Exploring the effects of project-based learning in secondary mathematics education

This mixed-method, longitudinal study investigated the benefits of project-based learning (PBL) on secondary-mathematics students' academic skill development and motivated strategies for learning (i.e., cognitive, social, and motivational). The focus of this study was academic skill development (algebra- and geometry-assessment scores) and other factors related to secondary mathematics learning, with comparable traditional high schoolers serving as the control group. In addition, the relationship between PBL and racially/ethnically and economically diverse secondary students was investigated. Results showed that at-risk and minority students benefited greatly from PBL in learning mathematics. The academic performance gap was present, but its width diminished significantly. Compared to their public school counterparts, PBL students were more intrinsically motivated, showed significantly higher critical thinking skills, and appreciated peer learning. Impact of socioeconomic status on the PBL approach needs further investigation.     

Does attending a deeper learning school promote student motivation,engagement, perseverance,and achievement?

The evolving economic landscape of the 21st century demands graduates who possess deeper learning (DL) competencies such as critical thinking and collaboration skills. Despite their importance, little work has examined the motivational mechanisms through which DL predicts essential academic outcomes. The current study (N = 1,288) used an ethnically diverse sample of students (53% Hispanic) to explore self-efficacy and mastery goal orientation as potential mediators of the relationship between (a) enrollment in a DL school and (b) academic engagement, perseverance, and mathematics achievement. Results showed that students who attended DL schools, compared with students in non-DL schools, reported higher self-efficacy, mastery goal orientation, and academic engagement. Path analyses revealed that attending a DL school was associated with higher academic engagement and self-efficacy. However, enrollment in a DL school was not directly related to mathematics achievement. Overall, results provide evidence that attending a DL school can lead to valuable motivation- and engagement-related benefits.     

Academic responding during instruction and reading outcomes for kindergarten students at-risk for reading difficulties

The purpose of this study was to investigate the academic responding of students at-risk for reading difficulties in beginning reading instruction. Opportunities for kindergarten students at-risk for reading difficulties to respond academically during teacher-facilitated reading instruction in the general education classroom were examined in relation to student reading achievement as well as social behaviors. Student academic responding during teacher-facilitated instruction significantly predicted end of year reading achievement. Teacher perceptions of students’ social skills (positive correlation) and problem behaviors (negative correlation) were significantly correlated with academic responding. When academic responding and teacher perceptions of social behaviors were examined together, only teacher perceptions of academic competence and problem behaviors predicted spring outcomes.     

Evaluation of Broward County Alliance of Quality Schools Project

This article examines the evaluation of the Alliance of Quality Schools project, a 5-year project focusing on at-risk students in Broward County, Florida. The purpose of the evaluation was to determine the effect that the project had on selected academic and behavioral student indicators after its 5th year of implementation. This article focuses only on the findings related to the effect that the project has had on reading performance. Findings related to mathematics performance and student behavior can be found by reviewing the 5th-year evaluation report (Ligas, 1999). The project's mission, based on the philosophy that all children can learn, is to help the greatest number of at-risk students achieve at their highest performance level. In addition to a strong emphasis on Direct Instruction (DI), the Alliance of Quality Schools (AQS) initiative utilizes Accelerated Reader and Computer Assisted Instruction. The project has been evaluated yearly, from the 1994-1995 school year to the 1998-1999 school year. Fifth-year evaluation findings related to student achievement indicated that the effect of the project on academic achievement for elementary and middle school students enrolled at the Alliance schools has varied by grade level and year. The highest increases in student performance occurred at the 4th-grade level for reading and at the 5th-grade level for mathematics. These increases seem to be closely aligned to the grade levels targeted for school accountability by the state of Florida.     

Investigating the Unique Predictors of Word-Problem Solving Using Meta-Analytic Structural Equation Modeling

The purpose of the present study is to clarify the contributions of cognitive skills (nonverbal reasoning, language comprehension, working memory, attention, processing speed) and academic skills (mathematics facts retrieval, mathematics computation, mathematics vocabulary, reading comprehension) in performing mathematics word problems among elementary school students. With the two-stage meta-analytic structural equation modeling approach, I synthesized 112 correlation matrices from 98 empirical studies (N?=?111,346) and fitted the hypothesized partial mediation model. Overall, path analysis indicated that language comprehension, working memory, attention, mathematics vocabulary, and mathematics computation were unique predictors of word-problem solving. Subgroup analysis demonstrated different unique predictors for younger and older students to perform word problems (K-2nd grades versus 3rd–5th grades). Implications, limitations, and future directions are discussed.

     

The Development and Validation of Scales Assessing Students' Achievement Goal Orientations

Achievement goal theory has emerged as a major new direction in motivational research. A distinction is made among conceptually different achievement goal orientations including the goal to develop ability (task goal orientation), the goal to demonstrate ability (ability-approach goal orientation), and the goal to avoid the demonstration of lack of ability (ability-avoid goal orientation). Scales assessing each of these goal orientations were developed over an eight year period by a group of researchers at the University of Michigan. The results of studies conducted with seven different samples of elementary and middle school students are used to describe the internal consistency, stability, and construct validity of the scales. Comparisons of these scales with those developed by Nicholls and his colleagues provide evidence of convergent validity. Confirmatory factor analysis attests to the discriminant validity of the scales.     

Peer Coaching of At-Risk Students in a Remedial Mathematics Course

Remedial mathematics at the college level has evidenced strikingly low retention and passing rates. It has been shown that at least 25% of the variation in student performance is explained by students’ affective variables such as attitudes, study skills, and mathematics anxiety. This study endeavored to address affective variables by: (a) incorporating the teaching of study skills into an elementary algebra course; and (b) identifying at-risk students and assigning these students “coaches,” who functioned both as tutors and counselors, providing regular personalized assistance. The results showed that the attrition rate was significantly lower in the treatment groups, and the overall passing rate for coached students was significantly higher.     

Motivational and affective determinants of self-regulatory strategy use in elementary school mathematics

The aim of the study was to investigate the relationships between elementary students’ reported use of self-regulatory strategies in mathematics and their motivational and affective determinants. Participants of the study were 344 fifth- and sixth-grade Greek students. Students were asked to complete self-reported measures regarding the strategies they use to self-regulate mathematics learning, their achievement goals in relation to mathematics, their self-efficacy concerning mathematics learning and achievement, the value they attribute to mathematics as a subject domain and their enjoyment of mathematics learning. Structural equation modelling confirmed a mediation model, that is, students’ mathematics self-efficacy, value beliefs about mathematics and enjoyment mediated the effects of achievement goals on reported strategy use. Results are discussed in terms of implications for elementary students’ self-regulated learning skills.     

Students' perfectionistic profiles: Stability,change, and associations with achievement goal orientations

In this study, we examined what kind of perfectionistic profiles (i.e., different patterns of perfectionistic strivings and concerns) can be identified among general upper‐secondary school students, how stable those profiles are over the school year, and how they are connected with students' motivation (i.e., achievement goal orientations). Four distinct profiles were identified. Students with high strivings and low concerns had their focus mainly on mastery, while students with an opposite profile emphasized performance‐avoidance and work‐avoidance orientations. Students with high strivings and concerns favored both performance‐ and mastery‐related goals, whereas students characterized by low strivings and low concerns did not display a dominant tendency toward any orientation. Perfectionistic profiles were relatively stable over time, with the majority of students reporting similar tendencies across the measurements, and with no extreme changes observed. Some indications of more students displaying less adaptive perfectionistic tendencies by the end of the school year were nevertheless found. Our findings demonstrate not only stability in perfectionistic tendencies, but also their motivational relevance in the academic context where students' goals and performance concerns play an important role.     

The Synergistic Effects of Self-Regulation Tools and the Flipped Classroom

ABSTRACT

Students at open-enrollment institutions enter college with a wide range of academic preparedness and are often required to take developmental classes to increase their academic skills to be successful in higher education. Further, few students possess self-regulated learning skills to aid in their learning. Researchers posited that academically at-risk students benefit from gains in self-regulated learning skills when a modeling and scaffolding approach is used to implement self-regulated learning tools. Self-regulated skills coupled with an active learning environment like the flipped classroom provide positive synergistic effects for academically at-risk students. This study compared several iterations of the flipped classroom in a general chemistry class at an open-enrollment college where high school class rank and mathematics placement level varied significantly. The results of the multiple regression analysis indicated that mathematics level and class rank were significant when predicting overall course grade regardless of the learning environment. The results of a paired-samples t test did not reveal a significant difference upon addition of note-taking and exam wrappers in a flipped classroom learning environment. However, students graduating high school in the top third, middle third, and bottom third of their graduating class increased their overall course grades in a flipped classroom using self-regulated tools by 7%, 3%, and 6%, respectively. To enhance the quantitative results, the author provides student comments on note-taking and the use of exam wrappers.     

Students’ transition from elementary to high school and changes of the relationship between motivation and academic performance

336 students, 186 girls and 150 boys were met at the end of the school year, both at grade six and at Secondary one, in order to examine the impact of the transition from elementary to secondary school on various motivational variables. Analyses showed changes in self-efficacy beliefs and learning goals, whatever students’ level of achievement and gender. However, self-efficacy beliefs appeared as the most powerful predictor of academic performance at both school levels. In addition, the pattern of relations between academic performance and the variables examined was relatively similar at both times of measurement. The discussion focuses on changes in self-efficacy beliefs and learning goals and on their relations to academic performance.     

Promoting cognitive and soft skills acquisition in a disadvantaged public school system: Evidence from the Nurture thru Nature randomized experiment

It is widely acknowledged that our public schools have failed to produce sufficient levels of high quality STEM education. The mathematics and science performance of minority and disadvantaged students has been especially troubling with blacks and Hispanics substantially underrepresented in the STEM labor market. In this paper we examine the impacts of a STEM enhancement program called Nurture thru Nature (NtN) on the cognitive (academic grades) and soft skills development of 139 elementary school students who attended the program over an eight year period (2010–2017). Utilizing a randomized experimental design or RCT with a control group of 491 elementary school students, we find that NtN slows the deterioration in students’ math and science grades relative to controls and improves soft skills such as conscientiousness, higher order thinking, empathy, and pro-social behavior.     

Changes in self-reported academic cheating across the transition from middle school to high school

Changes in early adolescents' self-reported cheating behaviors in mathematics before and after the transition from middle school to high school are examined. Students were surveyed in school regarding their cheating behaviors in math, and the motivational goal structures perceived in their math classrooms. Surveys were completed twice during the eighth grade (during middle school) and once at the end of the ninth grade (at the end of the first year in high school). Results indicated that self-reported cheating did not change in the year prior to the high school transition, but that reported cheating increased after the transition. Additional analyses indicated that across the high school transition, self-reported cheating in math increased for students who moved from high mastery to low mastery-oriented classes after the transition, and for students who moved from low performance to high performance-oriented classes; in contrast, self-reported cheating decreased for students who moved from low to high mastery-oriented math classrooms.     

The prevalence,development and domain specificity of elementary school students’ achievement goal profiles

This study’s aim was to examine the prevalence, development and domain specificity of fifth- and sixth-grade elementary school students’ achievement goal profiles. Achievement goals were measured for language and mathematics among 722 pupils at three points in time. These data were analysed through latent profile analysis and latent transition analysis. Results indicated that three similar goal profiles could be discerned at all measurement waves for both language and mathematics. Profiles were labelled ‘multiple goals’, ‘approach oriented’ and ‘moderate/indifferent’. In both mathematics and language, around 80% of the participants remained stable in their goal profiles across measurements. Students who transitioned between goal profiles mostly moved from less to more favourable profiles. Profile membership and transitions between profiles were found to be relatively domain general with 60% overlap between domains. The high level of stability over time and across domains suggests that students’ goal profiles represent relatively stable personal dispositions.     

Basic Competence in Mathematics: Swedish and English 16 year olds

The transition to mass participation in post-16 education, which had occurred considerably earlier in other European countries, has finally taken place in England. However, high drop-out and failure rates persist, particularly on vocational qualification routes. Our hypothesis is that an important factor is the lack of basic competence of lower-achieving English students in the key skills - English language and mathematics - required for success in further study. Our research addresses the validity of the argument by investigating whether any significant difference can be detected between the skills of English students entering post-compulsory education and those of students in countries where drop-out and failure rates are low. The country investigated in this study was Sweden where participation of 16 year olds in post-compulsory upper-secondary education is currently over 90%; and where some 90% of those enrolling normally obtain an academic or vocational qualification. Some General Certificate of Secondary Education (GCSE) mathematics questions were incorporated into the national test taken by Swedish 16 year olds at the end of compulsory schooling; and significant differences were found in the scores of the lower 40% of the cohort in the two countries. The results are consistent with the hypothesis; and also go beyond previous Swedish-English comparisons, which reflect the general emphasis in international studies on younger age groups (typically 9 and 13 year olds).     

Educational goals of teachers in heterogeneous and homogeneous classes in elementary and junior high school

Teachers (N = 108) of low-achieving homogeneous, high-achieving homogeneous, and academically heterogeneous classes in nine elementary schools and 10 junior high schools in Israel were interviewed to determine their allegiance to academic, personal, and social goals for students. In contrast to results of American research, the academic goal dominated for teachers in all settings. Only for teachers of heterogeneous classes in elementary school was a tendency towards balance in goal orientations apparent. Several explanations for the results are discussed.     

Experimental Effects of Word Generation on Vocabulary,Academic Language,Perspective Taking,and Reading Comprehension in High-Poverty Schools

Abstract

With a sample of 7,752 fourth- to seventh-grade students in 25 schools which were randomized at the school level to condition, this article reports experimental impacts of an enhanced version of Word Generation on student outcomes at the end of Year 1 and of Year 2. Word Generation employs analysis, synthesis, critique, and problem-solving activities to build students’ academic language, perspective taking, and ultimately their reading comprehension. Results indicate that the program improves the proximate outcome of academic vocabulary included in the curriculum after the first and second year of implementation for all students (Y1 effect size (ES)?=?.22, Y2?=?.28 for fourth and fifth graders; Y1 ES?=?.13, Y2?=?.16 for sixth and seventh graders). For those in the fourth and fifth grades, their perspective positioning skills also improved at the end of the first year (ES?=?.14), and their academic language skills (ES?=?.06), perspective articulation and positioning skills (ES?=?.12, .19), and reading comprehension (ES?=?.15) improved at the end of the second year. Among sixth and seventh graders, there were improvements in perspective positioning skills (ES?=?.19) and reading comprehension (ES?=?.10) at the end of Year 2. Effects after both Years 1 and 2 were stronger in high-exposure classrooms.     

Mathematics Learning Development: the Role of Long-Term Retrieval

This study assessed the relation between long-term memory retrieval and mathematics calculation and mathematics problem solving achievement among elementary, middle, and high school students in nationally representative sample of US students, when controlling for fluid and crystallized intelligence, short-term memory, and processing speed. As hypothesized, structural equation modeling comparing elementary school students and middle and high school students revealed that long-term retrieval skills became a better predictor of both mathematics calculation and mathematics problem solving as age and grade increased. Future research should focus on the effectiveness of interventions to improve long-term retrieval skills in general, and arithmetic facts retrieval and problem solving procedures in particular, at all grades, including high school.     

Within-year changes in children’s intrinsic and extrinsic motivational orientations: Contextual predictors and academic outcomes

The present study was designed to investigate the nature, timing, and correlates of motivational change among a large sample (N = 1051) of third- through eighth-grade students. Analyses of within-year changes in students’ motivational orientations revealed that both intrinsic and extrinsic motivations decreased from fall to spring, with declines in intrinsic motivation especially pronounced for the adolescents and declines in extrinsic motivation especially pronounced for the elementary students. These changes in motivation were explained, in part, by shifts in students’ perceptions of the school goal context. Findings suggested that typical age-related declines in intrinsic motivation may be minimized by a school-wide focus on mastery goals. Finally, the potential academic consequences of students’ motivational orientations were examined with a series of hierarchical multiple regressions. Intrinsic motivation and classroom achievement appeared to influence one another in a positive and reciprocal fashion. Poor classroom performance minimally predicted higher levels of extrinsic motivation, but extrinsic motivation was not a source of low classroom grades.