Improved Appreciation of Mathematics Through an IBL Liberal Arts Mathematics Course

Abstract

The author has taught an inquiry-based liberal arts mathematics class using the text “The Heart of Mathematics: An Invitation to Effective Thinking” by Edward B. Burger and Michael Starbird a total of 20 times since Spring 2001. The students in this class have almost all been in non-technical majors and many started the semester with negative or ambivalent attitudes toward mathematics based on their prior experiences. The author has gathered responses from students in this class that illustrate significant changes in their attitudes towards mathematics during the course. In particular, the responses gathered at the end of the semester are often eloquent about understanding the great ideas of mathematics that students confronted in this course and about seeing many more and varied connections between mathematics and the “real world” than they had previously realized existed.     

Identifying patterns in students’ scientific argumentation: content analysis through text mining using Latent Dirichlet Allocation

Constructing scientific arguments is an important practice for students because it helps them to make sense of data using scientific knowledge and within the conceptual and experimental boundaries of an investigation. In this study, we used a text mining method called Latent Dirichlet Allocation (LDA) to identify underlying patterns in students written scientific arguments about a complex scientific phenomenon called Albedo Effect. We further examined how identified patterns compare to existing frameworks related to explaining evidence to support claims and attributing sources of uncertainty. LDA was applied to electronically stored arguments written by 2472 students and concerning how decreases in sea ice affect global temperatures. The results indicated that each content topic identified in the explanations by the LDA— “data only,” “reasoning only,” “data and reasoning combined,” “wrong reasoning types,” and “restatement of the claim”—could be interpreted using the claim–evidence–reasoning framework. Similarly, each topic identified in the students’ uncertainty attributions— “self-evaluations,” “personal sources related to knowledge and experience,” and “scientific sources related to reasoning and data”—could be interpreted using the taxonomy of uncertainty attribution. These results indicate that LDA can serve as a tool for content analysis that can discover semantic patterns in students’ scientific argumentation in particular science domains and facilitate teachers’ providing help to students.

     

The effect of students’ subject discipline on their m-learning application preferences

The effect of students’ subject discipline on their preferences toward m-learning applications was investigated by using a mixed-method research design. A questionnaire on students’ preferences of m-learning application features was used to collect data from 181 undergraduate students. One-way analysis of variance found a significant difference among perceptions of students from different subject disciplines related to the “collaboration” and “learning” features. Follow-up interviews were carried out to further investigate students’ perceptions. Content analysis revealed that “availability” and “ease of use” were the most preferred features, and “collaboration” and “entertaining” were the least preferred ones. Interview results related to universities’ readiness for m-learning were categorized into (i) universities’ infrastructures, (ii) instructors’ skills and (iii) students’ skills for m-learning. Students indicated their universities’ infrastructures as “moderately ready” for m-learning. They ranked their instructors’ skills as “low”. However, students assessed their own skills as “moderate” for utilizing m-learning in their respective universities.     

Student connections with academic texts: a phenomenographic study of reading

Concerns about the ability of post-secondary students to read scholarly materials are well documented in the literature. A key aspect of reading at the deeper level expected of these students is connecting new information to prior knowledge. This study is based on an activity where students were explicitly required to make such connections as part of an in-class workshop on reading. Phenomenographic analysis of these connections showed that students could establish links between the scholarly article and their personal and academic knowledge. It also showed that students read at both surface and deep levels, making connections to the words in the text or on a deeper level, to the meaning of the text. These insights suggest ways of encouraging students to deepen their engagement with academic texts.     

图式理论在高职英语听力教学的运用

根据图式理论,任何文本,不论是口头文本还是书面文本,本身并不表达任何信息,而是靠人的先验知识赋予文本信息。听力则是文本输入与大脑中固有知识间的动态交互过程。将图式理论运用到英语听力教学中,通过在“听前”激活图式,在“听中”建构图式以及在“听后”巩固图式,帮助学生建立固有知识与新知识间的桥梁,不断提高其英语听力水平。     

CHILDREN'S SPIRITUALITY AND “THE GOOD SHEPHERD EXPERIENCE”

This article aims to explore the connections between a religious education curriculum's methodology in the Catholic Archdiocese of Melbourne, Australia and some contemporary theories about children's spirituality. “The Good Shepherd Experience” curriculum is intended for use with 5- and 6-year-old children in the first years of formal schooling. It forms a part of the To Know, Worship and Love religious education text based curriculum, directed for use by schools in the Archdiocese of Melbourne as a key text in the religious education curricula. In exploring connections with children's spirituality, this article analyzes “The Good Shepherd Experience” in terms of wonder (mystery-sensing, contingency, and dependability), play and imagination, and the ability to use religious language and concepts.     

Analyzing teaching quality in Botswana and South Africa

This study focuses on quantifying the quality of mathematics teaching in 183 randomly selected sixth grade classrooms: 100 from the North West province of South Africa and 83 from South East Botswana. The teaching quality is measured by coding videotaped lessons for three different components: mathematical proficiency, level of cognitive demand, and observed teacher knowledge. Results suggest that the overall teaching quality is about the same in both regions. Some variation was observed at the level of each component. For example, in the South Africa sample the students engage more in tasks that just involve “memorization” and less in tasks that involve “procedures without connections” in comparison with the Botswana students. Teachers in Botswana implement the official curriculum more faithfully than do those in North West. In both countries most of the learners engaged only in low-level tasks (very little activity involved “procedures with connections”) and teachers demonstrated a lack of knowledge about how to integrate mathematical content with effective pedagogical techniques.     

Relational Analysis of College Science‐Major Students’ Epistemological Beliefs Toward Science and Conceptions of Learning Science

In recent years, there has been an increasing interest among educational researchers in exploring the relationships between learners’ epistemological beliefs and their conceptions of learning. This study was conducted to investigate these relationships particularly in the domain of science. The participants in this study included 407 Taiwanese college science‐major students. All of them responded to two major questionnaires, one assessing their scientific epistemological beliefs (SEBs) and the other one probing their conceptions of learning science (COLS). The SEB questionnaire included four factors: “certainty,” “source,” “development,” and “justification” of science knowledge. The COLS survey consisted of six factors in a hierarchical order, that is, learning science as “memorizing,” “preparing for tests,” “calculating and practicing,” “increasing one’s knowledge,” “application,” and “understanding and seeing in a new way.” The students’ confidence and interest toward learning science were also assessed by additional questionnaire items. Stepwise regression analyses, in general, showed coherence between students’ SEBs and their COLS, indicating that the sophistication of SEBs was consistent with less agreement with lower‐level COLS (such as “memorizing” and “preparing for tests”) as well as more agreement with higher‐level COLS (such as “understanding and seeing in a new way”). However, the SEB’s “justification” factor was positively related to almost all of COLS factors from the lower‐level to higher‐level. This study finally found that among all of the SEB and COLS factors, the “preparing for tests” factor in COLS was the solely significant variable for predicting students’ interest in science and confidence toward learning science.     

“以学生为中心”的理念在高中国际课程融合教学中的实践与思考

随着基础教育阶段国际化的不断深入,在坚持立足本土、兼容并包的课程融合实践中,研究提出了高中国际课程融合教学实践的三个支点和四个突出特点以及课程融合教学实践中采用的“差异化教学”“混合式学习”“多元化评价”三个策略。“以学生为中心”并不是要弱化教师的作用;要真正落实“眼中有人,心中有人”;“以学生为中心”是为了学生,而不是站在学生的立场上。     

大学辅学体系的新实践:“精确评价—精准指导”

“精确评价—精准指导”辅助学生发展体系是评价学生与指导发展的新方案、新实践。该体系修正了传统的评价体系,从学生自身、同学、导师三者入手设定“自己眼中的自己”“同学眼中的自己”“老师眼中的自己”“自己认为别人眼中的自己”四个评价模块,挖掘学生学业成绩、努力程度等13项评价数据,利用EXCEL、赋权频数统计、大数据原理等方法进行统计与整合,用雷达图分析法对整合后数据进行了精准化分析,并提出个性化发展建议。该体系有助于发现学生的优势与不足,有利于高校将人才素质和人才特性与因材施教合理匹配,促成差异化管理、因材管理理念的实现,从而达到“人尽其才、人适其位、人位相宜”这一较为理想的模式。     

Students’ Perception of Interdisciplinary,Problem‐Based Learning in a Food Biotechnology Course

Abstract: Students’ perception of 8 criteria (rationale of the problem; interdisciplinary learning; facilitator asked essential questions; learner's skills; assessments; facilitation procedures; team's use of resources [team collaboration], and facilitator within a problem‐based learning context) were assessed for a food biotechnology course that was part of a 3rd year biotechnology program. The mean score for “perceived learner's skills” was the lowest whereas those for “facilitation” and “facilitator” were the highest. Selected qualitative comments from students were also analyzed. This study demonstrated interdisciplinary learning as the students could make meaningful connections across different science disciplines. Further investigation is needed to develop possible strategies to accommodate the challenges in making meaningful connections across science disciplines as well as to develop a defined hybrid method for analysis of students’ responses.     

CAN READABILITY FORMULAS BE USED TO SUCCESSFULLY GAUGE DIFFICULTY OF READING MATERIALS?

A grade level of reading material is commonly estimated using one or more readability formulas, which purport to measure text difficulty based on specified text characteristics. However, there is limited direction for teachers and publishers regarding which readability formulas (if any) are appropriate indicators of actual text difficulty. Because oral reading fluency (ORF) is considered one primary indicator of an elementary aged student's overall reading ability, the purpose of this study was to assess the link between leveled reading passages and students’ actual ORF rates. ORF rates of 360 elementary‐aged students were used to determine whether reading passages at varying grade levels are, as would be predicted by readability levels, more or less difficult for students to read. Results showed that a small number of readability formulas were fairly good indicators of text, but this was only true at particular grade levels. Additionally, most of the readability formulas were more accurate for higher ability readers. One implication of the findings suggests that teachers should be cautious when making instructional decisions based on purported “grade‐leveled” text, and educational researchers and practitioners should strive to assess difficulty of text materials beyond simply using a readability formula.     

Exploring the difficulty of mathematics examination questions for weaker readers

This research investigated the difficulty of examination questions for students with weaker reading skills. Item level performance data were obtained for all candidates who took a maths examination (for 16 year olds). A sub-group of students who had access to a reader was identified (students with proven reading difficulties are permitted to have an adult available to read the examination questions aloud). A matched control group of students was also identified. Facility values were calculated for the “Reader” and “Matched” groups and used to compare item difficulty between groups. Questions for which there was a statistically significant difference between scores for the two groups were selected for more detailed analysis of the responses given by 100 candidates from each group. The analyses attempted to identify the question features likely to have contributed to relative difficulty or ease for those with weaker reading skills. This can inform future question-writing practice.     

互文性：文本社会学的理论之核

文本社会学是奥地利学者皮埃尔·V·齐马提出的社会学批评理论。他充分地汲取了巴赫金的对话理论、克里斯特娃的符号学,在文本与社会之间、文本各层次之间、文本生产与接受之同、文类体系与社会体系之间构建了互文性。文本社会学将“互文性”作为其理论核心,不仅给我们提供了一种既经验又批判的社会学批评方法,可以成为中国21世纪文学理论多元化中的一元,而且还能为文学研究和文化研究的和谐沟通提供一种精致而有效的理论范式。     

How Dynamic Visualization Technology can Support Molecular Reasoning

This paper reports the results of a study aimed at exploring the advantages of dynamic visualization for the development of better understanding of molecular processes. We designed a technology-enhanced curriculum module in which high school chemistry students conduct virtual experiments with dynamic molecular visualizations of solid, liquid, and gas. They interact with the visualizations and carry out inquiry activities to make and refine connections between observable phenomena and atomic level processes related to phase change. The explanations proposed by 300 pairs of students in response to pre/post-assessment items have been analyzed using a scale for measuring the level of molecular reasoning. Results indicate that from pretest to posttest, students make progress in their level of molecular reasoning and are better able to connect intermolecular forces and phase change in their explanations. The paper presents the results through the lens of improvement patterns and the metaphor of the “ladder of molecular reasoning,” and discusses how this adds to our understanding of the benefits of interacting with dynamic molecular visualizations.     

Special Education Teachers Integrating Reading with Eighth Grade U.S. History Content

This research replicates an earlier study and extends it by shifting instructional responsibility from researchers to special education teachers, who implemented reading instruction that included multisyllabic word decoding, academic vocabulary, and three comprehension strategies (generating main ideas, comparing and contrasting people and events, and identifying cause and effect relations) with their intact eighth grade history classes, using history text as the reading material. Participants included 73 eighth grade students with disabilities (77 percent with learning disabilities, 72 percent males, and 45 percent English language learners) and four teachers. Compared to students with disabilities in typical special education history classes, students in the treatment outperformed controls on researcher‐developed measures of word‐ and text‐level reading comprehension, as well as in the history content that students in both conditions studied. Across reading strategies, implementation of “nearly all lesson components” ranged from 72 percent to 83 percent.     

大数据背景下高校图书馆书评工作实施策略

大数据背景下,大学生阅读不可避免地受到“碎片化”“快餐化”影响。好的书评,能传播馆藏信息、引导阅读倾向、倡导先进价值观。高校图书馆要重视新书通告、文本推介、书海导航、热点点评、“大家”之言、大学生书评等各类书评工作,引发大学生阅读兴趣,推进大学生整体阅读,提升大学生使用图书馆和深层次阅读的能力。     

The research of social-design-based maker education: based upon “The old man and the sea” text

Since 2015, the Taiwan government has endeavoured to uphold maker education for all-level schools. In addition to “learning by doing” or “learning through play”, maker education believed to have varied features that set it apart from preceding pedagogical approaches and have possibility to reform learners’ requisite competencies for future. Engaging with “social care” as the mind-set for example, it could drive maker movement towards a value-oriented disposition. This paper discusses the theoretical roots of maker education, collates its beliefs about the whole, and probes the correlation between social design and maker education. We studied how the experimental pedagogy of social-design-based making based on the text of “The Old Man and The Sea” was used at the 2017 New Taipei City Maker Workshop in Taiwan. And we constructed a case study to document its effects within the classroom context. The study revealed that the teaching model of social-design-based maker education would be the sequence as “topic choosing, problem defining, sympathy triggering, conception outputting, prototype making, integrating and sharing”, the proportion of teachers’/students’ roles in maker courses should be in half of the overall lessons, and teachers’ instructions should be concentrated on offering key questions and assisting on integrating learning points mainly.     

Improving Students' Data Analysis and Presentation Skills: The Ocean State Circuits,Inc. Forecasting Project

Many potential employers expect that newly hired students will arrive on‐the‐job with the ability to analyze data, utilize spreadsheets, and communicate findings and recommendations. We designed the Ocean State Circuits, Inc. Forecasting Project to address these gaps in our students’ knowledge of analytical tools (such as the vlookup() function and pivot tables), their ability to write mathematical formulas in a spreadsheet, their understanding of more advanced data analysis features (e.g., regression, correlation), and their ability to communicate and present managerial conclusions. The exercise requires student teams to act as “consultants” and utilize spreadsheets to analyze and forecast the demand for a hypothetical set of products and then communicate their findings to “management” in a professionally formatted report document. A survey of students that have completed the exercise indicates that their knowledge level of the tools used in the project increased significantly from before to after they completed the case. Similarly, anecdotal feedback from employers suggests that students that have completed the exercise seem more capable of dissecting data when investigating business issues.     

Learning from scientific texts: personalizing the text increases transfer performance and task involvement

In an experiment with 65 high-school students, we tested the hypothesis that personalizing learning materials would increase students’ learning performance and motivation to study the learning materials. Students studied either a 915-word standard text on the anatomy and functionality of the human eye or a personalized version of the same text in which 60 definite articles (e.g., “the eye”) were replaced with 60 second-person possessive pronouns (e.g., “your eye”). Afterwards, participants answered comprehension and transfer questions. One week later, the participants were asked to restudy the text and to answer the same questions again with the aim to improve their performance. In the personalized text condition, students showed higher transfer performance, spent more time on restudying the text, and reported being more motivated than students in the standard text condition. However, only duration of restudying (not self-reported motivation) mediated the effect of personalization on transfer performance.