Misconceptions in rational numbers, probability, algebra, and geometry.

In this study, the author examined the relationship of probability misconceptions to algebra, geometry, and rational number misconceptions and investigated the potential of probability instruction as an intervention to address misconceptions in all 4 content areas. Through a review of literature, 5 fundamental concepts were identified that, if misunderstood, create persistent difficulties across content areas: rational number meaning, additive/multiplicative structures, absolute/relative comparison, variable meaning, and spatial reasoning misconceptions. Probability instruction naturally provides concrete, authentic experiences that engage students with abstract mathematical concepts, establish relationships between mathematical topics, and connect inter-related problem solving strategies. The intervention consisted of five probability lessons about counting principles, randomness, independent and dependent event probability, and probability distributions. The unit lasted approximately two weeks. This study used mixed methodology to analyze data from a randomly assigned sample of students from an untreated control group design with a switching replication. Document analysis was used to examine patterns in student responses to items on the mathematics knowledge test. Multiple imputation was used to account for missing data. Structural equation modeling was used to examine the causal structure of content area misconceptions. Item response theory was used to compute item difficulty, item discrimination, and item guessing coefficients. Generalized hierarchical linear modeling was used to explore the impact of item, student, and classroom characteristics on incorrect responses due to misconceptions. These analyses resulted in 7 key findings. (1) Content area is not the most effective way to classify mathematics misconceptions; instead, five underlying misconceptions affect all four content areas. (2) Mathematics misconception errors often appear as procedural errors. (3) A classroom environment that fosters enjoyment of mathematics and value of mathematics are associated with reduced misconception errors. (4) Higher mathematics self confidence and motivation to learn mathematics is associated with reduced misconception errors. (5) Probability misconceptions do not have a causal effect on rational numbers, algebra, or geometry misconceptions. (6) Rational number misconceptions do not have a causal effect on probability, algebra, or geometry misconceptions. (7) Probability instruction may not affect misconceptions directly, but it may help students develop skills needed to bypass misconceptions when solving difficult problems

The Quality of Mathematics Education Technology Literature

Background: The present study evaluated the quality of 1,165 scholarly literature papers about mathematics education technology literature.Purpose: The purpose of the present study was to determine the extent to which mathematics education technology literature reports the information needed to support the scientific basis of a study.Setting: N/AIntervention: N/AResearch Design: A systematic review was used to organize the data collection and analysis processes Data Collection and Analysis: A literature search was conducted to identify scholarly papers that addressed the use of technology in mathematics education. A coding process was developed to record descriptive information about each paper. The Quality Framework developed for this process provided a structure to identify key information across research types based on types of analyses conducted, assigning a certain number of possible points based on the type of research conducted.Findings: Dissertations accounted for a surprisingly high portion of the literature and research: 39.7% of the available literature and 57.0% of the research studies. The overall quality of the mathematics education technology literature was lower than we expected, averaging only 48.9% of the points possible. We noted that the quality of research papers, with respect to possible point values averaged 54.6% over four decades. For mathematics education technology researchers, manuscript reviewers, and editors, these results suggest that more attention is needed on the information being included and excluded from scholarly papers, especially with regard to connections to theoretical frameworks and research designs

Research in Mathematics Educational Technology: Current Trends and Future Demands

This systematic review of mathematics educational technology literature identified 1356 manuscripts addressing the integration of educational technology into mathematics instruction. The manuscripts were analyzed using three frameworks (Research Design, Teacher Knowledge, and TPACK) and three supplementary lenses (Data Sources, Outcomes, and NCTM Principles) to produce a database to support future research syntheses and meta-analyses. Preliminary analyses of student and teacher outcomes (e.g., knowledge, cognition, affect, and performance) suggest that the effects of incorporating graphing calculator and dynamic geometry technologies have been abundantly studied; however, the usefulness of the results was often limited by missing information regarding measures of validity, reliability, and/or trustworthiness

A Survey of Mathematics Education Technology Dissertation Scope and Quality: 1968–2009

We examined 480 dissertations on the use of technology in mathematics education and developed a Quality Framework (QF) that provided structure to consistently define and measure quality. Dissertation studies earned an average of 64.4% of the possible quality points across all methodology types compared to studies in journals that averaged 47.2%. Doctoral students as well as their mentors can play a pivotal role in increasing the quality of research in this area by attending to the QF categories as they plan, design, implement, and complete their dissertation studies. These results imply that the mathematics education research community should demand greater clarity in its published papers through the preparation of their own manuscripts and how they review the works of others.Keywords: Dissertations, Mathematics Education, Technology, Quality Framework, Research Qualit

Teaching Mathematics with Technology: TPACK and Effective Teaching Practices

This paper examines how 17 secondary mathematics teacher candidates (TCs) in four university teacher preparation programs implemented technology in their classrooms to teach for conceptual understanding in online, hybrid, and face to face classes during COVID-19. Using the Professional Development: Research, Implementation, and Evaluation (PrimeD) framework, TCs, classroom mentor teachers, field experience supervisors, and university faculty formed a Networked Improvement Community (NIC) to discuss a commonly agreed upon problem of practice and a change idea to implement in the classroom. Through Plan-Do-Study-Act cycles, participants documented their improvement efforts and refinements to the change idea and then reported back to the NIC at the subsequent monthly meeting. The Technology Pedagogical Content Knowledge framework (TPACK) and the TPACK levels rubric were used to examine how teacher candidates implemented technology for Mathematics conceptual understanding. The Mathematics Classroom Observation Protocol for Practices (MCOP2) was used to further examine how effective mathematics teaching practices (e.g., student engagement) were implemented by TCs. MCOP2 results indicated that TCs increased their use of effective mathematics teaching practices. However, growth in TPACK was not significant. A relationship between TPACK and MCOP2 was not evident, indicating a potential need for explicit focus on using technology for mathematics conceptual understanding

A longitudinal study of school connectedness and academic outcomes across sixth grade

The current longitudinal study examines the extent to which school connectedness (i.e., students\u27 perceptions of school support and the number of adults with whom they have a positive relationship) is associated with academic outcomes across sixth grade for students from high poverty neighborhoods. Data were collected from 330 sixth-grade students attending two middle schools in a large public school district. Specifically, students completed a survey to assess their perceived connection to the school environment, and academic information regarding students\u27 grades, attendance, and discipline referrals was obtained from school records. Results fromlatent growth curve modeling showed that, on average, students\u27 perceptions of school support declined significantly across the sixth-grade year. However, students who reported less decline, or growth, in school support across sixth grade had higher academic achievement at the end of the year than students who reported more decline in school support. Sixth-grade boys were at a greater risk for negative outcomes (i.e., lower school support, lower GPAs, and more discipline referrals) across the school year than girls. Results point to the importance of perceived connectedness to school in helping economically disadvantaged students experience a safe and successful transition to middle school

Changes in School Connectedness and Deviant Peer Affiliation among Sixth-Grade Students from High-Poverty Neighborhoods

This longitudinal study examined associations between changes in School Connectedness and changes in Affiliation With Deviant Peers among students from high-poverty backgrounds during the year immediately following the transition to middle school. Sixth-graders (N = 328) attending two middle schools in a large school district completed measures of School Connectedness and Affiliation With Deviant Peers at three points across the year. Results from parallel process modeling showed that students’ reports of School Support significantly declined across the school year, School Support and Affiliation With Deviant Peers were negatively associated at the beginning of the school year, and students who reported more declines in School Support were more likely to report growth in Affiliation With Deviant Peers across sixth grade. Gender differences were also found. Findings suggest that School Connectedness may be important for high-poverty students following the transition to middle school

Building Mathematics Learning through Inquiry Using Student-Generated Data: Lessons Learned from Plan-Do-Study-Act Cycles

This paper describes how plan-do-study-act cycles engaged a classroom mentor teacher and student teacher in a professional collaboration that resulted in two inquiry activities for high-school geometry classes. The PDSA cycles were carried out in four high school geometry classes, each with 30 to 35 students, in a mid-Atlantic urban school district in the U.S. The four geometry classes were co-taught by the second and third authors of this paper. The data consisted of classroom documents (e.g., activity prompts, tasks), classroom observations, student feedback about activities, and monthly PDSA reports. The PDSA cycles had a direct effect on the professional learning of the teachers. The resultant classroom activities used a data collection approach to engaging students in inquiry to learn about trigonometry functions and density. Student learning behaviors were noticeably improved during these activities compared with traditional mathematics instruction. We concluded that the data collection sequence provided an accessible entry point for students to begin scientific inquiry in mathematics. The process opened the conceptual space for students to develop curiosity about mathematical phenomena and to explore their own research questions. The use of culturally relevant topics was especially compelling to students, and the open-ended nature of these exploratory activities allowed students to see mathematics through their own cultural lenses

The Quality of Mathematics Education Technology Literature

Background: The present study evaluated the quality of 1,165 scholarly literature papers about mathematics education technology literature.Purpose: The purpose of the present study was to determine the extent to which mathematics education technology literature reports the information needed to support the scientific basis of a study.Setting: N/AIntervention: N/AResearch Design: A systematic review was used to organize the data collection and analysis processes Data Collection and Analysis: A literature search was conducted to identify scholarly papers that addressed the use of technology in mathematics education. A coding process was developed to record descriptive information about each paper. The Quality Framework developed for this process provided a structure to identify key information across research types based on types of analyses conducted, assigning a certain number of possible points based on the type of research conducted.Findings: Dissertations accounted for a surprisingly high portion of the literature and research: 39.7% of the available literature and 57.0% of the research studies. The overall quality of the mathematics education technology literature was lower than we expected, averaging only 48.9% of the points possible. We noted that the quality of research papers, with respect to possible point values averaged 54.6% over four decades. For mathematics education technology researchers, manuscript reviewers, and editors, these results suggest that more attention is needed on the information being included and excluded from scholarly papers, especially with regard to connections to theoretical frameworks and research designs

The Critical Role of a Well-Articulated, Coherent Design in Professional Development: an Evaluation of a State-Wide Two-Week Program for Mathematics and Science Teachers

This evaluation study examined a state-wide professional development program composed of two institutes, one for mathematics teachers and one for science teachers, each spanning two weeks. The program was designed to help teachers transform their practice to align with Common Core State Standards for Mathematics and Next Generation Science Standards. Data from this mixed-methods design consisted of observations, interviews, focus groups, institute documents and participant surveys. Participants experienced inquiry-based, content-specific, focused grade-band sessions, yet in some ways results indicated that the experiences fell short of having a potentially transformative effect on classroom teaching. The evaluation used a professional development framework to analyze how a seemingly well-designed program became disconnected from the participants’ classroom teaching experience. Recommendations focus on ways for policy-makers, school leaders and professional development facilitators to use the professional development framework to bridge gaps identified by the evaluation