Leah A. Nillas

Shying Away from Questioning: Discourse and Participation in Mathematics Classrooms

Sarah Wilson — Mon, 29 Aug 2011 18:38:22 PDT

Classroom discourse is a well researched instructional practice that has yet to be incorporated into many mathematics classrooms across the United States. Research has shown that "78% of mathematical content is taught without discourse activities or incentives" (Forrest, 2008, p. 23). My goal for this self-study was to investigate my questioning and discourse practices as well as the role of students' participation in discourse in relation to their mathematical understanding. I conducted research in One geometry and two algebra I classes which consisted of approximately fifty five students from a local high school. Through several surveys, video-taped lessons, and various exit slips, I found trends on discourse techniques, student comfort, and overall academic comprehension. Students' understanding was strengthened by discourse activities that were carried out in a classroom environment in which students felt comfortable conjecturing and explaining ideas.

Lesson Study: A Collaborative Process of Improving Instruction and Facilitating Students' Motivation

Danielle Wall et al. — Mon, 29 Aug 2011 18:36:03 PDT

Using Vocabulary to Enhance the Understanding of Mathematics as a Language

Jennifer Monaco — Mon, 29 Aug 2011 18:33:30 PDT

Mathematics vocabulary is not often a focus in the mathematics classroom; however, it is found that acquiring new vocabulary enables students to communicate better mathematically, which allows teachers to gauge student understanding. Bay-Williams and Livers (2009) discuss the importance of making connections between previous concepts and new material, so students can apply knowledge and explore and engage on an individual level. Monaco's self-study focuses on two main topics: types of activities that help students learn mathematical concepts and the advantages of reading, writing and speaking mathematics. She conducted the study in three geometry classes and one fundamental geometry class at a rural high school in central Illinois. Monaco incorporated different activities, gathered student feedback, collected student work, and analyzed her personal journal reflections to draw conclusions on vocabulary usage in the mathematics classroom. Many students are not accustomed to emphasis on vocabulary in the mathematics classroom so student feedback and personal reflection allow for growth to enhance student learning and understanding of mathematical concepts.

Implementing Group Interactions to Encourage Peer Teaching, Social Relationships, and Collaborative Problem Solving in Mathematics Classroom

Jessica Madigan — Mon, 29 Aug 2011 18:25:22 PDT

"Cooperative learning is a pedagogical practice that has attracted much attention because of a large body of research that indicates students gain both academically and socially when they have the opportunities to interact with others to accomplish shared goals" (Johnson & Johnson, 2002). I implemented a self-study focusing on small group interactions into everyday lessons throughout student teaching. The participants of my study were unfamiliar with group work, but had positive perceptions of group work. By encouraging an active involvement in mathematics, I was able to increase the presence of peer teaching, social relationships among students, and collaborative problem solving in the classroom. Through surveys, observation, teacher journals and video analysis, I learned that collaborative learning, when introduced effectively and implemented properly, could prompt students' mathematical understanding and promote learning communities in mathematics classrooms.

Being Smart about Smartboards: A Technological Pedagogical and Content Knowledge (TPACK) Analysis

Katie Dietrich — Mon, 29 Aug 2011 18:21:32 PDT

Many educators have concerns that although interactive whiteboards are beneficial in their presentational and motivational aspects, they only have a "limited value in improving subject understanding" (Glover & Miller, 2009). This research study investigated that exact question - how the use of an interactive whiteboard (IWB) influenced students' learning, and what types of IWB-based activities facilitated students' mathematical understanding. Lessons were presented to high school Algebra students and relied heavily on various SmartBoard applications to convey the concepts. In tum, the effectiveness of the IWB was determined through observations, reflections, assessments, and student responses. This qualitative data was analyzed using the Technological Pedagogical and Content Knowledge (TP ACK) framework (Mishra & Koehler, 2006). Results support that the use of an IWB improves students' understanding of mathematics. However, it is imperative that technical and school-wide support is widely available and that the teacher is trained in how to implement its applications appropriately.

Improving Students' Retention of Mathematics and Science Concepts: The Case of Two Teaching Experiments

Kristina Bennett et al. — Mon, 29 Aug 2011 18:07:39 PDT

This self-study conducted using teaching experiment methodology (Steffe & Thompson, 2000) examined high school students' retention of mathematics and science concepts. While there were differences between the mathematics and science classrooms, both studies used entrance and exit slips as primary forms of assessing short-term retention. Unit tests functions as assessment for long-term retention. The findings show that a variety of teaching strategies benefited students' retention of concepts in both mathematics and science. Results from these teaching experiments contribute to the expansion of limited research on students' retention of mathematics and science concepts.

Technology Integration in Secondary Mathematics Classrooms: Effect on Students’ Understanding

Megan Sheehan et al. — Mon, 08 Nov 2010 19:34:06 PST

Technology use in secondary mathematics courses has the potential to bring about broad changes in learning environment and teaching pedagogy, allowing students to communicate and collaborate in new ways and to conjecture, justify, and generalize findings. However, this potential is only realized when teachers use technology in ways encouraging these outcomes (Galbraith, 2006). The purpose of this study is to examine the integration of technology in secondary mathematics classrooms and to evaluate the effectiveness of its use in relation to students’ learning outcomes. This self study research was conducted in honors geometry and AP calculus classes. Data sources included transcripts of classroom discourse, student responses to both forced-response and open-ended surveys, and teacher journals. It was found that when students were the primary users of technology, they were more engaged in learning and higher attained higher levels of understanding, especially in relating different mathematical representations and generalizing patterns.

Fraction Operations: Pre-service Teachers’ Misconceptions and Perceptions about Problem Solving

Leah A. Nillas — Mon, 13 Sep 2010 08:55:58 PDT

This study investigated preservice teachers’ content knowledge involving fractions operations and their beliefs about problem-solving. Preservice teachers took a semester of instruction on problem-solving that emphasized the use of multiple representations and solutions, communication of mathematical ideas, and working collaboratively. Common misconceptions were discussed and preservice teachers’ beliefs about teaching mathematics were presented. Findings support initiatives to improve preservice teachers’ content knowledge and beliefs in teaching and learning with understanding.

KEYS to Successful Learning

Michael J. White, '09 et al. — Thu, 02 Sep 2010 12:24:29 PDT

A nationwide push for the use of technology has influenced classroom teaching in the United States. This study examined the use of technology in elementary classrooms. Specific aspects of technology such as PowerPoint and word processing were examined in relation to developing skills in writing. Data from 46 fifth and third grade students as well as self-evaluation interviews with teachers were used to understand the overall comprehensive value of technology in teaching how to write. I expect my results to support previous research findings which assert that using computer technology in writing motivates students to do better work and is less tedious than a "normal" routine lesson.

Student and Teacher Perceptions on Ability Grouping

Amy Cochran, '09 et al. — Thu, 02 Sep 2010 11:34:38 PDT

As a student teacher I became greatly motivated to examine ability grouping. Ability grouping is a popular practice among schools today where teachers group their students based on their academic performance in a given subject. My research focused on three main questions:

1) What are student and teacher perceptions of ability grouping?

2) Do students perform better academically when they are grouped by ability?

3) Are there any ethical or social conflicts involved when students are grouped based on ability?

Breaking Language Barriers: Connections between Foreign Language and English Language Arts

Lauren Booth, '09 — Thu, 02 Sep 2010 09:15:10 PDT

The purpose of this study was to investigate the relationships between foreign language and English language arts. In previous literature, foreign language has been shown to positively affect students' performance in other subject areas as well as developing their cognitive abilities. When I thought about my own teaching experiences, I made direct connections between foreign language and English language arts in terms of vocabulary acquisition and grammar. Through interviews I found that other teachers are also aware of those connections and deliberately use them to enhance their instruction and defend the study of a foreign language. Upon investigating foreign language standards across the country, I noticed that they also identify this relationship between foreign language and English language arts. The standards include goals that promote the comparison of languages to further students' understanding of languages as a whole and also to reinforce English concepts. Overall, I have found that there are positive benefits to studying a foreign language, particularly in terms of enhancing students' language art skills.

Basic Math Skills: Can High School Students Do the Math?

Samantha Sebastian, '09 et al. — Thu, 02 Sep 2010 08:51:48 PDT

My research questions for this project were: 1) What basic mathematics skills can students perform without a calculator? 2) How can a teacher assist students in reviewing basic skills?

Modern Novels: How to Make them More Relevant to High School Students

David Wendler, '09 — Thu, 02 Sep 2010 08:49:47 PDT

There have been numerous studies conducted researching ways to reinvent how we teach outdated texts that are increasingly losing relevance to the current generation of students because of gaps in interest and culture. Because of this irrelevancy, students do not understand these books as well and are not thinking critically about the issues that they present. My research follows along the same lines, but deals specifically with the increasing irrelevancy of modern novels. I distributed a questionnaire to the class I observe at a local high school. My findings have been that modern novels, while lacking relevance with many students, still have the potential to be connected relevantly to many students in the class by relating the story and the characters' experiences to similar experiences in the lives of the high school students.

Embracing and Implementing Multicultural Education

Jenna Passananti, '08 — Wed, 01 Sep 2010 12:51:38 PDT

As our nation continually becomes more diversified and the demographics of the classroom are changing every year, the need for culturally responsive pedagogy intensifies. This study examines how teachers, administrators and students are responding to the continuous diversification and asks how our current educators are implementing the idea of multicultural education in their classrooms and school communities. To begin to explore answers and generate conclusions to this study, previous research on multicultural education was reviewed in order to gain a strong understanding of the many perspectives and issues on the topic. In addition to the literature, three teachers, all from dissimilar school communities, were interviewed regarding the implementation of multicultural education in the classroom and local community. Finally, a student based discussion was conducted with high school foreign language students which addressed diversity and the importance of learning a second language in our multicultural society. As a result of the literature, teacher interviews and student based discussion, the study concludes that our current educators are recognizing the growing diversity and changing demographics in the classroom. Rather than perceiving diversity and the changing demographics as a challenge in the school community, teachers, school communities and students are responding proactively to this change through the implementation of multiculturalism on a classroom and school wide basis. In addition to the teachers, the high school students are taking action in response to the diversification of our nation through the acquisition of a second language. As a nation, we continue to inquire how we can embrace everyone's culture as a valuable learning tool rather than a barrier that separates us.

CHARACTERIZING PRESERVICE TEACHERS’ MATHEMATICAL UNDERSTANDING OF ALGEBRAIC RELATIONSHIPS

Leah A. Nillas — Wed, 01 Sep 2010 05:38:02 PDT

Qualitative research methods were employed to investigate characterization of preservice teachers’ mathematical understanding. Responses on test items involving algebraic relationships were analyzed using with-in case analysis (Miles and Huberman, 1994) and Pirie and Kieren’s (1994) model of growth of mathematical understanding. Five elementary and special education preservice teachers were the focus of this study. Analysis showed that preservice teachers demonstrated different levels of mathematical understanding. The nature of the mathematical tasks they completed in class provided contexts for their developing understanding. Findings support the need to engage preservice teachers in mathematical sense-making and reasoning in order to experience what it means to teach and learn for understanding.

The Impact of Extracurricular Activities on High School Students’ Academic Success

Nicholas Cooprider — Fri, 13 Aug 2010 10:57:35 PDT

“Although we cannot conclude from the data that extracurricular activities alone caused these improvements, we can say with virtual certainty that when we help a student move from no participation in extracurricular activities to engagement in three or four such activities, it does not harm academic performance” (Reeves, 2008, p.2). Previous research concluded that participation in extracurricular activities does correlate to academic achievement in the classroom. This research examined how students perceived their involvement in extracurricular activities affected their academic performance. Surveys were distributed to a local, rural high school and students were asked to document the amount of time they spent in extracurricular activities and whether it affected their academic performance. Students’ feelings about the effects of part-time employment and their sleep patterns on academic success were also investigated. Results showed a positive correlation between involvement in extracurricular activities and academic achievement. This study aims to enhance the research already done on the topic and open new doors for further research.

Literacy Work Stations: Effects on Students’ Reading Comprehension and Fluency

Amy Burns — Fri, 13 Aug 2010 10:54:58 PDT

According to the National Center for Educational Statistics, “Despite recent national attention to the importance of teaching early reading skills, many children in America continue to struggle with reading. Forty percent of U.S. fourth grade children read below a ‘basic level’ and have ‘little or no mastery’ of the knowledge of skills necessary to perform work at each grade level” (Choutka, Jitendra, Edwards, Starosta, Sacks & Jacobson, 2004). With this data in mind, the purpose of this research is to determine how literacy work stations are affecting students’ literacy skills.

This research was conducted in a fourth grade classroom at a rural, elementary school. Using two surveys, student participants were asked to reflect upon their interests and self-perceptions of their abilities in reading comprehension and reading fluency. Furthermore, students were asked about their views of literacy work stations. Student surveys, a teacher survey, and observation notes were analyzed for common themes and trends. Data showed that students enjoy participating in literacy work stations and believe in the stations’ ability to help improve their reading comprehension and fluency. Quantitative data confirmed these personal beliefs, as students’ words read per minute for fluency increased throughout the study’s one month span. Teacher comments confirmed increases made in students’ comprehension skills. This data suggests that literacy work stations should be implemented in today’s classrooms in order to increase students’ skills in reading.

Understanding English Homework from High School Students’ Perspectives

Laura Allen et al. — Fri, 13 Aug 2010 10:52:25 PDT

Current research on homework is missing the student perspective. This study aims to understand high school students’ perceptions of English homework and how we as teachers can promote students’ understanding and completion of homework. We surveyed fifty students, from two Midwestern high schools, to determine students’ feelings about homework, their motivation for completing assignments, and their preferences in homework design and assessment. Results suggest that students have negative associations with homework, despite thinking it is helpful and reinforces what is learned in class. In addition, grades are students’ primary motivation for completing homework, and time constraints due to extracurricular activities and other demanding classes is their primary reason for not completing their English homework. These findings suggest that students have the most positive experiences with English homework when they have adequate time to complete it, they receive formal feedback rather than completion points, assignments have a clear purpose that assists in students’ understanding of class material, and their preferences are acknowledged and taken into consideration when designing assignments.

Encouraging Higher Performance through an Inclusive Curriculum: A Case Study

Amanda Guidice — Fri, 13 Aug 2010 10:49:26 PDT

During student teaching, it became rather apparent to me that many very intelligent students choose to enroll in lower-level classes that are clearly not challenging enough to help them reach their maximum potentials. One student particularly stood out to me due to his excellent behavior within my remedial English class, in addition to the fact that he received over one hundred percent in the course at the end of the semester. Through a case study on this particular student, I sought to find out how I, as a novice teacher, can encourage students to enroll in average or higher level English courses that are more appropriate to their levels of intelligence and ability. To do so, I focused on motivation and engagement both through an in-depth literature review on similar topics and through my own research methods.

During my research process, I collected observations from student teaching and had the student complete two surveys, two interviews, and three journal entries. After analyzing my data and comparing it to the literature review, it seems that the student’s responses generally support those found in prior research. By incorporating student interests and experiences into class content, providing more options for completing projects, and using more humorous and interactive assignments, we can increase levels of student motivation and engagement within the classroom. Furthermore, the student supported prior findings regarding teacher personality traits that make students feel more comfortable and motivated, such as when teachers are understanding, knowledgeable, and approachable. These findings suggest that it is absolutely possible to further engage students within the classroom, and to increase their motivation to achieve. By paying attention to the needs and concerns of students, it seems more likely that teachers will be able to accommodate these diverse expectations. Although these results are specific to my case study student, the fact that his responses almost directly align with those within previous research suggests a commonality among many students. In the future, it might be beneficial to measure if beginning these accommodations early (perhaps in middle school or during freshman year in high school) would actually show a positive effect in terms of students enrolling in more difficult classes.

Making a Difference: Accommodating Students with Autism in a General Education Classroom

Luci Ottaviano — Fri, 13 Aug 2010 10:45:40 PDT

“Increasingly, parents and professionals are looking to inclusive settings to provide social interactions and opportunities for children with autism that might otherwise be lacking in a self-contained setting” (Boutot, Bryant, 2005). However, most general education high school teachers have limited experience and knowledge regarding autism, and the purpose of this study was to determine how to accommodate and modify curriculum to address the needs of students with autism. Data was collected in two phases: the first phase took place during student teaching and was comprised of observational journals from my experience; the second phase consisted of three interviews with special education teachers, and one guidance counselor. From the data analysis, six best practice themes became evident. The themes address the research questions and are as follows: the meaning of inclusion, benefits for students, the role of paraprofessionals and co-teachers, classroom modifications and accommodations, implementing inclusion and advice for novice teachers.