The acquisition of basic quantitative reasoning skills during adolescence: Learning or development?

Five items requiring use of proportional, probabilistic, and correlational reasoning were administered to students in grades 6, 8, 10, and 12. Proportions are taught in the school district in grades 7 and 8, probability in grade 10, and correlations are not taught. Based on the hypothesis that successful performance is due to classroom instruction, improvements on the proportions item were predicted between grades 6 and 10 and improvements on the probability items were predicted between grades 10 and 12. Actual gradewise improvements did not correspond well with predictions. Yet performance did correlate significantly with enrollment in classes such as chemistry, physics, and trigonometry. It is argued that successful qualitative reasoning arises as a consequence of the process of equilibration, and influences one's selection of course work. Specific instruction may initiate the equilibration process.     

定性实验与定量实验的区别及应用

从实验结果的性质进行分类,实验可分为定性实验和定量实验。定性实验是判断研究对象具有哪些性质,并判断某种物质的成分、结构或鉴别某种因素是否存在以及某些因素之问是否具有某种关系的一种实验方法。其特点是回答“有没有”或者“是不是”等问题。这种实验在中学教材中很普遍。定量实验是研究对象的性质、组成和影响因素之间的数量关系。     

Assumptions underlying quantitative and qualitative research: Implications for institutional research

For institutional researchers, the choice to use a quantitative or qualitative approach to research is dictated by time, money, resources, and staff. Frequently, the choice to use one or the other approach is made at the method level. Choices made at this level generally have rigor, but ignore the underlying philosophical assumptions structuring beliefs about methodology, knowledge, and reality. When choosing a method, institutional researchers also choose what they believe to be knowledge, reality, and the correct method to measure both. The purpose of this paper is to clarify and explore the assumptions underlying quantitative and qualitative research. The reason for highlighting the assumptions is to increase the general level of understanding and appreciation of epistemological issues in institutional research. Articulation of these assumptions should foster greater awareness of the appropriateness of different kinds of knowledge for different purposes.     

教师更应该关注学生什么

邻居的儿子亮亮是一名小学五年级的学生,他的上课时间和我们一样,都是八点钟,但是,每天早上我上班时,几乎很少看到亮亮,因为他已经提前上学走了。     

Learning analytics application to examine validity and generalizability of game-based assessment for spatial reasoning

Game-based assessment (GBA), a specific application of games for learning, has been recognized as an alternative form of assessment. While there is a substantive body of literature that supports the educational benefits of GBA, limited work investigates the validity and generalizability of such systems. In this paper, we describe applications of learning analytics methods to provide evidence for psychometric qualities of a digital GBA called Shadowspect, particularly to what extent Shadowspect is a robust assessment tool for middle school students' spatial reasoning skills. Our findings indicate that Shadowspect is a valid assessment for spatial reasoning skills, and it has comparable precision for both male and female students. In addition, students' enjoyment of the game is positively related to their overall competency as measured by the game regardless of the level of their existing spatial reasoning skills.

Practitioner notes

What is already known about this topic:

• Digital games can be a powerful context to support and assess student learning.
• Games as assessments need to meet certain psychometric qualities such as validity and generalizability.
• Learning analytics provide useful ways to establish assessment models for educational games, as well as to investigate their psychometric qualities.

What this paper adds:

• How a digital game can be coupled with learning analytics practices to assess spatial reasoning skills.
• How to evaluate psychometric qualities of game-based assessment using learning analytics techniques.
• Investigation of validity and generalizability of game-based assessment for spatial reasoning skills and the interplay of the game-based assessment with enjoyment.

Implications for practice and/or policy:

• Game-based assessments that incorporate learning analytics can be used as an alternative to pencil-and-paper tests to measure cognitive skills such as spatial reasoning.
• More training and assessment of spatial reasoning embedded in games can motivate students who might not be on the STEM tracks, thus broadening participation in STEM.
• Game-based learning and assessment researchers should consider possible factors that affect how certain populations of students enjoy educational games, so it does not further marginalize specific student populations.

     

Designs of concept maps and their impacts on readers' performance in memory and reasoning while reading

From the perspective of the Fuzzy Trace Theory, this study investigated the impacts of concept maps with two strategic orientations (comprehensive and thematic representations) on readers' performance of cognitive operations (such as perception, verbatim memory, gist reasoning and syntheses) while the readers were reading two history articles that argue from different perspectives about a historical incident that had a profound impact on Taiwan. The results show that the design and focus of the concept maps may influence the formation of mental representations, and that this may be facilitative or constraining in regard to the readers' memory formation and reasoning about the reading materials. Based on these findings, the meaning of constraining effects of concept maps is discussed, and an instructional method involving the progressive elaboration of concept map systems is recommended.     

Complex influences of mechanistic knowledge,worldview, and quantitative reasoning on climate change discourse: Evidence for ideologically motivated reasoning among youth

Anthropogenic climate change remains divisive in the United States, where skepticism of the scientific consensus is associated with conservative worldviews, resulting in political polarization. This study considers three hypotheses regarding U.S. polarization over climate change that have emerged from social psychology research and applies them to science education by showing how these hypotheses could relate to adolescents' science learning. We then test each hypothesis within an experimental educational intervention designed to study the influence of worldview, mechanistic knowledge, and quantitative reasoning on students' written arguments about climate change. We used mixed methods to analyze the results of this individually randomized trial with clustering involving 357 participants in grades 9–11 from 5 U.S. sites. Findings show that: (a) exposure to mechanistic knowledge about climate change increased odds of receptivity toward climate change; (b) increasingly conservative worldviews were associated with decreased odds of receptivity; (c) worldview and quantitative reasoning interacted, resulting in an amplified effect of worldview for students with greater quantitative reasoning. Results also suggest that the influence of worldview and mechanistic knowledge on receptivity work independently from one another in our dataset. This study demonstrates the value of teaching mechanistic understandings of climate change, yet also demonstrates the influence of worldview on receptivity to climate change for adolescents, as well as complex interactions between quantitative reasoning (something school science aims to develop) and worldview. It shows that moving the U.S. public toward the scientific consensus is complex and involves confronting ideologically motivated reasoning within science education.     

Novice use of qualitative versus quantitative problem solving in electrostatics

Problem-solving behavior of six novice subjects attempting to solve an electrostatics problem in second-semester calculus-based college physics was observed and recorded. Five of the subjects were characterized as “A” or “B” students and one subject as a “D” student in introductory college physics. Although the A or B subjects were able to arrive at a “correct” solution to the problem, they exhibited major misconceptions about the problem situation as well as minimal qualitative understanding of the problem situation. The A or B subjects were successful in identifying, either from memory or written notes, equations relevant to electrostatics, whereas the D subject was not. The implication of this study is that current instruction in introductory calculus-based college physics and the students' previous science learnings place a premium on acquisition of correct quantitative solutions at the expense of qualitative understanding of physics problem situations.     

Integrating qualitative and quantitative methods to monitor an intervention program

Teachers in one-teacher schools have often experienced problems when implementing enquiry-based science programs. An innovation was developed to address these problems in isolated one-teacher schools in the far-west of NSW. It consisted of 18 science kits and an associated teaching sequence. Each kit contained 15 student activity sheets, equipment and supplementary resources. An intervention program was designed to support the implementation of the innovation. The purpose of this study was to monitor the teacher's process of change and to ascertain the outcomes of the intervention program in one of the schools. Data were collected using, diagnostic dimensions from the Concerns-Based Adoption Model Project as well as qualitative methods. The results indicated that the teacher's concerns about the innovation focused on how it affected the students. The teacher used the innovation to support her student-centred teaching methods and the students had positive perceptions about learning science. Specializations: K-6 Science and Technology curriculum and instruction.     

Teaching and learning logic programming in virtual worlds using interactive microworld representations

Logic Programming (LP) follows the declarative programming paradigm, which novice students often find hard to grasp. The limited availability of visual teaching aids for LP can lead to low motivation for learning. In this paper, we present a platform for teaching and learning Prolog in Virtual Worlds, which enables the visual interpretation and verification of program results in a straightforward fashion and requires students to adopt a collaborative problem‐solving approach. The results of the pilot application and student‐centered evaluation of the platform are encouraging regarding group learning performance and user experience. The paper contributes to current practice of teaching and learning LP by proposing a metaphor and a system that can empower the educational process with toy world examples visualized in a shared 3D environment.     

Proportional reasoning and the linguistic abilities required for hypothetico-deductive reasoning

The hypothesis is advanced that a necessary, though not sufficient, condition for the acquisition of proportional reasoning during adolescence is the prior internalization of key linguistic elements of argumentation, essentially those used in hypothetico-deductive reasoning. This hypothesized internalization, which does not occur in all individuals, results in some who have acquired the ability to reflect upon the correctness of self-generated answers in a hypothetico-deductive manner, and others who have not. As an initial test of the hypothesis, 46 subjects (Ss) (mean age = 21.03 years) were classified into additive, transitional, or proportional reasoning categories based upon responses to a proportions task. Group differences were found in which proportional Ss performed better than transitional Ss who in turn performed better than additive Ss on a number of items testing Ss' abilities to identify, generate, and use the linguistic elements of argumentation. Further it was found that some Ss who were successful on the linguistic items failed the proportions task, but no Ss who were successful on the proportions task failed the linguistic items. This result supports the hypothesis that the internalization of linguistic elements of argumentation is a prerequisite for proportional reasoning and by inference other advanced reasoning schemata as well. Implications for science instruction are drawn.     

Entrepreneurial Community College Presidents: An exploratory qualitative and quantitative study

Tertiary Education and Management - This study examined the entrepreneurial, nontraditional fundraising behaviors and activities of 23 community college presidents using interview and survey data....     

Entrepreneurial Community College Presidents: An exploratory qualitative and quantitative study

This study examined the entrepreneurial, nontraditional fundraising behaviors and activities of 23 community college presidents using interview and survey data. The institutional characteristics that facilitate entrepreneurial action and how presidents are raising these new revenues were explored. “Best practices” and implications for future research and practice are provided. The results of this analysis revealed meaningful information that is beneficial for community college presidents seeking to transform their colleges through entrepreneurial leadership. These findings indicate entrepreneurial presidents do exist and their practices can be identified. The findings also indicate that presidents' engagement in certain specific entrepreneurial practices do result in increased nontraditional funding secured. A summary of these key findings may be used as a guide for current and future community college leaders who desire to become more entrepreneurial.     

Gender Differences in the Experience of Higher Education: quantitative and qualitative approaches

This paper reviews the evidence for differences between men and women in their experience of higher education. It is generally agreed that students manifest a number of different approaches to learning, and these have been operationalised in terms of quantitative measures derived from responses to formal questionnaires. Nevertheless, there is little consistent or valid evidence for gender differences in the responses to these instruments. Other researchers have used qualitative methodologies in order to identify different stages of intellectual development among students in higher education. Their findings indicate the existence of parallel, but distinct developmental schemes in male and female students.     

浅议定量研究与定性研究的对比与整合

定量研究和定性研究是教育科学研究领域的量大基本范式和方法,各自有着不同的概念,在本质、认识论、理论基础、研究程序和预先设计、研究目的、研究方法上也各不相同,本文在阐述两者的特点和优点的基础上,分析了两种研究范式结合的意义、条件和可能方式。     

Teaching children how to include the inversion principle in their reasoning about quantitative relations

The basis of this intervention study is a distinction between numerical calculus and relational calculus. The former refers to numerical calculations and the latter to the analysis of the quantitative relations in mathematical problems. The inverse relation between addition and subtraction is relevant to both kinds of calculus, but so far research on improving children’s understanding and use of the principle of inversion through interventions has only been applied to the solving of a + b − b = ? sums. The main aim of the intervention described in this article was to study the effects of teaching children about the explicit use of inversion as part of the relational calculus needed to solve inverse addition and subtraction problems using a calculator. The study showed that children taught about relational calculus differed significantly from those who were taught numerical procedures, and also that effects of the intervention were stronger when children were taught about relational calculus with mixtures of indirect and direct word problems than when these two types of problem were given to them in separate blocks.     

Examining the reciprocal relations of mathematics anxiety to quantitative reasoning and number knowledge in Chinese children

This study aimed to examine the longitudinal relations of mathematics anxiety to quantitative reasoning and number knowledge in Chinese children. Three hundred and sixteen 6-year-old Chinese children in Hong Kong participated in two waves of assessments, eight months apart. Cross-lagged panel analyses showed that prior quantitative reasoning and number knowledge predicted lower mathematics anxiety, even after the effects of gender, mothers’ educational levels, and general anxiety were taken into account. However, earlier mathematics anxiety did not predict later quantitative reasoning and number knowledge. Our findings were consistent with the Deficit Theory, which postulates that mathematics anxiety comes from poor mathematical competence but not vice versa. We also found a reciprocal association between quantitative reasoning and number knowledge, in which initial quantitative reasoning had a stronger prediction on later number knowledge. Taken together with previous research, this result highlights the importance of quantitative reasoning in children’s mathematics learning and its role in mathematics education.