Mathematics Majors’ Exploration of Famous Conjectures in a Transition-to-Proof Course

PRIMUS ◽  
2021 ◽  
pp. 1-34
Author(s):  
Jeffrey Pair ◽  
Gabe Calva
Keyword(s):  
Mathematics Majors ◽  
Transition To Proof

scholarly journals Creativity as a function of problem-solving expertise: posing new problems through investigations

ZDM ◽  
2021 ◽  
Author(s):  
Haim Elgrably ◽  
Roza Leikin
Keyword(s):  
Problem Solving ◽  
Dynamic Geometry ◽  
Problem Posing ◽  
Dynamic Geometry Environment ◽  
Mathematics Majors ◽  
Individual Interviews ◽  
University Mathematics ◽  
Domain Specific ◽  
Mathematics Test ◽  
Different Types

AbstractThis study was inspired by the following question: how is mathematical creativity connected to different kinds of expertise in mathematics? Basing our work on arguments about the domain-specific nature of expertise and creativity, we looked at how participants from two groups with two different types of expertise performed in problem-posing-through-investigations (PPI) in a dynamic geometry environment (DGE). The first type of expertise—MO—involved being a candidate or a member of the Israeli International Mathematical Olympiad team. The second type—MM—was comprised of mathematics majors who excelled in university mathematics. We conducted individual interviews with eight MO participants who were asked to perform PPI in geometry, without previous experience in performing a task of this kind. Eleven MMs tackled the same PPI task during a mathematics test at the end of a 52-h course that integrated PPI. To characterize connections between creativity and expertise, we analyzed participants’ performance on the PPI tasks according to proof skills (i.e., auxiliary constructions, the complexity of posed tasks, and correctness of their proofs) and creativity components (i.e., fluency, flexibility and originality of the discovered properties). Our findings demonstrate significant differences between PPI by MO participants and by MM participants as reflected in the more creative performance and more successful proving processes demonstrated by MO participants. We argue that problem posing and problem solving are inseparable when MO experts are engaged in PPI.

scholarly journals A Cross-Sectional Analysis of Mathematics Education Practices at Canadian Universities

2018 ◽  
Vol 12 (1) ◽  
pp. 1-20 ◽  
Author(s):  
Chester Weatherby ◽  
Donna Kotsopoulos ◽  
Douglas Woolford ◽  
Laaraib Khattak
Keyword(s):  
Mathematics Education ◽  
Standardized Testing ◽  
Secondary Mathematics ◽  
Online Information ◽  
Cross Sectional ◽  
Mathematics Scores ◽  
Canadian Universities ◽  
Mathematics Majors ◽  
Post Secondary ◽  
University Mathematics

In response to international standardized testing, many countries are examining mathematics education at virtually every level of instruction. Canada is no exception. Declines in mathematics scores in some international standardized tests have raised concerns amongst some stakeholders that a “crisis” may be unfolding and the readiness of students to study mathematics in university. These results raise questions about the ways in which students are streamed into university mathematics and the supports provided once they begin their studies. Our focus in this research was university-level mathematics education. To mimic how students, parents, counselors and son on are most likely to seek for mathematics support, we engaged in a web-based examination of departments of mathematics at 62 Canadian universities (including “university colleges”). Our objectives were to examine the types of degrees offered, admission protocols (including types of streaming or placement tests), methods for remedial support, accessibility of online information, mathematics help centers, courses for non-mathematics majors, and access initiatives as a preliminary step in analyzing the broader Canadian landscape in post-secondary mathematics education. Our findings reveal remarkably consistent practices across all institutions. A rethinking of practices may be necessary in order to support those students that appear to be underprepared for post-secondary mathematics.

scholarly journals Associative and Strategic Study Approaches: Their Significant Relationships to Solving Meta Cognitive Problems of Mathematics Majors

2013 ◽  
Vol 1 (1) ◽  
Author(s):  
Marvin S. Daguplo
Keyword(s):  
Word Problems ◽  
Strong Relationship ◽  
Male And Female ◽  
Mathematics Majors ◽  
Classroom Activities ◽  
Significant Relationships ◽  
Significant Difference ◽  
Mathematical Word Problems ◽  
Strategic Study ◽  
Cognitive Problems

University students still found difficulties in working successfully mathematical word problems. Some researchers attributed this to students’ weak cognitive and abstract thinking. To address such problem, this study aimed to understand student’s cognitive approaches in processing mathematics information to determine students’ level of cognition and come up with classroom activities that enhance the desired approaches in processing mathematical information which influences learning. A total of thirty-seven students of SLSU – Tomas Oppus were the respondents of this descriptive-correlational study. A standardized Mathematics Information Processing Scale (Cronbach’s alpha coefficient=.89) was utilized to gather the data for this study. Statistical analysis revealed that there is no significant difference in the performance of male and female mathematics majors in solving word problems who performed at below average level. The same finding is found between male and female mathematics majors in their approaches in processing mathematics information when solving metacognitive problems, when doing deep-associative study, and when doing strategic study. Correlational analysis revealed that a strong relationship exists between solving metacognitive problems and doing associative and strategic study approaches. This study concludes that students who apply associative and strategic study methods perform well in solving meta-cognitive problems.Keywords: Mathematics, Processing Mathematics Information, Action Research, Philippines

Exploring Reactions to Hacktivism Among STEM College Students: A Preliminary Model of Hacktivism Support and Resistance

2014 ◽  
Vol 33 (4) ◽  
pp. 479-497
Author(s):  
Lisa M. PytlikZillig ◽  
Shiyuan Wang ◽  
Leen-Kiat Soh ◽  
Alan J. Tomkins ◽  
Ashok Samal ◽  
...  
Keyword(s):  
Specific Context ◽  
Mathematics Majors ◽  
Mediation Analyses ◽  
Science Technology ◽  
Utilitarian Value ◽  
Preliminary Model ◽  
Midwestern University ◽  
Support Resistance ◽  
And Mathematics ◽  
Willingness To Report

This study investigated the predictors of support for and resistance to hacktivism in a sample of 78 science, technology, engineering, and mathematics majors at a Midwestern university. Results from surveys about real-world instances of hacktivism indicate different preexisting global attitudes predict specific situational hacktivism support (predicted by admiration) versus resistance (predicted by willingness to report). Also, participants gave greater weight to their perceptions of hacktivist (rather than target) trustworthiness/untrustworthiness. Comparisons among different facets of trustworthiness suggest perceptions of shared values with and integrity of the hacktivists are especially important for predicting support and resistance. Participants also were more supportive of hacktivism rated as having higher utilitarian value but not less supportive of hacktivism initiated for retribution. Mediation analyses indicated that situation perceptions significantly mediated the effects of global attitudes on hacktivism support/resistance, but that the significance of specific mediators was inconsistent across analyses. This suggests that the importance of mediators may depend on specific context.

Science fiction prototyping’s features and impact on college students’ perceptions of writing

2020 ◽  
Vol 10 (1) ◽  
pp. 128-164
Author(s):  
Justin Nicholes
Keyword(s):  
College Students ◽  
Creative Writing ◽  
Science Fiction ◽  
Science Writing ◽  
Post Intervention ◽  
Stem Majors ◽  
Emotional Tone ◽  
Mathematics Majors ◽  
English Majors ◽  
The Impact

Abstract The present study develops an applied literariness study by exploring both the features, and the impact, of science fiction prototyping (SFP) on college students’ perceptions of disciplinary, or field-specific, writing. College students (N = 83), who were English (n = 35) or STEM (science, technology, engineering, mathematics) majors (n = 48), composed micro-science fiction prototyping (µSFP), a genre that blends creative and science writing. Linguistic Inquiry and Word Count (LIWC2015) analysis demonstrated that, aside from a more positive average emotional tone, µSFP written fell psycho-linguistically between personal and science writing. English and STEM majors’ µSFP stories were similar in terms of analytical levels, clout, authenticity, emotional tone, and use of words. Mann-Whitney U tests indicated that, while English majors evaluated creative writing as significantly more relevant to their future career goals pre-intervention than did STEM majors (p = .04, r = .23), this difference vanished post-intervention. Additionally, while STEM majors evaluated science writing as significantly more worth their time to study (p = .042, r = .22) and relevant to their major (p = .01, r = .28) pre-intervention than did English majors, these differences disappeared post-intervention. Wilcoxon signed-ranks tests indicated that, while English majors’ ownership and evaluation of science and creative writing did not change, STEM majors’ evaluations of creative writing as relevant to their majors and future careers were significantly higher post-intervention (p = .015, r = .35)

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