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Tablet‐based technology has become a conduit for the administration of curriculum‐based measurement (CBM) tools. Using tablets to administer CBM probes has many advantages; however, little is known about how students perform on CBMs when administered via a tablet. The current investigation compared digits correct per minute obtained from 44 third‐grade students on CBM addition fluency probes administered via three different modalities. Students completed the probes using traditional paper and pencil, a tablet using their fingers to write the answer, or a tablet application using a keyboard to type the answer. A within‐subjects group design showed students performed significantly better on the tablet when using their finger to write the answer, even though most students (58%) indicated this was their least preferred modality. The discussion focuses on the implications for educators and the use of different CBM modalities for interindividual and intraindividual comparisons. Practitioner points: Third‐grade students responded to math facts faster when writing with their fingers on an iPad, even compared to paper and pencil.The results are inconsistent with other studies that found students were faster when using paper and pencil.Finally, most third‐grade students preferred answering addition facts with a pencil on paper. [ABSTRACT FROM AUTHOR]

This research addresses the issue of how to support students' representational fluency—the ability to create, move within, translate across, and derive meaning from external representations of mathematical ideas. The context of solving linear equations in a combined computer algebra system (CAS) and paper‐and‐pencil classroom environment is targeted as a rich and pressing context to study this issue. We report results of a collaborative teaching experiment in which we designed for and tested a functions approach to solving equations with ninth‐grade algebra students, and link to results of semi‐structured interviews with students before and after the experiment. Results of analyzing the five‐week experiment include instructional supports for students' representational fluency in solving linear equations: (a) sequencing the use of graphs, tables, and CAS feedback prior to formal symbolic transpositions, (b) connecting solutions to equations across representations, and (c) encouraging understanding of equations as equivalence relations that are sometimes, always, or never true. While some students' change in sophistication of representational fluency helps substantiate the productive nature of these supports, other students' persistent struggles raise questions of how to address the diverse needs of learners in complex learning environments involving multiple tool‐based representations. [ABSTRACT FROM AUTHOR]

This paper details a literature review of mathematics vocabulary intervention studies for students with mathematics difficulty. The primary aim was to identify instructional practices that support mathematics vocabulary development. We conducted a database search to identify mathematics intervention studies either focused exclusively on vocabulary or with an embedded vocabulary component. Ultimately, 13 studies with participants from kindergarten to Grade 8 were included in the review. The majority of included studies had dual foci on vocabulary and other mathematics content, including whole number computation, word problem solving, fractions, algebra, or geometry. All studies that measured mathematics vocabulary performance indicated positive student outcomes. In addition, multiple studies indicated positive effects on measures of other mathematics content beyond mathematics vocabulary knowledge. We noted six instructional practices across studies that bolstered the mathematics vocabulary performance of students with mathematics difficulty. From most to least common, these practices included formal vocabulary use, explicit instruction, use of representations, repeated exposures, pre‐teaching, and graphic organizers. Implications are addressed for both researchers and practitioners. [ABSTRACT FROM AUTHOR]

Dimensional comparisons are comparisons between different domains. They are well known in educational psychology. Here, they explain the seemingly paradoxical finding that students' math and verbal self‐concepts of ability usually show correlations close to zero, although students' math and verbal achievements show strong positive correlations. This finding can be explained by the fact that students overemphasize potential differences between their math and verbal achievements when they form their self‐concepts. However, dimensional comparisons also take place and affect self‐evaluations outside the educational context, and the number of studies examining dimensional comparisons in different contexts has significantly increased during the last few years. This paper provides an up‐to‐date overview of findings on dimensional comparisons. It presents findings from studies that have examined effects of dimensional comparisons (as most studies dealing with dimensional comparisons have done so far), as well as studies that have focused on an understanding of the psychological processes involved in dimensional comparison (which relatively few studies have done so far). It is hoped that this paper will help broaden awareness of dimensional comparisons and stimulate further research on this type of comparison, especially in disciplines other than educational psychology. [ABSTRACT FROM AUTHOR]

We examine how incentives for test prep varied between math and English language arts (ELA) on U.S. state accountability exams. We collected data on exam structure for grade 3 to 8 tests in six states that are the setting for most U.S. research in literatures where accountability matters. We show that math exams typically measured ability more precisely for students on the margin of achieving proficiency. This gave educators an incentive to spend more time preparing students for math tests than for ELA tests, consistent with the common finding of larger math effects in the literature. [ABSTRACT FROM AUTHOR]

While an abundance of evidence‐based mathematics interventions are available to support students' mathematics fluency, research suggests that they are not often implemented within schools. Moreover, national data suggests that most students in the United States are not meeting grade level expectations in mathematics. This underperformance coupled with limited implementation of evidence‐based practices emphasizes the need to provide schools with effective, efficient, and resource friendly interventions to support students' mathematics achievement. The purpose of this study was to compare the effects of reciprocal peer tutoring, iPad delivered flashcards, and a combined intervention condition on the multiplication fluency of 72 third grade students enrolled in two public schools in the midwestern region of the United States using a randomized pretest–posttest design. Students received 10 min of intervention after their core instruction 4 days per week for 5 weeks. Results suggest that there were few differences between treatment groups on both proximal and distal measures. Moreover, all groups demonstrated significant growth from pre‐ to posttest on proximal measures. Assessment response rates across modalities and student engagement are discussed along with implications for research and practice. Practitioner points: Students across all treatment groups (peer tutoring, iPad flashcards, and a combined intervention) improved their multiplication fact fluency.There were few differences between groups at posttest on proximal measures of multiplication fluency and distal measures of math achievement between groups.Students across treatment groups scored consistently higher in digits correct per minute when completing the paper‐pencil curriculum‐based measure (CBM) compared with the iPad CBM. [ABSTRACT FROM AUTHOR]

Although the educational potential of social media has been widely acknowledged, it remains unclear whether social media use might present opportunities for the development of math identity. This study drew on the socialization framework of math identity to examine the relationships between social media use for math learning, bicultural identity integration, ethnic‐math beliefs and math identity among ethnic minority high school students in China. Structural equation modelling results showed that (a) social media use was positively related to math identity; (b) high bicultural identity integration was positively associated with math identity, while biased ethnic‐math beliefs were negatively related to math identity and (c) social media use suppressed the socialization process of math identity, weakening the maladaptive roles of low bicultural identity integration and biased ethnic‐math beliefs in shaping math identity. Our findings highlight the beneficial role of social media use in student math learning. Theoretical and practical implications are discussed. Practitioner notesWhat is already known about this topicSocial media use for learning is associated with students' academic motivation, engagement and academic achievement.Social media use may have affordances for identity development, especially for ethnic minorities.The formation of ethnic minority students' math identity is intertwined with their math and ethnic socialization.What this paper addsSocial media use for math learning was directly and positively related to ethnic minorities' math identity.This study quantitatively confirmed the associations of bicultural identity integration and ethnic‐math beliefs with math identity.Social media use suppressed the relations of bicultural identity integration and ethnic‐math beliefs with math identity.Implications for practice and/or policyPromoting social media use for math learning benefits ethnic minority students' math identity.Social media use for math learning could alleviate the maladaptive role of low bicultural identity integration and biased ethnic‐math beliefs in math identity development.Ethnic minority students' math identity socialization processes merit attention. [ABSTRACT FROM AUTHOR]

The mathematics education community has routinely called for mathematics tasks to be connected to the real world. However, accomplishing this in ways that are relevant to students' lived experiences can be challenging. Meanwhile, mathematical modeling has gained traction as a way for students to learn mathematics through real‐world connections. In an open problem to the mathematics education community, this paper explores connections between the mathematical modeling and the nature of what is considered relevant to students. The role of empathy is discussed as a proposed component for consideration within mathematical modeling so that students can further relate to real‐world contexts as examined through the lens of Ecological Systems Theory. This is contextualized through a classroom‐tested example entitled "Tiny Homes as a Solution to Homelessness" followed by implications and conclusions as they relate to mathematics education. [ABSTRACT FROM AUTHOR]

This paper presents the results of an observational study developed on lessons taught by 128 teachers for a national teaching assessment program in Chile and whose practice was identified as outstanding. Specifically, we studied which strategies teachers used to promote students' self‐regulation and autonomy during segments involving teacher‐led public talk, student‐led public talk, shared engagement, and private work. Additionally, we examined whether the instructional practices targeting self‐regulation that occur throughout these segments can be accounted for based on two overall dimensions of teacher practices, namely one of promotion of metacognition and one of promotion of motivation. During public segments, teachers encouraged student participation; during private work segments, teachers offered clues for problem solving. Thus, there was a stronger focus on motivational regulation instructional strategies during public segments and on metacognitive instructional strategies during private ones. A confirmatory factor analysis supported the hypothesis of two distinctive but related factors behind the observed self‐regulation promotion strategies, one motivational, and one cognitive. [ABSTRACT FROM AUTHOR]

This paper examines 'resilience' of mathematics students in transition from a sociocultural perspective, in which resilience is viewed as relational and in particular as a function of the social and cultural capital students may bring to the new field. We draw on two students' stories of transition, in which we recognise elements traditionally viewed as 'risks' for mathematics students in transition into institutions where new demands are made. However, in each case it seems that some of their apparent background 'risk factors'-coming from poorer socioeconomic backgrounds and disadvantaged schools-have come to serve to constitute capital, buttressing their particular resilience, as they provide a crucial kind of autonomy that is particularly valued in the new institution. We identify the learners' reflexivity as having been crucial to this accumulation of capital and we discuss some educational implications. [ABSTRACT FROM AUTHOR]

We bound the distribution of treatment effects under plausible and testable assumptions on the joint distribution of potential outcomes, namely that potential outcomes are mutually stochastically increasing. We show how to test the empirical restrictions implied by those assumptions. The resulting bounds substantially sharpen bounds based on classical inequalities. We apply our method to estimate bounds on the distribution of effects of attending a Knowledge is Power Program (KIPP) charter school on student achievement, and find that a substantial majority of students' math achievement benefited from attendance, especially those who would have fared poorly in a traditional classroom. [ABSTRACT FROM AUTHOR]

Despite pervasive educational efforts, student interest in STEM careers continues to decline in many countries. The present study seeks to better understand this phenomenon by examining how internal factors (gender) and external factors (school grades, grade level, family size) relate to Kazakh students' STEM career interests. To this end, a newly developed instrument (STEM Career Interest Survey) based on social cognitive career theory was used to assess interest in STEM careers among middle‐ and secondary students in Kazakhstan. The survey was completed by a sample of 396 Kazakh students in grades 7 to 12. Our statistical analyses revealed that (1) female students were generally less interested in STEM careers than male students; (2) students with higher grades in physics classes were significantly more interested in STEM careers than low‐performing students; (3) students at higher grade levels were generally more interested in STEM careers than those in lower grade levels; (4) the number of siblings was positively associated with student interest in mathematics careers; and, (5) family support and role models were significantly correlated with student STEM career interest. Our findings suggest that student development of interest in STEM careers constitutes an epigenetic phenomenon that involves complex interactions between internal factors (e.g., self‐efficacy) and external factors (e.g., gender stereotypes). Based on this, it is argued that the promotion of student interest in STEM careers is a multifaceted problem whose resolution requires, among other things, dispelling stereotypes in students' sociocultural context through systematic renegotiation of traditional gender‐technology relations characteristic of a country's culture. [ABSTRACT FROM AUTHOR]

There is an increased demand for useful measures that capture students' math learning during intervention. Similarly, there is an awareness of the importance of researchers observing guidelines for study quality in publishing intervention results, including information related to outcome measures. We investigated the characteristics of outcome measures to assist researchers and practitioners in selecting appropriate outcome measures for early numeracy interventions. We also explored the level of quality regarding how studies reported outcome measure information. To do this, we analyzed 94 outcome measures of math achievement across 25 kindergarten early numeracy intervention studies. Overall, studies met 84% of the quality indicators related to outcome measures. Fewer studies met the recommendation to include multiple measures (i.e., proximal and distal measures; 60%) or provide validity information about measures (39%). Ultimately, the results of this study provide researchers with valuable information for developing and selecting outcome measures to determine the effectiveness of early numeracy interventions. Practitioner Points: Overall, the 94 math outcome measures met 84% of the quality indicators.Fewer studies met the recommendation to include multiple measures (i.e., proximal and distal measures; 60%) or provide validity information about measures (39%).Future studies should aim to include validity information as this indicator was the least reported in intervention studies among the seven outcome measure quality indicators. [ABSTRACT FROM AUTHOR]

We investigated the relationship between students' perceived stress and investment in learning and tested the role of future time perspective (FTP) as a moderator. We expected that FTP would serve as a protective factor in the association between students' perceived stress and investment in learning. Perceived stress was gauged by assessing students' mathematics anxiety related to class, learning, and tests, and investment in learning was gauged by measuring investment in learning with respect to mathematics. To measure FTP, we focused on the FTP in school and professional career. A total of N = 349 secondary school students from the Netherlands participated in this study. Results revealed negative associations between students' investment in learning and their anxiety in class, during learning, and while taking tests. The moderating effects of FTP were also found to be significant. Contrary to our expectations, higher levels of FTP were associated with a stronger negative relationship between anxiety and investment in learning. Moreover, we found negative associations between FTP and class anxiety and learning anxiety and a positive association between FTP and investment in learning. Overall, our results may suggest that FTP motivates students to learn, but students' anxiety weakens the motivating effect of FTP. Key points: •Students who reported feeling anxious about learning for mathematics, classes, or tests invested less in their learning for mathematics.•FTP moderated the relationship between students' anxiety and investment in learning for mathematics: for students with a high FTP score, anxiety had a stronger negative relationship with their investment in learning.•In addition, when the interaction effect of FTP and anxiety was disregarded, students' FTP had a positive effect in decreasing their class and learning anxiety and in increasing their learning. [ABSTRACT FROM AUTHOR]

This article introduces the term Apache mathematics to define mathematics used by Apache people. Using ethnographic, autoethnographic, and qualitative interviews, the author highlights the cultural production of mathematics in the San Carlos Apache community, contrasting hegemonic Eurocentric claims to mathematics. Findings contributes Apache perspectives on the cultural uses of mathematics, as strength and intelligence central for shifting school‐based pedagogy meted to Apache students in current contexts of gross educational inequities. [ABSTRACT FROM AUTHOR]

Mathematics is one of the fundamental subjects for engineering students. While learning mathematics, students often find it difficult or lose interest due to the complexity of the subject. Augmented reality (AR) could aid students to learn certain concepts or theories that were difficult to understand in the classroom and also has the capability to enhance the instructional/learning material. In this study, an AR‐based learning setting named geometry learning assistant (GLA) was developed to teach geometry to students in a mathematics course. GLA provides an interactive and immersive experience to the students that helped them to learn about 3D vectors and direction ratios. The application includes vector addition, cross product, position vector, direction ratios, and dot product with real‐time examples for better learning. Experimental research was organized to investigate the impact of AR intervention on learner's memory retention abilities and learning. Eighty 1st‐year polytechnic students participated in the study and they were divided randomly into two groups: experimental group (N = 40) and control group (N = 40). Students of the experimental group were made to learn using AR‐based GLA, whereas the students from the control group were treated using interactive simulation (IS). The experimental results showed that the learners from the experimental group have better memory retention abilities after 2 and 4 weeks of the learning activity. AR‐based GLA provided a 3D immersive learning experience to the students that enhanced their visualization of the core concepts, which additionally improved their memory retention abilities. [ABSTRACT FROM AUTHOR]

Background: Graduation rates in engineering programs continue to be a concern in higher education. Prior research has documented an association between students' experiences in first‐year mathematics courses and graduation rates, but the influences of the mathematics courses completed and the grades earned are not fully understood. Purpose: The purpose of this study was to investigate the relationship among the first undergraduate mathematics course a student completes, the grade they earn in this course, and the likelihood of graduating with a degree in engineering within six years. Method: The study involved 1504 students from five consecutive cohorts of first‐year students enrolled in an engineering degree program at a medium‐sized Midwestern public university. Logistic regression was used to model the interrelationship between course and grade in predicting the relative likelihood of graduation for students enrolled in 16 different mathematics courses. Results: Overall, students who take Calculus I or a more advanced mathematics course as their first mathematic course and who are more successful in their first mathematics course are more likely to graduate with a degree in engineering. However, considering grade and course together, some groups of students who are more successful in lower‐level mathematics courses are as likely to graduate as students who are less successful in upper‐level mathematics courses. Conclusions: Evidence from this study helps to dispel the myth that beginning with higher‐level mathematics courses is the optimal course‐taking strategy when pursuing an engineering degree. Findings have implications for student advising, curriculum and instruction, high school course‐taking, and broadening participation in engineering. [ABSTRACT FROM AUTHOR]

Background: Given the importance of engineers to a nation's economy and potential innovation, it is imperative to encourage more students to consider engineering as a college major. Previous studies have identified a broad range of high school experiences and demographic factors associated with engineering major choice; however, these factors have rarely been ranked or ordered by relative importance. Purpose/Hypothesis: This study leveraged comprehensive, longitudinal data to identify which high school‐level factors, including high school characteristics and student high school experiences as well as student demographic characteristics and background, rank as most important in terms of predictive power of engineering major choice. Design/Method: Using data from a nationally representative survey, the High School Longitudinal Study of 2009, and the random forest method, a genre of machine learning, the most important high school‐level factors in terms of predictive power of engineering major choice were ranked. Results: Random forest results indicate that student gender is the most important variable predicting engineering major choice, followed by high school math achievement and student beliefs and interests in math and science during high school. Conclusions: Gender differences in engineering major choice suggest wider ranging cultural phenomena that need further investigation and systemic interventions. Research findings also highlight two other areas for potential interventions to promote engineering major choice: high school math achievement and beliefs and interests in math and science. Focusing interventions in these areas may lead to an increase in the number of students pursuing engineering. [ABSTRACT FROM AUTHOR]

A solid foundation in math is important for children's long‐term academic success. Many factors influence children's math learning—including the math content students are taught in school, the quality of their instruction, and the math attitudes of students' teachers. Using a large and diverse sample of first‐grade students (n = 551), we conducted a large‐scale replication of a previous study (Proceedings of the National Academy of Sciences of the USA, 2010, 1860; n = 117), which found that girls in classes with highly math anxious teachers learned less math during the school year, as compared to girls whose math teachers were less anxious about math. With a larger sample, we found a negative relation between teachers' math anxiety and students' math achievement for both girls and boys, even after accounting for teachers' math ability and children's beginning of year math knowledge, replicating and extending those previous results. Our findings strengthen the support for the hypothesis that teachers' math anxiety is one factor that undermines children's math learning and could push students off‐track during their initial exposure to math in early elementary school. [ABSTRACT FROM AUTHOR]

Neoliberal logics, a form of racial capitalism, adjudicate children as smart, able, and desirable (or not) in schools. I explore the social processes and structural arrangements by which such logics position a Latina mathematics student as "undesirable" in her class. Drawing on data collected over a year, the analysis lays bare how undesirability is both a requirement of neoliberalism and an emergent position that she, her low‐track class, and her school come to occupy. [ABSTRACT FROM AUTHOR]

When we look at the theoretical relationships between the three types of geometry, we find that the most primitive type is topology and that both Euclidean and projective geometry are derived from this earlier type. Therefore, Piaget described the first stage or level of understanding geometry as topological understanding. In this study, the geometric thinking conditions of mathematics teacher candidates were examined and what they think about the topology course was determined by surveying their opinions about the undergraduate courses. The participants of the study consisted of 36 teacher candidates studying in the Mathematics Department of the Faculty of Science attached to a university in Turkey. The findings of the study revealed that none of the teacher candidates used topological thinking to solve the questions in the data collection instrument. Those candidates who considered topology as an abstract course did not associate topology with geometry. A thorough understanding of the meaning of topology and topological thought is an advantage to young children as well as college‐age students; improving mathematics curricula on this topic, particularly at the graduate level, will ensure that all future teachers are appropriately trained for their future responsibility of educating others. We believe that it is necessary to give Topology and topological thought the place they deserve in the educational process. [ABSTRACT FROM AUTHOR]

Metaphors have been widely used to investigate the perspectives of teachers and students in mathematics. In this report, an instrument was developed, the metaphor continuums, to provide a space for four prospective teachers to discuss their projective identities as teachers and mathematics teacher. Using an argumentation perspective on identity, the responses to the instrument were investigated to determine a tentative manifestation of the participants' projective identity. The participants' provided some evidence of their projective identities as teacher and mathematics teachers being aligned. One participant did not provide evidence of distinguishing between her identity as a mathematics teacher and a teacher. The vehicles, or subject of the metaphors, given to the participants provided varying ways for them to explore their ideas of teaching and learning mathematics. The metaphor continuums showed potential for mathematics teacher educators to receive initial information to help in determining targeted interventions for their students. [ABSTRACT FROM AUTHOR]

A study involving 916 students spanning grades 5–8 was conducted to investigate indicators that may contribute to enjoyment and confidence in mathematics. For this group of middle school students, mathematics enjoyment, mathematics confidence, and attitudes toward school were found to generally decline across grade levels. Mathematics enjoyment and confidence were also found to differ significantly based upon student preferences for future careers. Gender differences as well as similarities regarding predictors of mathematics enjoyment and confidence were identified. Specifically, the best predictor for end of year mathematics enjoyment for males was beginning of year attitude toward school, while the most significant predictor of end of year enjoyment for females was beginning of year dispositions toward mathematics (semantic perception). A strong relationship between mathematics enjoyment and confidence overall was found, with indications that activities that increase mathematics enjoyment contribute to increased confidence, and also that activities that increase mathematics confidence contribute to increased enjoyment. [ABSTRACT FROM AUTHOR]

Negative relationships between mathematics anxiety and achievement appear in many countries globally (Lee, 2009; OECD, 2013), suggesting that mathematics anxiety could be an underconsidered factor in regions with persistently low mathematics achievement. We draw on a national sample of students and their teachers in Belize to examine relations between mathematics anxiety and achievement. The data replicated the negative relationships between students' math anxiety and achievement observed in many higher achieving, higher resourced regions, and importantly also revealed that teachers' mathematics anxiety predicted their students' mathematics attitudes and sometimes achievement. The effects were small overall so the robustness of this relationship is not clear, but they provide novel data toward building a comprehensive theory of mathematics anxiety's relationship to achievement across cultural, gender and age contexts, and offer insight into how addressing mathematics anxiety might improve mathematics teaching and achievement in low resourced countries. Lay abstract: Anxiety about mathematics has been shown in many regions to have the potential to reduce math achievement as well as to impact math learning and teaching, so could be an important yet under‐considered aspect of educational improvement in low resourced nations. A national sample of students and teachers was used to examine relations among math achievement, anxiety, and confidence in Belize. Data revealed that math anxiety was related to lower achievement in this region, and that teachers' math anxiety was related to their students having more math anxiety and lower achievement, though those relationships were quite small and not apparent in all of the data. These data are therefore only suggestive, but provide motivation to further examine and alleviate math anxiety as a part of national efforts to improve mathematics achievement, as well as within theories of mathematical teaching and learning. [ABSTRACT FROM AUTHOR]

The associations among parenting behaviors, effortful control, and student engagement in math were examined in a sample of Chinese children. The sample was composed of 778 students (Mage = 10.43 years, SD = 0.99) from Grades 4 to 6 in Shanghai, China. Children completed questionnaires to assess parental warmth and hostility, effortful control, and student engagement in math. The results indicated that parental warmth was positively correlated with math engagement whereas parental hostility was negatively correlated with math engagement. In addition, mediational analyses indicated that effortful control fully mediated the association between parental hostility and math engagement, but partially mediated the association between parental warmth and math engagement. This study offers insights into a mediating mechanism linking the relationships among parenting behaviors, effortful control, and math engagement. [ABSTRACT FROM AUTHOR]

More than half of students in the USA perform below a proficient level in math. Although evidence suggests that intervention in elementary school is critical to supporting struggling learners, and there are several research‐supported instructional practices to support students with math difficulties, the existing research is limited with regard to the impact of motivational strategies designed to improve students' math skills. This study examined the effectiveness of specific motivational strategies used in the small‐group Accelerating Mathematics Performance through Practice Strategies (AMPPS‐SG) intervention program. A multiple baseline design was used with three instructional groups of second grade students to compare the relative effectiveness of three different conditions on students' math computation skills. Condition 1 included all of the AMPPS‐SG instructional components. Condition 2 included all instructional procedures as well as goal‐setting, performance feedback, and reinforcement for performance. Condition 3 included all components used in Condition 2, as well as a group‐based reward contingency. Results showed that students' performance during Condition 3 was significantly better than performance during Conditions 1 and 2. [ABSTRACT FROM AUTHOR]

We describe the summative assessment component within a K–12 assessment program and our development of a validity argument to support its claims with respect to intended uses and interpretations. First, we describe the Winsight® assessment program theory of action, a logic model elucidating mechanisms for how use of the assessment components can lead to improved student learning in mathematics and English language arts (ELA) and defining the roles of key groups of stakeholders. We explain our process of developing the validity argument that enumerates sources of validity evidence supporting the Winsight summative assessment claims drawn from the theory of action. We examine candidate structures for the argument, describe the steps in which we unpacked stakeholder‐level claims and defined subclaims to operationalize components, and discuss types and sources of validity evidence to meet the goals of professional and federal guidelines. Finally, we discuss the research agenda and operational analyses that will provide this validity evidence. Report Number: ETS RR–19‐26 [ABSTRACT FROM AUTHOR]

In a technologically driven society, math and science students in the United States are falling further and further behind their international counterparts, resulting in an influx of STEM focused, reformed K‐12 schools, including schools focused on project‐based learning (PBL). This article reports a study of the effectiveness of PBL on high school students' performance on state mandated standardized mathematics and science achievement measures. Manor New Tech High School is a nationally recognized model STEM school, with a diverse student population, where all instruction is delivered through PBL. Although there is ample research suggesting that PBL is advantageous for increasing STEM learning compared to conventional teaching approaches, there is a lack of studies randomly assigning students to receive PBL. Further, some of the effects observed for students attending project‐based schools could be due to a self‐selection bias for students or parents that choose such an alternative learning environment. This study addresses both of these concerns and found that students taught through PBL, as a group, matched performance of conventionally taught students on all science 11th grade and mathematics 9th, 10th, and 11th grade TAKS achievement measures and exceeded performance by a scale score increase of 133 for the 10th grade science TAKS measure by (B = 133.082, t = 3.102, p < .05). One possible explanation of the differences observed in this study could be the TAKS instrument used to capture student math and science achievement that interprets "real‐life applications" of content differently between math and science questions. These results align with literature on the effects of PBL and deepen our understanding of these effects by providing a controlled study with random assignments to the PBL experience. Future research looking at the effect of PBL on achievement on the PISA could be beneficial in identifying benefits of PBL implementation in schools. [ABSTRACT FROM AUTHOR]

Data‐based decision making (DBDM) is presumed to improve student performance in elementary schools in all subjects. The majority of studies in which DBDM effects have been evaluated have focused on mathematics. A hierarchical multiple single‐subject design was used to measure effects of a 2‐year training, in which entire school teams learned how to implement and sustain DBDM, in 39 elementary schools. In a multilevel modeling approach, student achievement in mathematics and spelling was analyzed to broaden our understanding of the effects of DBDM interventions. Student achievement data covering the period from August 2010 to July 2014 were retrieved from schools' student monitoring systems. Student performance on standardized tests was scored on a vertical ability scale per subject for Grades 1 to 6. To investigate intervention effects, linear mixed effect analysis was conducted. Findings revealed a positive intervention effect for both mathematics and spelling. Furthermore, low‐SES students and low‐SES schools benefitted most from the intervention for mathematics. [ABSTRACT FROM AUTHOR]

Spatial abilities, which are described by Linn and Petersen as "skills in representing, transforming, generating, and recalling symbolic, nonlinguistic information" are, as such, not trained or taught in schools. Nevertheless, the importance of highly developed abilities for science, technology, engineering, and mathematics students has been scientifically proven, which implies that spatial abilities can have a significant impact on success in studying STEM subjects and, later, STEM careers. The developed experimental program employing GeoGebra 5 ran for 4 weeks and was conducted at the Faculty of Science and Education in Mostar. The sample consisted of first‐year students, aged 18 to 20, with 35 male and 17 female students in the experimental and 33 male and 19 female students in the control group (CG). A spatial test was administered before the program and once again at the end, along with one more spatial test and a questionnaire, which consisted of possible highly developed spatial abilities predictors. The differences between the control and the experimental group (EG) at initial testing of spatial abilities were not statistically significant regarding any subsample. No significant correlations between the questionnaire and the initial spatial test were found. The correlation between average grade in mathematics in high school and the scores on the initial spatial test was not significant. Results showed that a statistically significant jump in performance on the posttest regarding the EG has occurred, whereas no statistically significant changes in performance have been noted regarding the CG. [ABSTRACT FROM AUTHOR]

Co‐teaching is an instructional teaching model that provides an opportunity for students to receive instruction in the least restrictive environment. An extensive literature review was completed in order to identify best practices and effective co‐teaching practices in mathematics classrooms. A clearly defined purpose for co‐teaching and selecting co‐teaching partners is a key to the success of co‐teaching. Also, student and teacher perceptions impact the implementation of co‐teaching. The effectiveness of co‐teaching is further impacted by co‐teaching practices, along with the use of effective mathematical teaching strategies. The balance of maintaining effective co‐teaching practices and mathematical teaching strategies is integral to the success of co‐teaching. The literature revealed a lack of a consistent definition of what effective co‐teachers are. Also, there is generally a lack of focus on student outcomes in co‐teaching research. Finally, there is minimal research on co‐teaching in mathematics. [ABSTRACT FROM AUTHOR]

This study examines how student perceptions of teacher practices contribute to female high school students' math beliefs and achievement. Guided by the expectancy–value framework, we hypothesized that students' motivation beliefs and achievement outcomes in mathematics are fostered by teachers' emphasis on the relevance of mathematics and constrained by gender‐based differential treatment. To examine these questions, structural equation modeling was applied to a longitudinal panel of 518 female students from the Maryland Adolescent Development in Context Study. While controlling for prior achievement and race, gendered differential treatment was negatively associated with math beliefs and achievement, whereas relevant math instruction was positively associated with these outcomes. These findings suggest inroads that may foster positive math motivational beliefs and achievement among young women. [ABSTRACT FROM AUTHOR]

Place value understanding requires the same activity that students use when developing fractional and algebraic reasoning, making this understanding foundational to mathematics learning. However, many students engage successfully in mathematics classrooms without having a conceptual understanding of place value, preventing them from accessing mathematics that is more sophisticated later. The purpose of this exploratory study is to investigate how upper elementary students' unit coordination related to difficulties they experience when engaging in place value tasks. Understanding place value requires that students coordinate units recursively to construct multi‐digit numbers from their single‐digit number understandings through forms of unit development and strategic counting. Findings suggest that students identified as low‐achieving were capable of only one or two levels of unit coordination. Furthermore, these students relied on inaccurate procedures to solve problems with millennial numbers. These findings indicate that upper elementary students identified as low‐achieving are not to yet able to (de)compose numbers effectively, regroup tens and hundreds when operating on numbers, and transition between millennial numbers. Implications of this study suggest that curricula designers and statewide standards should adopt nuances in unit coordination when developing tasks that promote or assess students' place value understanding. [ABSTRACT FROM AUTHOR]

In the transition to middle school, and during the middle school years, students' motivation for mathematics tends to decline from what it was during elementary school. Formative assessment strategies in mathematics can help support motivation by building confidence for challenging tasks. In this study, the authors developed and piloted a professional development program, Learning to Use Formative Assessment in Mathematics with the Assessment Work Sample Method (AWSM) to build middle school math teachers' understanding of the characteristics of high‐quality formative assessment processes and increases their ability to use them in their classrooms. AWSM proved to be feasible to implement in the middle school setting. It improved teachers' practice of formative assessment, especially in their feedback practices, regardless of their pedagogical content knowledge at entry. Results from focus groups suggested that teachers were better able to implement ungraded practice and student self‐ and peer‐assessment after AWSM, and that students were more willing to engage in complex problem solving. [ABSTRACT FROM AUTHOR]

Teachers' abilities to design mathematics lessons are related to their capability to mobilize resources to meeting intended learning goals based on their noticing. In this process, knowing how teachers consider Students' thinking is important for understanding how they are making decisions to promote student learning. While teaching, what teachers notice influences their decision-making process. This article explores the mathematics lesson planning practices of four 4th-grade teachers at the same school to understand how their consideration of Students' learning influences planning decisions. Case study methodology was used to gain an in-depth perspective of the mathematics planning practices of the teachers. Results indicate the teachers took varying approaches in how they considered students. One teacher adapted instruction based on Students' conceptual understanding, two teachers aimed at producing skill-efficient students, and the final teacher regulated learning with a strict adherence to daily lessons in curriculum materials, with little emphasis on student understanding. These findings highlight the importance of providing professional development support to teachers focused on their noticing and considerations of Students' mathematical understandings as related to learning outcomes. These findings are distinguished from other studies because of the focus on how teachers consider Students' thinking during lesson planning. This article features a . Please click on the supporting information link below to access. [ABSTRACT FROM AUTHOR]

In this article, we present findings from a study that investigated the relationship between all-girls classes, all-boys classes, and coeducational classes on student mathematics self-concept and student perception of classroom environment. Further, we compared responses of girls in all-girls classes to girls in coeducational classes and responses of boys in all-boys classes to boys in coeducational classes. Using the Mathematics Attitude Scale and the What Is Happening in This Class? questionnaire, we found no significant differences in student responses on any of the subscales or domains for any of the subgroups, except for Math as a Male Domain. Our findings indicate that student mathematics self-concept and student perception of the classroom environment are similar regardless of whether students are in a single-sex or a coeducational class. [ABSTRACT FROM AUTHOR]

This study compared the characteristics of second graders' mathematical writing between an intervention and comparison group. Two six-week Project M2 units were implemented with students in the intervention group. The units position students to communicate in ways similar to mathematicians, including engaging in verbal discourse where they themselves make sense of the mathematics through discussion and debate, writing about their reasoning on an ongoing basis, and utilizing mathematical vocabulary while communicating in any medium. Students in the comparison group learned from the regular school curriculum. Students in both the intervention and comparison groups conveyed high and low levels of content knowledge as indicated in archived data from an open-response end-of-the-year assessment. A multivariate analysis of variance indicated several differences favoring the intervention group. Both the high- and low-level intervention subgroups outperformed the comparison group in their ability to (a) provide reasoning, (b) attempt to use formal mathematical vocabulary, and (c) correctly use formal mathematical vocabulary in their writing. The low-level intervention subgroup also outperformed the respective comparison subgroup in their use of (a) complete sentences and (b) linking words. There were no differences between groups in their attempt at writing and attempts at and usage of informal mathematical vocabulary. [ABSTRACT FROM AUTHOR]

Increasing the number of students who study mathematics once it is no longer compulsory remains a priority for England. A longitudinal cohort from England (1085 students) was surveyed at Years 10 and 12. Students' self-beliefs of ability influenced their GCSE mathematics grades and their intended and actual mathematics subject-choices; the degree of under-confidence or over-confidence related to these self-beliefs was also influential. Additional factors that significantly influenced students' intentions at Year 10 to study mathematics in Year 12 were the advice or pressure to do so, the extrinsic motivation associated with mathematics, their gender and the emotional response associated with doing mathematics. These same factors were also significant influences on students' intentions at Year 12 to study mathematics at university, with the addition of their intrinsic motivation associated with mathematics. Although gender was not a significant influence on GCSE mathematics grades or whether students actually studied A-Level mathematics, boys were associated with higher intentions to study mathematics into Year 12, 13 and university. Additionally, girls were generally more under-confident than boys in their self-beliefs. [ABSTRACT FROM AUTHOR]

When learning a new math concept, should learners be first taught the concept and its associated procedures and then solve problems, or solve problems first even if it leads to failure and then be taught the concept and the procedures? Two randomized-controlled studies found that both methods lead to high levels of procedural knowledge. However, students who engaged in problem solving before being taught demonstrated significantly greater conceptual understanding and ability to transfer to novel problems than those who were taught first. The second study further showed that when given an opportunity to learn from the failed problem-solving attempts of their peers, students outperformed those who were taught first, but not those who engaged in problem solving first. Process findings showed that the number of student-generated solutions significantly predicted learning outcomes. These results challenge the conventional practice of direct instruction to teach new math concepts and procedures, and propose the possibility of learning from one's own failed problem-solving attempts or those of others before receiving instruction as alternatives for better math learning. [ABSTRACT FROM AUTHOR]

The Long- Term Trend ( LTT) mathematics assessment of the National Assessment of Educational Progress ( NAEP) used the same set of items from 1982 through 2004, including 20 items that were administered to 9- and 13-year-olds, 29 items that were administered to 13- and 17-year-olds, and 4 items that were administered at all three ages. This study used these items to identify areas of mathematics that had substantial gain from one age level to the next and to identify patterns of gain by age and how those patterns changed over time. Findings included the facts that older students usually did better on items than younger students, although item context and wording was often as important as mathematical knowledge in explaining differences in performance by age. LTT NAEP included a unique set of estimation items and analysis of performance on those items showed that students at all levels could identify an appropriate estimate only when numbers were small and the context for the estimate was familiar. The LTT data also indicated that addition and subtraction skills of 9-year-olds increased and the estimation skills of 13- and 17-year olds improved in some contexts from 1982 through 2004. [ABSTRACT FROM AUTHOR]

Background Self-explanation, or generating explanations to oneself in an attempt to make sense of new information, can promote learning. However, self-explaining takes time, and the learning benefits of this activity need to be rigorously evaluated against alternative uses of this time. Aims In the current study, we compared the effectiveness of self-explanation prompts to the effectiveness of solving additional practice problems (to equate for time on task) and to solving the same number of problems (to equate for problem-solving experience). Sample Participants were 69 children in grades 2-4. Methods Students completed a pre-test, brief intervention session, and a post- and retention test. The intervention focused on solving mathematical equivalence problems such as 3 + 4 + 8 = _ + 8. Students were randomly assigned to one of three intervention conditions: self-explain, additional-practice, or control. Results Compared to the control condition, self-explanation prompts promoted conceptual and procedural knowledge. Compared to the additional-practice condition, the benefits of self-explanation were more modest and only apparent on some subscales. Conclusions The findings suggest that self-explanation prompts have some small unique learning benefits, but that greater attention needs to be paid to how much self-explanation offers advantages over alternative uses of time. [ABSTRACT FROM AUTHOR]

Aim. This study examined whether teachers' use of fear appeals in the classroom, attempts to motivate students to perform well in high-stakes examinations by highlighting the educational, and/or occupational consequences of failure did indeed motivate students or whether it contributed to an increase in worry, anxiety, and fear of failure. Sample. A total of 132 secondary school students. Method. Self-report data were collected for teachers' use of fear appeals, test anxiety, and achievement goals in the context of Mathematics at the end of Years 10 and 11, the final 2 years of compulsory schooling. Results. The frequency with which teachers were reported to make fear appeals was unrelated to future test anxiety and achievement goals. When fear appeals were perceived to be threatening, however, they were related to an increase in the worry and tension components of test anxiety and increases in performance-avoidance and mastery-approach goals. Conclusion. Fear appeals appear to have competing positive and negative outcomes, resulting in both anxiety and a fear of failure, and a mastery-approach goal. [ABSTRACT FROM AUTHOR]

Background. Boredom has been found to be an important emotion for students' learning processes and achievement outcomes; however, the precursors of this emotion remain largely unexplored. Aim. In the current study, scales assessing the precursors to boredom in academic achievement settings were developed and tested. Sample. Participants were 1,380 grade 5-10 students in mathematics classes. Method. The Precursors to Boredom Scales were tested for structural and convergent validity with multi-level confirmatory factor analyses (ML-CFA), and differences in the perception of the precursors of boredom due to gender were investigated. Results. The first ML-CFA found support for the structural validity of the Precursors to Boredom Scales. In a second ML-CFA, the newly developed boredom scales showed good convergent validity with several key aspects of instructional quality. Finally, the results supported previous research that found no gender differences in academic self-concept and interest. Conclusion. The precursors contained in our scales are empirically separable. Implications of the current findings for research on boredom among students are discussed. [ABSTRACT FROM AUTHOR]