An official website of the United States government
Background/Context: After-school programs that focus on integrating computer programming and mathematics in authentic environments are seldomly accessible to students from culturally and linguistically diverse backgrounds, particularly bilingual Latina students in rural contexts. Providing a context that broadens Latina students’ participation in mathematics and computer programming requires educators to carefully examine how verbal and nonverbal language is used to interact and to position students as they learn new concepts in middle school. This is also an important stage for adolescents because they are likely to make decisions about their future careers in STEM. Having access to discourse and teaching practices that invite students to participate in mathematics and computer programming affords them opportunities to engage with these fields. Purpose/Focus of Study: This case study analyzes how small-group interactions mediated the positionings of Cindy, a bilingual Latina, as she learned binary numbers in an after-school program that integrated computer programming and mathematics (CPM). Setting: The Advancing Out-of-School Learning in Mathematics and Engineering (AOLME) program was held in a rural bilingual (Spanish and English) middle school in the Southwest. The after-school program was designed to provide experiences for primarily Latinx students to learn how to integrate mathematics with computer programming using Raspberry Pi and Python as a platform. Our case study explores how Cindy was positioned as she interacted with two undergraduate engineering students who served as facilitators while learning binary numbers with a group of three middle school students. Research Design: This single intrinsic case focused on exploring how small-group interactions among four students mediated Cindy’s positionings as she learned binary numbers through her participation in AOLME. Data sources included twelve 90-minute video sessions and Cindy’s journal and curriculum binder. Video logs were created, and transcripts were coded to describe verbal and nonverbal interactions among the facilitators and Cindy. Analysis of select episodes was conducted using systemic functional linguistics (SFL), specifically language modality, to identify how positioning took place. These episodes and positioning analysis describe how Cindy, with others, navigated the process of learning binary numbers under the stereotype that female students are not as good at mathematics as male students. Findings: From our analysis, three themes that emerged from the data portray Cindy’s experiences learning binary numbers. The major themes are: (1) Cindy’s struggle to reveal her understanding of binary numbers in a competitive context, (2) Cindy’s use of “fake it until you make it” to hide her cognitive dissonance, and (3) the use of Spanish and peers’ support to resolve Cindy’s understanding of binary numbers. The positioning patterns observed help us learn how, when Cindy’s bilingualism was viewed and promoted as an asset, this social context worked as a generative axis that addressed the challenges of learning binary numbers. The contrasting episodes highlight the facilitators’ productive teaching strategies and relations that nurtured Cindy’s social and intellectual participation in CPM. Conclusions/Recommendations: Cindy’s case demonstrates how the facilitator’s teaching, and participants’ interactions and discourse practices contributed to her qualitatively different positionings while she learned binary numbers, and how she persevered in this process. Analysis of communication acts supported our understanding of how Cindy’s positionings underpinned the discourse; how the facilitators’ and students’ discourse formed, shaped, or shifted Cindy’s positioning; and how discourse was larger than gender storylines that went beyond classroom interactions. Cindy’s case reveals the danger of placing students in “struggle” instead of a “productive struggle.” The findings illustrated that when Cindy was placed in struggle when confronting responding moves by the facilitator, her “safe” reaction was hiding and avoiding. In contrast, we also learned about the importance of empathetic, nurturing supporting responses that encourage students’ productive struggle to do better. We invite instructors to notice students’ hiding or avoiding and consider Cindy’s case. Furthermore, we recommend that teachers notice their choice of language because this is important in terms of positioning students. We also highlight Cindy’s agency as she chose to take up her friend’s suggestion to “fake it” rather than give up.
more »
« less
Cognitive agency and computer-based tasks
As computer-focused policies and trends become more popular in schools, more students access math curriculum online. While computer-based programs may be responsive to some student input, their algorithmic basis can make it more difficult for them to be prepared for divergent student thinking, especially in comparison to a teacher. Consider programs that assess student work by judging how well it matches pre-set answers. Unless designed and enacted in classrooms with care, computer-based curriculum materials might encourage students to think about mathematics in pre-determined ways. How do students approach the process of mathematics while using online materials, especially in terms of engaging in original thought? Drawing on Pickering’s (1995) dance of agency and Sinclair’s (2001) conception of students as path-finders or track-takers, I define two modes of mathematical behavior: trail-taking and bushwhacking. While trail-taking, students follow an established approach, often relying on Pickering’s (1995) disciplinary agency, wherein the mathematics “leads [them] through a series of manipulations” (p. 115). The series of manipulations can be seen as a trail that a student may choose to follow. Bushwhacking, on the other hand, refers to actions a student takes of their own invention. It is possible that, unknown to the student, these actions have been taken before by others. In bushwhacking, the student possesses agency, which Pickering (1995) describes as active (rather than passive) and as hallmarked by “choice and discretion” (p. 117). In this study, students worked in several dynamic geometric environments (DGEs) during a geometry lesson about the midline theorem. The lesson was originally recorded as part of a larger study designing mathematically captivating lessons. Students accessed both problems and online addresses for corresponding DGEs via a printed packet. Students interacted with the DGEs on individual laptops, but were seated in groups of three or four. Passages of group conversations in which students transitioned between trail-taking and bushwhacking were selected for closer analysis, which involved identifying evidence of each mode and highlighting the curricular or social forces that may have contributed to shifts between modes. Of particular interest were episodes in which students asked one another to share results, which led to students reconsidering previously set approaches, and episodes in which students interacted with DGEs containing a relatively high proportion of drag-able components, which corresponded to some students working in bushwhacking mode, spontaneously suggesting and revising approaches for manipulating the DGE (e.g., “unless you make this parallel to the bottom, but I don’t think you... yes you can.”). Both types of episodes were found in multiple groups’ conversations. Further analysis of student interactions with tasks, especially with varying levels of student control and sharing, could serve to inform future computer-based task design aimed to encourage students to productively engage in bushwhacking while problem-solving.
more »
« less
- Award ID(s):
- 1652513
- PAR ID:
- 10084136
- Date Published:
- Journal Name:
- Proceedings of the 40th annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education
- Page Range / eLocation ID:
- 1011
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
More Like this
-
-
Lamberg, T.; Moss, D. (Ed.)The positive relationship between students’ attitudes toward mathematics and mathematics achievement is well documented. Yet there is a worsening problem of low appeal of mathematics especially at the secondary level. Therefore, in this paper we focus on three high school students who report a strong dislike of mathematics. By analyzing student surveys, interviews, and lesson observation data, we examined how some mathematical lessons improved these students’ experiences (i.e., their aesthetic dimensions). We found that while student preferences varied, each student was interested in lessons that centered them as sense-makers and in which the content unfolded with suspense. Such lessons led to positive aesthetic responses such as surprise, curiosity, and satisfaction. Thus, lessons can be designed in which even students with the most negative views of mathematics can find mathematical concepts interesting.more » « less
-
Transcripts of teaching episodes can be effective tools to understand discourse patterns in classroom instruction. According to most educational experts, sustained classroom discourse is a critical component of equitable, engaging, and rich learning environments for students. This paper describes the TalkMoves dataset, composed of 567 human annotated K-12 mathematics lesson transcripts (including entire lessons or portions of lessons) derived from video recordings. The set of transcripts primarily includes in-person lessons with whole-class discussions and/or small group work, as well as some online lessons. All of the transcripts are human-transcribed, segmented by the speaker (teacher or student), and annotated at the sentence level for ten discursive moves based on accountable talk theory. In addition, the transcripts include utterance-level information in the form of dialogue act labels based on the Switchboard Dialog Act Corpus. The dataset can be used by educators, policymakers, and researchers to understand the nature of teacher and student discourse in K-12 math classrooms. Portions of this dataset have been used to develop the TalkMoves application, which provides teachers with automated, immediate, and actionable feedback about their mathematics instruction.more » « less
-
This complete research paper examines the connection between student beliefs about engineering as a profession, as well as the perceptions of their family and friends, to their reported self-efficacy, career expectations, and grittiness. The student responses examined were obtained from non-calculus ready engineering students at a large land grant institution in the Mid-Atlantic region. The students participated in a well-established program focused on cohort formation, mentorship, professional skill development, and fostering a sense of inclusion and belonging in engineering. The program, consisting of a one-week pre-fall bridge experience and two common courses, was founded in 2012 and has been operating with National Science Foundation (NSF) S-STEM funding since 2016. Students who received S-STEM funded scholarships are required to participate in focus groups, one-on-one interviews, and complete LAESE, MSLQ, and GRIT questionnaires each semester. The researchers applied qualitative coding methods to evaluate student responses from focus groups and one-one-one interviews which were conducted from 2017 to 2019. Questions examined in this paper include: 1) How would you describe an engineer? 2) Please describe what you think an engineer does on a daily basis. 3) What do you think your friends/family think of engineering? 4) What skills or characteristics do you think good engineers have? 5) What types of careers do you believe are filled by degree holding engineers? Student responses on the aforementioned questions were related to the self-efficacy, career expectation, and grit values obtained from the LAESE, MSLQ, and GRIT instruments. The nature of this longitudinal study allows the evolution of student responses to also be examined as they matriculate through their education. Additional analysis was performed to identify themes and numerical trends associated with student populations such as, underrepresented minorities, females, and first-generation college students. Results of this research are presented in an effort to further highlight the importance of exposure to STEM fields during an individual’s K-12 education, and express how student perceptions, self-efficacy, GRIT, and career expectations evolve over their undergraduate education.more » « less
-
null (Ed.)Applications of Generative Machine Learning techniques such as Generative Adversarial Networks (GANs) are used to generate new instances of images, music, text, and videos. While GANs have now become commonplace on social media, a part of children’s lives, and have considerable ethical implications, existing K-12 AI education curricula do not include generative AI. We present a new module, “What are GANs?”, that teaches middle school students how GANs work and how they can create media using GANs. We developed an online, team-based game to simulate how GANs work. Students also interacted with up to four web tools that apply GANs to generate media. This module was piloted with 72 middle school students in a series of online workshops. We provide insight into student usage, understanding, and attitudes towards this lesson. Finally, we give suggestions for integrating this lesson into AI education curricula.more » « less
- Free Publicly Accessible Full Text
-
Accepted Manuscript1.0
- Conference Paper:
- The DOI is not currently available.
