Motivation and Attitude of Preservice Elementary Teachers toward Mathematics

This study investigated preservice elementary teachers' achievement goal orientations for learning mathematics and the relationship of those goals to their attitudes toward mathematics. Self‐report instruments were administered to assess three achievement goals—mastery, performance‐approach, and performance‐avoid, and three constructs of attitude—confidence in learning mathematics, usefulness of mathematics, and mathematics as a male domain. The preservice teachers were higher in mastery goals than in performance goals, and performance‐avoid goals were higher than performance‐approach goals. Mastery goals correlated positively to all three constructs of attitude. Since mathematics classes are traditionally performance‐oriented, these results suggest a mismatch between personal and classroom goals that could result in negative attitudes and the adoption of maladaptive performance‐avoid goals. These findings suggest that mathematics content courses for preservice elementary teachers should be taught in a classroom climate that supports and encourages mastery goals.     

Middle School Mathematics Teachers’ Perceptions of the Common Core State Standards for Mathematics and Its Impact on the Instructional Environment

This study examines Middle School Mathematics Teachers’ (MSMTs') (N = 1,241) perceptions of the Common Core State Standards for Mathematics (CCSSM) and its impact on the instructional environment. A total of eight factors appear in the data. These factors include professional support, teachers’ use of district‐adopted and non‐district‐adopted curricular resources, influence of CCSSM assessment and teacher evaluation on the instructional environment, influence of the CCSSM on classroom instruction, teachers’ planning practices, and perceived rigor of the CCSSM. The data suggest that teachers’ use of digital resources located online was disconnected from their district‐adopted resources suggesting a lack of curricular coherence. MSMTs note that the CCSSM had caused them to incorporate more reform‐oriented practices such as exploration and productive struggle into their daily instruction. MSMTs also perceive that the CCSSM includes new content that is more rigorous than previous state standards. Sampled MSMTs state that while state assessments will measure CCSSM content, they are less likely to include more complex problems or the standards for mathematical practice. Teachers are more likely to read teacher resources than student textbook activities online and to use digital resources for remediation instead of inquiry activities. Over one‐third of MSMTs wanted more CCSSM professional development.     

Preservice Teachers of High School Mathematics: Success,Failure, and Persistence in the Face of Mathematical Challenges

The goal of this study was to identify variables related to success and resilience in an undergraduate, high school mathematics teacher education program. Over a five‐year period, we tracked the academic performance and achievement motivation goals of multiple cohorts of students. Students who successfully completed their degrees had higher grade point average (GPAs) upon entering the program, earned higher grades in their first college mathematics course, and failed fewer courses than students who left the program or university. Learning and performance motivational goals did not predict success in the program. Performance goals decreased over time. Nearly half the successful students repeated one or more mathematics courses. Ten students completed their degrees, obtained a teaching license, and are teaching despite the need for multiple repetitions of the same mathematics courses. These persistent students did not differ from their peers in motivational goals. Our results suggest that although students with higher GPAs and initial mathematics grades were more likely to complete the program, students who experienced challenges in mathematics courses were able to succeed. We discuss the implications of these results for recruiting, advising, and retention of students in mathematics education programs.     

How Common Is the Common Core? A Global Analysis of Math Teaching and Learning

The U.S. educational system is undergoing rapid and substantial changes with many states grappling with the adoption of the Common Core State Standards in Mathematics (CCSSM). Important research questions remain unanswered regarding the potential efficacy of the CCSSM to improve student math performance compared with students around the globe. This article utilized TIMSS 2007 8th‐grade math assessment results and curricular frameworks to (1) measure the degree of overlap between the CCSSM and TIMSS standards, and (2) use this finding to create a predictive model to determine the potential efficacy of the CCSSM in improving the U.S. 8th‐grade student math performance compared with six culturally matched, TIMSS‐assessed countries, provinces, and states. Comparisons of CCSSM and TIMSS‐assessed jurisdictions show that the CCSSM holds many items in common with TIMSS‐assessed jurisdictions, but lacks rigor in some key areas. The CCSSM deficiencies include algebraic knowledge and problem solving at the 8th‐grade level, and are a significant detractor from the CCSSM when compared with TIMSS.     

Gender Differences in Learning Constructs,Shifts in Learning Constructs,and Their Relationship to Course Achievement in a Structured Inquiry,Yearlong College Physics Course for Life Science Majors

This study investigated differences and shifts in learning and motivation constructs among male and female students in a nonmajors, yearlong structured inquiry college physics course and examined how these variables were related to physics understanding and course achievement. Tests and questionnaires measured students' learning approaches, motivational goals, self‐efficacy, epistemological beliefs, scientific reasoning abilities, and understanding of central physics concepts at the beginning and end of the course. Course achievement scores were also obtained. The findings showed that male students had significantly higher self‐efficacy, performance goals, and physics understanding compared to females, which persisted throughout the course. Differential shifts were found in students' meaningful learning approaches, with females tending to use less meaningful learning from beginning to end of the course; and males using more meaningful learning over this time period. For both males and females, self‐efficacy significantly predicted physics understanding and course achievement. For females, higher reasoning ability was also a significant predictor of understanding and achievement; whereas for males, learning goals and rote learning were significant predictors, but in a negative direction. The findings reveal that different variables of learning and motivation may be important for females' success in inquiry physics compared to males. Instructors should be cognizant of those needs in order to best help all students learn and achieve in college physics.     

The Effect of a Horseshoe Crab Citizen Science Program on Middle School Student Science Performance and STEM Career Motivation

The purpose of the present quasi‐experimental study was to examine the impact of a horseshoe crab citizen science program on student achievement and science, technology, engineering, and mathematics (STEM) career motivation with 86 (n = 86) eighth‐grade students. The treatment group conducted fieldwork with naturalists and collected data for a professional biologist studying horseshoe crab speciation and a mock survey. The comparison group studied curriculum related to horseshoe crabs in the science classroom. A series of measures related to self‐efficacy, interest, outcome expectations, choice goals, and content knowledge were given to participants before and after the intervention. It was hypothesized that students would report higher motivational beliefs regarding science and show higher levels of achievement following the intervention than the comparison group. Support was shown for most of the hypotheses. In addition, path analyses indicated that students' motivational beliefs influence content knowledge and outcome expectations, which in turn affect their career goals. These results have implications for incorporating authentic fieldwork within a formal school structure as an effective method for promoting student achievement and STEM career motivation.     

Science as a Learner and as a Teacher: Measuring Science Self‐Efficacy of Elementary Preservice Teachers

Academic science achievement of U.S. students has raised concerns regarding our ability as a nation to compete in a global economy. Additionally, research has shown that many elementary teachers have weak science content backgrounds and had poor/negative experiences as students of science, resulting in a lack of confidence regarding teaching science. However, efforts to increase science self‐efficacy (SE) in preservice teachers can help to combat these issues. This study looked at a sample of preservice elementary teachers engaged in a semester‐long science content course, using Bandura's concept of SE as a conceptual framework. Our quantitative data showed significant increases in science SE on both subscales (personal efficacy and outcome expectancy). Our qualitative data showed that students communicated an increased sense of confidence with regard to the discipline of science. In addition, students reported learning science pedagogy through the instructor's modeling. Combining our findings resulted in several meta‐inferences, one of which showed students growing as both confident learners of science and teachers of science simultaneously. We created a construct new to the literature to describe this phenomenon: “teacher‐learner,” for students are both learning science and learning to teach science simultaneously through the content course experience, resulting in increased science SE.     

Preservice mathematics teachers' conceptions and enactments of modeling standards

Mathematical modeling has been highlighted recently as Common Core State Standards for Mathematics (CCSSM) included Model with Mathematics as one of the Standards for Mathematical Practices (SMP) and a modeling strand in the high school standards. This common aspect of standards across most states in the United States intended by CCSSM authors and policy makers seems to mitigate the diverse notions of mathematical modeling. When we observed secondary mathematics preservice teachers (M‐PSTs) who learned about the SMP and used CCSSM modeling standards to plan and enact lessons, however, we noted differences in their interpretations and enactments of the standards, despite their attendance in the same course sections during a teacher preparation program. This result led us to investigate the ways the M‐PSTs understood modeling standards, which could provide insights into better preparing teachers to teach mathematical modeling. We present the contrasting ways in which M‐PSTs presented modeling related to their conceptions of mathematical modeling, choices of problems, and enactments over an academic year, connecting their practices to extant research. We consider this teaching and research experience as an opportunity to make significant changes in our instruction that may result in our students enhanced implementation of mathematical modeling.     

Common Core State Standards in the Middle Grades: What's New in the Geometry Domain and How Can Teachers Support Student Learning?

The Common Core State Standards for Mathematics (CCSSM) is a primary focus of attention for many stakeholders' (e.g., teachers, district mathematics leaders, and curriculum developers) intent on improving mathematics education. This article reports on specific content shifts related to the geometry domain in the middle grades (6–8) mathematics curriculum. The methodology employed allows for comparisons of content across multiple standards documents. We report on some dramatic changes with regards to the geometry content taught in the middle grades. We found 52% of the middle grades geometry CCSSM learning expectations will be new to the respective grade level at which they are taught in at least six of the eight states analyzed in this study (57% in grade 6, 50% in grade 7, and 50% in grade 8). We also highlight three areas that represent “new” geometry content at the middle grades based on our analysis of CCSSM and pre‐CCSSM state standards.     

Statistical Association: Alignment of Current U.S. High School Textbooks with the Common Core State Standards for Mathematics

This study examined the alignment of three selected U.S. high school textbooks series with the Common Core State Standards for Mathematics (CCSSM) regarding the treatment of statistical association. A framework grounded in the literature for inclusion and exclusion of reasoning about association topics was developed, and textbook entries were compared with the CCSSM learning expectations (LEs). Across the three series, about 77–90% of the 582 association problems addressed two numerical variables. All CCSSM LEs were covered by two of the three series. However, additional association LEs not found in the CCSSM were included in the textbooks. Implications for curriculum revision and development, and content analysis are suggested. The study challenges the notion of CCSSM‐aligned curricula.     

Relationships Between Inquiry‐Based Teaching and Physical Science Standardized Test Scores

This exploratory case study investigates relationships between use of an inquiry‐based instructional style and student scores on standardized multiple‐choice tests. The study takes the form of a case study of physical science classes taught by one of the authors over a span of four school years. The first 2 years were taught using traditional instruction with low levels of inquiry (non‐inquiry group), and the last 2 years of classes were taught by inquiry methods. Students' physical science test scores, achievement data, and attendance data were examined and compared across both instructional styles. Results suggest that for this teacher the use of an inquiry‐based teaching style did not dramatically alter students' overall achievement, as measured by North Carolina's standardized test in physical science. However, inquiry‐based instruction had other positive effects, such as a dramatic improvement in student participation and higher classroom grades earned by students. In additional inquiry‐based instruction resulted in more uniform achievement than did traditional instruction, both in classroom measures and in more objective standardized test measures.     

Evaluating efficacy of environmental education programming

The Clark Fork Watershed Education Program (CFWEP) goals are: (a) increasing students’ understanding of the nature of ecological impacts within their watershed as related to historic mining damage; and (b) increasing students’ sense of stewardship of newly restored landscapes. Data from 2012 to 2016 were evaluated for student knowledge gains (46 trials representing 2,395 student pre‐surveys; 2,409 student post‐surveys). Data from 2013 to 2016 were evaluated for students’ attitudes toward science and disposition toward caring for the environment (38 trials representing 1,479 pre‐surveys; 1,460 post‐surveys). The results of this study support that the program’s goals are being achieved. Students achieved statistically significant gains on knowledge surveys with a 33.4% overall gain pre‐ to posttest (p < 0.0001). Students also moved toward greater positive responses in both attitudes toward science and disposition toward caring for the environment with Cohen’s d effect sizes of “medium effect” for caring toward the environment (d = 0.52) and “small effect” of positive disposition toward science (d = 0.24).     

The Mathematics Attitudes and Perceptions Survey: an instrument to assess expert-like views and dispositions among undergraduate mathematics students

One goal of an undergraduate education in mathematics is to help students develop a productive disposition towards mathematics. A way of conceiving of this is as helping mathematical novices transition to more expert-like perceptions of mathematics. This conceptualization creates a need for a way to characterize students' perceptions of mathematics in authentic educational settings. This article presents a survey, the Mathematics Attitudes and Perceptions Survey (MAPS), designed to address this need. We present the development of the MAPS instrument and its validation on a large (N = 3411) set of student data. Results from various MAPS implementations corroborate results from analogous instruments in other STEM disciplines. We present these results and highlight some in particular: MAPS scores correlate with course grades; students tend to move away from expert-like orientations over a semester or year of taking a mathematics course; and interactive-engagement type lectures have less of a negative impact, but no positive impact, on students' overall orientations than traditional lecturing. We include the MAPS instrument in this article and suggest ways in which it may deepen our understanding of undergraduate mathematics education.     

Instructional Supports for Representational Fluency in Solving Linear Equations with Computer Algebra Systems and Paper‐and‐Pencil

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.     

Linking Preservice Teachers' Mathematics Self‐Efficacy and Mathematics Teaching Efficacy to Their Mathematical Performance

This study examined preservice teachers' mathematics self‐efficacy and mathematics teaching efficacy and compared them to their mathematical performance. Participants included 89 early childhood preservice teachers at a Midwestern university. Instruments included the Mathematics Self‐Efficacy Scale (MSES), Mathematics Teaching Efficacy Beliefs Instrument (MTEBI), and the Illinois Certification Testing System (ICTS) Basic Skills Test. The results indicate that preservice teachers' mathematics self‐efficacy is positively correlated to their personal mathematics teaching efficacy. In addition, their mathematical performance is related to their mathematics self‐efficacy and mathematics teaching efficacy. In regard to affecting student outcomes, only those preservice teachers who are very confident in their ability to teach believe they can have an effect on their students. Implications on teacher education programs are discussed.     

High School Students' Goals for Working Together in Mathematics Class: Mediating the Practical Rationality of Studenting

In this article I explore high school students' perspectives on working together in a mathematics class in which they spent a significant amount of time solving problems in small groups. The data included viewing session interviews with eight students in the class, where each student watched video clips of their own participation, explaining and justifying their behaviors. Analysis of data involved an investigation of students' goals for working together, which were found to vary along multiple dimensions. The dimensions that emerged from these data were mathematical versus nonmathematical goals, individual versus group goals, and personal versus normative goals. I present cases of four individual students to illustrate these dimensions. Such goals are important for illuminating how students' practical rationality is mediated by their personal goals for working together; additionally, these goal dimensions can be used as tools for considering challenges involved with using small group collaboration in high school classes where students' goals may be diverse.     

A Comparison of Calculator Use in Eighth‐Grade Mathematics Classrooms in the United States,Japan, and Portugal: Results From the Third International Mathematics and Science Study

The study used data from the Third International Mathematics and Science Study to determine trends in calculator use among Population 2 (13‐year‐olds) students in Japan, the United States, and Portugal. While relatively high levels of calculator use were observed for the US and Portugal, virtually no calculator use was found for the Japanese sample. Hierarchical Linear Model analysis determined a statistically significant negative relationship between students' frequency of calculator use and student performance in Japan; no statistically significant relationship was detected for the US and Portuguese samples. US student achievement was positively associated with each of the five reported ways in which calculators are used; however, a statistically significant negative relationship was found between student performance and Japanese students' use of calculators on tests. Plausible explanations are explored.     

Relationships between emotional dispositions and mathematics achievement moderated by instructional practices: analysis of TIMSS 2015

ABSTRACT

This research is a secondary analysis with Korean students’ data collected in the TIMSS 2015 to describe the moderation effects of instructional practices on the relationships between students’ emotional dispositions toward mathematics and mathematics achievement. From the TIMSS 2015 database, we collected mathematics achievement scores, a student-level contextual scale for students’ emotional disposition, and teacher-level contextual scales representing teachers’ instructional practices. We applied hierarchical linear modelling to construct multilevel models. The findings showed that the achievement gap between emotional dispositions – like and dislike – became smaller when teachers more frequently implemented certain instructional practices like asking students to complete challenging exercises, decide their own problem-solving procedures, and express their ideas in class. Students who disliked mathematics were likely to have higher scores as their teachers implemented each of those practices more frequently. Findings provide important implications to teachers regarding: It is important to encourage students to reason through instructional practices like asking them to decide their own problem-solving procedures and to solve challenging problems.     

The Effects of Metacognitive Reflective Assessment on Fifth and Sixth Graders' Mathematics Achievement

The purpose of this experimental study was to investigate the effects of metacognitive reflective assessment instruction on student achievement in mathematics. The study compared the performance of 141 students who practiced reflective assessment strategies with students who did not. A posttest‐only control group design was employed, and results were analyzed by conducting one‐way analysis of variance (ANOVA) and nonparametric procedures. On both a posttest and a retention test, students who practiced reflective strategies performed significantly higher than students who did not use the strategies. A within‐subjects ANOVA was also conducted six weeks following the intervention to assess how the factor of time affected retention levels. No significant difference was found between the posttest and retention test results for the experimental groups or the control group.