scholarly journals A calculus student’s understanding of graphical approach to the derivative through quantitative reasoning

2021 ◽  
Vol 9 (1) ◽  
Author(s):  
Aytug Ozaltun-Celik
Keyword(s):  
Mathematical Modelling ◽  
Rate Of Change ◽  
Quantitative Reasoning ◽  
First Year ◽  
Instantaneous Rate ◽  
Graphical Approach ◽  
Global View ◽  
Concept Of Function ◽  
Support Students ◽  
Mental Actions

The concept of derivative is used in many areas including applied problems and requiring mathematical modelling in different disciplines. One of the most important approaches for teaching the derivative is to support students in visualizing the concept. Also, it is necessary to shift researchers and teachers’ focuses to students’ dynamic mental actions while learning derivative in order to conduct effective teaching process. With this necessity, I focused on the perspective of quantitative reasoning related to the graphical approach to the derivative. This study aims to reveal a calculus student’s mental actions related to the graphical approach to the derivative. The data were collected from a first-year calculus student engaged in the task requiring graphical interpretation of the derivative. Results showed that the student’s understanding of the slope shaped her inferences about the tangent line because the quantity of ratio is prior knowledge for learning the instantaneous rate of change. Besides, as the student had the idea of correspondence related to the concept of function, she had difficulties in interpreting the global view of the derivate. This result suggests that having global view of the derivative requires a strong understanding of function and rate.

scholarly journals Identifying the structure of students’ argumentation in covariational reasoning of constructing graphs

2020 ◽  
Vol 13 (1) ◽  
pp. 61-80
Author(s):  
Sutini Sutini ◽  
Iffana Fitrotul Aaidati ◽  
Kusaeri Kusaeri
Keyword(s):  
Average Rate ◽  
Rate Of Change ◽  
Interview Data ◽  
The Other ◽  
Mental Action ◽  
Instantaneous Rate ◽  
Covariational Reasoning ◽  
Mental Actions ◽  
Grade 11

[English]: This study aimed to identify students’ claim, evidence, and reasoning in covariational reasoning of constructing the graphs of a function. Covariational reasoning is one of the approaches to solve the problems of function. The study involved thirty grade 11 students. Data was collected through a covariation test and interview. The results of the test were grouped based on the criteria of mental action of covariational reasoning (Carlson et al., 2002), then the students who solve correctly two or three problems in the test were selected as the subjects. The interview data were analyzed to confirm and further dig students' structure of argumentation. The findings of this study indicate that only one student fulfils five mental actions of covariational reasoning; meanwhile, the other three students have similar components of argumentation which do not meet the mental actions. The claim and reasoning used by the latter students in covariational reasoning to construct graph are not identified in mental action 5 and the evidence is not found in mental action 3 (major coordination of change), mental action 4 (coordination the average rate of change), and mental action 5 (coordination of the instantaneous rate of change). Keywords: Argumentation, Claim, Evidence, Reasoning, Covariational reasoning [Bahasa]: Penelitian ini bertujuan untuk mengidentifikasi klaim, bukti, dan alasan siswa pada penalaran kovariasional dalam mengonstruk grafik fungsi. Penalaran kovariasional merupakan salah satu pendekatan dalam menyelesaikan permasalahan fungsi. Penelitian ini melibatkan 30 siswa kelas 11. Pengumpulan data dilakukan menggunakan tes kovariasi dan wawancara. Data hasil hasil tes kovariasi siswa dikelompokkan berdasarkan kriteria aksi mental penalaran kovariasional (Carlson et al., 2002), kemudian dipilih siswa yang mampu menyelesaikan minimal dua soal kovariasi. Data hasil wawancara dianalisis untuk mengonfirmasi dan menggali lebih dalam argumentasi siswa. Hasil penelitian menunjukkan hanya satu siswa yang memenuhi lima aksi mental penalaran kovariasional sedangkan ketiga siswa lain memiliki persamaan komponen argumentasi yang tidak memenuhi aksi mental. Untuk ketiga siswa tersebut, klaim dan alasan yang digunakan dalam membangun grafik fungsi tidak berada pada aksi mental 5 sedangkan bukti tidak berada pada aksi mental 3 (koordinasi besar perubahan), aksi mental 4 (koordinasi laju perubahan rata-rata), dan aksi mental 5 (koordinasi laju perubahan sesaat). Kata kunci: Argumentasi, Klaim, Bukti, Alasan, Penalaran kovariasional

scholarly journals Learning Scenario to Promote Comprehension of the Meaning of Subtraction

2021 ◽  
Vol 11 (12) ◽  
pp. 757
Author(s):  
Ricardo Silva ◽  
Fernando Martins ◽  
Cecília Costa ◽  
José Cravino ◽  
Joaquim Bernardino Lopes
Keyword(s):  
Mathematical Modelling ◽  
Structural Characteristics ◽  
Self Regulation ◽  
Virtual Manipulatives ◽  
First Year ◽  
School Students ◽  
Mathematical Connections ◽  
Post Test ◽  
Principles Of Design ◽  
Support Students

The integration of virtual manipulatives in classroom practices facilitates student learning processes. For this, the teacher must understand how to support students in establishing mathematical connections between the manipulation and their interpretations of the representations. We present a learning scenario that integrates the use of virtual manipulatives in mathematical modelling tasks. It was designed and implemented during initial teacher training, with the aim of helping a group of first-year elementary school students to overcome difficulties identified in their comprehension of the meaning of subtraction. The research, following the principles of design-based research, included three distinct moments: an individual written pre-test, an intervention phase with six micro-cycles, and an individual written post-test. The analysis of the collected data—audio, screen recordings, and written productions—allowed us to identify the most influential structural characteristics of the learning scenario: mathematical communication, collaborative learning, self-regulation, and co-regulation of learning. Our results suggest that differentiated instruction, minimal guidance, and scaffolding played an important role in the support provided by the pre-service teacher to students in the mathematical modelling activities that integrated virtual manipulatives.

scholarly journals Building Connections in the First-year Undergraduate Experience

2013 ◽  
Vol 4 (2) ◽  
Author(s):  
June Countryman ◽  
Andrew Zinck
Keyword(s):  
First Year ◽  
First Year Students ◽  
The Past ◽  
Core Courses ◽  
Big Ideas ◽  
Undergraduate Experience ◽  
New Students ◽  
Research Findings ◽  
Transition From High School ◽  
Support Students

Concerned about the success rate of new students in our program we designed and implemented a compulsory set of experiences which aim to support students in their transition from high school to university by 1) developing their sense of belonging to a community of learners and by 2) articulating with them the interrelationships among their first year core courses. We initiated various strategies which we have refined in response to student feedback over the past three years. In this paper we describe the pedagogical moves that constitute our initiative and the lessons we learned. We explore essential academic and personal issues that first-year students in all programs face. We share our research findings and address the big ideas that could be applied to any discipline or multi-disciplinary program. Préoccupés par les taux de rétention des étudiants de première année, les auteurs ont conçu et mis en oeuvre un ensemble d’expériences obligatoires dont le but est d’aider les étudiants à effectuer la transition entre l’école secondaire et l’université. Ils ont établi deux objectifs : (a) développer chez les étudiants le sens d’appartenance à une communauté d’apprenants et (b) démontrer les corrélations qui existent entre les cours de base de première année que les étudiants suivent. Diverses stratégies ont été entreprises et plus tard améliorées, à partir des rétroactions fournies par les étudiants au cours de l’étude de deux ans. Cet article présente une explication des actions pédagogiques de cette initiative et explore les questions essentielles académiques et personnelles auxquelles sont confrontés les étudiants de première année dans tous les programmes. Les résultats de cette étude sont résumés et les idées générales qui peuvent s’appliquer à n’importe quelle discipline ou à des programmes multidisciplinaires sont présentées en détail.

scholarly journals Correlates of Depression in First-Year College Students

2017 ◽  
Vol 47 (1) ◽  
pp. 114-136
Author(s):  
Aude Villatte ◽  
Diane Marcotte ◽  
Alexandra Potvin
Keyword(s):  
College Students ◽  
Depressive Symptoms ◽  
Emotional Adjustment ◽  
First Year ◽  
Personal Goals ◽  
Adjustment To College ◽  
First Year College ◽  
First Year College Students ◽  
High Level ◽  
Support Students

This study aimed to identify and rank the personal, family-related, social, and academic correlates of depressive symptoms in first-year college students. A questionnaire that included the Beck Depression Inventory-II (BDI-II) was administered to 389 first-year college students (mean age = 18.9; SD = 3.38; 59.4% female). Eight variables contributed uniquely to the variance of depressive symptoms and were, in decreasing order of importance: (1) the absence of personal goals, (2) a high level of anxiety and (3) of dysfunctional thoughts regarding success, (4) a lack of emotional adjustment to college, (5) being female, (6) receiving little warmth and encouragement of autonomy from one’s mother and (7) from one’s father, and (8) being attracted to members of the opposite or both sexes. These results suggest that a multimodal intervention is required to support students’ mental health.  

scholarly journals SOLVING INVERSE PROBLEM OF CHEMICAL KINETICS WITH USE OF CUBIC SPLINES

2020 ◽  
Vol 63 (7) ◽  
pp. 61-66
Author(s):  
Nikolay I. Kol'tsov
Keyword(s):  
Experimental Data ◽  
Inverse Problem ◽  
Chemical Kinetics ◽  
Good Accuracy ◽  
Cubic Splines ◽  
Rate Of Change ◽  
Reference Points ◽  
Additional Advantage ◽  
Instantaneous Rate ◽  
Relaxation Curves

A simple effective method for solving the inverse problem of chemical kinetics based on non-stationary experiments for multistage reactions occurring in an isothermal reactor of ideal mixing is described. The idea of the method is based on taking into account the distinctive features (informativeness) of different fragments of relaxation curves for chemical reactions with arbitrary (non-monotonic) kinetics and their as accurate approximation as possible. For this purpose, non-linear (cubic) splines are used to describe different informative fragments of relaxation curves, which allow to approximate and interpolate experimental data as accurately as possible. An additional advantage of cubic splines, from the point of view of the implementation of the described method, is their continuity at all given points up to and including second-order derivatives (smoothness). This allows us to calculate with good accuracy not only the concentration of reagents, but also the instantaneous rate of change at any time. The consequence of this is the possibility of a sufficiently accurate solution of the inverse problem based on the data of non-stationary experiments. The correctness of the mathematical model used and the stability of the method were tested using variations of the original data. An example of using the method for determining the intervals of physical values of the rate constants of the stages of a two-stage reaction is given. The influence of the method of selecting the reference points (structure) of the spline and measurement errors (noise) of experimental data on the error of determining the speed constants of the stages is estimated. The efficiency of application and good accuracy of the method for solving the inverse problem of chemical kinetics of multistage reactions occurring in non-gradient systems with taking into account of noise is shown.

scholarly journals Introduction to the special issue “Climate of the past 2000 years: regional and trans-regional syntheses”

2019 ◽  
Vol 15 (2) ◽  
pp. 611-615
Author(s):  
Chris S. M. Turney ◽  
Helen V. McGregor ◽  
Pierre Francus ◽  
Nerilie Abram ◽  
Michael N. Evans ◽  
...  
Keyword(s):  
Regional Differences ◽  
Global Climate ◽  
Rate Of Change ◽  
Global Changes ◽  
Special Issue ◽  
The Past ◽  
Global View ◽  
Past 2000 Years ◽  
Recent Climate ◽  
Observational Record

Abstract. This PAGES (Past Global Changes) 2k (climate of the past 2000 years working group) special issue of Climate of the Past brings together the latest understanding of regional change and impacts from PAGES 2k groups across a range of proxies and regions. The special issue has emerged from a need to determine the magnitude and rate of change of regional and global climate beyond the timescales accessible within the observational record. This knowledge also plays an important role in attribution studies and is fundamental to understanding the mechanisms and environmental and societal impacts of recent climate change. The scientific studies in the special issue reflect the urgent need to better understand regional differences from a truly global view around the PAGES themes of “Climate Variability, Modes and Mechanisms”, “Methods and Uncertainties”, and “Proxy and Model Understanding”.

scholarly journals Early Introduction of Sugar-Sweetened Beverages and Caries Trajectories from Age 12 to 48 Months

2020 ◽  
Vol 99 (8) ◽  
pp. 898-906 ◽  
Author(s):  
E. Bernabé ◽  
H. Ballantyne ◽  
C. Longbottom ◽  
N.B. Pitts
Keyword(s):  
Dental Caries ◽  
Young Children ◽  
Later Life ◽  
Rate Of Change ◽  
First Year ◽  
Sugar Sweetened Beverages ◽  
Sweetened Beverages ◽  
The Mean ◽  
First Year Of Life ◽  
Over Time

Early exposure to sweet tastes predicts similar food preferences and eating behavior in later life and is associated with childhood obesity. The aim of this study was to explore the associations of early (during the first year of life) and subsequent intake of sugar-sweetened beverages (SSBs) with 4-y caries trajectories among Scottish young children. We used data from 1,111 Scottish children who were followed annually from age 12 to 48 mo (4 sweeps in total). SSB intake was reported by parents in every sweep. SSB intake was broken down into 2 components, the initial SSB intake and the deviation over time from that initial value. Childhood dental caries was clinically determined (including noncavitated and cavitated lesions) every year. The association of SSB intake with baseline decayed, missing, and filled tooth surfaces (dmfs) (intercept) and rate of change in dmfs over time (slope) was examined in 2-level linear mixed-effects models, with repeated observations nested within children. Both the initial SSB intake and the deviation from the initial SSB intake were positively associated with steeper caries trajectories. By sweep 4, the predicted mean dmfs difference was 1.73 between children with low and high initial SSB intake (1 standard deviation below and above the mean) and 1.17 between children with low and high deviation from their initial SSB intake (1 SD below and above the mean). The findings of this prospective study among Scottish young children provide evidence that the introduction of SSBs during the first year of life can put children in a trajectory of high levels of dental caries. They support current recommendations to avoid sugars for very young children and interventions targeting early feeding practices for caries prevention.

scholarly journals A height resolved global view of dust aerosols from the first year CALIPSO lidar measurements

2008 ◽  
Vol 113 (D16) ◽  
Author(s):  
Dong Liu ◽  
Zhien Wang ◽  
Zhaoyan Liu ◽  
Dave Winker ◽  
Charles Trepte
Keyword(s):  
First Year ◽  
Dust Aerosols ◽  
Global View ◽  
Lidar Measurements

Helping Students to Identify and Achieve Appropriate Learning Targets

2002 ◽  
Vol 39 (3) ◽  
pp. 219-229
Author(s):  
Warren Houghton
Keyword(s):  
Learning Outcomes ◽  
First Year ◽  
Wide Range ◽  
Support Mechanisms ◽  
Support Students ◽  
Different Levels

In order to support students with a wide range of attainment expectations, within a common first year of a range of engineering programmes, intending learning outcomes have been set out in detail at different levels and support mechanisms put in place to help them plan their own learning targets.

scholarly journals A dynamical time operator in Dirac's relativistic quantum mechanics

2014 ◽  
Vol 29 (06) ◽  
pp. 1450036 ◽  
Author(s):  
M. Bauer
Keyword(s):  
Quantum Mechanics ◽  
Wave Packet ◽  
Phase Velocity ◽  
Relativistic Quantum ◽  
Rate Of Change ◽  
Time Operator ◽  
Relativistic Quantum Mechanics ◽  
Instantaneous Rate ◽  
Expectation Value ◽  
Dynamical Time

A self-adjoint dynamical time operator is introduced in Dirac's relativistic formulation of quantum mechanics and shown to satisfy a commutation relation with the Hamiltonian analogous to that of the position and momentum operators. The ensuing time-energy uncertainty relation involves the uncertainty in the instant of time when the wave packet passes a particular spatial position and the energy uncertainty associated with the wave packet at the same time, as envisaged originally by Bohr. The instantaneous rate of change of the position expectation value with respect to the simultaneous expectation value of the dynamical time operator is shown to be the phase velocity, in agreement with de Broglie's hypothesis of a particle associated wave whose phase velocity is larger than c. Thus, these two elements of the original basis and interpretation of quantum mechanics are integrated into its formal mathematical structure. Pauli's objection is shown to be resolved or circumvented. Possible relevance to current developments in electron channeling, in interference in time, in Zitterbewegung-like effects in spintronics, graphene and superconducting systems and in cosmology is noted.

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