College Studens´ Views of Fraction Arithmetic

2019 ◽  
pp. 36-41
Author(s):  
Brianna Bentley
Keyword(s):  
College Students ◽  
Conceptual Understanding ◽  
Correct Answer ◽  
Mathematics Courses ◽  
Critical Thought ◽  
Procedural Understanding ◽  
Direct Reflection

College students view mathematics, specifically fraction arithmetic, as a series of tricks that can lead them to the correct answer. This view of mathematics is a direct reflection of their lack of conceptual understanding of fraction arithmetic and their reliance on procedural understanding. College students have an imprecise remembrance of fraction arithmetic and instead rely on tricks they vaguely remember and cannot explain. This reliance on procedural processes that they do not fully understand causes them to make mistakes in their arithmetic. If we do not require students to think critically about the mathematical processes they are completing when first taught a subject and require this critical thought as students progress through mathematics courses, mathematics loses meaning and our students will not have the ability to think critically or conceptually about mathematics.

scholarly journals On being examined: do students and faculty agree?

2015 ◽  
Vol 39 (4) ◽  
pp. 320-326 ◽  
Author(s):  
Andrew Perrella ◽  
Joshua Koenig ◽  
Henry Kwon ◽  
Stash Nastos ◽  
P. K. Rangachari
Keyword(s):  
Conceptual Understanding ◽  
Correct Answer ◽  
Transfer Of Learning ◽  
Learning Experience ◽  
Health Sciences ◽  
Faculty Members ◽  
Point Scale ◽  
New Information ◽  
Good Learning ◽  
Level Of Agreement

Students measure out their lives, not with coffee spoons, but with grades on examinations. But what exams mean and whether or not they are a bane or a boon is moot. Senior undergraduates (A. Perrella, J. Koenig, and H. Kwon) designed and administered a 15-item survey that explored the contrasting perceptions of both students ( n = 526) and faculty members ( n = 33) in a 4-yr undergraduate health sciences program. A series of statements gauged the level of agreement on a 10-point scale. Students and faculty members agreed on the value of assessing student learning with a variety of methods, finding new information to solve problems, assessing conceptual understanding and logical reasoning, having assessments with no single correct answer, and having comments on exams. Clear differences emerged between students and faculty members on specific matters: rubrics, student choice of exam format, assessing creativity, and transfer of learning to novel situations. A followup questionnaire allowed participants to clarify their interpretation of select statements, with responses from 71 students and 17 faculty members. All parties strongly agreed that exams should provide a good learning experience that would help them prepare for the future (students: 8.64 ± 1.71 and faculty members: 8.03 ± 2.34).

Mathematical Background and Attitudes toward Statistics in a Sample of Spanish College Students

2005 ◽  
Vol 97 (1) ◽  
pp. 53-62 ◽  
Author(s):  
José Carmona ◽  
Rafael J. Martínez ◽  
Manuel Sánchez
Keyword(s):  
Social Sciences ◽  
College Students ◽  
Multivariate Analyses ◽  
Affective Responses ◽  
Mathematics Courses ◽  
Mathematical Background ◽  
Attitudes Toward Statistics

To examine the relation of mathematical background and initial attitudes toward statistics of Spanish “college students in social sciences the Survey of Attitudes Toward Statistics was given to 827 students. Multivariate analyses tested the effects of two indicators of mathematical background (amount of exposure and achievement in previous courses) on the four subscales. Analysis suggested grades in previous courses are more related to initial attitudes toward statistics than the number of mathematics courses taken. Mathematical background was related with students' affective responses to statistics but not with their valuing of statistics. Implications of possible research are discussed.

scholarly journals Investigating the Different Dimensions of Preservice Mathematics Teachers’ Understanding – The Case of Factorisation

2020 ◽  
Vol 45 (10) ◽  
pp. 73-94
Author(s):  
Olivia Fitzmaurice ◽  
◽  
Jacqueline Hayes ◽  
Keyword(s):  
Teacher Education ◽  
Preservice Teachers ◽  
Secondary School ◽  
Conceptual Understanding ◽  
Mathematics Teachers ◽  
Teacher Educators ◽  
Education Programme ◽  
Procedural Understanding ◽  
Different Dimensions ◽  
Preservice Mathematics Teachers

This paper reports on a study designed to investigate preservice teachers’ understanding of factorisation, a topic not explicitly taught within their teacher education programme, but one they will be required to teach when they graduate. We query if the knowledge they bring from secondary school, prepares them sufficiently to teach their future students for understanding. 83 preservice secondary school mathematics teachers’ procedural and conceptual understanding of quadratic factorisation were assessed using Usiskin’s Framework for understanding mathematics (2012) which identifies several dimensions of understanding. The study provides evidence that the preservice mathematics teachers have a strong procedural understanding, and while some conceptual understanding does exist, there was very limited conceptual understanding within most of the dimensions of the framework (Usiskin, 2012). We conclude the paper by considering how teacher educators can address the issues of preservice teacher knowledge and understanding of content not formally covered within their teacher education programmes.

scholarly journals Transition Process of Procedural to Conceptual Understanding in Solving Mathematical Problems

2016 ◽  
Vol 9 (9) ◽  
pp. 182 ◽  
Author(s):  
Fatqurhohman Fatqurhohman
Keyword(s):  
Conceptual Understanding ◽  
Transition Process ◽  
Fifth Grade ◽  
Procedural Understanding ◽  
Fifth Grade Students ◽  
Mathematical Problems

<p class="apa">This article aims to describe the transition process from procedural understanding to conceptual understanding in solving mathematical problems. Subjects in this study were three students from 20 fifth grade students of SDN 01 Sumberberas Banyuwangi selected based on the results of the students’ answers. The transition process from procedural to conceptually based on three aspects: (1) identify problems in the use of an algorithm, (2) the process algorithm, (3) connect multiple concepts to transform into another shape through the symbolic/picture representations. The results showed that the majority of students (18 students out of 20 students) only meets two (2) aspects of 10 students (50%) can identify the algorithms and the use of algorithms, 8 students (40%) able to use algorithms and connect with other forms. While other students (two students from 20 students) of 10% that meet only three aspects of the transitions. Thus, understanding the procedural has an important role in developing a conceptual understanding. Because the component/aspect of procedural understanding exist on components/aspects of conceptual understanding. Thus, the association acquired several components/aspects that support the process of transition from procedural understanding to a conceptual understanding.</p>

Prove It! Engaging Teachers as Learners to Enhance Conceptual Understanding

2008 ◽  
Vol 15 (2) ◽  
pp. 68-73
Author(s):  
Julie Sweetland ◽  
Meghann Fogarty
Keyword(s):  
Elementary School ◽  
Staff Development ◽  
Conceptual Understanding ◽  
Correct Answer ◽  
Mathematics Problem

The faculty of an elementary school gathered for a staff development workshop and quickly completed the first mathematics problem assigned by the facilitator: “What is 1/5 × 1/4?” Within a few seconds, every teacher in the room arrived at the correct answer: 1/20. The follow-up question, at first glance, seemed to be equally simple: “How did you get your answer?”

scholarly journals A Comparison of Pedagogical Practices and Beliefs in International and Domestic Mathematics Teaching Assistants

2014 ◽  
Vol 4 (1) ◽  
pp. 74-88
Author(s):  
Minsu Kim
Keyword(s):  
Conceptual Understanding ◽  
Mathematics Teaching ◽  
Teaching Assistants ◽  
The Body ◽  
Pedagogical Practices ◽  
Development Programs ◽  
Substantial Portion ◽  
Mathematics Courses ◽  
Body Of Knowledge ◽  
New Concepts

International and domestic mathematics teaching assistants (MTAs) are a critical part of mathematics education because they teach a substantial portion of low-level mathematics courses at research institutions. Even if there are several factors to build on MTAs’ pedagogical practices, MTAs’ beliefs significantly influence the MTAs’ practices. The purpose of this study is to explore different beliefs and pedagogical practices between international and domestic MTAs. The findings reveal that there is consistency between the MTAs’ beliefs and their pedagogical practices. In addition, the two groups adopt significantly different approaches of how to teach new concepts, definitions, and problem-solving for students’ conceptual understanding and how to interact with their students. These results contribute to the body of knowledge of MTAs and the adaptation of professional development programs of MTAs. In addition, faculty in mathematics has an opportunity to understand the differences in beliefs and pedagogical practices between IMTAs and DMTAs.

scholarly journals GeoGebra as a Means for Understanding Limit Concepts

2017 ◽  
Vol 7 (2) ◽  
pp. 71-84
Author(s):  
Puspita Sari
Keyword(s):  
Conceptual Understanding ◽  
Learning Trajectory ◽  
Complete Understanding ◽  
Procedural Understanding ◽  
Common Misconception ◽  
Limit Problems ◽  
Geometric Representations ◽  
The Common ◽  
Dynamic Software ◽  
Support Students

Limit is a major concept in calculus that underpins the concepts of derivatives and integrals. The common misconception about limits is that students treat the value of a limit of a function as the value of a function at a point. This happens because usually the teaching of limit only leads to a procedural understanding (Skemp, 1976) without a proper conceptual understanding. Some researchers suggest the importance of geometrical representations to a meaningful conceptual understanding of calculus concepts. In this research, GeoGebra as a dynamic software is used to support students’ understanding of limit concepts by bridging students' algebraic and geometrical thinking. In addition to this, realistic mathematicseducation (RME) is used as a domain theory to develop an instructional design regarding how GeoGebra could be used to illustrate and explore the limit concept of so that students will have a meaningful understanding both algebraically and geometrically. Therefore, this research aims to explore the hypothetical learning trajectory in order to develop students’ understanding of limit concepts by means of GeoGebra and an approach based on RME.The results show that students are able to solve limit problems and at the same time they try to make sense of the problem by providing geometrical representations of it. Thus, the use of geometric representations by GeoGebra and RME approach could provide a more complete understanding of the concepts of limit. While the results are interesting and encouraging and provide some promising directions, they are not a proof and a much larger study would be needed to determine if the results are due to this approach or due to the teachers’ enthusiasm, the novelty effect or what is known as the Hawthorne Effect.

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