Analysis of Students’ Misconceptions and Error Patterns in Mathematics: The Case of Fractions

This study analyzed three fifth grade students’ misconceptions and error patterns when working with equivalence, addition and subtraction of fractions. The findings revealed that students used both conceptual and procedural knowledge to solve the problems. They used pictures, gave examples, and made connections to other mathematical concepts and to daily life topics. Error patterns found include using addition and subtraction of numerators and denominators, and finding the greatest common factor.

Establishing a baseline of psychometric estimates of measurement of intercultural competence of Ukrainian faculty: Setting the stage for domestic and global intercultural understanding

Post-Soviet Ukraine is in a time of upheaval and transition. Internal relations between pro-Western and pro-Russian supporters have deteriorated in the light of recent political events of Euro Revolution, Russia's occupation of the Crimean peninsula, and the militant confrontations in the southeastern regions of the country. In the light of these developments, intercultural competence is greatly needed to alleviate domestic tensions and enable effective intercultural communication with the representatives of different cultures within the country and beyond its borders.^ This study established a baseline of psychometric estimates of intercultural competence of Ukrainian higher education faculty. A sample of 276 professors of different academic majors from one university in Western Ukraine participated in the research. The Global Perspective Inventory (GPI; Merrill, Braskamp, & Braskamp, 2012) was chosen as a research instrument to measure intercultural competence of the faculty members. The GPI takes into account cognitive, intrapersonal, and interpersonal domains, each of which contains two scales reflective of theories of cultural development and intercultural communication – Cognitive-Knowing, Cognitive-Knowledge, Intrapersonal-Identity, Intrapersonal-Affect, Interpersonal-Social Responsibility, and Interpersonal-Social Interaction. Because the research instrument has neither been previously used as a measure of intercultural competence, nor administered in Ukraine, it was cross-validated using a Table of Specification (Newman, Lim, & Pineda, 2013) and two sets of factor analyses. As a result, a modified version of the GPI was created for use in Ukraine.^ Multiple linear regression analyses were used to test relationships between the participants' GPI scores on intercultural competence, and several independent variables that consisted of academic discipline, intercultural experience, and how long the participants taught at the university. The analyses determined a positive relationship between the scores on three out of six scales of the original version and two out of five scales of the modified version of the GPI and all the independent variables simultaneously. The relationship between the faculty responses on the six scales of both GPI versions and the independent variables controlling for each other produced mixed results. A unique role of intercultural professional development in predicting intercultural competence was discussed.^

The effects on students' self-efficacy beliefs regarding their comprehension of American literature when aesthetic reading and reader response strategy are implemented

High-stakes testing and accountability have infiltrated the education system in the United States; the top priority for all teachers must be student progress on standardized tests. This has resulted in the predominance of reading for test-taking, (efferent reading), in the English, language arts, and reading classrooms. Authentic uses of print activities, like aesthetic reading, that encourage students to engage individually with a text, have been pushed aside. ^ During a 3-week time period, regular level, English 3/American literature students in a Title I magnet high school, participated in this quasi-experimental study (N = 62). It measured the effects of an intervention of reading American literature texts aesthetically and writing aesthetically-evoked reader responses on students' self-efficacy beliefs regarding their comprehension of American literature. One trained teacher and the researcher participated in the study: student participants were pre- and post- tested using the Confidence in Reading American Literature Survey which examined their self-efficacy beliefs regarding their comprehension of American literature. Several statistical analyses were performed. The results of the linear regression analyses partially supported a positive relationship between aesthetically-evoked reader responses and students' self-efficacy beliefs regarding their comprehension of American literature. Additionally, the results of the 2 (sex) x 2 (treatment) ANCOVAs conducted to test group differences in self-efficacy beliefs regarding the comprehension of American literature between treatment and control groups indicated a main effect for treatment (but not sex; nor was there a significant sex x treatment interaction), suggesting the treatment was partially effective in increasing students' self-efficacy beliefs. Seven of the twelve ANCOVAs indicated a statistically significant increase in the treatment group's adjusted group mean self-efficacy belief scores as a result of being exposed to the intervention. In six of these seven analyses, increases in self-efficacy beliefs occurred in tasks that required three or more higher-order levels of thinking/learning. The results are discussed in terms of theoretical, empirical and practical significance. Future research is recommended to extend the intervention beyond the narrow confines of a Title I magnet school to settings where the intervention could be tested longitudinally, e. g., honors and gifted students, elementary and middle schools.^

Undergraduate Students’ Perceptions of Study Abroad and Their Level of Achievement of Global Learning Outcomes

This study expanded on current research on study abroad and global learning, using the Global Perspective Inventory (GPI), and conducted at Florida International University (FIU) in Miami, FL. The GPI assesses the holistic development of a global perspective in higher education within three domains and their respective FIU-determined equivalents: cognitive (global awareness), intrapersonal (global perspective), and interpersonal (global engagement). The main purpose of this study was to assess FIU’s undergraduate students’ perceptions of study abroad on their level of achievement of global awareness, global perspective, and global engagement. The secondary purpose was to determine how the students described their study abroad experience and achievement of global learning. The research design for this study consisted of parallel mixed methods. The quantitative component was an ex post facto with hypothesis design, using a pretest/posttest nonequivalent group methodology. FIU undergraduates (N=147) who studied abroad for one semester or more completed the GPI pre- and post-tests. Descriptive statistics and paired t-tests were conducted to compare the means. The interviews included 10 students, and were analyzed through Structural coding, Saldaña’s In Vivo coding, and Value coding. Quantitative analyses indicated positive changes in the students’ global awareness and global perspective. These analyses also showed that the FIU students achieved higher post-test means on all the domains of the GPI compared to other studies. Qualitative analyses showed that the students’ experiences incorporated all three global learning outcomes, most notably global awareness and perspective.

Comparison of Linear Functions in Middle Grades Textbooks from Singapore and the United States

Many U.S. students do not perform well on mathematics assessments with respect to algebra topics such as linear functions, a building-block for other functions. Poor achievement of U.S. middle school students in this topic is a problem. U.S. eighth graders have had average mathematics scores on international comparison tests such as Third International Mathematics Science Study, later known as Trends in Mathematics and Science Study, (TIMSS)-1995, -99, -03, while Singapore students have had highest average scores. U.S. eighth grade average mathematics scores improved on TIMMS-2007 and held steady onTIMMS-2011. Results from national assessments, PISA 2009 and 2012 and National Assessment of Educational Progress of 2007, 2009, and 2013, showed a lack of proficiency in algebra. Results of curriculum studies involving nations in TIMSS suggest that elementary textbooks in high-scoring countries were different than elementary textbooks and middle grades texts were different with respect to general features in the U.S. The purpose of this study was to compare treatments of linear functions in Singapore and U.S. middle grades mathematics textbooks. Results revealed features currently in textbooks. Findings should be valuable to constituencies who wish to improve U.S. mathematics achievement. Portions of eight Singapore and nine U.S. middle school student texts pertaining to linear functions were compared with respect to 22 features in three categories: (a) background features, (b) general features of problems, and (c) specific characterizations of problem practices, problem-solving competency types, and transfer of representation. Features were coded using a codebook developed by the researcher. Tallies and percentages were reported. Welch's t-tests and chi-square tests were used, respectively, to determine whether texts differed significantly for the features and if codes were independent of country. U.S. and Singapore textbooks differed in page appearance and number of pages, problems, and images. Texts were similar in problem appearance. Differences in problems related to assessment of conceptual learning. U.S. texts contained more problems requiring (a) use of definitions, (b) single computation, (c) interpreting, and (d) multiple responses. These differences may stem from cultural differences seen in attitudes toward education. Future studies should focus on density of page, spiral approach, and multiple response problems.

The Relationship between Classroom Interactions and Exclusionary Discipline as a Social Practice: A Critical Microethnography

Exclusionary school discipline results in students being removed from classrooms as a consequence of their disruptive behavior and may lead to subsequent suspension and/or expulsion. Literature documents that nondominant students, particularly Black males, are disproportionately impacted by exclusionary discipline, to the point that researchers from a variety of critical perspectives consider exclusionary school discipline an oppressive educational practice and condition. Little or no research examines specific teacher-student social interactions within classrooms that influence teachers’ decisions to use or not use exclusionary discipline. Therefore, this study set forth the central research question: In relation to classroom interactions in alternative education settings, what accounts for teachers’ use or non-use of exclusionary discipline with students? A critical social practice theory of learning served as the framework for exploring this question, and a critical microethnographic methodology informed the data collection and analysis. Criterion sampling was used to select four classrooms in the same alternative education school with two teachers who frequently and two who rarely used exclusionary discipline. Nine stages of data collection and reconstructive data analysis were conducted. Data collection involved video recorded classroom observations, digitally recorded interviews of teachers and students discussing selected video segments, and individual teacher interviews. Reconstructive data analysis procedures involved hermeneutic inferencing of possible underlying meanings, critical discourse analysis, interactive power analysis and role analysis, thematic analysis of the interactions in each classroom, and a final comparative analysis of the four classrooms. Four predominant themes of social interaction (resistance, conformism, accommodation, and negotiation) emerged with terminology adapted from Giroux’s (2001) theory of resistance in education and Third Space theory (Gutiérrez, 2008). Four types of power (normative, coercive, interactively established contracts, and charm), based on Carspecken’s (1996) typology, were found in the interactions between teacher and students in varying degrees for different purposes. This research contributes to the knowledge base on teacher-student classroom interactions, specifically in relation to exclusionary discipline. Understanding how the themes and varying power relations influence their decisions and actions may enable teachers to reduce use of exclusionary discipline and remain focused on positive teacher-student academic interactions.

Factors Surgical Team Members Perceive Influence Choices of Wearing or not Wearing Personal Protective Equipment During Operative/Invasive Procedures

Exposure to certain bloodborne pathogens can prematurely end a person’s life. Healthcare workers (HCWs), especially those who are members of surgical teams, are at increased risk of exposure to these pathogens. The proper use of personal protective equipment (PPE) during operative/invasive procedures reduces that risk. Despite this, some HCWs fail to consistently use PPE as required by federal regulation, accrediting agencies, hospital policy, and professional association standards. The purpose of this mixed methods survey study was to (a) examine factors surgical team members perceive influence choices of wearing or not wearing PPE during operative/invasive procedures and (b) determine what would influence consistent use of PPE by surgical team members. Using an ex post facto, non-experimental design, the memberships of five professional associations whose members comprise surgical teams were invited to complete a mixed methods survey study. The primary research question for the study was: What differences (perceptual and demographic) exist between surgical team members that influence their choices of wearing or not wearing PPE during operative/invasive procedures? Four principal differences were found between surgical team members. Functional (i.e., profession or role based) differences exist between the groups. Age and experience (i.e., time in profession) differences exist among members of the groups. Finally, being a nurse anesthetist influences the use of risk assessment to determine the level of PPE to use. Four common themes emerged across all groups informing the two study purposes. Those themes were: availability, education, leadership, and performance. Subsidiary research questions examined the influence of previous accidental exposure to blood or body fluids, federal regulations, hospital policy and procedure, leaders’ attitudes, and patients’ needs on the use of PPE. Each of these was found to strongly influence surgical team members and their use of PPE during operative/invasive procedures. Implications based on the findings affect organizational policy, purchasing and distribution decisions, curriculum design and instruction, leader behavior, and finally partnership with PPE manufacturers. Surgical team members must balance their innate need to care for patients with their need to protect themselves. Results of this study will help team members, leaders, and educators achieve this balance.

Stereotype Threat and the Standardized Testing Experiences of African American Children at an Urban Elementary School

Stereotype threat (Steele & Aronson, 1995) refers to the risk of confirming a negative stereotype about one’s group in a particular performance domain. The theory assumes that performance in the stereotyped domain is most negatively affected when individuals are more highly identified with the domain in question. As federal law has increased the importance of standardized testing at the elementary level, it can be reasonably hypothesized that the standardized test performance of African American children will be depressed when they are aware of negative societal stereotypes about the academic competence of African Americans. This sequential mixed-methods study investigated whether the standardized testing experiences of African American children in an urban elementary school are related to their level of stereotype awareness. The quantitative phase utilized data from 198 African American children at an urban elementary school. Both ex-post facto and experimental designs were employed. Experimental conditions were diagnostic and non-diagnostic testing experiences. The qualitative phase utilized data from a series of six focus group interviews conducted with a purposefully selected group of 4 African American children. The interview data were supplemented with data from 30 hours of classroom observations. Quantitative findings indicated that the stereotype threat condition evoked by diagnostic testing depresses the reading test performance of stereotype-aware African American children (F[1, 194] = 2.21, p < .01). This was particularly true of students who are most highly domain-identified with reading (F[1, 91] = 19.18, p < .01). Moreover, findings indicated that only stereotype-aware African American children who were highly domain-identified were more likely to experience anxiety in the diagnostic condition (F[1, 91] = 5.97, p < .025). Qualitative findings revealed 4 themes regarding how African American children perceive and experience the factors related to stereotype threat: (1) a narrow perception of education as strictly test preparation, (2) feelings of stress and anxiety related to the state test, (3) concern with what “others” think (racial salience), and (4) stereotypes. A new conceptual model for stereotype threat is presented, and future directions including implications for practice and policy are discussed.

Geographical Literacy, Attitudes, and Experiences of Freshman Students: A Qualitative Study at Florida International University

The purpose of the study was to explore the geography literacy, attitudes and experiences of Florida International University (FIU) freshman students scoring at the low and high ends of a geography literacy survey. The Geography Literacy and ABC Models formed the conceptual framework. Participants were freshman students enrolled in the Finite Math course at FIU. Since it is assumed that students who perform poorly on geography assessments do not have an interest in the subject, testing and interviewing students allowed the researcher to explore the assumption. In Phase I, participants completed the Geography Literacy Survey (GLS) with items taken from the 2010 NAEP Geography Subject Area Assessment. The low 35% and high 20% performers were invited for Phase II, which consisted of semi-structured interviews. A total of 187 students participated in Phase I and 12 in Phase II. The primary research question asked was what are the geography attitudes and experiences of freshman students scoring at the low and high ends of a geographical literacy survey? The students had positive attitudes regardless of how they performed on the GLS. The study included a quantitative sub-question regarding the performance of the students on the GLS. The students’ performance on the GLS was equivalent to the performance of 12th grade students from the NAEP Assessment. There were three qualitative sub-questions from which the following themes were identified: the students’ definition of geography is limited, students recall more out of school experiences with geography, and students find geography valuable. In addition, there were five emergent themes: there is a concern regarding a lack of geographical knowledge, rote memorization of geographical content is overemphasized, geographical concepts are related to other subjects, taking the high school level AP Human Geography course is powerful, and there is a need for real-world applications of geographical knowledge. The researcher offered as suggestions for practice to reposition geography in our schools to avoid misunderstandings, highlight its interconnectedness to other fields, connect the material to real world events/daily decision-making, make research projects meaningful, partner with local geographers, and offer a mandatory geography courses at all educational levels.

The effect of a reform on a school organizational culture after receiving a failing Florida Comprehensive Assessment Test rating

The purpose of this research was to explore the effects of a reform that took place in an elementary school during 2000/2001 as a result of a failure rating on the Florida Comprehensive Assessment Test on the structure and the personnel of the organization. The exploration took place over a period of 10 months starting in August 2000 until June 2001. It focused on the effect of the failure rating on the: (a) structure and operation of the school; (b) morale, beliefs, behaviors, and daily lives of teachers and the principal; and (c) the effect of the reform effort on the leadership style of the principal, whether she became a transactional or a transformative leader. The researcher assumed the role of a participant observer. Data sources were her personal recollections of major events that took place during the year of the reform, interviews, observations, and school documents. The sample included 15 teachers present during the time of the reform. Ten taught second through fifth grade. The remaining five participants were the music teacher, the counselor, and the writing, reading and technology specialists. Together they represented the instructional team or represented special education areas. The findings indicated that the reform effort had an effect on the structure and the operation of the school. The changes included reorganization of the physical set up, changes in curriculum and instruction, changes in the means of communication among the staff, and the addition of new staff members including an official agent of change. The reform had a greater effect on the daily lives of teachers and their morale than on their beliefs and behaviors. Teachers reported that during the effort their daily lives were stressful and their morale very low due to the enormous expectations that they had to meet. On the other hand, the reform effort had a positive effect on the daily life, morale, beliefs, and behaviors of the principal. It energized her. She spoke positively about the change. She functioned as an effective, positive, resilient transactional leader who did what was necessary in order to enable the teachers to cope with the complex situation.

An evaluation of a curriculum response to the State of Florida mandate for computer literacy at a large comprehensive high school in Dade County, Florida

Minimum Student Performance Standards in Computer Literacy and Science were passed by the Florida Legislature through the Educational Reform Act of 1983. This act mandated that all Florida high school graduates receive training in computer literacy. Schools and school systems were charged with the task of determining the best methods to deliver this instruction to their students. The scope of this study is to evaluate one school's response to the state of Florida's computer literacy mandate. The study was conducted at Miami Palmetto Senior High School, located in Dade County, Florida. The administration of Miami Palmetto Senior High School chose to develop and implement a new program to comply with the state mandate - integrating computer literacy into the existing biology curriculum. The study evaluated the curriculum to determine if computer literacy could be integrated successfully and meet both the biology and computer literacy objectives. The findings in this study showed that there were no significant differences between biology scores of the students taking the integrated curriculum and those taking a traditional curriculum of biology. Student in the integrated curriculum not only met the biology objectives as well as those in the traditional curriculum, they also successfully completed the intended objectives for computer literacy. Two sets of objectives were successfully completed in the integrated classes in the same amount of time used to complete one set of objectives in the traditional biology classes. Therefore, integrated curriculum was the more efficient means of meeting the intended objectives of both biology and computer literacy.

The Effect of Authentic Literacy Experiences as Book Buddies with Hispanic Fourth Graders on Preservice Teachers’ Literacy Content Knowledge and Reading Maturity

From a sociocultural perspective, individuals learn best from contextualized experiences. In preservice teacher education, contextualized experiences include authentic literacy experiences, which include a real reader and writer and replicate real life communication. To be prepared to teach well, preservice teachers need to gain literacy content knowledge and possess reading maturity. The purpose of this study was to examine the effect of authentic literacy experiences as Book Buddies with Hispanic fourth graders on preservice teachers’ literacy content knowledge and reading maturity. The study was a pretest/posttest design conducted over 12 weeks. Preservice teacher participants, the focus of the study, were elementary education majors taking the third of four required reading courses in non-probabilistic convenience groups, 43 (n = 33 experimental, n = 10 comparison) Elementary Education majors. The Survey of Preservice Teachers’ Knowledge of Teaching and Technology (SPTKTT), specifically designed for preservice teachers majoring in elementary or early childhood education and the Reading Maturity Survey (RMS) were used in this study. Preservice teachers chose either the experimental or comparison group based on the opportunity to earn extra credit points (experimental = 30 points, comparison = 15). After exchanging introductory letters preservice teachers and Hispanic fourth graders each read four books. After reading each book preservice teachers wrote letters to their student asking higher order thinking questions. Preservice teachers received scanned copies of their student’s unedited letters via email which enabled them to see their student’s authentic answers and writing levels. A series of analyses of covariance were used to determine whether there were significant differences in the dependent variables between the experimental and comparison groups. This quasi-experimental study tested two hypotheses. Using the appropriate pretest scores as covariates for adjusting the posttest means of the subcategory Literacy Content Knowledge (LCK), of the SPTKTT and the RMS, the mean adjusted posttest scores from the experimental group and comparison group were compared. No significant differences were found on the LCK dependent variable using the .05 level of significance, which may be due to Type II error caused by the small sample size. Significant differences were found on RMS using the .05 level of significance.

The Mathematics Anxiety of Bilingual Community College Students

Math anxiety levels and performance outcomes were compared for bilingual and monolingual community college Intermediate Algebra students attending a culturally diverse urban commuter college. Participants (N = 618, 250 men, 368 women; 361 monolingual, 257 bilingual) completed the Abbreviated Math Anxiety Scale (AMAS) and a demographics instrument. Bilingual and monolingual students reported comparable mean AMAS scores (20.6 and 20.7, respectively) and comparable proportions of math anxious individuals (50% and 48%, respectively). Factor analysis of AMAS scores, using principal component analysis by varimax rotation, yielded similar two-factor structures for both populations -- assessment and learning content -- accounting for 65.6% of the trace for bilingual AMAS scores. Statistically significant predictor variables for levels of math anxiety for the bilingual participants included (a) preparatory course enrollment (β = .236, p = .041) with those enrolled in prior preparatory courses scoring higher, (b) education major (β = .285, p = .018) with education majors scoring higher, and (c) business major (β = .252, p = .032) with business majors scoring higher. One statistically significant predictor variable emerged for monolingual students, gender (β = -.085, p = .001) with females ranking higher. Age, income, race, ethnicity, U.S. origin, science or health science majors did not emerge as statistically significant predictor variables for either group. Similarities between monolingual and bilingual participants included statistically significant negative linear correlations between AMAS scores and course grades for both bilingual (r = -.178, p = .017) and monolingual participants (r = -.203, p = .001). Differences included a statistically significant linear correlation between AMAS scores and final exam grades for monolingual participants only (r = -.253, p < .0009) despite no statistically significant difference in the strength the linear relationship of the AMAS scores and the final exam scores between groups, z = 1.35, p = .1756. The findings show that bilingual and monolingual students report math anxiety similarly and that math anxiety has similar associations with performance measures, despite differences between predictor variables. One of the first studies on the math anxiety of bilingual community college students, the results suggest recommendations for researchers and practitioners.

Theoretical Foundations of Developing Modeling Instruction Curriculum for College Biology Courses

Modeling Instruction (MI) has been successfully implemented in high school science classes. Moreover, MI curriculum for introductory physics has also been developed at a university level. Noticing the gap, the author will provide theoretical foundations to support the statement that MI curriculum should be developed for college biology courses.

Florida's Voluntary Prekindergarten (VPK) Program's Influence on Preschool Teachers' Beliefs and Practices

Three veteran preschool teachers told their stories about navigating the implementation of VPK. Even with parents' misconceptions about VPK's goals, teachers were able to meet its standards by continuing to embrace a play-based, hands-on philosophy that also emphasized children's social and emotional needs.