scholarly journals Developing Number Sense: An Approach to Initiate Algebraic Thinking in Primary Education

Mathematics ◽  
2021 ◽  
Vol 9 (5) ◽  
pp. 518
Author(s):  
Natividad Adamuz-Povedano ◽  
Elvira Fernández-Ahumada ◽  
M. Teresa García-Pérez ◽  
Jesús Montejo-Gámez
Keyword(s):  
Teaching And Learning ◽  
Number Sense ◽  
Methodological Approach ◽  
Number System ◽  
Algebraic Thinking ◽  
First Year ◽  
Symbolic Language ◽  
Decimal Number ◽  
Language Characteristic ◽  
Theoretical Foundations

Traditionally, the teaching and learning of algebra has been addressed at the beginning of secondary education with a methodological approach that broke traumatically into a mathematical universe until now represented by numbers, with bad consequences. It is important, then, to find methodological alternatives that allow the parallel development of arithmetical and algebraic thinking from the first years of learning. This article begins with a review of a series of theoretical foundations that support a methodological proposal based on the use of specific manipulative materials that foster a deep knowledge of the decimal number system, while verbalizing and representing quantitative situations that underline numerical relationships and properties and patterns of numbers. Developing and illustrating this approach is the main purpose of this paper. The proposal has been implemented in a group of 25 pupils in the first year of primary school. Some observed milestones are presented and analyzed. In the light of the results, this well-planned early intervention contains key elements to initiate algebraic thinking through the development of number sense, naturally enhancing the translation of purely arithmetical situations into the symbolic language characteristic of algebraic thinking.

Modeling 10-ness using Tech-knowledgy

2012 ◽  
Vol 18 (9) ◽  
pp. 574-578 ◽  
Author(s):  
Jennifer Suh ◽  
Padmanabhan Seshaiyer
Keyword(s):  
Number Sense ◽  
Number System ◽  
Place Value ◽  
Teaching Mathematics ◽  
Technology Knowledge ◽  
Knowledge For Teaching ◽  
Decimal Number

Foundational in understanding place value and our decimal number system, this concept is explored through a practiced-based activity designed to develop teachers' technology knowledge for teaching mathematics. The activity focuses on number sense using online applets and various related models and representations.

scholarly journals Third Grade Students’ Use of Relational Thinking

Mathematics ◽  
2021 ◽  
Vol 9 (2) ◽  
pp. 187
Author(s):  
Marta Molina ◽  
Encarnación Castro
Keyword(s):  
Number Sense ◽  
Number System ◽  
Teaching Experiment ◽  
Third Grade ◽  
Relational Thinking ◽  
Arithmetic Properties ◽  
Third Grade Students ◽  
Decimal Number ◽  
Mathematics Curricula ◽  
Arithmetic Expressions

Current mathematics curricula have as one of their fundamental objectives the development of number sense. This is understood as a set of skills. Some of them have an algebraic nature such as acquiring an abstract understanding of relations between numbers, developing awareness of properties and of the structure of the decimal number system and using it in a strategic manner. In this framework, the term relational thinking directs attention towards a way of working with arithmetic expressions that promotes relations between their terms and the use of properties. A teaching experiment has allowed to characterize the way in which third grade students use this type of thinking for solving number equalities by distinguishing four profiles of use. These profiles inform about how students employ relations and arithmetic properties to solve the equalities. They also ease the description of the evolution of the use of relational thinking along the sessions in the classroom. Uses of relational thinking of different sophistication are distinguished depending on whether a general known rule is applied, or relations and properties are used in a flexible way. Results contribute to understanding the process of developing the algebraic component of number sense.

A Compass During the Storm: Offering Students Critical Rigor for Polarizing Times

2021 ◽  
pp. 1-5
Author(s):  
Andrew M. Wender ◽  
Valerie J. D’Erman
Keyword(s):  
Higher Education ◽  
Critical Thinking ◽  
Civic Engagement ◽  
Political Science ◽  
Cognitive Processes ◽  
Teaching And Learning ◽  
Thinking Skills ◽  
Critical Thinking Skills ◽  
Learning Objective ◽  
First Year

ABSTRACT Teaching and learning in higher education is occurring, unavoidably, within the broader civic context of today’s extraordinarily polarizing political times. We seek to help students situate themselves with respect to and, above all, thoughtfully assess others’ as well as their own perspectives on issues of profound contention, without contributing to exacerbated polarization ourselves. Specifically, we offer students in our first-year exploratory political science course a vital tool—critical rigor—for navigating but not being inundated by the storm. This article discusses our experiences in teaching the course titled, “The Worlds of Politics,” as we attempt to help students deeply engage in cognitive processes of critical thinking and analysis, without undue infringement from their own—and least of all our own—personal political biases. Our focal learning objective is the cultivation of critical-thinking skills that promote students’ drawing of distinctions between advocacy and analysis, as well as their discerning civic engagement.

scholarly journals Comparative Dynamics of Above-Ground Litter Production and Decomposition from Eucalyptus Grandis Hill ex Maiden and Pinus Taeda L., and Their Contribution to Soil Organic Carbon

Forests ◽  
2021 ◽  
Vol 12 (3) ◽  
pp. 349
Author(s):  
Andrés Baietto ◽  
Jorge Hernández ◽  
Amabelia del Pino
Keyword(s):  
Pinus Taeda ◽  
Decomposition Rate ◽  
Methodological Approach ◽  
Eucalyptus Grandis ◽  
Isotopic Analysis ◽  
Forest Litter ◽  
First Year ◽  
Litter Production ◽  
Forest Species ◽  
Pinus Taeda L

The replacement of native pasture by exotic commercial forest species is an infrequent situation worldwide. In these systems, a new component is introduced, forest litter, which constitutes one of the main ways of incorporating carbon into the soil–plant system. The present work seeks to establish a methodological approach to study the dynamics of litter production and decomposition in an integrated way. The general objective was to characterize and compare the litter production dynamics in 14-year-old Eucalyptus grandis Hill ex Maiden and Pinus taeda L. commercial plantations. During two years, seasonal evaluations of fall, decomposition and accumulation of litter were carried out in stands of both species. In turn, the contribution of carbon from forest species to the soil through isotopic analysis techniques was quantified. Litterfall in E. grandis showed maximums during the spring of the first year and in the spring and summer of the second. In P. taeda, the maximums occurred in summer of the first year and in autumn of the second. In relation to the decomposition rate, the results based on short periods of evaluation between 15 and 21 months did not show differences between species, nor for the different moments of beginning of the evaluation, obtaining average values of 0.0369 month−1 for E. grandis and 0.0357 month−1 for P. taeda. In turn, both the decomposition rate of the material as a whole and the estimates of accumulated biomass in equilibrium state did not show significant differences between the species. Additionally, there was a relevant incorporation of carbon into the soil by forest species, fundamentally in the first few centimeters, substituting an important proportion of the carbon inherited by the original cover of native pastures. Finally, it is necessary to specify that the scope of the findings obtained is greatly limited by the sample size used in this study.

An exploration of the factors that contribute to learning satisfaction of first-year anatomy and physiology students

2015 ◽  
Vol 39 (3) ◽  
pp. 158-166 ◽  
Author(s):  
Saramarie Eagleton
Keyword(s):  
Learning Community ◽  
Teaching And Learning ◽  
Community Support ◽  
First Year ◽  
Learning Effectiveness ◽  
Anatomy And Physiology ◽  
Learning Satisfaction ◽  
Use Of Technology ◽  
Teaching Anatomy ◽  
Physiology Students

Lecturers have reverted to using a “blended” approach when teaching anatomy and physiology. Student responses as to how this contributes to their learning satisfaction were investigated using a self-administered questionnaire. The questionnaire consisted of closed- and open-ended questions that were based on three determinants of learning satisfaction: perceived course learnability, learning community support, and perceived learning effectiveness. Regarding course learnability, students responded positively on questions regarding the relevance of the subject for their future careers. However, students identified a number of distractions that prevented them from paying full attention to their studies. As far as learning community support was concerned, respondents indicated that they were more comfortable asking a peer for support if they were unsure of concepts than approaching the lecturing staff. Most of the students study in their second language, and this was identified as a stumbling block for success. There was a difference in opinion among students regarding the use of technology for teaching and learning of anatomy and physiology. From students' perceptions regarding learning effectiveness, it became clear that students' expectations of anatomy and physiology were unrealistic; they did not expect the module to be so comprehensive. Many of the students were also “grade oriented” rather than “learning oriented” as they indicated that they were more concerned about results than “owning” the content of the module. Asking students to evaluate aspects of the teaching and learning process have provided valuable information to improve future offerings of anatomy and physiology.

scholarly journals A virtual alternative to molecular model sets: a beginners’ guide to constructing and visualizing molecules in open-source molecular graphics software

2021 ◽  
Vol 14 (1) ◽  
Author(s):  
Siripreeya Phankingthongkum ◽  
Taweetham Limpanuparb
Keyword(s):  
General Chemistry ◽  
Open Source ◽  
Undergraduate Students ◽  
Teaching And Learning ◽  
Molecular Model ◽  
Bond Line ◽  
First Year ◽  
Molecular Graphics ◽  
Model Sets ◽  
Graphics Software

Abstract Objective The application of molecular graphics software as a simple and free alternative to molecular model sets for introductory-level chemistry learners is presented. Results Based on either Avogadro or IQmol, we proposed four sets of tasks for students, building basic molecular geometries, visualizing orbitals and densities, predicting polarity of molecules and matching 3D structures with bond-line structures. These topics are typically covered in general chemistry for first-year undergraduate students. Detailed step-by-step procedures are provided for all tasks for both programs so that instructors and students can adopt one of the two programs in their teaching and learning as an alternative to molecular model sets.

PEER FEEDBACK TECHNIQUE IN IMPROVING THE STUDENTS’ WRITING ABILITY OF THE FIRST GRADE STUDENTS IN SMA NEGERI BALIKPAPAN

2020 ◽  
Vol 3 (1) ◽  
pp. 117-131
Author(s):  
Dayang Suriani
Keyword(s):  
Learning Process ◽  
Teaching And Learning ◽  
Peer Feedback ◽  
First Grade ◽  
First Year ◽  
First Year Students ◽  
Writing Ability ◽  
Preliminary Study ◽  
Academic Year ◽  
Writing Practice

This study is directed to obtain information how peer feedback can improve students’ ability in writing. Specifically, it is directed to investigate whether peer feedback works and can improve students’ writing ability in writing sentences and narrative paragraphs, at the first year students of SMA Negeri 1 Balikpapan. The study was conducted based on the result of preliminary study at the school. It is found that the students’ ability in the language skills especially in writing is still insufficient. In the teaching and learning process the teacher provides fewer portions in writing activities for the students in class. In addition, the strategies used in the teaching and learning process are uninteresting because the students have to do the writing activities in under pressure. To answer the problems, a classroom action research is conducted. The teacher as a researcher works in planning the action, implementing the action, observing, and analyzing and reflecting the action. The subjects of the study are the second year students (X-IPA-1) of 2019/2020 academic year consisting of 40 students. The results shows that peer feedback obviously can improve the students’ ability in writing sentences and narrative paragraphs at the first year students of SMA Negeri 1 Balikpapan. It has been observed that the improvements are caused by the regular writing practice done by the students and the teacher’s response given to their writing. It becomes a sort of on going dialogue.

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