Many students entering college in the United States need assistance in at least one academic area, causing remedial courses to be commonplace in higher education. This study evaluated the impact of video instruction in learning the content found in an online remedial math course. The instructional videos were created using the guidelines of Universal Design and cognitive load theory. A quantitative, quasi-experimental method was used to evaluate a dataset made available by a regionally accredited private New England college's online division. The online division offers undergraduate and graduate degree programs and certifications, and the students are located all over the world. The dataset started with 203 participants, with 78 completing the first module, 36 completing the second module, and 17 completing the third module. Paired t tests revealed that while both text and video instruction improved the scores between the pre- and posttests, there was no statistically significant difference between those two groups. However, the end sample size was small, with many students not completing all three modules. This limited the interpretation to the results of the pre- and posttest scores of the first module only. These findings inform faculty teaching remedial online math courses, as well as course designers, seeking to improve these courses and increase the success rate for students passing the course. This has implications for social change because student success in these remedial math courses may in turn increase persistence, retention and graduation.

In the city selected for this study, only 29% of inner-city students scored proficiently on standardized tests, whereas 71% of their peers at nearby suburban and affluent schools achieved the proficiency level. To address the gap, the local district implemented ability grouping in one charter school. The purpose of this ex post facto quasi-experimental study was to examine the effect of ability grouping among inner-city students in mathematics as an instructional intervention for improving student achievement. Ability grouping theory as an instructional strategy was used as the theoretical framework for this study. The criterion measure of mathematics improvement was provided by the test results from the Northwest Evaluation Association's Measure of Academic Progress (NWEA-MAP), a computer-adaptive assessment of mathematics. Using population data for 2012-2014 inner-city 8th graders who took the pretest and posttest NWEA-MAP (N = 234), two 1-way analyses of variances were used to test for mean differences in the NWEA-MAP improvement scores between ability-grouped (n = 115) and non-ability-grouped (n = 115) students, then specifically between students who were grouped as high ability (n = 55) and low ability (n = 55). The ability-grouped students had significantly higher improvement scores than did the nongrouped students. For those students who were ability grouped, no statistically significant difference existed in improvement between the high and low ability groups. A position paper was developed recommending student grouping to improve academic performance of inner-city school students. Positive social change will occur as the achievement gap is closed for students who attend inner-city schools.

Algebra test scores of the Maldivian students from grade 6 through 12 are the lowest compared to any other area of mathematics. Algebra is a fundamental topic in mathematics and lays the foundation for mathematical reasoning and complex problem-solving. Research shows that strengthening algebra instruction could improve student achievement. This concurrent mixed methods study examined the algebraic content and pedagogical knowledge of 5 sixth grade mathematics teachers who teach in 5 different schools across the Maldives. Shulman's major categories of teacher knowledge and Ball, Thames, and Phelps' domains of mathematical knowledge for teaching guided this study. The research questions examined the relationship between teachers' perceptions of their mastery of algebraic content and pedagogical knowledge, and what teachers actually know about algebraic content and pedagogy. Purposive sampling was used to select the 5 participants. Quantitative data were collected using the Diagnostic Teacher Assessments of Mathematics and Science - Middle Mathematics Teacher Assessments and qualitative data were gathered through lesson observations, interviews, and analysis of teachers' lesson plans and notes. All participants believed that they were proficient in both algebraic content and pedagogical knowledge. However, the results of this study showed that all participants lacked both algebraic content and pedagogical knowledge. Findings of this study were used to inform and design mathematics professional development to meet the needs of the participants. This mathematics professional development is expected to improve the instructional delivery of algebra through enhanced algebraic content and pedagogical knowledge. This could positively contribute to the improvement of student achievement in algebra.

The sustainability of improved pedagogy gained through professional development (PD) of mathematics teachers has undergone little empirical study. In a midsized urban school district in the Northeastern United States, all high school mathematics teachers attended a 3-year mandatory PD program. Although an external evaluator studied this program immediately after completion, there had been no longitudinal study of the perceptions of its participants regarding the sustained benefits of the program. This qualitative study offered a follow-up study of the participants in the Math and Science Partnership (MSP) PD program to provide insight to administrators regarding the sustainability of benefits gained through the MSP program. The conceptual framework for the study consisted of Desimone's model for evaluating PD and Kleining's framework of systematic exploration and inquiry. The participants (N =7) were asked about their perceptions of the value, applicability, longevity, and efficacy of their MSP PD and their suggestions to improve the program. Data were organized and analyzed using Patton's semistructured systematic framework to reveal general consensus as well as anecdotal evidence. The perceptions of the mathematics teachers provided pertinent information that administrators could use to determine the format of future PD. Teachers participating in this study indicated that having a college professor present a combination of content knowledge and pedagogy skills made the MSP program highly effective and long-lasting. Using this feedback, district leaders could institute improved PD, giving their teachers the skill and knowledge to lift their students academically. Closing the mathematics achievement gap may open employment and college opportunities to students which allow them to escape poverty and lead more successful lives.

Although educators have embraced technology in mathematics inclusion classrooms, students with math learning disabilities (MLD) still have anxiety and negative attitudes about mathematics and score lower than their counterparts. The purpose of this qualitative single case study was to investigate and describe the experiences of middle school 8th grade inclusion iPad math app users. The technological pedagogical content knowledge model, the universal design for learning model, and the experiential learning theory provided the conceptual framework of technology integration. The research questions addressed the experiences of middle school inclusion teachers and students with MLD regarding iPad use in a Common Core standards-based math curriculum. Two inclusion co-teachers and 8 special education students from 2 inclusion classes in a middle school participated in the study. Data were collected from direct lesson observations, document analysis, and individual teacher and student interviews. An interpretative approach of clustering codes and categories was employed to identify emerging themes. Findings indicated that iPads increased student engagement and student access to the Common Core math curriculum. Teachers and students using iPads faced some challenges including lack of knowledge of using text-to-speech and keeping up with relevant new apps. Educators may use findings to understand how technology integration can provide equal access to the Common Core standards-based math curriculum for students with MLD and can reduce learning barriers for all students

The purpose of this study was to characterize ways in which teaching practice in classroom undergoing first semester implementation of an argument-based inquiry approach changes in whole-class discussion. Being that argument is explicitly called for in the Next Generation Science Standards and is currently a rare practice in teaching, many teachers will have to transform their teaching practice for inclusion of this feature. Most studies on Argument-Based Inquiry (ABI) agree that development of argument does not come easily and is only acquired through practice. Few studies have examined the ways in which teaching practice changes in relation to the big idea or disciplinary core idea (NGSS), the development of dialogue, and/or the development of argument during first semester implementation of an argument-based inquiry approach. To explore these areas, this study posed three primary research questions: (1) How does a teacher in his first semester of Science Writing Heuristic professional development make use of the "big idea"?, (1a) Is the indicated big idea consistent with NGSS core concepts?, (2) How did the dialogue in whole-class discussion change during the first semester of argument-based inquiry professional development?, (3) How did the argument in whole-class discussion change during the first semester of argument-based inquiry professional development? This semester-long study that took place in a middle school in a rural Midwestern city was grounded in interactive constructivism, and utilized a qualitative design to identify the ways in which the teacher utilized big ideas and how dialogue and argumentative dialogue developed over time. The purposefully selected teacher in this study provided a unique situation where he was in his first semester of professional development using the Science Writing Heuristic Approach to argument-based inquiry with 19 students who had two prior years' experience in ABI. Multiple sources of data were collected, including classroom video with transcripts, teacher interview, researcher field notes, student journals, teacher lesson plans from previous years, and a student questionnaire. Data analysis used a basic qualitative approach. The results showed (1) only the first time period had a true big idea, while the other two units contained topics, (2) each semester contained a similar use for the given big idea, though its role in the class was reduced after the opening activity, (3) the types of teacher questions shifted toward students explaining their comprehension of ideas and more students were involved in discussing each idea and for more turns of talk than in earlier time periods, (4) understanding science term definitions became more prominent later in the semester, with more stating science terms occurring earlier in the semester, (5) no significant changes were seen to the use of argument or claims and evidence throughout the study. The findings have informed theory and practice about science argumentation, the practice of whole-class dialogue, and the understanding of practice along four aspects: (1) apparent lack of understanding about big ideas and how to utilize them as the central organizing feature of a unit, (2) independent development of dialogue and argument, (3) apparent lack of understanding about the structure of argument and use of basic terminology with argument and big ideas, (4) challenges of ABI implementation. This study provides insight into the importance of prolonged and persistent professional development with ABI in teaching practice.

Research suggests that scientific models and modeling should be topics covered in K-12 classrooms as part of a comprehensive science curriculum. It is especially important when talking about topics in weather and climate, where computer and forecast models are the center of attention. There are several approaches to model based inquiry, but it can be argued, theoretically, that science models can be effectively implemented into any approach to inquiry if they are utilized appropriately. Yet, it remains to be explored how science models are actually implemented in classrooms. This study qualitatively looks at three middle school science teachers' use of science models with various approaches to inquiry during their weather and climate units. Results indicate that the teacher who used the most elements of inquiry used models in a way that aligned best with the theoretical framework than the teachers who used fewer elements of inquiry. The theoretical framework compares an approach to argument-based inquiry to model-based inquiry, which argues that the approaches are essentially identical, so teachers who use inquiry should be able to apply model-based inquiry using the same approach. However, none of the teachers in this study had a complete understanding of the role models play in authentic science inquiry, therefore students were not explicitly exposed to the ideas that models can be used to make predictions about, and are representations of, a natural phenomenon. Rather, models were explicitly used to explain concepts to students or have students explain concepts to the teacher or to each other. Additionally, models were used as a focal point for conversation between students, usually as they were creating, modifying, or using models. Teachers were not observed asking students to evaluate models. Since science models are an important aspect of understanding science, it is important that teachers not only know how to implement models into an inquiry environment, but also understand the characteristics of science models so that they can explicitly teach the concept of modeling to students. This study suggests that better pre-service and in-service teacher education is needed to prepare students to teach about science models effectively.

The purpose of this study was to explore the development of students' understanding through writing while immersed in an environment where there was a strong emphasis on a language-based argument inquiry approach. Additionally, this study explored students' spoken discourse to gain a better understanding of what role(s) talking plays in the development of understanding through writing. Finally, the study proposed a new concept of Discourse Space, which enabled researchers to improve their understanding of the characteristics of the development of student cognition through writing, and of the roles talking plays in cognitive development through writing. This study was guided by the research question: What patterns of the development of fifth grade students' cognition over time emerge in their private and public negotiations under a teacher who is ranked as a low-level implementer of the SWH approach? This question was divided into two sub-questions: (a) Throughout a unit, Ecosystems, what patterns emerge regarding the development of six fifth grade students' understanding through writing, and b) What patterns of the development of Discourse Space emerge through talking in three different contexts. In order to answer these questions, this qualitative research employed a generic qualitative study. Twenty-one fifth grade students participated in this study, and six students were purposefully selected through which to further investigate the development of an understanding of science through private negotiation while immersed in a language-based argument inquiry approach. Major data sources included students' writing samples, informal conversations with the teacher, researcher's field notes, and classroom videos. Additionally, the teacher's modified RTOP scores and semi-structured interviews were used to deepen the contextual understanding of the learning environment and the teacher's instructional performance. The data analysis was conducted by utilizing discourse analysis of writing and talking. The results showed (1) students' low level of engagement in evaluation impacted their reasoning and use of sources for making meanings, as well as their understanding of the topic. Compared to the results of a previous study, students' complexity of reasoning was relatively less developed, and similarly students' use of reflective sources was generally observed relatively less often. (2) The teacher and students in this study engaged in limited public negotiation, which focused more on articulating than on evaluating ideas. The limited public negotiation that was represented by the dialogical patterns in this study cannot support the development of understanding through writing or the practice of the roles of constructor and critiquer, which play a core function in the comprehension of scientific practice. This study has several implications for teacher education and research. Teacher education needs to be centered more on how to encourage students' engagement in the process of evaluation, since this plays an important function not only in the development of understanding, but also in providing opportunities to perform the roles of both constructor and critiquer. Teachers can use writing as an argumentative activity to encourage or foster students' engagement in the process of evaluation or critique. Additionally, this study provides insight into the importance of the learning environment in which the teacher and students create and develop; this learning environment needs to provide not only opportunities but also demands for students to engage in both constructing and critiquing ideas.

Research indicates that many elementary students do not comprehend that the equal sign is an indication that an equality relation exists between two structures. Instead, they perceive the equal sign as an indication that a particular procedure is to be performed. As students mature, and as their exposure to the equal sign and equality relations in multiple contexts increases, most obtain the ability to interpret the equal sign as an indicator of an equivalence relation. Incorrect usages of the equal sign, however, by post-algebra students indicate a tendency for students to regress back to a comprehension of the equal sign as an operator symbol or to ignore the equal sign altogether. The purpose of this project was to develop an instrument that is relevant to objectives associated with the interpretation of the equals relation, and to perform a test reliability analysis to assess measurement reliability and construct validity for the instrument. The model that was utilized to develop items for the instrument followed a general item development and validity assessment model proposed by Cangelosi. This model requires an iterative process that includes a peer review of objectives and instrument items by a panel of experts and a revision of the items based upon recommendations from the panel. A pilot test was synthesized from the revised items and administered to a group of subjects, and an instrument reliability analysis and an item efficiency analysis were performed. The quantitative and qualitative data obtained from this process were used to create the 18-item instrument entitled, Wheeler Test for Comprehension of Equals. The researcher recommends further validity assessments for the instrument across multiple settings and subject groups.

An educational researcher sought to collaborate with a classroom instructor to introduce problem-based learning as a new teaching intervention. First, a classroom instructor was approached to consider how a problem-based learning instructional approach might fit with their existing curriculum plan. The researcher and the classroom teacher used a discussion framework to decide together how to best design a professional learning course meant to prepare the teacher to use the new techniques in their classroom. The teacher took the professional learning course and subsequently designed his own problem-based learning course. That course was then delivered to undergraduate students in a college senior thermo-fluids lab course. Quantitative and qualitative data describe how students recognized the connection between the lab course and their perceptions of a future career as engineers. Preliminary findings suggest the researcher and teacher professional learning codesign process contributed positively to the classroom teachers developing and delivering their own PBL course that was perceived by students to contribute positively to their content knowledge, motivation and perception of their future career as engineers.