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Background: Providing students with worked out problem solutions is a beneficial instructional technique in STEM disciplines, and studying examples that have been worked out incorrectly may be especially helpful for reducing misconceptions in students with low prior content knowledge. However, past results are inconclusive and the effects of incorrect worked examples alone or in combination with correct examples remains unclear. Objectives: We aim to address whether studying incorrect examples alone or in combination with correct examples can support the reduction of students' fraction misconceptions, operationalized as errors made with high confidence. Methods: After incorrectly solving a sampling problem, 130 students in 4th through 11th grade in the U.S. were randomly assigned to a condition in an online problem set focused on fraction equivalence. Students studied either single‐type worked examples (i.e., correct or incorrect; n = 49) or combination‐type worked examples (correct and incorrect; n = 41) or engaged in a problem‐solving control (n = 50). Results: Studying a combination of correct and incorrect worked examples was as effective as the problem‐solving control with feedback at improving fraction equivalence knowledge and reducing the rate of high‐confidence errors. Students in both the combination condition and the problem‐solving with feedback condition outperformed those who studied either correct or incorrect worked examples alone. Conclusions: Results support the inclusion of a combination of correct and incorrect worked examples when teaching students with low prior content knowledge. Studying a combination of example types within an online tutor helps to reduce misconceptions about fractions, a topic students commonly struggle with. A problem‐solving task with corrective feedback worked equally well. Lay Description: What is already known about this topic: Studying worked examples of mathematical solutions improves student learning.Incorrect examples, either alone or in combination with correct examples, are particularly effective for improving learning for students with low prior knowledge in the target content.Comparing correct and incorrect examples is also effective at improving problem‐solving but this effect may be specific to those with high prior knowledge.Still unknown are the impacts of these different combinations of examples on misconceptions in particular. What this paper adds: We show that studying a combination of correct and incorrect examples reduces math misconceptions.Problem‐solving with corrective feedback within an online tutor also has this effect. Implications for practice and/or policy: Using a combination of example types will help reduce students' misconceptions about fractions. [ABSTRACT FROM AUTHOR]

Background: Valuable safeguards against fast‐spreading conjectures about learning in times of fear and uncertainty are evidence‐based approaches to the assessment of the impact of sudden and unforeseen disruptions on learning practices. The present research focused on physics learning in such times because conceptual and computational literacy in physics is critical to the development of a scientifically and technologically literate society. Objectives: The present research aimed (a) to offer an objective assessment of whether performance differences in a physics course of the general education curriculum existed between the face‐to‐face medium (familiar mode of instruction) and the online medium (unfamiliar mode of instruction) for both male and female students, and then (b) to develop a response to the evidence collected to ensure a quality education for all parties involved. The research intended to fill two critical gaps in the extant literature: mixed findings concerning students' performance in the face‐to‐face and online mediums as well as scarce coverage of specific domains of knowledge that are critical to STEM learners. Methods: Students' performance was examined as a function of the type of assessment (formative and summative), instructional mode (online and face‐to‐face), and gender. An understudied student population of STEM students of Middle Eastern descent without prior formal exposure to online instruction was targeted. Results and Conclusions: In both formative and summative assessments, male students performed better online than face‐to‐face, whereas the performance of female students was either higher online or equivalent between instructional mediums. The evidence collected suggested that consideration be given to remedies that foster academic success in the face‐to‐face instructional medium, particularly for male students. Takeaways: An evidence‐based approach to learning dismantled emotion‐driven expectations regarding the impact of the online medium on physics learning, and encouraged new perspectives about instruction. Lay Description: What is already known?: Ongoing debates on the impact of the pandemic on students' learning shape decisions regarding future reliance on the online medium for instruction. What this paper adds: The extant literature is mixed concerning performance in the face‐to‐face and online mediums, including particular domains of knowledge critical to STEM learning.This study focused on physics learning in an understudied population of STEM students who were unaccustomed to online instruction.Performance was higher online than face‐to‐face, but gender differences emerged. Implications for practice: Lessons learned focused on the flexibility of online learning and on the need to develop materials to enhance learning in males enrolled in face‐to‐face or hybrid/blended classes. [ABSTRACT FROM AUTHOR]

This paper examines the relationships among the quality and quantity of parent-child shared book reading (SBR) engagements and children's reading and mathematics outcomes in preschool. Additionally, we explore how child and family characteristics predict the quality and quantity of SBR. Quantity was measured using parental reports of the frequency of SBR. Quality was measured by observational protocols evaluating for questioning, vocabulary, and discussion depth. A structural equation model was estimated using data from a nationally representative sample of 700 children living in the United States from the Early Childhood Longitudinal Study-Birth cohort. Results indicated that the quality of book reading was associated with children's mathematics outcomes, and the quantity was associated with reading outcomes controlling for contextual variables. Socioeconomic status, race or ethnicity, and children's age predicted the quality and quantity of book reading experiences. These findings indicate that frequent exposure to high-quality book reading may positively impact children's mathematics and reading development, but that variation in SBR exists. SBR is a common practice among many parents; helping parents understand the multiple benefits of the practice may further increase the frequency and quality of the engagement. Implications for research and practice are addressed. Highlights This paper describes the relationship between parental book reading practices, mathematics, and reading outcomes., Structural equation models reveal relationships between the quantity of book reading and children's reading outcomes, as well as the quality of book reading and children's mathematics outcomes., High-quality book reading may positively impact academic achievement in multiple domains, but results may vary based on contextual factors. [ABSTRACT FROM AUTHOR]

The number of students who leave U.S. schools mathematically underprepared has prompted widespread concern. Low achieving students, many of whom have been turned off mathematics, are often placed in low tracks and given remedial, skills-oriented work. This study examines a different approach wherein heterogeneous groups of students were given responsibility and agency and asked to engage in a range of mathematical practices collaboratively. The teaching intervention, which was introduced in the first paper, took place as part of a summer class on algebra, and it gave students the opportunity to participate with mathematics in changed ways. This paper will report evidence that the vast majority responded with increased engagement, achievement, and enjoyment. The students chose collaboration and agency as critical to their improved relationships with mathematics. [ABSTRACT FROM AUTHOR]

In recent years, US curriculum policy has emphasized standards‐based conceptions of curricula in mathematics and science. This paper explores the data from the Third International Mathematics and Science Study (TIMSS) to argue that the presence of content standards is not sufficient to guarantee curricula that lead to high‐quality instruction and achievement. An examination of the content topics covered in each grade of a group of six of the highest‐achieving TIMSS countries in mathematics and science shows a pattern in which new topics are gradually introduced, are a part of instruction for a few grades, and then often leave the curriculum as separate topics. This contrasts sharply with mapping of topics in the various US national standards in mathematics and science. Topics enter and linger, so that each grade typically devotes instructional attention to many more topics than is typical of the six high‐achieving countries; in addition, each topic stays in the curriculum for more grades than in the high‐achieving countries. An examination of mathematics and science content standards from 21 states and 50 districts in the US shows a pattern more like that of the US national standards than those of the high‐achieving TIMSS countries. While content standards have become integral to US curriculum development and reform, they have yet to reflect the coherence that is typical of countries that achieved significantly better than the US in the TIMSS study. [ABSTRACT FROM AUTHOR]