Thesis (Ed.M.)--Boston University

This study compares results of sighting, control, suppression and wink tests of visual dominance with a dissociation test administered to 240 high-achieving (ninetieth percentile and above academically) and low-achieving (twenty-fifth percentile and below academically) students at grades four, eight, and twelve. The study examines differences between visual dissociation and other visual-dominance tests. In so doing, the study tests the proportion of consistent dominance revealed by each test among underachievers with a high incidence of dominance variations, examines possible influences on choice of dominant eye, and compares distributions of dominance functions in high- and low-achieving populations.

Detta examensarbete har undersökt hur låg- respektive högpresterande elever påverkas av problemlösningsuppgifter i matematikundervisningen. Är det främst de relativt högpresterande eleverna som har störst nytta av matematisk problemlösning för att få en djupare förståelse i matematik? Kan problemlösning användas för att få upp intresset för lågpresterande elever? Spelar det någon roll hur problemuppgifter är formulerade? Arbetet har genomförts genom en begränsad systematisk litteraturöversikt genom en databassökning via sökmotorerna DiVA, ERIC och Springer följt av en narrativ analys av tolv utvalda artiklar. Resultatet från detta examensarbete tyder på det främst är de relativt högpresterande eleverna som har störst nytta av matematisk problemlösning för att få en djupare förståelse i matematik. Det är främst dessa elever som möter problemlösning i sin matematikundervisning, vilket gör att de blir mer vana vid problemlösning än andra elever. De lågpresterande eleverna ges inte samma möjligheter att utveckla sin förmåga att lösa matematiska problem. Problemlösning kan dock användas för att få upp intresset för lågpresterande elever. Gruppsammansättningar kan här ha en stor betydelse för hur bra elever kan prestera. Lågpresterande elever presterar t.ex. bättre efter samverkan i en heterogen grupp tillsammans med mer högpresterande eleverna. Resultatet tyder också på att det har betydelse hur problemuppgifter är formulerade för att öka elevernas förutsättning att utveckla sina förmågor att lösa matematiska problem. Textbaserade problemlösningsuppgifter anpassas sällan till elevernas kunskapsnivå. Problemlösningsuppgifter bör därför vara konstruerade så att de inte är för svåra utan är anpassade till elevens kunskapsnivå. Det finns t.ex. en tydlig koppling mellan textbaserad problemlösning och elevernas läsförståelse. Examensarbetet drar också slutsatsen att elever får begränsade förutsättningar att skapa lösningsmetoder eftersom uppgifterna i deras läroböcker mycket sällan kräver ett kreativt matematiskt resonemang för att kunna lösas. Läroböckerna behöver därför kompletteras med flera problemlösningsuppgifter, särskilt på en enklare nivå och i sammanhang som eleverna kan relatera till. / This thesis has investigated how low- and high-achieving students are affected by problem-solving tasks in mathematics education. Is it primarily the relatively high-achieving students who benefit most from mathematical problem solving to gain a deeper understanding in mathematics? Can problem solving be used to raise the interest of low-achieving students? Does it matter how problem solving tasks are formulated? The work has been carried out through a rapid systematic literature review through a database search via the search engines DiVA, ERIC and Springer, followed by a narrative analysis of twelve selected articles. The results from this thesis indicate that it is primarily the relatively high-achieving students who benefit most from mathematical problem solving to gain a deeper understanding in mathematics. It is mainly these students who encounter problem solving in their mathematics teaching, which means that they become more accustomed to problem solving than other students. The low-achieving students are not given the same opportunities to develop their ability to solve mathematical problems. However, problem solving can be used to raise the interest of low-achieving students. Here, group compositions can have a major impact on how well students can perform. Low-achieving students perform e.g. better after collaboration in a heterogeneous group together with higher performing students. The results also indicate that it is important how problem tasks are formulated to increase the students' prerequisites for developing their abilities to solve mathematical problems. Text-based problem-solving tasks are rarely adapted to the students' level of knowledge. Problem solving tasks should therefore be constructed so that they are not too difficult but are adapted to the student's level of knowledge. There is e.g. a clear connection between text-based problem solving and students' reading comprehension. The thesis also concludes that students are given limited opportunities to create solution methods because the tasks in their textbooks very rarely require creative mathematical reasoning in order to be solved. The textbooks therefore need to be supplemented with several problem-solving tasks, especially at a simpler level and in contexts that the students can relate to.

abstract: The focus of the study was to identify secondary school students' difficulties with aspects of linearity and linear functions, and to assess their teachers' understanding of the nature of the difficulties experienced by their students. A cross-sectional study with 1561 Grades 8-10 students enrolled in mathematics courses from Pre-Algebra to Algebra II, and their 26 mathematics teachers was employed. All participants completed the Mini-Diagnostic Test (MDT) on aspects of linearity and linear functions, ranked the MDT problems by perceived difficulty, and commented on the nature of the difficulties. Interviews were conducted with 40 students and 20 teachers. A cluster analysis revealed the existence of two groups of students, Group 0 enrolled in courses below or at their grade level, and Group 1 enrolled in courses above their grade level. A factor analysis confirmed the importance of slope and the Cartesian connection for student understanding of linearity and linear functions. There was little variation in student performance on the MDT across grades. Student performance on the MDT increased with more advanced courses, mainly due to Group 1 student performance. The most difficult problems were those requiring identification of slope from the graph of a line. That difficulty persisted across grades, mathematics courses, and performance groups (Group 0, and 1). A comparison of student ranking of MDT problems by difficulty and their performance on the MDT, showed that students correctly identified the problems with the highest MDT mean scores as being least difficult for them. Only Group 1 students could identify some of the problems with lower MDT mean scores as being difficult. Teachers did not identify MDT problems that posed the greatest difficulty for their students. Student interviews confirmed difficulties with slope and the Cartesian connection. Teachers' descriptions of problem difficulty identified factors such as lack of familiarity with problem content or context, problem format and length. Teachers did not identify student difficulties with slope in a geometric context. / Dissertation/Thesis / Ph.D. Curriculum and Instruction 2011

The purpose of this study was to examine how academic stress affects Chinese high achieving secondary students’ mental health. Potential moderating effects of perceived social support and gender on the relationship between academic stress and depression were also examined. Current literature suggests Chinese high school students report greater academic stress and depression than their counterparts overseas (Sun, Dunne, Hou, & Xu, 2013), but it is unclear about the status of high achieving Chinese students as well as how social support works as a protective factor on this particular population. In order to fill this gap, the current study recruited a diverse sample of 133 Key school students and 99 IB students from eight classrooms of two schools during Fall 2017, and administered questionnaires on participants’ academic stress, depression level, perceived social support, and demographic information. Result indicated IB students experience more academic stress and depression compared to Key school students, and female IB students experience more depression than male IB students. Although perceived social support was negatively related to academic stress and depression for both Key and IB students, it was not an effective moderator for either group. Female Key school students were more likely to report higher level of depression compared to male students when they were experiencing similar level of academic stress. This study highlighted the importance of mental health services to high achieving students, discussed appropriate intervention programs for this group of students, and suggested directions for the future research.

High school students in accelerated academic curricula including Advanced Placement (AP) courses and International Baccalaureate (IB) programs are faced with unique challenges associated with their rigorous academic demands, in addition to normative adolescent stressors. Because of the increasing popularity of AP and IB among high-achieving youth and benefits realized by students who successfully manage such curricula, there remains a need to better understand the experiences of stress and coping among this population. The current study used longitudinal and cross-sectional comparisons to (a) investigate the degree to which students in accelerated curricula experience environmental stressors and employ coping strategies to manage academic stressors, and (b) determine which stressors and coping strategies were associated with student success. The longitudinal sample consisted of 184 students from six high schools within three school districts who completed the six-factor Student Rating of Environmental Stressors Scale (StRESS) and 16-factor Coping with Academic Demands Scale (CADS) at Time 1 (grades 9-11) and one year later, at Time 2 (grades 10-12). The cross-sectional sample included 2,379 students (grades 9-12) from 19 high schools within five school districts who also completed the StRESS, CADS, and the Students Life Satisfaction Scale (SLSS); grade point averages (GPAs) were gleaned from school records. Findings indicate that AP and IB students reported more frequent stressors specific to academic requirements over time, while older students (e.g., 11th and12th grade) also reported experiencing more frequent stress due to academic and social struggles and financial issues than their younger counterparts. Regarding coping strategies, findings from longitudinal and cross-sectional comparisons suggested students tend to respond to higher stress by increasing their use of maladaptive strategies including reliance on substance use, reduce effort on schoolwork, and deterioration. Predictive analyses indicated that environmental stressors explained 4-7% and 17-23% of the variance in academic achievement and life satisfaction, respectively. High-achieving students' stress due to academic requirements was related to greater academic success, while it did not appear to compromise life satisfaction. Moreover, while stress due to academic and social struggles was predictive of diminished life satisfaction, stress within this domain was not predictive of poorer academic outcomes. Coping strategies used to manage academic demands accounted for 13-20% and 23-32% of the variance in achievement and life satisfaction, respectively. Students who employed time and task management, sleep, and deterioration to cope were more likely to experience higher academic achievement, while those who coped by seeking academic support, skipping school, engaging in social and creative diversions, using substances, reducing effort on schoolwork, and handling problems alone were less likely to be academically successful. Additionally, those who used cognitive reappraisal, turning to family, and social and athletic diversions were more likely to experience high life satisfaction, while those relying on creative diversions, reduce effort on schoolwork, handle problems alone, and deterioration were less likely to have high life satisfaction. Implications of findings for key stakeholders, including schools psychologists, and future directions for research are discussed.

The purpose of this study was to examine differences in math problem solving among students with learning disabilities (LD), low-achieving (LA) students, and average-achieving (AA) students. The primary interest was to analyze the problem representation processes students use to translate and integrate problem information as they solve math word problems. Problem representation processes were operationalized as (a) paraphrasing the problem and (b) visually representing the problem. Paraphrasing accuracy (i.e., paraphrasing relevant information, paraphrasing irrelevant linguistic information, and paraphrasing irrelevant numerical information), visual representation accuracy (i.e., visual representation of relevant information, visual representation of irrelevant linguistic information, and visual representation of irrelevant numerical information), and problem-solving accuracy were measured in eighth-grade students with LD (n = 25), LA students (n = 30), and AA students (n = 29) using a researcher-modified version of the Mathematical Processing Instrument (MPI). Results indicated that problem-solving accuracy was significantly and positively correlated to relevant information in both the paraphrasing and the visual representation phases and significantly negatively correlated to linguistic and numerical irrelevant information for the two constructs. When separated by ability, students with LD showed a different profile as compared to the LA and AA students with respect to the relationships among the problem-solving variables. Mean differences showed that students with LD differed significantly from LA students in that they paraphrased less relevant information and also visually represented less irrelevant numerical information. Paraphrasing accuracy and visual representation accuracy were each shown to account for a statistically significant amount of variance in problem-solving accuracy when entered in a hierarchical model. Finally, the relationship between visual representation of relevant information and problem-solving accuracy was shown to be dependent on ability after controlling for the problem-solving variables and ability. Implications for classroom instruction for students with and without LD are discussed.

This study investigated the mental health of high school students enrolled in the International Baccalaureate (IB) High School Diploma Program (n =139) in a large, southeastern high school. Mental health was assessed using both positive indicators (life satisfaction, academic achievement, academic self-efficacy) and negative indicators (psychopathology) indicators of adolescent social-emotional and school functioning. Findings from this study include that IB students perceive more stress than their general education peers, yet maintain mental health that is equivalent or superior to that of their general education peers. The role of coping in predicting mental health outcomes in IB students was also investigated. Findings indicate that specific coping styles are differentially related to mental health outcomes in this sub-population of adolescents. Furthermore, coping styles moderate the influence of stress on global life satisfaction and internalizing psychopathology. These findings suggest that participation in the academically rigorous and time-intensive IB program is not harmful to the mental health of high school students, and in fact may be beneficial, as evidenced by the superior academic functioning of students in the IB program.

Student engagement is a multifaceted construct gaining increased interest within the fields of psychology and education. Current literature suggests that student engagement is linked to important student outcomes including academic achievement, psychopathology, and mental wellness; however, there is a dearth of studies that have examined all components of student engagement simultaneously as they relate to the aforementioned outcomes. Additionally, past literature has found support for a decreasing trend in student engagement across the school years, but less attention has been paid to student engagement in the high school years. Among high school students, a particular subgroup has been virtually ignored: high-achieving students enrolled in college-level curricula such as International Baccalaureate (IB) and Advanced Placement (AP). Research questions answered in the current study pertain to: (a) differences in the components of student engagement among IB and AP students, (b) differences in the components of student engagement of IB and AP students across grade level, (c) the extent to which student engagement relates to academic achievement, and (d) the extent to which student engagement relates to mental health. To answer these questions, self-report surveys and school records data from 727 IB and AP high school students were analyzed. Several main effects for program type and grade level were found among the various dimensions of engagement, as well as two interactions between program type and grade level. Regarding predictive relationships, results indicate that the linear combination of all seven indicators of student engagement accounted for 19.56% of the variance in students' academic achievement, 17.47% of the variance in students' life satisfaction, and 6.17% of the variance in students' anxiety. Implications for school psychologists and future directions are discussed.

This thesis reports on two different investigations. The first is a systematic review of pedagogical and organizational practices associated with gifted pupils’ education in mathematics, and on the empirical basis for those practices. The review shows that certain practices – for example, enrichment programs and differentiated instructions in heterogeneous classrooms or acceleration programs and ability groupings outside those classrooms – may be beneficial for the development of gifted pupils. Also, motivational characteristics of and gender differences between mathematically gifted pupils are discussed. Around 60% of analysed papers report on empirical studies, while remaining articles are based on literature reviews, theoretical discourses and the authors’ personal experiences – acceleration programs and ability groupings are supported by more empirical data than practices aimed for the heterogeneous classroom. Further, the analyses indicate that successful acceleration programs and ability groupings should fulfil some important criteria; pupils’ participation should be voluntary, the teaching should be adapted to the capacity of participants, introduced tasks should be challenging, by offering more depth and less breadth within a certain topic, and teachers engaged in these practices should be prepared for the characteristics of gifted pupils. The second investigation reports on the interaction of mathematical abilities and the role of mathematical memory in the context of non-routine problems. In this respect, six Swedish high-achieving students from upper secondary school were observed individually on two occasions approximately one year apart. For these studies, an analytical framework, based on the mathematical ability defined by Krutetskii (1976), was developed. Concerning the interaction of mathematical abilities, it was found that every problem-solving activity started with an orientation phase, which was followed by a phase of processing mathematical information and every activity ended with a checking phase, when the correctness of obtained results was controlled. Further, mathematical memory was observed in close interaction with the ability to obtain and formalize mathematical information, for relatively small amounts of the total time dedicated to problem solving. Participants selected problem-solving methods at the orientation phase and found it difficult to abandon or modify those methods. In addition, when solving problems one year apart, even when not recalling the previously solved problem, participants approached both problems with methods that were identical at the individual level. The analyses show that participants who applied algebraic methods were more successful than participants who applied particular methods. Thus, by demonstrating that the success of participants’ problem-solving activities is dependent on applied methods, it is suggested that mathematical memory, despite its relatively modest presence, has a pivotal role in participants’ problem-solving activities. Finally, it is indicated that participants who applied particular methods were not able to generalize mathematical relations and operations – a mathematical ability considered an important prerequisite for the development of mathematical memory – at appropriate levels. / <p>At the time of the doctoral defense, the following paper was unpublished and had a status as follows: Paper 4: In press.</p>