established work in algebra contexts from the mathematics education
research community. Such a framework can support innovation that can catalyze
deeper mathematical conceptualizations of signed quantities in the introductory
courses and beyond

### Framework for the natures of negativity in introductory physics

Mathematical reasoning skills are a desired outcome of many introductory physics courses, particularly calculus-based physics courses. Novices can struggle to understand the many roles signed numbers play in physics contexts, and recent evidence shows that unresolved struggle can carry over to subsequent physics courses. Positive and negative quantities are ubiquitous in physics, and the sign carries important and varied meanings. The mathematics education research literature documents the cognitive challenge of conceptualizing negative numbers as mathematical objectsâ€”both for experts, historically, and for novices as they learn. We contribute to the small but growing body of research in physics contexts that examines student reasoning about signed quantities and reasoning about the use and interpretation of signs in mathematical models. In this paper we present a framework for categorizing various meanings and interpretations of the negative sign in physics contexts, inspired by established work in algebraic contexts from the mathematics education research community. Such a framework can support innovation that can catalyze deeper mathematical conceptualizations of signed quantities in the introductory courses and beyond

### Exploring student facility with "goes like'' reasoning in introductory physics

Covariational reasoning -- reasoning about how changes in one quantity relate
to changes in another quantity -- has been examined extensively in mathematics
education research. Little research has been done, however, on covariational
reasoning in introductory physics contexts. We explore one aspect of
covariational reasoning: ``goes like'' reasoning. ``Goes like'' reasoning
refers to ways physicists relate two quantities through a simplified function.
For example, physicists often say that ``the electric field goes like one over
r squared.'' While this reasoning mode is used regularly by physicists and
physics instructors, how students make sense of and use it remains unclear. We
present evidence from reasoning inventory items which indicate that many
students are sense making with tools from prior math instruction, that could be
developed into expert ``goes like'' thinking with direct instruction.
Recommendations for further work in characterizing student sense making as a
foundation for future development of instruction are made.Comment: under review for Physics Education Research Conference Proceedings
202

### Online administration of a reasoning inventory in development

We are developing a new research based assessment (RBA) focused on
quantitative reasoning -- rather than conceptual understanding -- in physics
contexts. We rapidly moved administration of the RBA online in Spring 2020 due
to the COVID-19 pandemic. We present our experiences with online, unproctored
administration of an RBA in development to students enrolled in a
large-enrollment, calculus-based, introductory physics course. We describe our
attempts to adhere to best practices on a limited time frame, and present a
preliminary analysis of the results, comparing results from the online
administration to earlier results from in-person, proctored administration. We
include discussion of online administration of
multiple-choice/multiple-response (MCMR) items, which we use on the instrument
as a way to probe multiple facets of student reasoning. Our initial comparison
indicates little difference between online and paper administrations of the
RBA, consistent with previous work by other researchers.Comment: PERC 202

### Toward a valid instrument for measuring physics quantitative literacy

We have developed the Physics Inventory of Quantitative Literacy (PIQL) as a
tool to measure students' quantitative literacy in the context of introductory
physics topics. We present the results from various quantitative analyses used
to establish the validity of both the individual items and the PIQL as a whole.
We show how examining the results from classical test theory analyses, factor
analysis, and item response curves informed decisions regarding the inclusion,
removal, or modification of items. We also discuss how the choice to include
multiple-choice/multiple-response items has informed both our choices for
analyses and the interpretations of their results. We are confident that the
most recent version of the PIQL is a valid and reliable instrument for
measuring students' physics quantitative literacy in calculus-based
introductory physics courses at our primary research site. More data are needed
to establish its validity for use at other institutions and in other courses.Comment: accepted for publication: 2020 Physics Education Research Conferenc

### The Physics Inventory of Quantitative Literacy: A tool for assessing mathematical reasoning in introductory physics

One desired outcome of introductory physics instruction is that students will
develop facility with reasoning quantitatively about physical phenomena. Little
research has been done regarding how students develop the algebraic concepts
and skills involved in reasoning productively about physics quantities, which
is different from either understanding of physics concepts or problem-solving
abilities. We introduce the Physics Inventory of Quantitative Literacy (PIQL)
as a tool for measuring quantitative literacy, a foundation of mathematical
reasoning, in the context of introductory physics. We present the development
of the PIQL and evidence of its validity for use in calculus-based introductory
physics courses. Unlike concept inventories, the PIQL is a reasoning inventory,
and can be used to assess reasoning over the span of students' instruction in
introductory physics. Although mathematical reasoning associated with the PIQL
is taught in prior mathematics courses, pre/post test scores reveal that this
reasoning isn't readily used by most students in physics, nor does it develop
as part of physics instruction--even in courses that use high-quality,
research-based curricular materials. As has been the case with many inventories
in physics education, we expect use of the PIQL to support the development of
instructional strategies and materials--in this case, designed to meet the
course objective that all students become quantitatively literate in
introductory physics