Critical Thinking to Justify an Answer in Mathematics Classrooms

Students\u27 critical thinking in mathematics was a concern for grade 5 through 8 teachers at a Title 1 public school in the northeastern United States because of the students\u27 poor performance on constructed response questions on the state\u27s mathematics exam. In this exam, students were required to justify their answers in writing. When teachers recognize the connection between writing and critical thinking, they can devise strategies to help students develop mathematical literacy. The purpose of this qualitative case study was to explore how 5th through 8th grade mathematics teachers use the GoMath mathematics literacy program to teach the critical thinking skills students need to justify an answer in writing. The conceptual framework of critical thinking theory drove this study examining critical thinking pedagogy in general and special education mathematics classrooms. Qualitative data were collected from pre- and post-observation interviews and classroom observations from 4 purposefully selected mathematics teachers in grades 5 through 8 who taught GoMath. Thematic analysis was used to analyze the data. Teachers reported that oral communication among students before writing justifications and students\u27 critical thinking skills were integral components in solving mathematics problems. Based on the findings, it is recommended that ongoing professional development be adopted to assist teachers in developing strategies for teaching critical thinking skills to help students justify answers in writing when solving mathematics problems. This endeavor may contribute to positive social change by providing teachers with the necessary skills and strategies to enhance students\u27 communication and critical thinking, thus, increasing their academic performance in mathematics

The Phenomenon of Abstract Cognition Among Scholastic Chess Participants: A Case Study

A qualitative investigation was conducted to explore the phenomenon of abstract cognition among a purposive sample of 5 secondary scholastic chess club participants. The case study enabled the researcher to explore the faculties of abstract cognition among students of contrasting skills and abilities in playing chess. The study also allowed for the consideration of potential visual-spatial, logical, academic, social competency and life benefits of chess play. Through analysis of interviews, chess simulations, blindfold chess play, and narration of chess lines and sequences, the investigator was able to extract meaning and code schemata into a holistic understanding of the phenomenon of abstract cognition within the context of Piaget’s Formal Operations Stage. Scholastic chess systematically engages the student in a stimuli-enriched environment in which the participant must exercise optimal cognitive control in processing and anticipating chess lines and sequences, thus facilitating the manifestation and phenomenon of abstract cognition. Abstract cognition as a phenomenon may elicit increased academic, scholarly, and life potential. Participation in scholastic chess may produce both scholarly and critical thinking individuals. Suggestions for future research include continuing qualitative research in the area of abstract cognition among chess players and developing a stronger understanding of cognitive growth in students

Comparative Multiple Case Study into the Teaching of Problem-Solving Competence in Lebanese Middle Schools

This multiple case study investigates how problem-solving competence is integrated into teaching practices in private schools in Lebanon. Its purpose is to compare instructional approaches to problem-solving across three different programs: the American (Common Core State Standards and New Generation Science Standards), French (Socle Commun de Connaissances, de Compétences et de Culture), and Lebanese with a focus on middle school (grades 7, 8, and 9). The project was conducted in nine schools equally distributed among three categories based on the programs they offered: category 1 schools offered the Lebanese program, category 2 the French and Lebanese programs, and category 3 the American and Lebanese programs. Each school was treated as a separate case. Structured observation data were collected using observation logs that focused on lesson objectives and specific cognitive problem-solving processes. The two logs were created based on a document review of the requirements for the three programs. Structured observations were followed by semi-structured interviews that were conducted to explore teachers' beliefs and understandings of problem-solving competence. The comparative analysis of within-category structured observations revealed an instruction ranging from teacher-led practices, particularly in category 1 schools, to more student-centered approaches in categories 2 and 3. The cross-category analysis showed a reliance on cognitive processes primarily promoting exploration, understanding, and demonstrating understanding, with less emphasis on planning and executing, monitoring and reflecting, thus uncovering a weakness in addressing these processes. The findings of the post-observation semi-structured interviews disclosed a range of definitions of problem-solving competence prevalent amongst teachers with clear divergences across the three school categories. This research is unique in that it compares problem-solving teaching approaches across three different programs and explores underlying teachers' beliefs and understandings of problem-solving competence in the Lebanese context. It is hoped that this project will inform curriculum developers about future directions and much-anticipated reforms of the Lebanese program and practitioners about areas that need to be addressed to further improve the teaching of problem-solving competence

Multiliteracies in the Classroom: An Explanatory Sequential Mixed Methods Approach to Teachers\u27 and Students\u27 Perspectives Toward Integration of Technology

An increased number of students graduating from high school lack college and career readiness skills to earn credit in entry-level college courses or begin a career in an entry-level position. Many schools across America have prepared to address students\u27 college and career readiness with the adoption of Common Core State Standards. Twenty-five teachers and 92 students participated in this dissertation study conducted at a high school (grades 10-12) in the southern United States. The purpose of this study was to describe and explain teachers\u27 and students\u27 perspectives toward the integration of technology that enhances multiliteracies in the classroom. An explanatory sequential mixed methods approach was used to guide this study. Data were collected from surveys to describe teachers\u27 and students\u27 beliefs, perceived barriers, and technology skill levels associated with multiliteracies enhanced by technology in the classroom. Descriptive statistics and independent t-tests were used for analysis of the quantitative data. Open thematic coding and axial coding were used for analysis of the qualitative data. Teachers\u27 and students\u27 interviews and classroom observations were used to further explain, clarify, and enhance the data collected from the surveys. Data results indicated that teachers and students strongly support the integration of technology in the classroom. Teachers and students indicated a statistically significant difference in technology skills associated with Social literacy and multimedia. Teachers perceived time as the most significant barrier to integrating technology into the classroom; students viewed the school filter as the most significant barrier. Teachers viewed the role of technology as a tool to support students\u27 cognitive development, to obtain and maintain students\u27 attention, to facilitate administrative tasks, and to facilitate and promote students\u27 college and career readiness. Students viewed the role of technology as a tool to gather information from the Internet and to enhance students\u27 cognitive learning processes

A SEMIOTIC ANALYSIS OF LINGUISTIC AND CONCEPTUAL DEVELOPMENT IN MATHEMATICS FOR ENGLISH LANGUAGE LEARNERS

This study explores how an elementary mathematics teacher supported English language leaners’ (ELLs’) academic language and concept development in the context of current high- stakes school reform. The conceptual frameworks informing this study include Halliday’s theory of systemic functional linguistics (e.g., Halliday & Matthiessen, 2014) and Vygotsky’s sociocultural theory of concept development (Vygotsky, 1986). Specifically, this study analyzes the interplay between academic and everyday language and how this interplay can facilitate the development of what Vygotsky referred to as “real” or complete concepts as students shift from “spontaneous” to more “scientific” understanding of phenomenon (Vygotsky, 1986, p.173). This year-long qualitative study combines case study methods with discourse analysis using SFL tools. Participants included an English-as-Second-Language teacher and her 14 ELL students. At the time of the study these students had varying degrees of English proficiency and were enrolled in a mix-aged classroom in an urban elementary school in Massachusetts. In SFL terms, the findings from this investigation indicate that the teacher used language in a structured way to interweave everyday language connected with familiar or “Given” information with academic language regarding “New” information. In addition, the data suggest that student talk, over time, mirrored the way the teacher used language to “bind” everyday language representing spontaneous concepts with academic language representing mathematical concepts. Moreover, mathematics classroom discourse in this context often related multiple semiotic resources as “Token” to their meanings as “Value.” Drawing Halliday and Matthiessen’ (2014) concept of “decoding” and “encoding” activities associated with Token-Value relationships, students were guided in verbalizing mathematical reasoning that promoted both spontaneous and scientific concept development. In addition, the participant teacher made linguistic choices differently depending on the multisemiotic resources she used during instruction. The findings of this study suggest that teachers’ use of language plays a pivotal role in developing students’ language and mathematical conceptual knowledge simultaneously. Drawing teachers’ attention to the role discourse plays in classroom interactions and students’ disciplinary literacy development is especially consequential given the discourses of high-stakes testing, standardization, and accountability systems in K-12 schools in the United States

Fifth Grade Teachers Use of Cooperative Learning in Science

This study aimed to explore Cooperative Learning theories and practice by examining the relationships among three aspects: Experience, Practice and Perceptions. The data were from interview records from eight science teachers. As a student-centered active pedagogical trend, cooperative learning has become part of one of the most effective and efficient educational trends that has illuminated constructivist science classrooms in South Texas. This method is conducive in the field of education. Students, in general, are encouraged to cooperatively get involved and to collaboratively participate in problem solving, discussions, and/or productions in group sessions to build a sense of community with the teacher’s facilitation to incorporate cooperative learning strategies. This qualitative case study will examine scholarly frameworks of the Cooperative Learning Model for Academic Achievement and the link between 5th grade Science teachers’ instructional expertise. Therefore, cooperative learning is significant enough that it can develop and/or sustain a constructive learning environment conducive for all learners alike. Cooperative learning is a constructive pedagogical trend that can be effectively applied to elementary science

The Effects of Digital Game-Based Learning on Algebraic Procedural and Conceptual Understanding and Motivation Towards Mathematics

This study examined the impact of digital game-based learning (DGBL) on procedural and conceptual understanding of algebraic expressions and equations and the motivation of students towards classroom mathematics. The mixed-methods sequential explanatory design was used in this study to collect data to determine the effectiveness of DGBL in a 7th grade STEM class. Following a pre-test and pre-motivation survey, students were assigned to either the DGBL group or the non-gaming computer applications as supplemental to mathematics instruction. In order to address both procedural targets and conceptual targets students would be using the technology interventions in addition to traditional math instruction as part of their daily math class, and a problem-based unit taught as part of their STEM class. Following the treatment, a post-test, post-motivation survey, and a conceptual assessment were administered, as well as a digital questionnaire. No significant differences were detected between their understanding of procedural or conceptual problems, nor was there a significant impact to their motivation towards mathematics based on the quantitative data gathered. Students displayed an enthusiastic response to the DGBL environment based on their transcripts from the follow-up questionnaire. The results of the study imply that there is a need for further development of DGBL systems and scaffolded supports to assist students in making connections from the digital environment to classroom mathematics. It further indicates that enjoyment of the DGBL environment does not necessarily transfer to motivation to learn the subject matter in the non-digital environment

Preservice Teachers’ Perceived Preparedness to Integrate Technology Into Teaching of Mathematics: A Mixed Method Study

This study explored preservice teachers’ (PTs’) perceptions of their preparedness to effectively integrate technology into mathematics teaching and the pedagogical strategies that contributed to developing their competencies in this regard. Their perceived preparedness was examined in terms of their knowledge within the TPACK domains and self-efficacy beliefs. Using a concurrent mixed method design, data were collected from 59 PTs in their last semester of study at a Canadian university. Quantitative data were collected through an online survey via three widely used instruments, namely: the TPACK survey, the Computer Technology Integration Survey (CTIS), and the Synthesis of Qualitative Evidence (SQD) Scale. Qualitative data obtained from three open-ended survey questions and follow-up interviews with six participants provided broader insights about PTs’ experiences and activities regarding technology integration into mathematics teaching. The results of descriptive statistics and thematic analysis indicated that PTs perceived their knowledge and self-efficacy beliefs related to integrating technology into mathematics teaching at a moderate to a high level. Correlation analysis also indicated positive relationships between the seven subscales of the TPACK domains and the confidence scale. Participants shared that while their respective programs’ ICT for Teaching and Learning course played an important role in developing their knowledge in the TK and TPK domains, activities such as coding processes, math games, dynamic mathematics software, and graphic calculators were effective tools that encouraged them to use technology in their teaching of mathematics (TPCK). Experiential learning, including practicum experiences, role modeling strategy, and collaboration with peers were identified by participants as effective pedagogical strategies that developed their preparedness to integrate technology into their teaching of mathematics. Some recommendations of this study for teacher education programs include providing math-specific technology courses; incorporating appropriate instructional design that connects the content course to curriculum to promote PTs’ active engagement in meaningful technology-rich learning activities; and using all six pedagogical strategies presented in the SQD model to prepare future teachers to effectively use technology in mathematics teaching

An Urban Education Study: Implementing Problem-Solving Strategies in Mathematics as a Function of Teacher\u27s Learning Styles

This qualitative research was designed to ascertain the impact of teachers\u27 learning styles on an active teaching program. Using grounded theory procedures, the researcher explored the second-year implementation of Moretti and associates\u27 Problem Solver Program by 67 second- through fifth-grade teachers in order to gain information on the major research question: How effective are teachers with different learning styles in implementing problem-solving strategies in mathematics that require an active teaching style? Three Concerns Based Adoption Model (CBAM) instruments were used in this study. Two quantitative instruments were used: The Stages of Concern (CBAM) to determine the degree of program implementation and the Gregorc Style Delineator to determine the teachers\u27 learning styles. Other instruments used to gather information during the interviews and observations were the Innovation Configurations Checklist (CBAM), the Levels of Use (CBAM), and the Classroom Observation Checklist. The data showed that the ordering dimensions of the teachers\u27 learning styles divided them into three distinct groups: sequential, random, and mixed. Data analysis revealed that the random-ordering group implemented The Problem Solver Program more effectively than did the sequential or mixed-ordering groups of teachers. These findings indicate a clear association between a teacher\u27s learning style and the degree of success with which the Problem Solver Program is implemented. The most significant implication from this study is that active teaching and learning programs will only become institutionalized to the extent to which the concerns of the teachers are met