Southern Methodist University
Teaching and Learning
This study examined sources of inconsistency between teachers’ and researchers’ interpretations of survey items. We analyzed cognitive interview data from 12 middle school mathematics teachers to understand their interpretations of... more
This study examined sources of inconsistency between teachers’ and researchers’ interpretations of survey items. We analyzed cognitive interview data from 12 middle school mathematics teachers to understand their interpretations of survey items focused on one aspect of their practice: the content of their advice-seeking interactions. Through this analysis we found that prior conceptualizations of sources of misinterpretation within teacher surveys (e.g., structural complexity, use of reform language) did not adequately account for all of the inconsistencies between the survey items and teachers’ interpretations. We found it useful to reconceptualize the broader source of many of the misinterpretations as an issue of fit between the researchers’ intended interpretation and teachers’ professional practice.
Utilizing Ruiz’s (1984, 1995) language orientation and language policy work, this ethnographic study compared two intercultural bilingual education (IBE) schools located in two Wichí-Weenhayek communities on both sides of the... more
Utilizing Ruiz’s (1984, 1995) language orientation and language policy work, this ethnographic study compared two intercultural bilingual education (IBE) schools located in two Wichí-Weenhayek communities on both sides of the Argentinean-Bolivian border. We examined Wichí-Weenhayek and non-Indigenous teachers’ profiles, teacher-student interactions, and school-community relations. Findings showed that Wichí-Weenhayek teachers in Argentina played only teacher-aid roles and were unable to promote the Wichí language as resource. Although the Wichí-Weenhayek teachers in Bolivia taught in both languages and were in charge of instruction, these teachers did not have enough pedagogical training or materials to meet the language-as-right and
language-as-resource goals of their IBE program. Regarding teacher-students interactions, the non-Indigenous teachers in Argentina used a teacher-centered model of instruction, while in Bolivia, teachers commonly interacted with their students using Wichí and employed more student-centered strategies. Finally, the school-community relationship in Argentina only happened in school because the non-Indigenous principal and teachers did not live in the same town as their students. In Bolivia, on the other hand, children and families commonly interacted with their Wichí-Weenhayek teachers inside and outside the school because all of them lived in the same town. Implications for the development of IBE programs that serve transnational Indigenous communities are discussed here.
language-as-resource goals of their IBE program. Regarding teacher-students interactions, the non-Indigenous teachers in Argentina used a teacher-centered model of instruction, while in Bolivia, teachers commonly interacted with their students using Wichí and employed more student-centered strategies. Finally, the school-community relationship in Argentina only happened in school because the non-Indigenous principal and teachers did not live in the same town as their students. In Bolivia, on the other hand, children and families commonly interacted with their Wichí-Weenhayek teachers inside and outside the school because all of them lived in the same town. Implications for the development of IBE programs that serve transnational Indigenous communities are discussed here.
We investigated the experiences of 12 bilingual teacher candidates as they participated in a non-traditional teacher education program implemented in the context of a partnership between a university, a non-profit organization, and an... more
We investigated the experiences of 12 bilingual teacher candidates as they participated in a non-traditional teacher education program implemented in the context of a partnership between a university, a non-profit organization, and an urban school district. Using the lens of Cultural Historical Activity Theory and Latinx Critical Race Theory, we analyzed participating teachers' interviews, reflection logs, and partnership artifacts. Findings showed that teacher candidates identified positive and negative affordances from participating in the teacher education partnership. Bilingual teacher candidates reported that urban schools were challenging settings to develop their practice and that they had less access to instructional resources and mentors than general education (English-only) teachers. Additional negative affordances included inconsistent expectations between the partnership members with respect to high-quality bilingual education and a mismatch between candidates' educational backgrounds and the subjects they were assigned to teach. Positive affordances of the partnership were being part of a cohort of teachers, having access to specialized bilingual mentors, and getting training relevant to their practices. Bilingual teacher candidates reported that these positive affordances allowed them to discuss issues of equity in their schools and identify ways to advocate for their students. Factors regarding equity in the allocation of educational resources and ways to bridge the gap between research and practice in designing programs that prepare bilingual teachers in urban settings via non-traditional programs are discussed.
Informal formative assessments (IFAs) are classroom interactions teachers use to gather information about their students' learning, interpret it, and act on this information to achieve academic goals. One of the responses science teachers... more
Informal formative assessments (IFAs) are classroom interactions teachers use to gather information about their students' learning, interpret it, and act on this information to achieve academic goals. One of the responses science teachers can enact as the result of IFA is constructing explanations to clarify science concepts to their students. Yet, there is scant research on the characteristics of IFA and the explanation practices that could support English Learners in their language and science knowledge development. In this study, we explored the IFA practices of one elementary and one secondary science teacher as they engaged with their students in constructing science explanations. Key findings indicate that teachers frequently co-constructed explanations with their English Learners as a response to IFA interactions. Yet, both teachers used explanations as a response to IFA unsystematically and not as a science development goal. In fact, both teachers used IFA mostly to assess students' language knowledge rather than their science understanding. Even when explanations were constructed to support English Learners' language, these explanations were only constructed orally and teachers' corrections mostly focused on language form (e.g., vocabulary, correct syntax) rather than on language function (i.e., how language is used to construct clear explanations). Finally, our study shows that for explanations to be effectively used with English Learners, teachers need to conduct adequate sampling of their students' science knowledge and language skills by creating structures that allow them to participate in classroom interactions. Implications for IFA and science explanations research and practice are discussed here.
This study contributes to a growing research base investigating how teachers interact and learn from each other in online communities of practice. It specifically investigates the online mentoring conversations between five cohorts of... more
This study contributes to a growing research base investigating how teachers interact and learn from each other in online communities of practice. It specifically investigates the online mentoring conversations between five cohorts of in-service mentor teachers that participated in graduate-level courses about language pedagogy and their mentee pre-service teachers, while they discussed effective practices for English learner (EL) students. The authors used qualitative methods to ask what types of knowledge and skills related to ELs' instruction the participating mentor teachers displayed when they were situated in the role of online mentors of mentee pre-service teachers. Findings showed that mentor teachers demonstrated knowledge and skills in adjusting general learning strategies to support ELs, in applying language development strategies to teach academic language in English, and in using emotional strategies to offer ELs a welcoming environment. Findings also showed that me...
This study contributes to a growing research base investigating how teachers interact and learn from each other in online communities of practice. It specifically investigates the online mentoring conversations between five cohorts of... more
This study contributes to a growing research base investigating how teachers interact and learn from each other in online communities of practice. It specifically investigates the online mentoring conversations between five cohorts of in-service mentor teachers that participated in graduate-level courses about language pedagogy and their mentee pre-service teachers, while they discussed effective practices for English learner (EL) students. The authors used qualitative methods to ask what types of knowledge and skills related to ELs' instruction the participating mentor teachers displayed when they were situated in the role of online mentors of mentee pre-service teachers. Findings showed that mentor teachers demonstrated knowledge and skills in adjusting general learning strategies to support ELs, in applying language development strategies to teach academic language in English, and in using emotional strategies to offer ELs a welcoming environment. Findings also showed that mentor teachers found a favorable space in the online mentoring environment to position themselves as teacher leaders and ELs' advocates.
Due to demographic changes, there is a growing number of adolescent students who learn in classrooms in which their teacher and peers come from cultural and linguistic backgrounds that are different from theirs. In these diverse... more
Due to demographic changes, there is a growing number of adolescent students who learn in classrooms in which their teacher and peers come from cultural and linguistic backgrounds that are different from theirs. In these diverse classrooms, teachers need to be able to facilitate language learning spaces that are welcoming for all children, regardless of their backgrounds. Considering this need, the purpose of this study is to examine how 11 teachers, acting as language mentors of 11 high school English learners, demonstrated intercultural communication and cultural responsiveness during their participation in a 10-week telecollaboration project. To this end, online interactions and the teacher mentors' weekly reflection journals were analyzed. From these analyses, three highly productive relationships were selected and their interactions were analyzed to better understand teachers' approaches to intercultural communication and cultural responsiveness and the role that the identities of teachers and students displayed in both processes. The study findings show that teachers who displayed an online identity as friends or as joint learners offered student mentees the opportunity to lead the conversation, to be recognized as they wanted to be recognized online, and to participate in learning tasks that reflected and engaged them. This study highlights the different needs of adolescent English learners, the complexity of their identities, and the importance of English teachers' dispositions to be humble and open to learn about both.
Schools are increasingly using technology to connect with families. Yet, we still know little about how technology shapes parent engagement—particularly for low-income Latinx families. Garnering insights from the Ecologies of Parental... more
Schools are increasingly using technology to connect with families. Yet, we still know little about how technology shapes parent engagement—particularly for low-income Latinx families. Garnering insights from the Ecologies of Parental Engagement framework and wide-ranging qualitative data, we explore Latinx engagement at an urban, high-tech elementary school. Findings suggest that technology and language independently and concurrently shaped engagement. Within school-based spaces (e.g., cafeteria, classroom), engagement also manifested differently depending on parents’ resources and the particular space’s rules and norms. In each space, parents overcame barriers to interact and invest—virtually or physically—in their children’s schooling. Implications are discussed.
A considerable body of research has suggested that without appropriate supports and learning opportunities on the job, beginning teachers are unlikely to develop effective instructional practices and find success. Informal supports, such... more
A considerable body of research has suggested that without appropriate supports and learning opportunities on the job, beginning teachers are unlikely to develop effective instructional practices and find success. Informal supports, such as teachers' advice networks, have received less attention in research and policy yet can serve as substantial supports for teachers' development. In this study, we follow Baker-Doyle and define a teacher's intentional professional network (IPN) to be the set of people to whom the teacher chooses to go for advice or information about teaching. In this study, we investigated how first-year teachers participating in an alternative certification partnership were supported by different individuals over the course of their first year of teaching. In particular, we analyzed their IPNs, col
Schools are increasingly using technology to connect with families. Yet, we still know little about how technology shapes parent engagement-particularly for low-income Latinx families. Garnering insights from the Ecologies of Parental... more
Schools are increasingly using technology to connect with families. Yet, we still know little about how technology shapes parent engagement-particularly for low-income Latinx families. Garnering insights from the Ecologies of Parental Engagement framework and wide-ranging qualitative data, we explore Latinx engagement at an urban, high-tech elementary school. Findings suggest that technology and language independently and concurrently shaped engagement. Within school-based spaces (e.g., cafeteria, classroom), engagement also manifested differently depending on parents' resources and the particular space's rules and norms. In each space, parents overcame barriers to interact and invest-virtually or physically-in their children's schooling. Implications are discussed.
Purpose A central issue in mathematics education relates to grounding, or the question of how abstract, mathematical ideas can be connected to students' prior knowledge and experience, such that their meaning becomes connected with... more
Purpose A central issue in mathematics education relates to grounding, or the question of how abstract, mathematical ideas can be connected to students' prior knowledge and experience, such that their meaning becomes connected with concrete, perceptual referents that can be readily understood (Goldstone & Son, 2005; Koedinger, Alibali, & Nathan, 2008).
- by Caroline "Caro" Williams and +2
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Methods We adopted the sort-re-sort procedure used by Medin et al.(1997). In one-on-one interviews, participants were presented with a set of cards that contained numbers or geometric shapes, the selections of which were based upon the... more
Methods We adopted the sort-re-sort procedure used by Medin et al.(1997). In one-on-one interviews, participants were presented with a set of cards that contained numbers or geometric shapes, the selections of which were based upon the varying of dimensions identified by previous research (Feldman, 2000; Miller & Gelman, 1983; see Figure 1).
- by Caroline "Caro" Williams and +2
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The role of reasoning and proof in mathematics is undeniably crucial, and yet research in mathematics education has repeatedly indicated that students struggle with proof production. Our research shows that proof activities can be... more
The role of reasoning and proof in mathematics is undeniably crucial, and yet research in mathematics education has repeatedly indicated that students struggle with proof production. Our research shows that proof activities can be illuminated by newly considering action and gesture as a modality for crucial aspects of mathematical communication. We share two examples that highlight the importance of gesture and action in supporting students' mathematical proof.
- by Caroline "Caro" Williams and +2
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In this study, we used two computerized text analysis tools, Coh-Metrix and the Linguistic Inquiry and Word Count (LIWC) software, to explore how language use relates to the validity of undergraduates’ mathematical proofs. We analyzed 240... more
In this study, we used two computerized text analysis tools, Coh-Metrix and the Linguistic Inquiry and Word Count (LIWC) software, to explore how language use relates to the validity of undergraduates’ mathematical proofs. We analyzed 240 transcripts of students’ justifications of two mathematical tasks: the triangle inequality conjecture and the parity principle of gears. We investigated the significant correlations between linguistic categories from the text analysis programs and incidence of correct proofs in order to explore where critical language-based differences between valid and invalid proofs may lie. Results showed distinct linguistic patterns for correct and incorrect proofs; multiple regression analysis showed that these categories were significantly predictive of the validity of a proof. Specifically, using conditional statements and building an argument by repeating domain-specific words predicts a correct proof, while using more self-conscious statements predicts an incorrect proof. This study contributes to our understanding of the role of language in mathematical reasoning and proof production. It also demonstrates the vast potential for text analysis tools to elucidate linguistic aspects of students’ emerging disciplinary discourse practices.
Theories of grounded and embodied cognition posit that situated actions are central constituents in cognitive processes. We investigate whether grounding actions influence reasoning, and how pedagogical language influences the... more
Theories of grounded and embodied cognition posit that situated actions are central constituents in cognitive processes. We investigate whether grounding actions influence reasoning, and how pedagogical language influences the action-cognition relationship. Undergraduate students (N = 120) generated proofs for two mathematical tasks after performing either grounding or non- grounding actions. Grounding actions facilitated key mathematical insights for both tasks, but did not lead to superior proofs. Pedagogical language in the form of prompts (prospective statements) and hints (retrospective statements) accompanying grounding actions enhanced proof performance on one task but not the other. Results from transfer tasks suggested that participants learned to apply their mathematical insights to new contexts. The findings suggest that relations between action and cognition are reciprocal: actions facilitate insight, while pedagogical language strengthens the influence of task-relevant actions for proof production. Pedagogically supported grounding actions offer alternative ways of fostering mathematical reasoning.
Many students entering higher education are under-prepared for college-level mathematics courses and require developmental mathematics. However, students struggle to complete the prescribed sequence of developmental courses. Reform... more
Many students entering higher education are under-prepared for college-level mathematics courses and require developmental mathematics. However, students struggle to complete the prescribed sequence of developmental courses. Reform initiatives suggest promising models for developmental coursework, yet insufficient evidence exists to support that these models are effective at scale. In this paper, we present a five-year longitudinal examination of a cohort of community college mathematics students and provide information as to what paths through developmental math were most successful. An accelerated format and initial placement in the developmental sequence were significant predictors of success in credit-level mathematics.
Many past studies of mathematical thinking and learning highlight the importance of gesture in reasoning and communication. This research explores the nature of speech that accompanies dynamic depictive gestures: gestures representing... more
Many past studies of mathematical thinking and learning highlight the importance of gesture in reasoning and communication. This research explores the nature of speech that accompanies dynamic depictive gestures: gestures representing transformations of physical and conceptual objects through bodily movement. Prior work has shown that such gestures can contribute to valid proof production. Automated text analysis tools, Coh-Metrix and LIWC, helped identify discourse processes associated with dynamic gesture production during proof. Analyses found that speakers were more likely to produce dynamic gestures when using connective words and less likely to produce dynamic gestures when they made self-conscious statements articulating a lack of knowledge or poor comprehension. Implications are offered for classroom formative assessment and for theories of language and gesture.
Solving mathematics story problems requires text comprehension skills. However, previous studies have found few connections between traditional measures of text readability and performance on story problems. We hypothesized that recently... more
Solving mathematics story problems requires text comprehension skills. However, previous studies have found few connections between traditional measures of text readability and performance on story problems. We hypothesized that recently developed measures of readability and topic incidence measured by text-mining tools may illuminate associations between text difficulty and problem-solving measures. We used data from 3,216 middle and high school students from 10 schools using the Cognitive Tutor Algebra program; these schools were geographically, socioeconomically, racially, and ethnically diverse. We found that several indicators of the readability and topic of story problems were associated with students’ tendency to give correct answers and request hints in Cognitive Tutor. We further examined the individual skill of writing an algebraic expression from a story scenario, and examined students at the lowest performing schools in the sample only, and found additional associations for these subsets. Key readability and topic categories that were related to problem-solving measures included word difficulty, text length, pronoun use, sentence similarity, and topic familiarity. These findings are discussed in the context of models of mathematics story problem solving and previous research on text comprehension
Twenty middle-school students participated in semistructured interviews in which they were asked to assess the validity of two mathematical conjectures. In addition to being free to develop a valid proof as a justification, students were... more
Twenty middle-school students participated in semistructured interviews in which they were asked to assess the validity of two mathematical conjectures. In addition to being free to develop a valid proof as a justification, students were also asked to generate numeric examples to test the conjecture. Students demonstrated strategic reasoning in their empirical approaches by varying the quantity, parity, magnitude, and typicality of the numbers selected. These strategies were more developed in students who initially believed in the truth of the conjecture as well as in students who generated a valid, deductive proof. Emphasizing students' strategic selection of diverse examples parallels inductive reasoning in other domains. Strategic use of examples in justifying conjectures has the potential to assist students' development of deductive proof strategies.
- by Charles Kalish and +1
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