Using assessment to individualize early mathematics instruction

Accumulating evidence suggests that assessment-informed personalized instruction, tailored to students' individual skills and abilities, is more effective than more one-size-fits-all approaches. In this study, we evaluate the efficacy of Individualizing Student Instruction in Mathematics (ISI-Math) compared to Reading (ISI-Reading) where classrooms were randomly assigned to ISI-Math or ISI-Reading. The literature on child characteristics X instruction or skill X treatment interaction effects point to the complexities of tailoring instruction for individual students who present with constellations of skills. Second graders received mathematics instruction in small flexible learning groups based on their assessed learning needs. Results of the study (n = 32 teachers, 370 students) revealed significant treatment effects on standardized mathematics assessments. With effect sizes (d) of 0.41–0.60, we show that we can significantly improve 2nd graders' mathematics achievement, including for children living in poverty, by using assessment data to individualize the mathematics instruction they receive. The instructional regime, ISI-Math, was implemented by regular classroom teachers and it led to about a 4-month achievement advantage on standardized mathematics tests when compared to students in control classrooms. These results were realized within one school year. Moreover, treatment effects were the same regardless of school-level poverty and students' gender, initial mathematics or vocabulary scores.     

Teachers' and students' verbal behaviours during cooperative and small‐group learning

Background. Teachers play a critical role in promoting interactions between students and engaging them in the learning process. This study builds on a study by Hertz‐Lazarowitz and Shachar (1990) who found that during cooperative learning teachers' verbal behaviours were more helpful to and encouraging of their students' efforts while during whole‐class instruction, their verbal behaviours tended to be more authoritarian, rigid, and impersonal. Aim. This study seeks to determine if teachers who implement cooperative learning engage in more facilitative learning interactions with their students than teachers who implement group work only. The study also seeks to determine if students in the cooperative groups model their teachers' behaviours and engage in more positive helping interactions with each other than their peers in the group work groups. Samples. The study involved 26 teachers and 303 students in Grades 8 to10 from 4 large high schools in Brisbane, Australia. Methods. All teachers agreed to establish cooperative, small‐group activities in their classrooms for a unit of work (4 to 6 weeks) once a term for 3 school terms. The teachers were audiotaped twice during these lessons and samples of the students' language, as they worked in their groups, were also collected at the same time. Results. The results show that teachers who implement cooperative learning in their classrooms engage in more mediated‐learning interactions and make fewer disciplinary comments than teachers who implement group work only. Furthermore, the students model many of these interactions in their groups. Conclusions. The study shows that when teachers implement cooperative learning, their verbal behaviour is affected by the organizational structure of the classroom.     

Group Counseling Intervention for Solving Problems on the Job

This article reports the effects of a group counseling intervention on the social problem solving by and employment preparation of Grade 9 and Grade 10 students. Mathematics teachers implemented the intervention on problem solving on the job within a unit on mathematics problem solving. The intervention used a cognitive approach to counseling, specifically cognitive strategy instruction with teacher modeling and students' thinking aloud to a partner. Both pretest and posttest scores and analyses of interviews with 4 students showed the success of the intervention. An interview with the peer coach of the teachers highlighted teacher experiences in implementing successful group counseling.     

Effect of Teachers' Stereotyping on Students' Stereotyping of Mathematics as a Male Domain

Abstract

This multilevel analysis used data from a representative sample from Grades 6, 7, and 8 in public schools in Switzerland. The data included information on (a) 6,602 students (3,307 girls, 3,295 boys) nested within 338 classes and (b) 321 mathematics teachers of these classes. The teachers and the students tended to stereotype mathematics as a male domain, and the teachers' stereotypes significantly affected the students' stereotypes after the author controlled for achievement, interest, and self-confidence in mathematics and for school grade and schooling track.     

How Much Does Creative Teaching Enhance Elementary School Students' Achievement?

This study examined the relationship between creative teaching and elementary students' achievement gains. Forty‐eight upper elementary school teachers' classroom instruction was observed and evaluated over the course of 8 different lessons throughout the year. For each teacher, during each lesson, both a creative teaching frequency score and a quality score were derived. These scores were then used as predictor variables in a structural equation model to determine the magnitude of the relationship between creative teaching and classroom achievement gains in reading, language, and mathematics. Our results demonstrated that (a) the majority of teachers do not implement any teaching strategies that foster student creativity; (b) teachers who elicit student creativity turn out students that make substantial achievement gains; and (c) classrooms with high proportions of minority and low‐performing students receive significantly less creative teaching.     

The Influence of Guided Error-Based Learning on Motor Skills Self-Efficacy and Achievement

The authors investigated the role of errors in motor skills teaching, specifically the influence of errors on skills self-efficacy and achievement. The participants were 75 undergraduate students enrolled in pétanque courses. The experimental group (guided error-based learning, n = 37) received a 6-week period of instruction based on the students' errors, whereas the control group (correct motion instruction, n = 38) received a 6-week period of instruction emphasizing correct motor skills. The experimental group had significantly higher scores in motor skills self-efficacy and outcomes than did the control group. Novices' errors reflect their schema in motor skills learning, which provides a basis for instructors to implement student-centered instruction and to facilitate the learning process. Guided error-based learning can effectively enhance beginners' skills self-efficacy and achievement in precision sports such as pétanque.     

Teaching Very Large Classes

The editor of Teaching Theology and Religion facilitated this reflective conversation with five teachers who have extensive experience and success teaching extremely large classes (150 students or more). In the course of the conversation these professors exchange and analyze the effectiveness of several active learning strategies they have employed to overcome the passivity and anonymity of the large lecture format. A major point of debate emerges that contrasts the dynamically performative and highly informed and skilled lecturer with the “wasted time and money” that results from encouraging students to participate through various active learning strategies. Other themes include the importance of story telling in the religious studies classroom, the significance of the differences between students' learning styles, and the challenge of teaching and assessing critical thinking and communication skills.     

Fostering reading comprehension in fifth grade by explicit instruction in reading strategies and peer tutoring

Background: Research reveals that explicit reading strategies instruction and engaging students in interaction about texts promote students' reading comprehension ability. The present intervention study combines both aspects. Aims: The study examines the educational benefits of explicit reading strategies instruction, followed by practice in (a) teacher‐led whole‐class activities (STRAT), (b) reciprocal same‐age (STRAT + SA), or (c) cross‐age peer tutoring activities (STRAT + CA) on fifth graders' reading comprehension achievement. Sample: Twenty‐two fifth‐grade teachers and their 454 students from 19 different schools throughout Flanders (Belgium) participated. Method: A quasi‐experimental pretest post‐test retention test design was used with three experimental (STRAT, STRAT + SA, and STRAT + CA) and a matched control group. The experimental interventions were implemented during an entire school year. Results: Multilevel analysis revealed that the STRAT and STRAT + CA condition made a significantly larger pretest to retention test progress than the control group. The significant major progress was especially situated from pretest to post‐test, during which the intervention took place. Concerning the STRAT + SA condition no significant differences with regard to the control group were detected. Pairwise comparisons of the experimental conditions indicated that the STRAT + CA condition's progress from pretest to retention test also exceeded the STRAT + SA condition's advancement significantly. Conclusion: The study corroborated the efficacy of the STRAT and STRAT + CA conditions' interventions as feasible tools to enhance fifth graders' reading comprehension achievement.     

Teaching and Learning in High School Reading Classes: Perspectives of Teachers and Students

This qualitative study investigated high school reading programs and participants focusing on the insider perspectives of teachers and their students. The study occurred in two sites, one in a Southern state and the other in an Eastern state. The participants, five high school reading teachers and two to three students in each of their reading classes, were interviewed individually by the researchers. Interview questions focused on reader identity, reading habits, reader strategies, content area reading, and the reading program. Findings indicate a disparity between teachers' and students' understanding about reading, variability in instruction, and need for engaged learning.     

Enhancing geometric reasoning

Geometry is an important part of the mathematics curriculum. However, students are not demonstrating strong conceptual knowledge of this subject. The research of Van Hiele and Van Hiele-Geldof has focused on the concept of thinking levels in geometry and the role of instruction in raising levels of thinking. This paper describes a field trial of a supplemental geometry unit intended to raise Van Hiele thinking levels in a group of 23 eighth-grade students by having them become more adept at using higher order thinking skills. Sample questions assessing particular Van Hiele thinking levels and attitudes toward geometry, as well as field-tested activities yielding the most positive results, are presented. Educators can benefit from this application of the Van Hiele model of geometric thinking, since the thought processes involved in learning geometry are explained, along with teaching techniques and tools for assessment. By having teachers become more aware of their students' cognitive skills, attitudes, and misconceptions, teaching practices and student achievement can be enhanced.     

English learners' achievement in mathematics and science: Examining the role of self-efficacy

The goals of the current study were twofold. The first goal was to describe levels of mathematics and science self-efficacy and achievement among a sample of students with varying levels of English language proficiency. The second goal was to examine the extent to which students' self-efficacy explains the relation between their English proficiency level and mathematics and science achievement. The sample consisted of 332 fifth graders (mean age = 10.46 years, SD = 0.38) and their 63 teachers in 20 schools. The student sample was linguistically diverse with parents reporting 22 different home languages. Based on district classification procedures, each student was coded into one of three English language proficiency level categories: English proficient-speaking students (English proficient), English Learner (EL) students who are reaching proficiency, yet are still being monitored (reaching proficiency), and EL students who are receiving English for Speakers of Other Languages services (ESOL; limited English proficient). Regression analyses indicated that students identified as limited English proficient consistently demonstrated lower achievement and self-efficacy across the content areas of mathematics and science as compared to their peers who were English proficient and reaching proficiency. In addition, students' self-efficacy partially explained the relation between limited English proficiency level and achievement for science, but not for mathematics. Results indicate that educators should consider variability in students' English proficiency levels as they select supports to promote both science achievement and self-efficacy. Findings also suggest promise for practices and programs that foster self-efficacy in addition to language and content skills.     

Designing Knowledge Scaffolds to Support Mathematical Problem Solving

We present a methodology for designing better learning environments. In Phase 1, 6th-grade students' (n = 223) prior knowledge was assessed using a difficulty factors assessment (DFA). The assessment revealed that scaffolds designed to elicit contextual, conceptual, or procedural knowledge each improved students' ability to add and subtract fractions. Analyses of errors and strategies along with cognitive modeling suggested potential mechanisms underlying these effects. In Phase 2, we designed an intervention based on scaffolding this prior knowledge and implemented the computer-based lessons in mathematics classes. In Phase 3, we used the DFA and supporting analyses to assess student learning from the intervention. The posttest results suggest that scaffolding conceptual, contextual, and procedural knowledge are promising tools for improving student learning.     

Do teachers’ cultural beliefs matter for students’ school adaptation? A multilevel analysis of students’ academic achievement and psychological school adjustment

Based on two large-scale studies from Germany, we examined how different types of teachers’ cultural beliefs are related to immigrant students’ school adaptation. Specifically, we investigated the relationship of teachers' multicultural beliefs appreciating cultural diversity, their egalitarian beliefs focusing on all students' similarities and their assimilationist beliefs that immigrant students should conform to the mainstream context with immigrant students' academic achievement and psychological school adjustment as indicators of their school adaptation. We also explored all of these associations for non-immigrant students. Study 1 used data on the multicultural, egalitarian, and assimilationist beliefs of German language (N_Teachers?=?220) and mathematics (N_Teachers?=?245) teachers and on students’ achievement and feelings of helplessness in German language classes (N_Students?=?2606) and mathematics classes (N_Students?=?2851) as well as students’ school satisfaction. Study 2 analyzed data on teachers’ multicultural and egalitarian beliefs (N_Teachers?=?456) and students’ achievement and self-concept in mathematics (N_Students?=?4722). Overall, multilevel analyses revealed no relationship between teachers’ cultural beliefs and any of the indicators of immigrant and non-immigrant students’ school adaptation. These findings challenge the notion that overall, teachers’ cultural beliefs effectively translate into students’ school adaptation.

     

USING NUMBER LINE PROCEDURES AND PEER TUTORING TO IMPROVE THE MATHEMATICS COMPUTATION OF LOW-PERFORMING FIRST GRADERS

Recommendations for mathematics instruction frequently include the use of manipulatives as a critical component. There are few experimental analyses of teaching strategies involving the use of manipulatives (e.g., the number line). This investigation used a multiple baseline design across three groups of students to examine the effectiveness of an experimental procedure for improving low-performing children's skills in solving missing addend arithmetic problems using the number line. To address concerns about inadequate time for instruction and insufficient practice in most mathematics instruction, trained peer tutors implemented the procedure. The results suggest that student performance improved when trained tutors taught the students number line procedures and gave them feedback on accuracy. Further, social validation data indicate that the students, their tutors, and their classroom teachers liked the procedures.     

Social emotional learning (SEL) practices in schools: Effects on perceptions of bullying victimization

The direct and indirect effects of student perceptions of the extent to which social emotional learning (SEL) instruction is provided on bullying at school and student victimization experiences were examined for 2832 public school students. Students in grades 4–12 completed several subscales of the Delaware School Climate Survey (Bear et al., 2016) at a single timepoint to assess their perceptions of the extent to which SEL instruction is used at their school, their own SEL skills, bullying at school, and personal victimization experiences. Structural equation modeling revealed that students' perceptions of SEL instruction were inversely related to their perceptions of bullying at school and students' personal experiences of victimization. Effects were direct and indirect, through students' self-reported perceptions of their SEL skills. Effects were stronger in late elementary and middle school than in high school. The indirect effects of student perceptions of the extent of SEL instruction on perceived bullying at school through students' SEL skills varied as a function of victimization severity. For students with low self-reported victimization, there was a negative relation between student self-reported SEL skills and perceptions of bullying at school. In contrast, for students who reported experiencing high levels of victimization, students' self-reported SEL skills related positively to perceptions of bullying at school; there was no significant relation between SEL skills and perceptions of bullying at school for students who reported moderate levels of victimization. Implications for teachers' inclusion of SEL instruction and its effects on positive youth development are discussed.     

Mapping Students' Perceptions of Interesting Class Lessons

Students' perspectives about their experiences as students are potentially valuable resources for teachers and researchers. In this study middle-school students were asked, ‘What are the features of interesting class lessons?’ Students' responses were allocated to categories of similar semantic meaning and representative statements were selected from each category. The students then sorted and ranked the representative statements, generating numerical data suitable for cluster anal-ysis and multidimensional scaling. The cluster analysis generated three main clusters: (a) teachers, (b) individual learning, and (c) social learning. Each main cluster contained smaller clusters that indicated students' concern with issues such as the personal qualities of teachers and self-efficacy. The multidimensional scaling analysis generated a perceptual map that was interpreted to contain two dimensions: (d) student-teacher and (e) individual-social learning. The structure of the perceptual map stimulates questions about the connections that students might make between students' learning and teachers' teaching strategies, as well as students' understandings about the learning opportunities provided by social learning activities.     

Effects of the Self-Regulation Empowerment Program (SREP) on middle school students' strategic skills,self-efficacy,and mathematics achievement

The current study examined the effectiveness of an applied self-regulated learning intervention (Self-Regulation Empowerment Program (SREP)) relative to an existing, school-based remedial mathematics intervention for improving the motivation, strategic skills, and mathematics achievement of academically at-risk middle school students. Although significant group differences in student self-regulated learning (SRL) were not observed when using self-report questionnaires, medium to large and statistically significant group differences were observed across several contextualized, situation-specific measures of strategic and regulatory thinking. The SREP group also exhibited a statistically significant and more positive trend in achievement scores over two years in middle school relative to the comparison condition. Finally, SREP students and coaches reported SREP to be a socially-valid intervention, in terms of acceptability and importance. The importance of this study and critical areas for future research are highlighted and discussed.