THE EFFECTS OF ERROR REFLECTION AND PERCEIVED FUNCTIONALITY OF ERRORS ON MIDDLE SCHOOL STUDENTS’ ALGEBRA LEARNING AND SENSE OF BELONGING TO MATHEMATICS
AuthorDoherty, Christina Barbieri
AdvisorBooth, Julie L.
Committee memberByrnes, James P.
Newton, Kristie Jones, 1973-
Schmitz, Mark F.
Incorrect Worked Examples
Learning From Errors
Perceived Functionality of Errors
Sense of Belonging
Permanent link to this recordhttp://hdl.handle.net/20.500.12613/2793
MetadataShow full item record
AbstractThe current study assessed an error reflection intervention on Algebra I students’ conceptual and procedural knowledge and sense of belonging to mathematics. Also of interest was whether perceptions of the functionality of errors mediated the effect of condition on learning and sense of belonging to mathematics. Middle school students (N = 207) were randomly assigned within classroom to one of four conditions: 1) a Problem-Solving Control group, 2) a Correct Examples Control group, 3) a Correct Examples Error Reflection condition that promoted reflection on hypothetical errors through self-explanation prompts, or 4) an Incorrect Examples Error Reflection condition that promoted reflection on displayed errors within the example through self-explanation prompts. Conceptual and procedural knowledge, sense of belonging to mathematics and perceived functionality of errors were measured pre- and post-intervention. After controlling for unanticipated clustering effects, results suggest that reflecting on and explaining errors within a worked examples intervention is just as effective at promoting learning as traditional problem solving alone or working with traditional correct worked examples and written self-explanation prompts. Students’ sense of belonging to mathematics or perceived functionality of errors for learning were high at the start of the study and remained so throughout the intervention. Perceptions of the functionality of errors were unrelated to learning and sense of belonging to mathematics. The limited size of the minority population in the sample did not allow for exploration of differential effects of condition for underrepresented minority (URM) students. However, these students reported lower feelings of belonging to mathematics than non-URM students. Implications for theory and practice are discussed.
ADA complianceFor Americans with Disabilities Act (ADA) accommodation, including help with reading this content, please contact firstname.lastname@example.org
Showing items related by title, author, creator and subject.
New Step Down Procedures for Control of the Familywise Error RateSarkar, S. K. (Sanat K.); Raghavarao, Damaraju; Hsuan, Francis C.; Chang, Steven (Temple University. Libraries, 2008)The main research topic in this dissertation is the development of the closure method of multiple testing procedures. Considering a general procedure that allows the underlying test statistics as well as the associated parameters to be dependent, we first propose a step-down procedure controlling the FWER, which is defined as the probability of committing at least one false discovery. Holm (1979) first proposed a step-down procedure for multiple hypothesis testing with a control of the familywise error rate (FWER) under any kind of dependence. Under the normal distributional setup, Seneta and Chen (2005) sharpened the Holm procedure by taking into account the correlations between the test statistics. In this dissertation, the Seneta-Chen procedure is further modified yielding a more powerful FWER controlling procedure. We then advance our research and propose another step-down procedure to control the generalized FWER (k-FWER), which is defined as the probability of making at least k false discoveries. We compare our proposed k-FWER procedure with the Lehmann and Romano (2005) procedure. The proposed k-FWER procedure is more powerful, particularly when there is a strong dependence in the tests. When the proportion of true null hypotheses is expected to be small, the traditional tests are usually conservative by a factor associated with pi0, which is the proportion of true null hypotheses among all null hypotheses. Under independence, two procedures controlling the FWER and the k-FWER are proposed in this dissertation. Simulations are carried out to show that our procedures often provide much better FWER or k-FWER control and power than the traditional procedures.
DESIGN FOR BIT ERROR RATE ESTIMATION OF HIGH SPEED SERIAL LINKSChiang, Chen Huan; Biswas, Saroj K.; Bai, Li (Temple University. Libraries, 2010)High-speed serial links in modern communication systems often require the Bit-Error-Rate (BER) to be at the level of 10 −12 or lower. From the industry perspective, major drawbacks in high volume production test for the serial links with low BER are the excessive test time for comparing each captured bit for error detection and costly instrumentation. In this thesis, we focus on developing a novel BER estimation methodology and its implementation. We propose a novel BER estimation methodology and an effective self-test system, which not only eliminates the usage of expensive measuring instruments, but also significantly reduces the test time. In the proposed BER estimation, we show that the total jitter (TJ) spectral information of a test SerDes is successfully estimated from the known TJ distribution of a golden SerDes. We propose a novel BER estimation formula that incorporates not only the TJ spectral information of the serial data, but also the TJ spectral information of the recovered clock. Our proposed estimation formula enables efficient BER estimation without excessive test time, and its accuracy does not depend on the jitter present in the serial data stream of the SerDes. The experimental results demonstrate that the test time for the proposed BER estimation is in the order of seconds, which translates to the test time savings of more than hundred times compared to the traditional BER measurement for the same accuracy. To implement the proposed BER estimation methodology, we have developed a novel time-to-digital converter (TDC). This design effectively measures the delay between two signals and converts it into the digital format. Performance of the TDC has been evaluated and presented using ModelSim and SPICE simulation.
Using Error Anticipation Exercises as an Instructional Intervention in the Algebra ClassroomNewton, Kristie Jones, 1973-; Booth, Julie L.; Ding, Meixia; McGinn, Kelly M. (Temple University. Libraries, 2019)Researchers and instructors have only recently embraced the role of errors as vehicles for learning in the algebra classroom. Studying a mixture of correct and incorrect worked examples has been shown to be beneficial relative to correct worked examples alone. This study examines the effectiveness of having students generate, or anticipate, errors another student might make. Five Algebra 1 sections at a suburban mid-Atlantic public high school participated amid an early equation-solving unit. During teacher-led instruction, all five sections examined 2-3 correct worked examples. The final example varied across conditions. One section received an additional correct worked example. Two sections examined an incorrect worked example. The remaining two sections engaged in an error anticipation exercise where the teacher wrote an equation on the board and asked the students to predict errors another student might make in solving. The study measured conceptual and procedural knowledge, encoding ability, and student-generated errors. Although no meaningful significant differences were found, students in the error anticipation condition saw no difference in performance in conceptual and procedural items versus those who examined incorrect worked examples. Analysis that combined the error anticipation and incorrect worked examples conditions showed that those students trended toward outperforming those who examined correct examples only on procedural items. These results support further examination of error anticipation as a worthwhile instructional activity.