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Many mathematics majors take a real analysis course, yet their experiences vary greatly. This article describes how one mathematics department is trying to improve its undergraduate real analysis course by listening to the experiences of underrepresented minority students. From student interviews, three main themes emerged: (1) real analysis feels discontinuous from every other course, (2) real analysis is a gatekeeping or gateway experience for math majors, and (3) students’ responsibilities outside of class influence how they engage in real analysis. We share lessons learned from students to help instructors and departments work toward equitable outcomes in pathways for mathematics majors.
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Mathematics is strongly connected to gambling through the mathematical models underlying any game of chance. Mathematics is reflected not only in games’ design/characteristics and their outcomes, but also in gamblers’ perception and knowledge of the mathematics-related facts of gambling – which influence their gambling behavior. The math-indispensability principle (Bărboianu, 2013) applies not only in problem-gambling research, but also in the gambling industry. The structural, informative, strategic, psychological, pathological, and ethical aspects of gambling have been identified to be grounded in the mathematics of games and gambling (Griffiths, 1993; Bărboianu 2014, 2015; Turner & Hobay, 2004; Harrigan, 2009, and others).In this theoretical framework, research is able to derive concrete norms and criteria to adequately reflect the mathematical dimension of gambling in the communication and texts associated with the gambling industry. These norms and criteria of adequacy will be further communicated to policy and decision makers in both governmental and private sectors, with the recommendation for implementation. Our study aims to evaluate qualitatively the reflection of the mathematical dimension of gambling in the content of gambling websites. This analysis is necessary in order to have an objective and concrete image of the actual state of this matter in the online industry and of the challenges that such research and application would face in the real world of gambling. A minimum number of 600 gambling websites will be reviewed annually for their content in that respect. A statistical analysis will record the presence of the mathematical dimension of gambling and its forms in the content of participating websites, and a qualitative research will analyze and assess the quality of the content with respect to that dimension.
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This dataset was collected through a survey conducted in 2021 and includes responses from 349 students (boys and girls) attending lower secondary schools in Norway. The primary objective of the data collection was to investigate how task difficulty labels influence students’ self-efficacy and performance in mathematics, with particular attention to gender differences. Variables included in the dataset: (1) Gender, (2) Self-efficacy related to three mathematics tasks, measured both before and after the tasks were presented with difficulty labels, (3) Performance on the same three mathematics tasks, (4) Task difficulty labels assigned to each task (experimental variable: easy, medium, or difficult). This dataset enables analysis of how labelling mathematics tasks as “easy”, “medium”, or “difficult” affects students’ self-efficacy and performance, and how these effects may differ across genders.
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The understanding of fractions can be challenging for primary school students. Music, like mathematics requires an understanding of subdivisions of numbers and proportional reasoning. Musical experience has been shown to enhance cognitive skills and most children like music (in contrast to maths). Yet, experimental work that has integrated the teaching of mathematical and musical concepts is scarce. In this study, we tested the feasibility of PlayMyMath in UK schools, an innovative EdTech approach that combines the teaching of fractions with the building of musical rhythms. We employed a mixed-methods approach: a qualitative strand explored implementation of PlayMyMath with teaching staff and a quasi-experimental pretest/post-test design study examined whether PlayMyMath can improve fraction skills in Year 4 students in the UK. We envisage this study as a precursor to further pilot and efficacy studies that will allow us to test the intended outcomes in a larger population.Uploaded here is the quantitative data derived from this project in an excel format.
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Dataset used in a meta-analysis examining the effects of educational technology on mathematics outcomes. Includes effects from 40 studies with codes for study and methodological features.
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Project Overview This research explores the complexity of secondary school mathematics through the perspectives of experienced in-service teachers and the framework of cognitive load theory. The research identifies sources of complexity in learning mathematics and compares them with the definitions of complexity within cognitive load theory. Semi-structured interviews with eleven secondary school mathematics teachers were conducted reaching empirical-driven saturation. The analysis of these interviews highlighted complexity sources related to the inherent intricacy of mathematics (knowledge complexity) and to the form in which tasks and instruction is presented and designed (task complexity). The findings offer insights into the nature of the difficulties students encounter while learning mathematics and thus provide an approximation to the sources of complexity that should be considered when assessing secondary school mathematics. The conclusions provide a bridge between academics and daily teaching, enhancing the applicability of cognitive load theory. Data and Data Collection Overview Participants and Recruitment Participants (N = 11) were experienced secondary school mathematics teachers from three different schools in Catalonia. All participants had at least five years of teaching experience in mathematics and taught across grades 7 to 12. Recruitment followed a convenience-sequential sampling strategy: initial participants were identified through professional teaching networks and institutional contacts within secondary schools in the Barcelona metropolitan area, and subsequent participants were added iteratively until data saturation was achieved. Teachers were selected based on accessibility and willingness to participate, and the sample was monitored continuously to determine when no new conceptual insights emerged in interview analysis. All participants provided written informed consent and retained the right to withdraw at any time without justification. Data Collection Procedure Interviews were face-to-face, conducted in Catalan or Spanish according to participants’ preference, and audio-recorded with consent. Each session lasted between 20 and 50 minutes. The interview protocol was semi-structured and designed to explore: The perceived sources of complexity that students experience in mathematics learning. Teachers’ comparisons of different mathematical topics and problems in terms of difficulty and cognitive demand. The factors contributing to task and knowledge complexity in classroom instruction.. To guide discussion, teachers analysed a learning sequence on fraction operations drawn from a Catalan Year-7 mathematics textbook aligned with the national curriculum. The interview included both conceptual questions about mathematics content (e.g., “Which topics do students find most complex?”) and applied tasks (e.g., “What aspects of this problem increase its complexity for students?”). All interviews were transcribed verbatim following O’Connell and Kowal’s (1999) standards for qualitative transcription. Selection and Organization of Shared Data The data files shared here consist of 11 interview transcripts. The documentation files shared comprise the interview guide, the consent form used in the study, this Data Narrative, and an administrative README file.
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We report on three approaches taken to incorporate collaborative activities into undergraduate mathematics classes. There is strong evidence from research in K-12 classrooms that these, and similar, approaches support a range of positive learning outcomes for students. Despite the potential benefits the cited studies have shown, research into the use of such methods at the tertiary level is limited. We describe the ways in which we have implemented research projects, collaborative tutorials, and team-based learning in a range of undergraduate mathematics classes in two countries. We present quantitative and qualitative evidence from these teaching experiences to support our claim that there is a definite mandate for significant opportunities within our courses for students to work cooperatively, talk together, and argue about mathematics.
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Abstract In this paper, we make an analysis of inequality handling, including both: the Chilean curriculum, through its plans and programs, and school texts. It has been decided to work on an exploratory research that follows a methodology of qualitative analysis, where the mathematical object will be equated with a complexity scheme of its own, allowing a visual analysis of what happens in Chile. Within the findings, we reveal some differences in the teaching progression for mathematical object under study, that is to say, the treatment given to the object in different courses would not cover it in its entirety. The missing contents could be addressed in classroom planning for every teacher with the aim of improving learning processes. Moreover, it is important to mention that the study process explained in this research can be also applied in the analysis of other mathematical objects.
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This dataset was collected as part of a study exploring high school mathematics teachers’ perceptions and use of artificial intelligence, with a particular focus on the perceived usefulness and perceived ease of use of artificial intelligence (AI) in teaching. ChatGPT was used as the artificial intelligence technology used in this study. The study employed a sequential explanatory mixed-methods design, guided by the Technology Acceptance Model 3 as a theoretical framework. Quantitative data were gathered through an online survey, in which structured Technology Acceptance Model 3 questionnaires were adapted and administered to examine participants' perceived usefulness and perceived ease of use of artificial intelligence, as well as the determinants. The quantitative data were analysed using the Statistical Package for the Social Sciences version 26. Descriptive statistics was used to interpret the data.Qualitative data were obtained through classroom observations and semi-structured interviews. Observations focused on how participants use artificial intelligence in their teaching, while the interviews provided deeper insights into their experiences and perspectives. All observations and interviews were recorded and subsequently transcribed for the dissertation. In order to open this data, Microsoft Excel, an MP4 video player, an audio player, and a portable document format reader will be needed.
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The graph shows the changes in the impact factor of ^ and its corresponding percentile for the sake of comparison with the entire literature. Impact Factor is the most common scientometric index, which is defined by the number of citations of papers in two preceding years divided by the number of papers published in those years.
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TwitterThis study examines the effect of the use of two Open Educational Resources (OER) (a Khan Academy online tutorial and an open textbook hosted on Wikibooks) on logical-mathematical outcomes for first and second-year students in higher education institutions in Chile. It also investigates perceptions of instructors and students about the use of OER, in order to understand how these resources are used and valued. Quantitative and qualitative methods were used to collect student performance data via a student survey, student focus groups, interviews with instructors, and sourcing institutional records.
Only the institutional records, focus group data and interview data are included in the final dataset. Student survey data is not made available for confidentiality reasons. Findings indicate that students in a contact-study mathematics course who used a Khan Academy online mathematics tutorial obtained better examination results than students who did not use any additional resources, or those who used the open textbook. Moreover, it was also found that instructors and students have positive perceptions about the use of Khan Academy and Wikibooks materials.This study is Sub-project 9 of the Research on Open Educational Resources for Development (ROER4D) project, hosted by the Centre for Innovation in Learning and Teaching (CILT) at the University of Cape Town, South Africa, and Wawasan Open University, Malaysia.
The interviews and survey data were conducted at one institution in Chile and are not representative of the country as a whole.
Individuals
The survey covered students and instructors in the single institution involved in the study.
Focus group and survey data
Face-to-face and internet [f2f-int]
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The Chicago School Staff Social Network Questionnaire Qualitative Interviews, 2006, is a part of the RETA: Distributed Leadership for Middle School Mathematics Education: Content Area Leadership Expertise in Practice study. The goal of RETA was to design and validate a series of research instruments to identify leadership for mathematics instruction in middle schools and for documenting instructional leadership practice. Adopting a distributed perspective on leadership, this work focused on both formally designated and informal leaders and their leadership routines. The objective was to develop valid and reliable instruments that make the day-to-day practice of school leadership for mathematics instruction more transparent, as well as measure changes in this practice over time. This project utilized Social Network Surveys, Experience Sampling Methods (ESM), and Daily Practice Logs. To validate these instruments, a combination of shadowing, end of day cognitive interviews, and semi-structured interviews was used. These instruments were used to describe and analyze when and how teachers and other educators solicit or provide instructional advice and the degree to which these resources influence their work.
In order to validate the survey, qualitative interviews were conducted with a subset of teachers at 6 of these 22 schools in early Spring 2006. A purposeful sample of schools was selected to maximize variation so that the sample included two public schools (an elementary and a middle school), two Catholic schools, and two charter schools. The interviewees were selected based on an analysis of the SSSNQ data. Using a purposeful sampling strategy, the following were selected in each school: formal leaders (i.e., Principal, Assistant Principal, Math Specialist, Literacy Specialist), informal leaders (i.e., two teachers who were not formally designated leaders but had more people go to them for math advice relative to other people in their school), and followers (i.e., two to four teachers who were not formal or informal leaders). Interviews with 49 staff members focused mainly on their advice-seeking practices around mathematics instruction. Using a semi-structured protocol, researchers asked interviewees about their advice or knowledge seeking related to mathematics instruction and their views of leadership and change efforts underway at the school.
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TwitterA unified introductory science curriculum that fully incorporates mathematics and quantitative thinking aimed to incorporate biology into the traditional quantitative cultures that have come to define the physical sciences and engineering.
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his project intends to find a correlation between the songs "Moonlight Sonata" and "Because" with the use of discrete mathematics. With music theory, the field of using math to analyze music, lacking exploration, our primary goal was to draw conclusions from what was found: analyze the data collected to better understand the behind the scenes mathematics in music. This was done by translating the sheet music into numbers using modular arithmetic (Mod 12) system; then, the numbers collected were classified into pitch class sets, normal form, and prime form. We also used matrices to test for the property of invariance. After thorough examination, it was clear that the songs were very similar in nature, which fundamentally demonstrates that a mathematical interpretation can be used to prove what is heard.
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AP Browning, JA Sharp, RJ Murphy, G Gunasingh, B Lawson, K Burrage, NK Haass, MJ Simpson. 2021 Quantitative analysis of tumour spheroid structure. eLife http://dx.doi.org/https://doi.org/10.7554/eLife.73020
Data comprises measurements relating to the size and inner structure of spheroids grown from WM793b and WM983b melanoma cells over up to 24 days.
Code, data, and interactive figures are available as a Julia module on GitHub:
Browning AP (2021) Github ID v.0.6.2. Quantitative analysis of tumour spheroid structure. https://github.com/ap-browning/Spheroids
(copy archived here)
Code used to process the experimental images is available on Zenodo:
Browning AP, Murphy RJ (2021) Zenodo Image processing algorithm to identify structure of tumour spheroids with cell cycle labelling. https://doi.org/10.5281/zenodo.5121093
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TwitterHigh quality postgraduate training in science, technology, engineering and mathematics (STEM) related disciplines in sub-Saharan Africa (SSA) is important to strengthen research evidence to advance development and ensure countries achieve the Sustainable Development Goals (SDGs). Equally, participation of women in STEM careers is vital, to ensure that countries develop economies that work for all their citizens. However, women and girls remain underrepresented in STEM due to gender stereotyping, lack of visible role models, and unsupportive policies and work environments. Therefore, there is a need to consolidate information on participation and experiences of women in STEM related postgraduate training and careers in SSA to enhance their contribution to realizing the SDGs. The primary objective of this study is to examine the participation and experiences of women in postgraduate training, and their subsequent recruitment, retention and progression in STEM careers in East Africa. A secondary objective is to establish the gender gaps in training and career engagement in selected STEM related academic disciplines in East Africa. The descriptive study will employ a mixed methods approach, including a scoping review, qualitative interviews, and quantitative analysis of secondary data. We will synthesize results to inform the development of an effective gendered approach and framework to improve participation and experiences of women in STEM training and career engagements in SSA. We will conduct the study over a period of five years.
Regional coverage (East Africa Region)
Individual Women in STEM
Qualitative data: Women in Science Technology Engineering and Mathematics (STEM) in postgraduate training and career Quantitative data: Postgraduate students, faculty, reseachers and supervisors (both men and women) in STEM in Inter-University Council for East Africa (IUCEA) member Universitiies
The study utilized a purposive sampling technique and targeted all universities that offered doctoral programs in applied sciences, technology, engineering, and mathematics. At the time, only 23 of the 74 universities in Kenya—equivalent to 30%—offered doctoral degrees in STEM. It was assumed that a similar or lower percentage would be found in the other five countries, namely Uganda, Tanzania, Rwanda, Burundi, and South Sudan.
Purposive sampling was used to recruit participants from purposively selected universities and national higher education commissions and agencies for the study. In universities, all students enrolled in doctoral programs in STEM were considered. Additionally, female and male students' lecturers, supervisors, mentors, and other faculty members and researchers in the identified institutions were also considered for participation in the study.
Purposive sampling of doctoral students, faculty, and early career researchers (post-doctoral fellows within the first six years since receiving their PhD) was conducted using the following inclusion criteria:
Inclusion criteria i. Worked in a STEM field/discipline ii. Enrolled in a doctoral program within a STEM field iii. Early career researchers in a STEM field in research organizations iv. Faculty in a STEM field at a university
Additionally, registrars, postgraduate training coordinators, heads of departments, and officials from national agencies and ministries related to postgraduate training and research were purposively selected from all the identified universities to provide input on existing policies, guidelines, and enrollment data. For each of the mentioned groups, 7-12 interviews were conducted, totaling 60 interviews.
Qualitative For the Key informant interviews one participant was interviewed from the engineers board despite the scope being Inter-University Council for East Africa (IUCEA) member Universities.
Quantitative The online survey was completed by some researchers not working/teaching in IUCEA member universities
Other [oth]
Quantitative data collection A. Online Survey This was carried out through an online survey questionnaire that was circulated via email and other digital platforms such as WhatsApp. The questionnaire had various parts: Part A - Participants characteristics This section mainly collected demographic details such as age, gender, nationality, residence, marital status, income, highest level of education completed, year of study, supervision and mentoship relationship, field of study in STEM (Science, Technology, Enginnering and Mathematics), mode of funding of postgraduate degree,
Part B - Status of Gender equality This section collected information on students enrollment and graduation in masters and PhD in STEM looking at gender distribution,
Part C - Factors that contribute to participation of women in STEM This section collected information on the factors or situations encountered while pursuing career in STEM in your specific discipline
Part D - Strategies for Optimizing Women's Engagement in STEM This section collected information on the strategies can maximize engagement of women in STEM training PhD level and subsequent careers
Part E - Effect of the COVID-19 pandemic on women's progression In this section collected information on COVID-19 pandemic affect on research progress or deadline for submission of thesis, COVID-19 pandemic affect on current research funding, COVID-19 pandemic caused researchers to work from home, working from affected progress in studies, any direct responsibilities caring for children, number of children being taken care of, change of domestic work responsibilities since the COVID-19 outbreak, change of domestic work responsibilities since the COVID-19 outbreak on studies, COVID-19 pandemic affect on access to these research tools which inlude: Computer or laptop, Reliable Internet, Assistive Technology, Laboratory equipment, University Library, Archives/special collections and Access to patients/research participants. It als collected information on: any benefits to COVID-19 pandemic for your work, some ways one thinks their supervisor or line manager could support or help one manage the impacts of COVID-19 on studies
The questionnaire was developed in English and was latertranslated into French to accommodate the French speaking countries i.e Burundi and Rwanda. The French questionnaire was backtlanslated to English to ensure the questions still maintained their original meaning. This work was done by an external consultant and the French questionnaires were reviewed by the research assistant from Burundi and tested among postgraduate students in Light University.
All questionnares and modules are provided as external resources.
Qualitative The data was collected through qualitative interviews (In-depth interviews) and focus group discussions. They were audio recorded and the recordings were transcribed on Ms Ofiice.The transcript were subjected to data quality checks and the clean transcripts were anonyzed for data protection.
QUANTITATIVE Secondary data The data was collected from the five countries in an Ms Excel designed data abstraction sheet. The data abstraction sheet helped the universities administrators and rergistrars to directly enter the data only in the required field and for the defined or specific variables. For the dataset that was in hardcopy format the data entry was also done using the data abstraction sheets. The data sets were subjected to data quality checks for data quality. We used a standard template to ensure data editing took place during data entry.
Online survey Data entry was in form of responding to the survey. Data editing was done while cleaning the data.
Quantitaive The online survey link was circulated using contacts within universities and research institutions in East Africa via email and social media platforms such as WhatApp hence it is impossible to track those who received the survey and hence it is not possible t calculate the survey response rate.
NA
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TwitterIn this project data were collected in parallel using essentially the same instruments but adjusted to optimise cultural validity. This means that cross culture comparisons must be made with caution and awareness of the differences between the instruments and between the two educational cultures. 20 Hong Kong and 17 English primary teachers representing 10 schools in each country took part. In HK the teachers were all mathematics teachers working with 400+ 10-11 year olds. In England the teachers were primary generalist teachers working with 200+ pupils in the 9 - 11 age range. The data collection includes: quantitative data on: - audit of teachers' mathematical knowledge and confidence at start of project (20 HK teachers and 17 English teachers) - pre and post intervention project data on teacher mathematical pedagogical self-efficacy -classroom observational data on pupil talk in groups - pre and post intervention pupil mathematics attainment data - post intervention attitudes to group work and mathematics data from the English pupils -qualitative data pre and post intervention interviews with the English teachers about their attitudes, experience and concerns on using group work in mathematics
This bilateral research project capitalises on Hong Kong primary teachers’ mathematics expertise and UK primary teachers’ use of collaborative groupwork, thereby recognising the two administrations’ respective concerns to develop interactive pedagogy and improve teachers’ subject knowledge. It complements the ESRC Teaching and Learning Research Programme project: ‘Improving Effectiveness of Pupil Groups in Classrooms’, which combined the social and cognitive aspects of groupwork into an effective social pedagogy. It aims to:
establish an intercultural community of practice between English and Hong Kong primary teachers and researchers for the sharing of knowledge and expertise
provide professional development for primary teachers in understanding and applying social pedagogic principles to groupwork in mathematics
determine the effects of carefully implemented groupwork on teachers’ self efficacy to teach mathematics and children’s higher order mathematical thinking.
To achieve these aims, the specific objectives are: (i) to assess a sample of primary school teachers' levels of mathematical and pedagogic knowledge and self-efficacy for teaching mathematics in Hong Kong and England (ii) to introduce and assess the use of social pedagogic-based groupwork skills with focused groups of primary school mathematics teachers in Hong Kong and England (iii) to compare for effects over time and between cultures of effective groupwork skills on teachers' self-efficacy for teaching mathematics, and teachers' and pupils' mathematics achievement demanding higher order thinking.
In both countries, ten teachers will learn to apply social pedagogical principles to their mathematics teaching, while ten more teachers and classes will form control groups. Face-to-face and digital communication will facilitate the sharing of pedagogical and subject knowledge in the local and inter-cultural communities of practice respectively. Teachers’ subject knowledge and teaching self-efficacy, pupil tests and classroom observations will form measures of professional development
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TwitterThis dataset contains the deidentified data used in the validation process for the Math-Biology Values Instrument (MBVI). MBVI_spring2016 contains data collected from undergraduate life science majors (via electronic survey) to develop the MBVI and was used for exploratory factor analyses and establishing convergent and divergent validity. MBVI_fall2016 contains data collected from a second independent sample of undergraduate life science majors (also via electronic survey) that was used for confirmatory factor analyses. The two "key" files contain survey item text, response options, and notes for all column headings in the data files. A full description of the data collection process and analyses can be found in the related publication cited below.
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Project Overview In this four-year project called Developing Preservice Elementary Teachers' Ability to Facilitate Goal-Oriented Discussions in Science and Mathematics via the Use of Simulated Classroom Interactions (GO Discuss), Educational Testing Service and Mursion developed, piloted, and validated a set of performance-based tasks delivered within a simulated classroom environment in order to improve preservice elementary teachers’ ability to orchestrate discussions. These tasks provided opportunities for preservice teachers in science and mathematics to facilitate discussions with five upper elementary student avatars (fifth grade) where the focus is on disciplinary argumentation within two content domains: fractions (mathematics) and structure/properties of matter (science). The overall goal of this research was to develop a validity basis for the use of such tools as formative assessment tasks that can be integrated within educator preparation programs to increase the amount, variety, and quality of clinical practice opportunities currently available to preservice elementary teachers. For this project, we developed eight performance-based tasks, four in mathematics and four in science, designed to be used by pre-service elementary teachers as they practice leading classroom discussions in the simulated classroom. Each task provides a scenario and specific details about the discussion, including the student learning goal, students’ background information, and what happened prior to the discussion. We also included the student work related to the mathematics problem or science investigation that was the focus within that task and a summary of important things that we wanted the pre-service elementary teachers to notice about the student work. This specific data project includes materials for one elementary mathematics task, called Ordering Fractions. In this task, the pre-service teacher leads a discussion on students’ responses to a problem asking them to order three fractions from least to greatest. Prior to this discussion, students worked in small groups to complete the problem, write an explanation for their answer, and consider whether their strategy could be applied more generally to other similar problems. The differences in the groups’ answers to the problem, strategies used, and claims about whether their strategies can be generalized form the basis for this discussion. Materials for pre-service teachers, resources for teacher educators, including sample videos, and task-specific simulation specialist training materials are included. For a complete description of the broader “Go Discuss” project, including a list of files for each task, as well as to read the detailed Terms of Use, please start by reading the Data Overview file. Some files appear in different formats with identical content. This is intentional. ETS wants to encourage adaptation of the deposited materials (which might be easier to implement in Word documents), but also wants to ensure that images and math notations are rendered correctly for secondary users (best preserved in PDF).
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Project Overview In this four-year project called Developing Preservice Elementary Teachers' Ability to Facilitate Goal-Oriented Discussions in Science and Mathematics via the Use of Simulated Classroom Interactions (GO Discuss), Educational Testing Service and Mursion developed, piloted, and validated a set of performance-based tasks delivered within a simulated classroom environment in order to improve preservice elementary teachers’ ability to orchestrate discussions. These tasks provided opportunities for preservice teachers in science and mathematics to facilitate discussions with five upper elementary student avatars (fifth grade) where the focus is on disciplinary argumentation within two content domains: fractions (mathematics) and structure/properties of matter (science). The overall goal of this research was to develop a validity basis for the use of such tools as formative assessment tasks that can be integrated within educator preparation programs to increase the amount, variety, and quality of clinical practice opportunities currently available to preservice elementary teachers. For this project, we developed eight performance-based tasks, four in mathematics and four in science, designed to be used by pre-service elementary teachers as they practice leading classroom discussions in the simulated classroom. Each task provides a scenario and specific details about the discussion, including the student learning goal, students’ background information, and what happened prior to the discussion. We also included the student work related to the mathematics problem or science investigation that was the focus within that task and a summary of important things that we wanted the pre-service elementary teachers to notice about the student work. This specific data project includes materials for one elementary mathematics task called Eight Divided by One-Fourth. In this task, students in small groups consider a new type of problem, dividing a whole number by a unit fraction. Prior to the discussion, students discussed a representative problem as a class and written responses in small groups. The pre-service teacher leads a discussion centered on the students’ strategies and the mathematical reasoning used in problems like this one. Materials for pre-service teachers, resources for teacher educators, including sample videos, and task-specific simulation specialist training materials are included. For a complete description of the broader “Go Discuss” project, including a list of files for each task, as well as to read the detailed Terms of Use, please start by reading the Data Overview file. Some files appear in different formats with identical content. This is intentional. ETS wants to encourage adaptation of the deposited materials (which might be easier to implement in Word documents), but also wants to ensure that images and math notations are rendered correctly for secondary users (best preserved in PDF).
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Many mathematics majors take a real analysis course, yet their experiences vary greatly. This article describes how one mathematics department is trying to improve its undergraduate real analysis course by listening to the experiences of underrepresented minority students. From student interviews, three main themes emerged: (1) real analysis feels discontinuous from every other course, (2) real analysis is a gatekeeping or gateway experience for math majors, and (3) students’ responsibilities outside of class influence how they engage in real analysis. We share lessons learned from students to help instructors and departments work toward equitable outcomes in pathways for mathematics majors.