Margret A. Hjalmarson

Teacher as Designer: A Framework for Teacher Analysis of Mathematical Model-Eliciting Activities

The study investigated tool development by three middle school mathematics teachers. The tools they designed were intended to support the use of model-eliciting activities (a form of instruction related to problem-based learning) and particularly the students’ presentations of their solutions for the whole class. The study examined the design and purposes for the presentation tools and resulted in a framework for categorizing teachers’ purposes for tools. The framework addressed the unit of analysis for the tools (individual students or groups of students) and the nature of teachers’ purposes for the tools. Design research was used as a theoretical perspective for conducting the

Comparing student understanding of signals and systems using a concept inventory, a traditional exam and interviews

Concept inventories play a growing role in assessing student understanding in engineering curricula. A common application of concept inventories is a pre/post- test assessment in a course. For this reason, it is important to confirm the validity of any new concept inventory, i.e., to verify that the inventory measures what it is designed to assess. The signals and systems concept inventory (SSCI) is a 25-question multiple-choice exam assessing core concepts in undergraduate signals and systems courses. This paper presents two analyses supporting the validity of the SSCI. The first analysis compares the responses of 40 students to final exam questions with their responses to related SSCI questions. This analysis finds statistically-significant correlations between the SSCI and the final exam for questions on convolution and Fourier transform properties. The second analysis examines the interview responses of 18 students to SSCI questions on frequency-selective filtering and convolution. The interviews suggest students have a strong understanding of high and low frequency, have some understanding of the relationship between time and frequency domains, but struggle to interpret frequency responses. The interviews also suggest that many students retain some conceptual understanding of convolution after their memory of the convolution integral has faded.

Students' interpretation of the importance and difficulty of concepts in signals and systems

Two ongoing challenges facing instructors when designing courses are (1) do students identify/understand important concepts in the course, and (2) what makes concepts difficult for students to understand? In particular, do students see the relationship between the procedures taught and the fundamental concepts they support? In this study, we use interviews with 39 undergraduate engineering students to address these questions in the context of a sophomore-level continuous-time signals and systems course. Each student interviewed was asked which concept in the course was most difficult, which was most important, and why. Student responses regarding the concepts and the reasons were qualitatively analyzed, and a codebook was developed. The results of the coding provide broad insight into what factors make a particular concept difficult and/or important from the student perspective. We conjecture that general elements drawn from the results obtained here can be applied beyond signals and systems and across the engineering curriculum.

Mathematics Curriculum Systems: Models for Analysis of Curricular Innovation and Development

Defining challenging curriculum first requires an examination of what is meant by curriculum. This discussion of challenging curriculum is motivated by the evaluation of the National Science Foundations Math and Science Partnership Program. Standards frameworks, textbooks, software, and pedagogy are some aspects of curricula. The level of challenge of a curriculum is a locally defined, qualitative characteristic that depends on the curriculum system. The structure of a curriculum system is proposed to investigate the purposes, representations, and conceptual systems inherent in models of curriculum that are part of mathematics teaching and learning initiatives. Three types of models are proposed: content focused, pedagogically focused, and learner centered. The models draw on examples from the Math and Science Partnership portfolio and from other areas of the literature on mathematics curriculum.

Item Response Analysis of the Continuous-Time Signals and Systems Concept Inventory

Item Response Theory was used to analyze version 3 of the Continuous-Time Signals and Systems Concept Inventory with a pool of 1276 students at 7 schools. The resulting estimates of question difficulty and student ability provide important data used to evaluate the design of the exam and prepare for the upcoming revision to version 4 of the inventory.

Workshop - The Signals and Systems Concept Inventory

The signals and systems concept inventory (SSCI) is a 25 question multiple choice exam designed to assess studentspsila conceptual understanding in signals and systems (S&S), a common core course in electrical and computer engineering curricula. The SSCI provides both formative assessment to instructors looking to improve studentspsila conceptual understanding in their courses, and summative assessment which can be used as part of the accreditation process. The SSCI is a mature instrument in its seventh year of development, given to over 1800 students by more than 30 instructors. This workshop will employ the active and collaborative learning techniques we advocate for improving studentspsila conceptual understanding. The workshop will describe the concepts assessed by the SSCI and the design of the SSCI questions. We will review the extensive pre-test/post-test data collected with the SSCI, including student gain data, the impact of instructional format on conceptual understanding, and the relative difficulty the SSCI questions. Wepsilall also discuss which misconceptions the SSCI finds to be most resistant to instruction. The workshop will provide examples of how other instructors have incorporated the SSCI into their research on S&S pedagogy.

Study of Self: The Self as Designer in Online Teacher Education

Abstract In this article we describe our engagement in self-study as part of an examination of design-based research for education. We focus on graduate-level online teacher education as an example of how self-study provided a means of examining deeply our teaching and our roles as teacher and designer in the learning environment. We posit that online learning environments are particularly well suited for self-study to enhance design perspectives because the interactions between teacher and students are informed by personal context and mediated by technological tools. The graduate students in our courses were teacher leaders in literacy or mathematics who were learning how to support professional development for other teachers. Throughout our self-study research we found ourselves drawing upon our previous design research experiences, which aided our ability to engage in self-study: We were part of the classroom system, focusing on our roles within the teaching and learning process as designers of the online learning environment. Three key design principles resulted from our self-study process: focusing on systems of learning and teaching, designing pedagogical tools and products, and using iterative processes. Engaging in self-study enhanced our understanding and implementation of synchronous online instruction, particularly regarding our use of technological tools to enhance student learning and support learning communities.

Implementation of interactive teaching strategies across STEM disciplines

We propose to present a collection of posters united by a single theme: the use of interactive teaching across STEM disciplines. The posters will be presented by Mason faculty and graduate students participating in the NSF-funded SIMPLE Project. The focus of the project is developing faculty communities of practice that promote evidence-based interactive teaching across STEM. As part of this project, participants have been trying new interactive teaching strategies in their classrooms and documenting the process in the form of a design memo. A design memo is a short, structured reflection on the implementation of a particular teaching strategy. In the context of the SIMPLE Project, design memos pursue two goals: prompting instructors to engage in reflection about their teaching, and serving as sharable artifacts for other instructors interested in adopting similar strategies. More information about the project and about design memos can be found on the project website: simple.onmason.com . Each poster at the session will provide a birds-eye view of the participant’s design memo; thus, it will include (but will not be limited to) a description of a strategy with examples, the instructor’s reasons to implement it, information on preparation needed for its use, discussion of potential pitfalls to avoid, and reflection on how the instructor would refine the technique for future implementations. Posters will be complemented by printed copies of design memos as handouts for attendees. By the end of the session, attendees will learn about various interactive teaching strategies and how they can be enacted in practice.