Pub Date : 2022-07-19DOI: 10.1007/s40753-022-00185-w
Alison S. Marzocchi, Roberto C. Soto
{"title":"Correction to: From the Front Lines of Active Learning: Lessons Learned from those who are Trying","authors":"Alison S. Marzocchi, Roberto C. Soto","doi":"10.1007/s40753-022-00185-w","DOIUrl":"https://doi.org/10.1007/s40753-022-00185-w","url":null,"abstract":"","PeriodicalId":42532,"journal":{"name":"International Journal of Research in Undergraduate Mathematics Education","volume":"9 1","pages":"556 - 556"},"PeriodicalIF":1.5,"publicationDate":"2022-07-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79535870","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
R. Álvarez-Arroyo, José Fernando Lavela Jiménez, Carmen Batanero Bernabeu
Se analiza el razonamiento probabilístico de 76 estudiantes de Bachillerato al interpretar una noticia sobre la COVID-19 tomada de los medios de comunicación. A partir de la noticia se plantean cinco preguntas que implican el cálculo o estimación de probabilidades simples, complementarias y compuestas y la toma de una decisión en función de la información presentada. Los resultados reflejan que los estudiantes calculan correctamente la probabilidad simple y la del suceso complementario, y muchos usan su conocimiento del contexto para dar respuesta a las preguntas, pero tienen grandes dificultades en el cálculo de la probabilidad compuesta. En la toma de decisión, no se tienen en cuenta los cálculos anteriores para proponer medidas de lucha contra los contagios, siendo la tendencia general el seguir las indicaciones que ya se conocen por parte de las autoridades sanitarias. Concluimos la importancia de educar el razonamiento probabilístico de los estudiantes para enfrentarse a situaciones extraescolares.
{"title":"Razonamiento probabilístico de estudiantes de bachillerato al interpretar datos de la COVID-19","authors":"R. Álvarez-Arroyo, José Fernando Lavela Jiménez, Carmen Batanero Bernabeu","doi":"10.17583/redimat.9741","DOIUrl":"https://doi.org/10.17583/redimat.9741","url":null,"abstract":"Se analiza el razonamiento probabilístico de 76 estudiantes de Bachillerato al interpretar una noticia sobre la COVID-19 tomada de los medios de comunicación. A partir de la noticia se plantean cinco preguntas que implican el cálculo o estimación de probabilidades simples, complementarias y compuestas y la toma de una decisión en función de la información presentada. Los resultados reflejan que los estudiantes calculan correctamente la probabilidad simple y la del suceso complementario, y muchos usan su conocimiento del contexto para dar respuesta a las preguntas, pero tienen grandes dificultades en el cálculo de la probabilidad compuesta. En la toma de decisión, no se tienen en cuenta los cálculos anteriores para proponer medidas de lucha contra los contagios, siendo la tendencia general el seguir las indicaciones que ya se conocen por parte de las autoridades sanitarias. Concluimos la importancia de educar el razonamiento probabilístico de los estudiantes para enfrentarse a situaciones extraescolares.","PeriodicalId":42532,"journal":{"name":"International Journal of Research in Undergraduate Mathematics Education","volume":"408 1","pages":""},"PeriodicalIF":1.5,"publicationDate":"2022-06-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82494537","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
J. Cervantes-Barraza, Maria Guadalupe Cabañas Sánchez
El estudio tiene como objetivo identificar las implicaciones de la refutación en argumentaciones con estudiantes de nivel primaria. Por lo que se presenta el análisis de los argumentos y refutaciones entre estudiantes de sexto grado de primaria en el contexto de la solución de tareas matemáticas relacionadas con la clasificación de triángulos según la medida de sus ángulos. Teóricamente el estudio se fundamenta sobre los conceptos base de la línea de investigación argumentación y prueba, de forma particular se abordan los conceptos de argumentación matemática, razonamiento y refutación. Los resultados del estudio documentan algunas implicaciones de la refutación de conclusiones en contextos de la resolución de tareas matemáticas a nivel primaria, y se reconoce que los estudiantes construyan argumentos mejoradas con base en características y propiedades de los triángulos.
{"title":"Argumentación matemática basada en refutaciones","authors":"J. Cervantes-Barraza, Maria Guadalupe Cabañas Sánchez","doi":"10.17583/redimat.4015","DOIUrl":"https://doi.org/10.17583/redimat.4015","url":null,"abstract":"El estudio tiene como objetivo identificar las implicaciones de la refutación en argumentaciones con estudiantes de nivel primaria. Por lo que se presenta el análisis de los argumentos y refutaciones entre estudiantes de sexto grado de primaria en el contexto de la solución de tareas matemáticas relacionadas con la clasificación de triángulos según la medida de sus ángulos. Teóricamente el estudio se fundamenta sobre los conceptos base de la línea de investigación argumentación y prueba, de forma particular se abordan los conceptos de argumentación matemática, razonamiento y refutación. Los resultados del estudio documentan algunas implicaciones de la refutación de conclusiones en contextos de la resolución de tareas matemáticas a nivel primaria, y se reconoce que los estudiantes construyan argumentos mejoradas con base en características y propiedades de los triángulos.","PeriodicalId":42532,"journal":{"name":"International Journal of Research in Undergraduate Mathematics Education","volume":"23 1","pages":""},"PeriodicalIF":1.5,"publicationDate":"2022-06-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76650229","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-06-24DOI: 10.1007/s40753-022-00171-2
Laura Broley, Nadia Hardy
{"title":"The Evolution of Students’ Learning from Calculus to Analysis: How Students Solve Analysis Tasks that look like Calculus Tasks","authors":"Laura Broley, Nadia Hardy","doi":"10.1007/s40753-022-00171-2","DOIUrl":"https://doi.org/10.1007/s40753-022-00171-2","url":null,"abstract":"","PeriodicalId":42532,"journal":{"name":"International Journal of Research in Undergraduate Mathematics Education","volume":"91 1","pages":"269 - 292"},"PeriodicalIF":1.5,"publicationDate":"2022-06-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86243099","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This study explores how hard of hearing students decided whether the shape was a polygon and which semiotic sources were used when the students engaged in explaining geometrical concepts. It was defined how the students interacted with geometric shapes using semiotic sources and examined how such multimodal interactions with geometric figures displayed their reasoning. The study was a case study and carried out three hard of hearing students. The data was collected through interviews and analyzed with content analysis. It was detected that the students paid attention to edge, angle, and vertex of the shapes in the process of identifying polygon. It was seen that the students used gesture, speech, sign language, inscriptions which are semiotic sources and personal or mathematical definitions to express polygon concept. However, it has been determined that students have some misconceptions in the process of explaining concepts. It is suggested that the words used in the concept definition should be selected carefully by the teachers to teach the concepts correctly and the teachers use hand signs for concepts in their lesson.
{"title":"How Must a Polygon Be According to Hard of Hearing Students? An Investigation with a Semiotic Approach","authors":"Nejla Gürefe","doi":"10.17583/redimat.6097","DOIUrl":"https://doi.org/10.17583/redimat.6097","url":null,"abstract":"This study explores how hard of hearing students decided whether the shape was a polygon and which semiotic sources were used when the students engaged in explaining geometrical concepts. It was defined how the students interacted with geometric shapes using semiotic sources and examined how such multimodal interactions with geometric figures displayed their reasoning. The study was a case study and carried out three hard of hearing students. The data was collected through interviews and analyzed with content analysis. It was detected that the students paid attention to edge, angle, and vertex of the shapes in the process of identifying polygon. It was seen that the students used gesture, speech, sign language, inscriptions which are semiotic sources and personal or mathematical definitions to express polygon concept. However, it has been determined that students have some misconceptions in the process of explaining concepts. It is suggested that the words used in the concept definition should be selected carefully by the teachers to teach the concepts correctly and the teachers use hand signs for concepts in their lesson.","PeriodicalId":42532,"journal":{"name":"International Journal of Research in Undergraduate Mathematics Education","volume":"47 1","pages":""},"PeriodicalIF":1.5,"publicationDate":"2022-06-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79114246","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The enrollment in lower-level mathematics courses has been on the increase in the last decade. It has been estimated that the DFW rate may rise to the level of 50% in courses that can be classified as college algebra. Numerous interventions have been utilized for college algebra and other mathematics classes to help students, including supplemental instruction, peer-led team learning, group learning, flipped classrooms, and integrating technology. In this study, we offered a half-semester course that implemented worked example worksheets, which were used in a previous full-semester intervention, to help students with the college algebra material. Results showed that the thirty students who participated in the worked example pass/fail mid-semester class significantly outperformed the college algebra students who did not participate in the intervention on total points in the course, quizzes, and tests 3 and 4. In addition, participants earned a significantly higher course GPA, attended significantly more regular class lectures, and earned a higher final exam score. Finally, we analysed the qualitative data to develop five themes about the worked examples and intervention. We conclude that the mid-semester intervention is a good just-in-time mechanism to implement after the semester has started to help students succeed in the class.
{"title":"Worked Example Mid-Semester Intervention in College Algebra","authors":"David Miller, Matthew Schraeder","doi":"10.17583/redimat.9645","DOIUrl":"https://doi.org/10.17583/redimat.9645","url":null,"abstract":"The enrollment in lower-level mathematics courses has been on the increase in the last decade. It has been estimated that the DFW rate may rise to the level of 50% in courses that can be classified as college algebra. Numerous interventions have been utilized for college algebra and other mathematics classes to help students, including supplemental instruction, peer-led team learning, group learning, flipped classrooms, and integrating technology. In this study, we offered a half-semester course that implemented worked example worksheets, which were used in a previous full-semester intervention, to help students with the college algebra material. Results showed that the thirty students who participated in the worked example pass/fail mid-semester class significantly outperformed the college algebra students who did not participate in the intervention on total points in the course, quizzes, and tests 3 and 4. In addition, participants earned a significantly higher course GPA, attended significantly more regular class lectures, and earned a higher final exam score. Finally, we analysed the qualitative data to develop five themes about the worked examples and intervention. We conclude that the mid-semester intervention is a good just-in-time mechanism to implement after the semester has started to help students succeed in the class.","PeriodicalId":42532,"journal":{"name":"International Journal of Research in Undergraduate Mathematics Education","volume":"59 8 1","pages":""},"PeriodicalIF":1.5,"publicationDate":"2022-06-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83214734","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This study was conducted to examine whether newly enrolled 9th grade students were ready to directly engage in the theoretical discursive process from the perspective of Duval’s Cognitive Model. The sample of the study was comprised of 51 newly-enrolled 9thgrade students between the ages of 14 and 15, who had not received any prior geometry instruction. These 51 students were posed two open-ended questions that would enable them to make a transition between perceptual and discursive apprehension. The qualitative data obtained from the open-ended questions were classified into three categories, and clinical interviews were held with three students from each category. According to the findings obtained from the study, many of the students could not display the necessary behaviors for theoretical discursive process. Students were mostly unsuccessful in converting discursive information into perceptual information, in writing discursive information based on perceptual information, and making inferences based on discursive information. These findings indicate that recent graduates of secondary school are not ready enough to directly engage in theoretical discursive process and, thus, they could experience difficulties in such high order skills as providing proof requiring the theoretical discursive process.
{"title":"Are 9th Grade Students Ready to Engage in the Theoretical Discursive Process in Geometry?","authors":"Yavuz Karpuz, Bülent Güven","doi":"10.17583/redimat.3667","DOIUrl":"https://doi.org/10.17583/redimat.3667","url":null,"abstract":"This study was conducted to examine whether newly enrolled 9th grade students were ready to directly engage in the theoretical discursive process from the perspective of Duval’s Cognitive Model. The sample of the study was comprised of 51 newly-enrolled 9thgrade students between the ages of 14 and 15, who had not received any prior geometry instruction. These 51 students were posed two open-ended questions that would enable them to make a transition between perceptual and discursive apprehension. The qualitative data obtained from the open-ended questions were classified into three categories, and clinical interviews were held with three students from each category. According to the findings obtained from the study, many of the students could not display the necessary behaviors for theoretical discursive process. Students were mostly unsuccessful in converting discursive information into perceptual information, in writing discursive information based on perceptual information, and making inferences based on discursive information. These findings indicate that recent graduates of secondary school are not ready enough to directly engage in theoretical discursive process and, thus, they could experience difficulties in such high order skills as providing proof requiring the theoretical discursive process. ","PeriodicalId":42532,"journal":{"name":"International Journal of Research in Undergraduate Mathematics Education","volume":"15 1","pages":""},"PeriodicalIF":1.5,"publicationDate":"2022-06-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78926541","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
El propósito de esta investigación fue el tratamiento de las unidades de medida no convencional promovidas en libros de texto de Matemáticas de la Educación Primaria en México. Se consideraron nociones teóricas y metodológicas del Programa Etnomatemática y el Enfoque Ontosemiótico (EOS). Como resultado se evidencia que, en los libros de texto se promueve el uso de unidades de medida de longitud (paso, codo, cuarta, dedo, vara, palmo, hilo o cordón y tira de papel); de capacidad (vaso y el molde de gelatina); de peso (sopeso, y balanza) y de tiempo (palmadas y reloj de arena).Donde las configuraciones epistémicas de objetos primarios permitieron caracterizar estas unidades de medida en términos de situaciones-problema, lenguaje, concepto-definición, procedimientos, proposiciones y argumentos. Se concluye que, las unidades de medida presentado en este estudio son el son el no convencional que ofrecen los materiales curriculares, para que los estudiantes y profesores, realicen procesos de medición, equivalencias y conversiones, así como resolver problemas extramatemáticos para contribuir al desarrollo de las competencias en torno al tema de la medida. Además, permite que el profesor reconozca la diversidad de unidades de medidas y las vincule con el contexto escolar de sus estudiantes.
{"title":"Medidas no convencionales en libros de texto mexicanos. Un análisis desde la Etnomatemática y el Enfoque ontosemiótico","authors":"Lizzet Morales-García, C. A. Rodríguez-Nieto","doi":"10.17583/redimat.8646","DOIUrl":"https://doi.org/10.17583/redimat.8646","url":null,"abstract":"El propósito de esta investigación fue el tratamiento de las unidades de medida no convencional promovidas en libros de texto de Matemáticas de la Educación Primaria en México. Se consideraron nociones teóricas y metodológicas del Programa Etnomatemática y el Enfoque Ontosemiótico (EOS). Como resultado se evidencia que, en los libros de texto se promueve el uso de unidades de medida de longitud (paso, codo, cuarta, dedo, vara, palmo, hilo o cordón y tira de papel); de capacidad (vaso y el molde de gelatina); de peso (sopeso, y balanza) y de tiempo (palmadas y reloj de arena).Donde las configuraciones epistémicas de objetos primarios permitieron caracterizar estas unidades de medida en términos de situaciones-problema, lenguaje, concepto-definición, procedimientos, proposiciones y argumentos. Se concluye que, las unidades de medida presentado en este estudio son el son el no convencional que ofrecen los materiales curriculares, para que los estudiantes y profesores, realicen procesos de medición, equivalencias y conversiones, así como resolver problemas extramatemáticos para contribuir al desarrollo de las competencias en torno al tema de la medida. Además, permite que el profesor reconozca la diversidad de unidades de medidas y las vincule con el contexto escolar de sus estudiantes.","PeriodicalId":42532,"journal":{"name":"International Journal of Research in Undergraduate Mathematics Education","volume":"116 1","pages":""},"PeriodicalIF":1.5,"publicationDate":"2022-06-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89854358","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Mara V. Martinez, Alison Castro-Superfine, Timothy Stoelinga
Our aim is to contribute to the body of research on learning trajectories (LTs) in mathematics by making visible a process for articulating a hypothetical learning trajectory implicit in a widely adopted, reform-based, middle-grades mathematics curriculum. In doing so, we highlight considerations, decisions, and challenges we faced as part of this work. By describing our LT articulation process, our aim is to highlight ways in which curriculum-specific LTs can be articulated to serve as a more proximal and instrumental tool for teachers’ instructional practice. Furthermore, to illustrate we describe how the products of the work were used in practice-based professional learning experiences with middle-grades mathematics teachers.
{"title":"A Curriculum-Based Approach to Learning Trajectories in Middle School Algebra","authors":"Mara V. Martinez, Alison Castro-Superfine, Timothy Stoelinga","doi":"10.17583/redimat.5539","DOIUrl":"https://doi.org/10.17583/redimat.5539","url":null,"abstract":"Our aim is to contribute to the body of research on learning trajectories (LTs) in mathematics by making visible a process for articulating a hypothetical learning trajectory implicit in a widely adopted, reform-based, middle-grades mathematics curriculum. In doing so, we highlight considerations, decisions, and challenges we faced as part of this work. By describing our LT articulation process, our aim is to highlight ways in which curriculum-specific LTs can be articulated to serve as a more proximal and instrumental tool for teachers’ instructional practice. Furthermore, to illustrate we describe how the products of the work were used in practice-based professional learning experiences with middle-grades mathematics teachers.","PeriodicalId":42532,"journal":{"name":"International Journal of Research in Undergraduate Mathematics Education","volume":"1 1","pages":""},"PeriodicalIF":1.5,"publicationDate":"2022-06-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"91096490","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-06-22DOI: 10.1007/s40753-022-00182-z
Mathilde Hitier, Alejandro S. González-Martín
{"title":"Derivatives and the Study of Motion at the Intersection of Calculus and Mechanics: a Praxeological Analysis of Practices at the College Level","authors":"Mathilde Hitier, Alejandro S. González-Martín","doi":"10.1007/s40753-022-00182-z","DOIUrl":"https://doi.org/10.1007/s40753-022-00182-z","url":null,"abstract":"","PeriodicalId":42532,"journal":{"name":"International Journal of Research in Undergraduate Mathematics Education","volume":"44 1","pages":"293 - 317"},"PeriodicalIF":1.5,"publicationDate":"2022-06-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89003387","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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