An Innovative Approach to Teaching Structural Induction for Computer Science

Proofs by induction are central to many computer science areas such as data structures, theory of computation, programming languages, program efficiency-time complexity, and program correctness. Proofs by induction can also improve students’ understanding of and performance with computer science concepts such as programming languages, algorithm design, and recursion, as well as serve as a medium for teaching them. Even though students are exposed to proofs by induction in many courses of their curricula, they still have difficulties understanding and performing them. This impacts the whole course of their studies, since proofs by induction are omnipresent in computer science. Specifically, students do not gain conceptual understanding of induction early in the curriculum and as a result, they have difficulties applying it to more advanced areas later on in their studies. The goal of my dissertation is twofold: 1. identifying sources of computer science students’ difficulties with proofs by induction, and 2. developing a new approach to teaching proofs by induction by way of an interactive and multimodal electronic book (e-book). For the first goal, I undertook a study to identify possible sources of computer science students’ difficulties with proofs by induction. Its results suggest that there is a close correlation between students’ understanding of inductive definitions and their understanding and performance of proofs by induction. For designing and developing my e-book, I took into consideration the results of my study, as well as the drawbacks of the current methodologies of teaching proofs by induction for computer science. I designed my e-book to be used as a standalone and complete educational environment. I also conducted a study on the effectiveness of my e-book in the classroom. The results of my study suggest that, unlike the current methodologies of teaching proofs by induction for computer science, my e-book helped students overcome many of their difficulties and gain conceptual understanding of proofs induction.

Teachers' knowledge, awareness, and pedagogy of global education in secondary schools

Professor Mohammed K. Farouk, Major Professor In 1979, the Florida State Board of Education approved the teaching of global education in the state of Florida. The purpose of this study was to examine the factors that contributed to teachers' global knowledge, global mindedness, and pedagogy in global education. The Hanvey model of teaching from a global perspective was the theoretical framework for the study. A total of 90 secondary teachers from Miami-Dade County Public Schools were randomly selected and placed in three groups: Globally Oriented Social Studies Program (GOSSE), Non-Globally Oriented Social Studies Program (non-GOSSE), and Teachers Who Teach Other Subjects (TWTOS). Seven teachers, two of whom team-taught a class, were selected for classroom observations and interviews. A mixed methods design that combined quantitative and qualitative data was used. ANOVA and Chi square techniques were used to determine whether the factors that contributed to teachers' global knowledge and global mindedness differ among groups. Classroom observations and interviews were conducted to determine whether the instructional strategies differ among the seven selected teachers. The findings of the study show that teachers who were trained in teaching from a global perspective differed in their global knowledge and used more appropriate instructional strategies than teachers who were not trained in teaching global perspectives. There was no significant difference in the combined global knowledge of the non-GOSSE and TWTOS groups when compared with the GOSSE group. There was no significant difference in the combined global knowledge of the GOSSE and non- GOSSE groups when compared with the TWTOS group. There was no significant difference among the teachers in their global mindedness. Observation and interview data indicate that current events, role-playing, simulations, open-ended discussion, debates, and projects were the predominant instructional strategies used by globally trained teachers. Cable networks, Internet, magazines, and newspapers were found to be the dominant tools for teaching global education. This study concluded that teachers who were trained in globally oriented programs had more global knowledge than teachers who were not. It is recommended that teacher education programs should incorporate a global perspective in the preparation of social studies teachers, with particular attention to developing their global attitudes.

The relationship between the teacher's experience, the teacher's college major, and the teacher's level of education in predicting classroom attitudes in high school science students

A review of the literature reveals few research has attempted to demonstrate if a relationship exists between the type of teacher training a science teacher has received and the perceived attitudes of his/her students. Considering that a great deal of time and energy has been devoted by university colleges, school districts, and educators towards refining the teacher education process, it would be more efficient for all parties involved, if research were available that could discern if certain pathways in achieving that education, would promote the tendency towards certain teacher behaviors occurring in the classroom, while other pathways would lead towards different behaviors. Some of the teacher preparation factors examined in this study include the college major chosen by the science teacher, the highest degree earned, the number of years of teaching experience, the type of science course taught, and the grade level taught by the teacher. This study examined how the various factors mentioned, could influence the behaviors which are characteristic of the teacher, and how these behaviors could be reflective in the classroom environment experienced by the students. The instrument used in the study was the Classroom Environment Scale (CES), Real Form. The measured classroom environment was broken down into three separate dimensions, with three components within each dimension in the CES. Multiple Regression statistical analyses examined how components of the teachers' education influenced the perceived dimensions of the classroom environment from the students. The study occurred in Miami-Dade County Florida, with a predominantly urban high school student population. There were 40 secondary science teachers involved, each with an average of 30 students. The total number of students sampled in the study was 1200. The teachers who participated in the study taught the entire range of secondary science courses offered at this large school district. All teachers were selected by the researcher so that a balance would occur in the sample between teachers who were education major versus science major. Additionally, the researcher selected teachers so that a balance occurred in regards to the different levels of college degrees earned among those involved in the study. Several research questions sought to determine if there was significant difference between the type of the educational background obtained by secondary science teachers and the students' perception of the classroom environment. Other research questions sought to determine if there were significant differences in the students' perceptions of the classroom environment for secondary science teachers who taught biological content, or non-biological content sciences. An additional research question sought to evaluate if the grade level taught would affect the students' perception of the classroom environment. Analysis of the multiple regression were run for each of four scores from the CES, Real Form. For score 1, involvement of students, the results showed that teachers with the highest number of years of experience, with masters or masters plus degrees, who were education majors, and who taught twelfth grade students, had greater amounts of students being attentive and interested in class activities, participating in discussions, and doing additional work on their own, as compared with teachers who had lower experience, a bachelors degree, were science majors, and who taught a grade lower than twelfth. For score 2, task orientation, which emphasized completing the required activities and staying on-task, the results showed that teachers with the highest and intermediate experience, a science major, and with the highest college degree, showed higher scores as compared with the teachers indicating lower experiences, education major and a bachelors degree. For Score 3, competition, which indicated how difficult it was to achieve high grades in the class, the results showed that teachers who taught non-biology content subjects had the greatest effect on the regression. Teachers with a masters degree, low levels of experience, and who taught twelfth grade students were also factored into the regression equation. For Score 4, innovation, which indicated the extent in which the teachers used new and innovative techniques to encourage diverse and creative thinking included teachers with an education major as the first entry into the regression equation. Teachers with the least experience (0 to 3 years), and teachers who taught twelfth and eleventh grade students were also included into the regression equation.

The impact of looping of fourth grade students on their reading achievement

This study examines the effects of looping (staying with the same teacher for two grade levels) on the reading achievement of fourth graders within a large, urban, multicultural school. Looping was expected to have a positive effect on reading achievement and reading qualities. Additional benefits, such as its effect on anxiety levels and self-concept were also assumed to accrue from looping. A causal-comparative design was employed. Four existing classrooms consisting of eighty-one fourth grade students comprised the treatment and comparison groups. The two "looping" treatment groups consisted of students who had the same teacher for their third and fourth grade school years. The remaining two classes comprised the comparison groups. Pre- and post-tests for reading achievement total scores and subscores for main idea and comparisons were obtained using the Florida Comprehensive Assessment Test (FCAT). Assessments were also obtained from the State-Trait Anxiety Inventory for Children, modified to reflect reading, and the Self- Perception Profile for Children. The difference in pre- and post-test FCAT scores were analyzed via a four group simple ANOVA to examine the effects of the looping model on reading achievement and reading qualities. Similar simple ANOVAs were performed to investigate the relationship of looping to anxiety and self-concept. The findings led to the conclusion that looping was significantly related to improvement in reading achievement and reading qualities. In addition, the hypothesized relationship of lower anxiety in the looping group compared to the comparison group was supported. There were no significant effects on self-concept for any of the comparisons. The study clearly demonstrated the positive effects of looping, on total reading achievement scores, on reading qualities of fourth grade students who participated in looping classes and on differences in students' anxiety. Looping did not have an effect on general self-concept. The results demonstrate the effects of looping on teaching methods. In looping practice teachers have the advantage of knowing their students and the students' readiness and can make adaptations of teaching methods accordingly. From the students' perspective, the looped students do not have to adapt to a new teacher and thus, experience lower anxiety.

The socialization of teachers who teach young students experiencing physical disability in physical education

The purpose of this study was to explore the socialization of teachers in physical education, with a focus on their experiences of teaching and learning to teach children living with physical disabilities. Data were collected using qualitative interviews and through analysis of program calendars for publicly-funded institutions offering pre-service teacher education programs. Despite being largely viewed as the least effective form of socialization, pre-service teacher education has the potential to influence a teacher’s confidence and performance in the classroom. Results of this study indicate that the socialization experiences of teachers continue to be strong indicators of performance, and that both specialist and generalist teachers lack positive socialization experiences that include students with physical disabilities in physical education. This limits the experience, knowledge and skills they have to draw on in their physical education teaching practice. Coupled with a lack of resources and expertise available, teachers are left under-prepared and without enough resources to provide high quality physical education to children living with physical disabilities.

A Jaworskian analysis of four senior class primary teachers endeavouring to teach mathematics from a constructivist-compatible perspective

A constructivist philosophy underlies the Irish primary mathematics curriculum. As constructivism is a theory of learning its implications for teaching need to be addressed. This study explores the experiences of four senior class primary teachers as they endeavour to teach mathematics from a constructivist-compatible perspective with primary school children in Ireland over a school-year period. Such a perspective implies that children should take ownership of their learning while working in groups on tasks which challenge them at their zone of proximal development. The key question on which the research is based is: to what extent will an exposure to constructivism and its implications for the classroom impact on teaching practices within the senior primary mathematics classroom in both the short and longer term? Although several perspectives on constructivism have evolved (von Glaserfeld (1995), Cobb and Yackel (1996), Ernest (1991,1998)), it is the synthesis of the emergent perspective which becomes pivotal to the Irish primary mathematics curriculum. Tracking the development of four primary teachers in a professional learning initiative involving constructivist-compatible approaches necessitated the use of Borko’s (2004) Phase 1 research methodology to account for the evolution in teachers’ understanding of constructivism. Teachers’ and pupils’ viewpoints were recorded using both audio and video technology. Teachers were interviewed at the beginning and end of the project and also one year on to ascertain how their views had evolved. Pupils were interviewed at the end of the project only. The data were analysed from a Jaworskian perspective i.e. using the categories of her Teaching Triad of management of learning, mathematical challenge and sensitivity to students. Management of learning concerns how the teacher organises her classroom to maximise learning opportunities for pupils. Mathematical challenge is reminiscent of the Vygotskian (1978) construct of the zone of proximal development. Sensitivity to students involves a consciousness on the part of the teacher as to how pupils are progressing with a mathematical task and whether or not to intervene to scaffold their learning. Through this analysis a synthesis of the teachers’ interpretations of constructivist philosophy with concomitant implications for theory, policy and practice emerges. The study identifies strategies for teachers wishing to adopt a constructivist-compatible approach to their work. Like O’Shea (2009) it also highlights the likely difficulties to be experienced by such teachers as they move from utilising teacher-dominated methods of teaching mathematics to ones in which pupils have more ownership over their learning.

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.

Perspectives of Teachers Regarding the Integration of Mathematics and Science at the Secondary School Level

The integration of mathematics and science in secondary schools in the 21st century continues to be an important topic of practice and research. The purpose of my research study, which builds on studies by Frykholm and Glasson (2005) and Berlin and White (2010), is to explore the potential constraints and benefits of integrating mathematics and science in Ontario secondary schools based on the perspectives of in-service and pre-service teachers with various math and/or science backgrounds. A qualitative and quantitative research design with an exploratory approach was used. The qualitative data was collected from a sample of 12 in-service teachers with various math and/or science backgrounds recruited from two school boards in Eastern Ontario. The quantitative and some qualitative data was collected from a sample of 81 pre-service teachers from the Queen’s University Bachelor of Education (B.Ed) program. Semi-structured interviews were conducted with the in-service teachers while a survey and a focus group was conducted with the pre-service teachers. Once the data was collected, the qualitative data were abductively analyzed. For the quantitative data, descriptive and inferential statistics (one-way ANOVAs and Pearson Chi Square analyses) were calculated to examine perspectives of teachers regardless of teaching background and to compare groups of teachers based on teaching background. The findings of this study suggest that in-service and pre-service teachers have a positive attitude towards the integration of math and science and view it as valuable to student learning and success. The pre-service teachers viewed the integration as easy and did not express concerns to this integration. On the other hand, the in-service teachers highlighted concerns and challenges such as resources, scheduling, and time constraints. My results illustrate when teachers perceive it is valuable to integrate math and science and which aspects of the classroom benefit best from the integration. Furthermore, the results highlight barriers and possible solutions to better the integration of math and science. In addition to the benefits and constraints of integration, my results illustrate why some teachers may opt out of integrating math and science and the different strategies teachers have incorporated to integrate math and science in their classroom.

A HARD PUSH FOR SOFT SKILLS: AN EXAMINATION OF POLICY AND RESEARCH ON NON-COGNITIVE SKILLS IN CANADIAN K-12 SCHOOLING

Non-cognitive skills have caught the attention of current education policy writers in Canada. Within the last 10 years, almost every province has produced a document including the importance of supporting non-cognitive skills in K-12 students in the classroom. Although often called different names (such as learning skills, cross curricular competencies, and 20th Century Skills) and occasionally viewed through different lenses (such as emotional intelligence skills, character skills, and work habits), what unifies non-cognitive skills within the policy documents is the claim that students that are strong in these skills are more successful in academic achievement and are more successful in post-secondary endeavors. Though the interest from policy-makers and educators is clear, there are still many questions about non-cognitive skills that have yet to be answered. These include: What skills are the most important for teacher’s to support in the classroom? What are these skills’ exact contributions to student success? How can teachers best support these skills? Are there currently reliable and valid measures of these skills? These are very important questions worth answering if Canadian teachers are expected to support non-cognitive skills in their classrooms with an already burdened workload. As well, it can begin to untangle the plethora of research that exists within the non-cognitive realm. Without a critical look at the current literature, it is impossible to ensure that these policies are effective in Canadian classrooms, and to see an alignment between research and policy. Upon analysis of Canadian curriculum, five non-cognitive skills were found to be the most prevalent among many of the provinces: Self-Regulation, Collaboration, Initiative, Responsibility and Creativity. The available research literature was then examined to determine the utility of teaching these skills in the classroom (can students improve on these skills, do these skills impact other aspects of students’ lives, and are there methods to validly and reliably assess these skills). It was found that Self-Regulation and Initiative had the strongest basis for being implemented in the classroom. On the other hand, Creativity still requires a lot more justification in terms of its impact on students’ lives and ability to assess in the classroom.

An analysis of beginning mentors’ critical incidents in English post-compulsory education: navigating stormy waters

This qualitative study explores the barriers and dilemmas faced by beginning and novice mentors in post-compulsory education in the southeast of England. It analyses critical incidents (Tripp, 2012) taken from the everyday practice of mentors who were supporting new teachers and lecturers in the southeast of England. It categorises different types of critical incidents that mentors encountered and describes the strategies and rationales mentors used to support mentees and (indirectly) their learners and colleagues. The study explores ways in which mentors' own values, beliefs and life experiences affected their mentoring practice.  Methodology As part of a specialist master’s-level professional development module, 21 mentors wrote about two critical incidents (Tripp, 2012) taken from their own professional experiences, which aimed to demonstrate their support for their mentee’s range of complex needs. These critical incidents were written up as short case studies, which justified the rationale for their interventions and demonstrated the mentors' own professional development in mentoring. Critical incidents were used as units of analysis and categorised thematically by topic, sector and mentoring strategies used. Findings The research demonstrated the complex nature of decision-making and the potential for professional learning within a mentoring dyad. The study of these critical incidents found that mentors most frequently cited the controversial nature of teaching observations, the mentor’s role in mediating professional relationships, the importance of inculcating professional dispositions in education, and the need to support new teachers so that they can use effective behaviour management strategies. This study contributes to our understanding of the central importance of mentoring for professional growth within teacher education. It identifies common dilemmas that novice mentors face in post-compulsory education, justifies the rationale for their interventions and mentoring strategies, and helps to identify ways in which mentors' professional development needs can be met. It demonstrates that mentoring is complex, non-linear and mediated by mentors’ motivation and values.

Concept maps as a tool to analyze the ideas of teacher training students regarding what to teach on human nutrition in Primary Education

Concept maps are a technique used to obtain a visual representation of a person's ideas about a concept or a set of related concepts. Specifically, in this paper, through a qualitative methodology, we analyze the concept maps proposed by 52 groups of teacher training students in order to find out the characteristics of the maps and the degree of adequacy of the contents with regard to the teaching of human nutrition in the 3rd cycle of primary education. The participants were enrolled in the Teacher Training Degree majoring in Primary Education, and the data collection was carried out through a training activity under the theme of what to teach about Science in Primary School? The results show that the maps are a useful tool for working in teacher education as they allow organizing, synthesizing, and communicating what students know. Moreover, through this work, it has been possible to see that future teachers have acceptable skills for representing the concepts/ideas in a concept map, although the level of adequacy of concepts/ideas about human nutrition and its relations is usually medium or low. These results are a wake-up call for teacher training, both initial and ongoing, because they shows the inability to change priorities as far as the selection of content is concerned.

Receptive Vocabulary of CLIL and Non-CLIL Primary and Secondary School Learners

CLIL instruction has been reported to be beneficial for foreign language vocabulary learning since CLIL students show higher vocabulary profiles than students of their same age in traditional EFL contexts. However, to our knowledge, the receptive vocabulary knowledge of CLIL and non-CLIL learners at the end of primary and secondary education has not been examined yet. Hence, this study aims at comparing the receptive vocabulary size 79 CLIL primary learners with the receptive vocabulary knowledge of 331 non-CLIL learners at the end of primary and secondary school. Sex-based differences were also analysed. The 2k Vocabulary Levels Test (VLT) was used for the purposes of the study. Results revealed that learners’ receptive vocabulary sizes lie within the most frequent 1000 words, non-CLIL secondary school students throw better results than primary students but the differences between the secondary group and the CLIL group are not statistically significant. As for sex-based differences, we found no significant differences among the groups. These findings led us to believe that the CLIL approach offers a benefit for vocabulary acquisition since CLIL learners have been exposed to the foreign language for a shorter period of time and the results are quite similar to their non-CLIL secondary school partners.

How using Technology Enhanced Learning could help modernise traditional large group teaching or Lecturing.

The efficiency of lecturing or large group teaching has been called into question for many years. An abundance of literature details the components of effective teaching which are not provided in the traditional lecture setting, with many alternative methods of teaching recommended. However, with continued constraints on resources large group teaching is here to stay and student’s expect and are familiar with this method.

Technology Enhanced Learning may be the way forward, to prevent educators from “throwing out the baby with the bath water”. TEL could help Educator’s especially in the area of life sciences which is often taught by lectures to engage and involve students in their learning, provide feedback and incorporate the “quality” of small group teaching, case studies and Enquiry Based Learning into the large group setting thus promoting effective and deep learning.

Addressing the theory practice gap in nurse education: evaluating teaching through audit against NMC standards and final management placement

Introduction
This paper outlines an innovative approach to auditing and evaluating the content of a management and leadership module for undergraduate nursing students after their final management clinical placement. Normally evaluations of teaching in a module take place at the end of a teaching module and therefore do not properly reflect the value of the teaching in relation to practical clinical experience.
Aim
This audit and evaluation sought to explore both the practical value of the teaching and learning, and also the degree to which it the teaching reflected against the NMC Standards of Education and Learning (2010 domain 3).
Methods
Having piloted the evaluative tool with an earlier cohort of nursing students, this evaluation explored both a quantitative assessment employing a Personal Response System (n =172), together with a qualitative dimension (n=116), thus delivering paper-based comments and reflections from students on the value and practicality of the module teaching theory to their final clinical management experience. The quantitative audit data were analysed for frequencies and cross tabulation and the qualitative audit data were thematically analysed.
Results
Results suggest a significant proportion of the students, appreciated the quality of the standard of teaching, but more importantly, ‘valued or highly valued’ the teaching and learning in relation to how it helped to significantly inform their management placement experience. A smaller proportion of the students underlined limitations and areas in which further improvement can be made in teaching and learning to the module.
Conclusion
Significantly positive evaluation by the students of the practical value of teaching and learning, to the theoretical management module. This has proved a useful auditing approach in assessing the theoretical teaching to student’s Level 3 clinical experience, and facilitated significant recommendations as far as developing the teaching and learning to better reflect the practice needs of nursing students

Troublesome Knowledge of SoTL

This study explores the Scholarship of Teaching and Learning (SoTL) as a form of troublesome knowledge (Perkins 1999) that continues to trouble its practitioners. Forty-eight higher education professionals from six countries described their understanding of SoTL in an online survey; ten individuals participated in follow-up interviews to consider how SoTL experiences shape, support, or hinder academic identity and knowing. We categorize our findings according to the dynamic factors—personal, relational, and contextual—identified by Lieff et al (2012); we argue that SoTL serves to illuminate and expose tensions created by competing values and that these values can lead to, or create, a troublesome space wherein promoting SoTL can be enabling and disabling.