Removing opportunities to calculate improves students' performance on subsequent word problems.

BackgroundIn two studies we investigated whether removing opportunities to calculate could improve students' subsequent ability to solve similar word problems. Students were first asked to write explanations for three word-problems that they thought would help another student understand the problems. Half of the participants explained typical word problems (i.e., problems with enough information to make calculating an answer possible), while the other half explained the same problems with numbers removed, making calculating an answer impossible. We hypothesized that removing opportunities to calculate would induce students to think relationally about the word problems, which would result in higher levels of performance on subsequent transfer problems.ResultsIn both studies, participants who explained the non-calculable problems performed significantly better on the transfer test than participants who explained the typical (i.e., calculable) problems. This was so in spite of the manipulation not fully suppressing students' desire to calculate. Many students in the non-calculable group explicitly stated that they needed numbers in order to answer the question or made up numbers with which to calculate. There was a significant, positive relationship between the frequency with which students made up numbers and their self-reported mathematics anxiety.ConclusionsWe hypothesized that the mechanism at play was a reduction in instrumental thinking (and an increase in relational thinking). Interventions designed to help students remediate prior mathematical failure should perhaps focus less on the specific skills students are lacking, and more on the dispositions they bring to the task of "doing mathematics.

Persistent Pedagogical Challenges in Developmental Education Reform

This chapter presents pedagogical challenges to reform in developmental education and observations of best practices gleaned from successful mathematics developmental education classrooms

What do teachers think about their students’ inclusion? Consistency of students’ self-reports and teacher ratings

The aim of this study was to investigate the consistency between the self-reports and teacher ratings of students’ emotional and social inclusion at school as well as for their academic self-concept. The German version of the Perceptions of Inclusion Questionnaire (PIQ) was administered to 329 grade 8 students (50.8% female, Mage = 14.5 years, SDage = 0.5 years) and their teachers. First, the three- dimensional structure of both PIQ versions was confirmed by confirmatory item factor analysis. The a and & coefficients demonstrated good reliability for all scales. Second, a correlated trait-correlated method minus one model provided evidence that the method specificity of teacher ratings was larger than the consistency between the self-reports and teacher ratings. Third, the results of a latent difference model indicated that general method effects can partly be explained by a student’s gender or special educational needs. Finally, the low consistency between self-reports and teacher rating is discussed

Practicing Connections: A Framework to Guide Instructional Design for Developing Understanding in Complex Domains

Research suggests that expert understanding is characterized by coherent mental representations featuring a high level of connectedness. This paper advances the idea that educators can facilitate this level of understanding in students through the practicing connections framework: a practical framework to guide instructional design for developing deep understanding and transferable knowledge in complex academic domains. We start by reviewing what we know from learning sciences about the nature and development of transferable knowledge, arguing that connectedness is key to the coherent mental schemas that underlie deep understanding and transferable skills. We then propose features of instruction that might uniquely facilitate deep understanding and suggest that the connections between a domain’s core concepts, key representations, and contexts and practices of the world must be made explicit and practiced, over time, in order for students to develop coherent understanding. We illustrate the practicing connections approach to instructional design in the context of a new online interactive introductory statistics textbook developed by the authors

Student Concerns and Perceived Challenges in Introductory Statistics, How the Frequency Shifted during COVID-19, and How They Differ by Subgroups of Students

ABSTRACTThe COVID-19 pandemic and shift to remote instruction disrupted students’ learning and well-being. This study explored undergraduates’ incoming course concerns and later perceived challenges in an introductory statistics course. We explored how the frequency of concerns changed with the onset of COVID-19 ([Formula: see text]1417) and, during COVID-19, how incoming concerns compared to later perceived challenges ([Formula: see text]524). Students were most concerned about R coding, understanding concepts, workload, prior knowledge, time management, and performance, with each of these concerns mentioned less frequently during than before COVID-19. Concerns most directly related to the pandemic—virtual learning and inaccessibility of resources—showed an increase in frequency. The frequency of concerns differed by gender and URM status. The most frequently mentioned challenges were course workload, virtual learning, R coding, and understanding concepts, with significant differences by URM status. Concerns about understanding concepts, lack of prior knowledge, performance, and time management declined from the beginning to the end of the term. Workload had the highest rate of both consistency and emergence across the term. Because students’ perceptions have an impact on their experiences and expectations, understanding and addressing concerns and challenges could help guide instructional designers and policymakers as they develop interventions

What is Effective Mathematics Teaching? International Educators' Judgements of Mathematics Lessons from the TIMSS 1999 Video Study

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Removing opportunities to calculate improves students' performance on subsequent word problems.

BackgroundIn two studies we investigated whether removing opportunities to calculate could improve students' subsequent ability to solve similar word problems. Students were first asked to write explanations for three word-problems that they thought would help another student understand the problems. Half of the participants explained typical word problems (i.e., problems with enough information to make calculating an answer possible), while the other half explained the same problems with numbers removed, making calculating an answer impossible. We hypothesized that removing opportunities to calculate would induce students to think relationally about the word problems, which would result in higher levels of performance on subsequent transfer problems.ResultsIn both studies, participants who explained the non-calculable problems performed significantly better on the transfer test than participants who explained the typical (i.e., calculable) problems. This was so in spite of the manipulation not fully suppressing students' desire to calculate. Many students in the non-calculable group explicitly stated that they needed numbers in order to answer the question or made up numbers with which to calculate. There was a significant, positive relationship between the frequency with which students made up numbers and their self-reported mathematics anxiety.ConclusionsWe hypothesized that the mechanism at play was a reduction in instrumental thinking (and an increase in relational thinking). Interventions designed to help students remediate prior mathematical failure should perhaps focus less on the specific skills students are lacking, and more on the dispositions they bring to the task of "doing mathematics.