scholarly journals Middle school students' and mathematicians' judgments of mathematical typicality

2018 ◽  
Vol 4 (1) ◽  
pp. 243-270
Author(s):  
Candace Walkington ◽  
Jennifer Cooper ◽  
Olubukola Leonard ◽  
Caroline Williams-Pierce ◽  
Chuck Kalish

K-12 students often rely on testing examples to explore and determine the truth of mathematical conjectures. However, little is known about how K-12 students choose examples and what elements are important when considering example choice. In other domains, experts give explicit consideration to the typicality of examples – how representative a given item is of a general class. In a pilot study, we interviewed 20 middle school students who classified examples as typical or unusual and justified their classification. We then gave middle school students and mathematicians a survey where they rated the typicality of mathematical objects in two contexts – an everyday context (commonness in everyday life) and a mathematical context (how likely conjectures that hold for the object are to hold for other objects). Mathematicians had distinct notions of everyday and mathematical typicality – they recognized that the objects often seen in everyday life can have mathematical properties that can limit inductive generalization. Middle school students largely did not differentiate between everyday and mathematical typicality – they did not view special mathematical properties as limiting generalization, and rated items similarly regardless of context. These results suggest directions for learning mathematical argumentation and represent an important step towards understanding the nature of typicality in math.

2000 ◽  
Vol 6 (3) ◽  
pp. 156-161
Author(s):  
John P. Smith ◽  
Elizabeth A. Phillips

NO PART OF THE K–12 MATHEMATICS curriculum is more fluid and controversial than introductory algebra. Content and assessment issues lie at the core of this debate: What algebra skills and understandings are important? What kind of evidence suggests that students possess these skills? Neither question can be answered in simple terms; in fact, no single “right” answer may exist for either one.


1999 ◽  
Vol 5 (1) ◽  
pp. 20-23
Author(s):  
Michaele F. Chappell ◽  
Denisse R. Thompson

During the past twenty years, documents have recommended that the mathematics curriculum include measurement for all grades, K–12 (NCTM 1980, 1989). Indeed, students interact daily with measurement in their physical environment, for example, by finding the distance from home to school, their height and weight, and wall space for posters. Adolescents bring to the classroom varied conceptions of measurement, which may be in the form of basic applications or general formulas. All too often, a fundamental understanding of these ideas is sacrificed while students learn general formulas. This situation is particularly true for attributes of perimeter and area. To what extent do middle school students possess a conceptual understanding of these measurement concepts?


Author(s):  
Wajeeh Daher

<blockquote>Although many researchers have examined knowledge building in traditional settings and distance learning, few have examined middle school students' building of mathematical knowledge using mobile phones. The present study uses two well-known models of knowledge building to carry out the examination: the interactive analysis model of knowledge building phases developed by Gunawardena, Lowe and Anderson (1997) and the six themes model of knowledge building characteristics developed by Scadamalia and Bereiter (2006). The findings show that the middle school students participating in this research went through all the knowledge building phases suggested by Gunawardena, Lowe and Anderson (1997). They further experienced other knowledge building phases that fit the authentic context in which they learned. Participants advanced their knowledge of ideas as a community, collaborating to carry out authentic activities using mobile phones. They demonstrated constructive and critical use of information in general and of authoritative information in particular. Participants worked as mathematicians, especially during the second part of the experiment, when they suggested real world phenomena to explore using the mobile phone. My conclusion suggests learning mathematics by carrying out authentic activities using mobile phones, to encourage and enrich the mathematics knowledge building of students in K-12.</blockquote><p> </p>


2020 ◽  
Vol 6 (1) ◽  
pp. 152-178
Author(s):  
Leslie Elizabeth Sprong ◽  
Sonya N. Martin

Abstract Quality environmental education (EE) is key for supporting sustainable development and use of resources. Educators in rural India face considerable challenges to teach EE in K-12 school settings. This study took place in Assam in Northeast India where non-governmental organization (NGO) educators are working to develop an EE program for students in rural areas. To reveal students’ perceptions of the environment, researchers administered the Draw-an-Environment Test (DAET) to 277 middle school students in government schools. Analysis of students’ drawings of the environment revealed that while students recognized humans have an impact on the environment, they did not fully understand the impact could often be negative and drawings did not necessarily reflect the reality of the local environment. Implications for how these findings can be used to develop responsive EE curriculum that challenges and extends students’ conceptions of the environment and the need for future research are discussed.


2011 ◽  
Vol 14 (1) ◽  
pp. 47-55 ◽  
Author(s):  
Aimee Faul ◽  
Karoline Stepensky ◽  
Brandi Simonsen

Prompting is a simple strategy that has been demonstrated to increase appropriate (and decrease inappropriate) behavior when used (a) as a stand-alone strategy with preschool students and individuals with disabilities and (b) in combination with other strategies (e.g., active supervision) with K-12 students in general education settings. Until now, no studies have specifically investigated the effectiveness of prompting as a stand-alone strategy in a general education setting. This study used a single-subject alternating treatment design, with a baseline phase, to explore the relationship between the presence (or absence) of prompting and off-task behavior of two male middle school students in general education. Study results document a decrease in off-task behavior with prompting. Results and implications are discussed in light of limitations.


Author(s):  
Melissa Burns

Competitive video games, or esports, have been making their way into high schools across Canada, though most middle school students have been left out of the game. This chapter will examine the identity and role of the various shared stakeholders at the middle years level, highlight the benefits of scholastic esports for middle school learners, and examine obstacles that may hinder the implementation of such programming, leaning on the experience of one such program in central Canada. The author will examine data collected over a span of four years on the impact of both coed and girls-only gaming environments in middle schools and how to support young female learners through gaming. Finally, this chapter will highlight the current landscape of K-12 scholastic esports with recommendations on how and why scholastic esports should have a place in Canadian schools.


2021 ◽  
Author(s):  
Andrew Patrick Cook

As a tangible and motivating medium for students to engage in computational thinking, robotics has drawn interest from educators and researchers as K-12 schools continue to integrate STEM into curriculum. Through this mixed methods study, the researcher sought to explore the effects of robotics instructional methods (task-based and project-based) on the computational thinking skills of middle school students, including the problem-solving strategies used and the role of peer collaboration. The quantitative results of this study indicated no significant difference in the computational thinking skills of students participating in task-based or project-based robotics instruction. Interviews consisted of open-ended questions in which problem-solving and collaboration in robotics were explored from the perspectives of the participants. In both groups, problem-solving strategies encompassed all aspects of computational thinking as students took an iterative approach to problem-solving in both tasks and projects. Peer collaboration was naturally occurring and frequent among both groups. In task-based robotics instruction, peer collaboration and problem-solving strategies were primarily focused on the programming of the robot. In project-based robotics, peer collaboration and problem-solving strategies were applied throughout the entire design process, including the building and the programming of the robot. Through this study, the researcher hoped to provide a roadmap for the implementation of robotics in schools for K-8 students. As schools are increasingly seeking ways to integrate robotics into school curriculum, further research in this area on a larger scale is recommended.


2018 ◽  
Vol 3 (4) ◽  
pp. 1
Author(s):  
Lauren Birney ◽  
Denise McNamara ◽  
Catherine Sanders ◽  
Hari Luintel ◽  
Joshua Penman

The CCERS partnership includes collaborators from universities, foundations, education departments, community organizations, and cultural institutions to build a new curriculum. As reported in a study conducted by the Rand Corporation (2011), partnerships among districts, community-based organizations, government agencies, local funders, and others can strengthen learning programs. The curriculum merged project-based learning and Bybee’s 5E model (Note 1) to teach core STEM-C concepts to urban middle school students through restoration science. CCERS has five interrelated and complementary programmatic pillars (see details in the next section). The CCERS curriculum encourages urban middle school students to explore and participate in project-based learning activities restoring the oyster population in and around New York Harbor. In Melaville, Berg and Blank’s Community Based Learning (2001) there is a statement that says, “Education must connect subject matter with the places where students live and the issues that affect us all”. Lessons engage students and teachers in long-term restoration ecology and environmental monitoring projects with STEM professionals and citizen scientists. In brief, partners have created curriculums for both in-school and out-of-school learning programs, an online platform for educators and students to collaborate, and exhibits with community partners to reinforce and extend both the educators’ and their students’ learning. Currently CCERS implementation involves:78 middle schools127 teachers110 scientist volunteersOver 5000 K-12 studentsIn this report, we present summative findings from data collected via surveys among three cohorts of students whose teachers were trained by the project’s curriculum and findings from interviews among project leaders to answer the following research questions:Do the five programmatic pillars function independently and collectively as a system of interrelated STEM-C content delivery vehicles that also effectively change students’ and educators’ disposition towards STEM-C learning and environmental restoration and stewardship?What comprises the "curriculum plus community enterprise" local model?What are the mechanisms for creating sustainability and scalability of the model locally during and beyond its five-year implementation?What core aspects of the model are replicable?Findings suggest the program improved students’ knowledge in life sciences but did not have a significant effect on students’ intent to become a scientist or affinity for science.Interviews with project staff indicated that the key factors in the model were its conservation mission, partnerships, and the local nature of the issues involved. The primary mechanisms for sustainability and scalability beyond the five-year implementation were the digital platform, the curriculum itself, and the dissemination (with over 450 articles related to the project published in the media and academic journals). The core replicable aspects identified were the digital platform and adoption in other Keystone species contexts.


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