The science education system currently in place in the United States does not adequately prepare students to compete well with international students. The development of new teaching methods is essential to ensure improvement of the system and provide its students with better scholastic achievements and employment opportunities. Various methods have been studied, with one implemented in a high school classroom to compare the results of the new method with the traditional method of instruction. Rather than the traditional lecture-based approach, Honors Chemistry students learned the theory of the gas laws using inquiry-based methods and hands-on activities. The students were then evaluated using the same assessment as in previous years where instruction was more direct. Preliminary results indicate a 3% increase in the final assessment score using the inquiry method rather than the straight lecture approach.

An increasing number of English Language Learners enrolling in the Washington County Virginia Public School System during the past several years prompted the idea of this thesis. These students are currently mainstreamed in the regular academic classroom. Adapting to their needs is a new challenge in education for teachers in Southwest Virginia. This thesis offers an opportunity for teachers to prepare for a multicultural classroom setting providing English Language Learners with learning strategies necessary to gain confidence in their mathematical ability and academic success in the areas of probability and statistics. Lesson plans have been specifically designed emphasizing teaching strategies, the role of an effective teacher, classroom environment, various cultures and relevant and authentic data.

Since becoming an educator and gaining extensive classroom experience, I have concluded that it would be beneficial to elementary school children to learn other number bases and their basic functions and operations. In this thesis, I have developed five units involving lesson plans for incorporating various number bases into the existing curriculum. The units are Decimal (Base 10), Duodecimal (Base 12), Quinary (Base 5), Binary (Base 2), and Octal (Base 8) which are all appropriate for the elementary level.

It is the author's belief that middle school mathematics is greatly taught in isolation with little or no mention of its origin. Teaching mathematics from a historical perspective will lead to greater understanding, student inspiration, motivation, excitement, varying levels of learning, and appreciation for this subject. This thesis will develop four units that will incorporate original source documents and selected historical topics surrounding computation, numbers, and early calculating devices. Many of the units will center on the Rhind Papyrus and The Treviso Arithmetic. These units will be appropriate to middle school, with an emphasis on 6th grade.

After being introduced to graph theory and realizing how it can be utilized to solve real-world problems, the author decided to create modules of study on graph theory appropriate for middle school students. In this thesis, four modules were developed in the area of graph theory: an Introduction to Terms and Definitions, Graph Families, Graph Operations, and Graph Coloring. It is written as a guide for middle school teachers to prepare teaching units on graph theory.

After becoming interested in the beauty of numbers and the intricate patterns of their behavior, the author concluded that it would be a good idea to make the subject available for students earlier in their educational experience. In this thesis, the author developed four units in combinatorics, namely Fundamental Principles, Permutations, Combinations, and Pascal's Triangle, which are appropriate for third grade level.

To capture a snapshot of the late-preterm academic phenotype in adolescence, and to address a research gap in empirical investigation, the researcher in the present study compared disability- and mathematics-related eighth-grade age outcomes of those born late-preterm (n = 330), to full-term (n = 5434) peers. Through an analysis of Early Childhood Longitudinal Study, Kindergarten Class of 1998-99 (ECLS-K) the researcher in the present study examined the impact of late-preterm birth on disability-related school outcomes in adolescent-age, as measured by (1) presence of special education services; (2) presence of learning disability or other disability; (3) and presence of increased behavioral or attention needs. The researcher examined the impact of late-preterm birth on mathematics-related school outcomes in adolescent-age, as measured by (1) adolescent participant performance in mathematics; (2) adolescent participant engagement in mathematics; (3) and adverse adolescent participant outcomes in mathematics. The researcher found adolescent participants born late-preterm had greater risk of school report of provided special education services; parent report of disability; mathematics teacher report of attention-related adverse outcomes; and mathematics teacher report of decreased ability, incongruent with student's typical performance on ECLS-K standardized assessment.

Today, many introductory computer science courses rely heavily on a specific programming language to convey fundamental programming concepts. For beginning students, the cognitive capacity required to operate with the syntactic forms of this language may overwhelm their ability to formulate a solution to a program. We recognize that the introductory computer science courses can be more effective if they convey fundamental concepts without requiring the students to focus on the syntax of a programming language. To achieve this, we propose a new teaching method based on the Design Recipe and Code Outlining (DRaCO) processes. Our new pedagogy capitalizes on the algorithmic intuitions of novice students and provides a tool for students to externalize their intuitions using techniques they are already familiar with, rather than with the syntax of a specific programming language. We validate the effectiveness of our new pedagogy by integrating it into an existing CS1 course at California Polytechnic State University, San Luis Obispo. We find that the our newly proposed pedagogy shows strong potential to improve students’ ability to program.

Due to the increasing diversity of mathematics classrooms today, teachers need guidance on how to support English Learners (ELs) in mathematics classes in a way that situates language learning within mathematical activity. Unfortunately, neither mathematics education research nor EL education research is sure how to navigate the complexity of teaching ELs mathematics while supporting both their language development and their mathematical development through their participation in mathematical activity. This study examined ELs' participation in mathematical Discourse, investigating both the mathematical purposes ELs accomplished by using multiple symbol systems, and the way ELs used non-English language (NEL) symbol systems to support their spoken English. The participants were college-aged ELs beginning their studies at the English Learning Center at an American university. The students all had fluency with basic conversational English, and had many different levels of mathematical experience. I identified five categories of purposes in which ELs engaged during mathematical Discourse. I also developed the Replace Augment Learn (RAL) framework that describes how ELs used NEL symbol systems to make up for their decreased English literacy and facilitate their participation in mathematical Discourse. Analysis of the data suggests ELs' use of NEL symbol systems (1) played a significant role in achieving many of the purposes associated with mathematical Discourse, and (2) opened up a space for effective language acquisition. These findings indicate that authentic mathematical activity can be a productive site for language development, and that ELs with basic conversational English and literacy with a variety of symbol systems can participate meaningfully in mathematical Discourse.

Task-based instruction has been a promising method of instruction advocated by mathematics education researchers over the past twenty years. However traditional curricula constitute a majority of the curricula utilized in the United States. The purpose of this study is to identify the problems reform oriented novice teachers face when utilizing a traditional curriculum to plan task-based lessons. In order to identify these problems three novice teachers' interactions with curricula were observed and characterized using the frameworks of past researchers. Through analysis of teachers' textbook interaction practices it was found that teachers struggled to plan task-based lessons due to issues encountered finding/constructing mathematical tasks, and due to problems associated with being naturally oriented toward procedures while utilizing a traditional curriculum.