Work In Progress: Combining Concept Inventories with Rapid Feedback to Enhance Learning

In this project our goal is to adapt the Concept Inventory for frequent classroom use, and to implement it in a system to provide rapid feedback to students of their understanding of key concepts being presented. The feedback system acts as the focal point and catalyst to encourage students, working in pairs, to assist each other in correcting misconceptions or deepening each other’s understanding of the topic at hand. Furthermore, the system allows the professor to assess the students’ level of comprehension (or misconception) in a just-in-time fashion, and thus guides his or her pacing and coverage of the material. The rapid feedback is enabled through wireless-networked handheld computers. In this first year of the study, we have implemented the system in a lower-level, core-engineering course (engineering mechanics: statics). This paper will focus on the motivation for and the design of this project; our presentation will describe results from the first implementation

Enhancing Student Learning in Mechanics Through Rapid-Feedback

In this project our goal is to improve student learning in engineering mechanics courses. The aim to improve learning was accomplished by providing rapid feedback to students of their understanding of key concepts and skills being taught. The feedback system acts as a catalyst to encourage students, working in pairs, to assist each other in correcting misconceptions or deepening each other’s understanding of the concept or skill at hand. Furthermore, the system allows the professor to assess the students’ level of comprehension or misconception in a just-in-time fashion, and thus guide the pace of covering the material. The feedback is enabled through wireless-networked handheld computers or color-coded flashcards. In the first two years of the study, the feedback system was implemented in two sections of a lower-level, core-engineering course, statics, as well as in follow-on courses of dynamics and solid mechanics

BLOCK DESIGNS: GENERAL OPTIMALITY RESULTS WITH APPLICATIONS TO SITUATIONS WHERE BALANCED DESIGNS DO NOT EXIST (EXPERIMENTAL, INFORMATION MATRIX, SCHUR-CONVEX)

The problem of optimally allocating v treatments to experimental units in b blocks of size k(,j) (l (LESSTHEQ) j (LESSTHEQ) b) when no balanced block design (BBD) exists is studied. The model is that of one-way elimination of heterogeneity where the expectation of an observation on treatment i in block j is (alpha)(,i) + (beta)(,j) and all observations are uncorrelated with common variance. Optimality is measured with criteria that are functions of the nonzero eigenvalues of the C-matrix derived from the reduced normal equations for the (alpha)(,i) (1 (LESSTHEQ) i (LESSTHEQ) v). The criteria include A-, D- and E-optimality, Cheng\u27s generalized type 1 optimality, and optimality over the class of Schur-convex functions that are nonincreasing in each eigenvalue. A main result is proved which says if a design d* has a C-matrix with eigenvalues of the form O \u3c a \u3c b = ... = b, is of maximum trace and as E-optimal for a class of designs, then d* is optimal over that class of designs for all Schur-convex functions nonincreasing in each eigenvalue. Several other results using similar techniques of weak supermajorization are given. This main result is applied to the case where all k(,j) = v-l and b-l blocks allow a balanced incomplete block design (BIBD) to be constructed, and with partial success where all k(,j) = 2 and b+l blocks allow a BIBD. A result of Cheng (1978) for eigenvalues of the form O \u3c a = ... = a \u3c b is applied to cases where all k(,j) = v-l but b-l blocks allow a BIBD, and all k(,j) = 2 but b+l blocks allows a BIBD. The main result is also applied in some cases of two situations with unequal block sizes. The first has k(,l) = ... = k(,b-l) = pv + q (p (GREATERTHEQ) O, O (LESSTHEQ) q (LESSTHEQ) v-l) and k(,b) = v-l with b-l blocks allowing a BBD to be constructed. The second has k(,1) = ... = k(,b-l) = pv + q and k(,b) = pv + q-l with b blocks of size pv + q allowing a BBD. Next two situations where all k(,j) = pv + q (p (GREATERTHEQ) l) are studied. In these b + m or b-m (l (LESSTHEQ) m (LESSTHEQ) v/q) blocks allow a BBD to be constructed. The main results is applied in some cases, and cases with eigenvalues of the form of Cheng (1978) are also investigated. For some cases of the above situation appropriate A-, D- or E-efficiencies are presented for designs of special interest, or which were not proved optimal. Finally the main result is used to extend an existing theorem for trend-free block designs generated by a BBD with k (LESSTHEQ) v. Important examples limit further extension for k \u3c v

Using Technology for Concepts Learning and Rapid Feedback in Statics

In this project our goal is to improve student learning in the foundation mechanics course Statics as well as improve knowledge retention (durability) and knowledge application in a different environment (transferability). We aim to do this by providing rapid feedback to students of their understanding of key concepts and skills being presented. The feedback system acts as the focal point and catalyst to encourage students to assist each other in correcting misconceptions or deepening each other’s understanding of the topic or skill at hand. Furthermore, the system allows the professor to assess the students’ level of comprehension (or misconception) in a just-in-time fashion, and thus guide his or her pacing and coverage of the material. The rapid feedback is enabled through wireless-networked handheld personal digital assistants (PDAs) or flashcards. In the first two years of the study, we have implemented the system in two sections of Statics using a crossover design of experiment, where one section receives the rapid feedback ‘treatment’ (i.e., use of the PDAs) while the other (the ‘control’ group) receives rapid feedback on the exact same topics, but only through the use of flashcards instead of PDAs. After a predetermined period, the sections swap their feedback treatment. Several swaps are achieved during the course, and in this manner each student acts as his or her own experimental control to assess the effectiveness of the treatment. This paper focuses on implementation and feedback methods in statics, a brief summary of statistical analysis, results of student learning and use of feedback in follow-on courses

Concepts Learning Using Technology for Rapid Feedback and Student Engagement

In this project our goal is to improve student learning in the foundation mechanics course Statics. In this case improved learning is defined as knowledge retention (durability) and knowledge application in a different environment (transferability). We aim to do this by providing rapid feedback to students of their understanding of key concepts and skills being presented. The feedback system acts as the focal point and catalyst to encourage students to assist each other in correcting misconceptions or deepening each other’s understanding of the topic or skill at hand. Furthermore, the system allows the professor to assess the students’ level of comprehension (or misconception) in a just-in-time fashion, and thus guiding his or her pacing and coverage of the material. The rapid feedback is enabled through wireless-networked handheld personal digital assistants (PDAs) or flashcards. In the first two years of the study, we have implemented the system in two sections of Statics using a crossover design of experiment, where one section receives the rapid feedback ‘treatment’ (i.e., use of the PDAs) while the other (the ‘control’ group) receives rapid feedback on the exact same topics, but only through the use of flashcards. After a predetermined period, the sections swap their feedback treatment. Several swaps are achieved during the course, and in this manner each student acts as his or her own experimental control to assess the effectiveness of the treatment. This paper focuses on our experimental methods, the statistical analysis of data, and results of student learning and student satisfaction from the first implementation

On the E- and MV-optimality of block designs having k≥v

Incidence matrix, C-matrix, eigenvalue, E-optimality, MV-optimality,