Key Mathematical Competencies From Arithmetic to Algebra

2020 ◽  
Author(s):  
Kristie J. Newton ◽  
Christina A. Barbieri ◽  
Julie L. Booth
Keyword(s):  
Mathematics Learning ◽  
Numerical Magnitude ◽  
Major Area ◽  
Equal Sign ◽  
Negative Numbers ◽  
Mathematical Ideas ◽  
Whole Numbers ◽  
Mathematical Competencies ◽  
Number Lines ◽  
Over Time

Mathematics learning encompasses a broad range of processes and skills that change over time. Magnitude and equivalence are two fundamental mathematical ideas that students encounter early and often in their mathematics learning. Numerical magnitude knowledge is knowledge of the relative sizes of numbers, including whole numbers, fractions, and negative numbers, within a given scale. Understanding mathematical equivalence means understanding that two or more specific quantities with the same value can be represented in a variety of ways and remain equal and interchangeable. A major area of research on equivalence is knowledge of the equal sign. Both equal sign knowledge and magnitude knowledge are foundational in that they predict later learning in mathematics, including algebra. Implications for practice include the use of number lines and more variation in the way that arithmetic problems are formatted.

scholarly journals A Field Guide to Whole Number Representations in Children’s Books

2021 ◽  
Vol 9 (4) ◽  
pp. 697-727
Author(s):  
Julie Nurnberger-Haag ◽  
Amy Scheurermann ◽  
Janis S. McTeer
Keyword(s):  
Mathematics Learning ◽  
Trade Books ◽  
Design Studies ◽  
Field Guide ◽  
Mathematical Ideas ◽  
Whole Numbers ◽  
Field Guides ◽  
Number Representations ◽  
Whole Number ◽  
Common Resource

Trade books are a common resource used to teach children mathematical ideas. Yet, detailed analyses of the mathematics content of such books to determine potential impacts on learning are needed. This study investigated how trade books represent whole numbers. A two-pronged approach was used a) one team documented every way 197 books represented numerical ideas and b) another team used standards to identify ideal representations. A third team validated the traits on 67 books. Greater variation than expected was documented (103 traits identified) and organized into a field guide for researchers to consult to design studies about how particular traits influence number learning. Studies could investigate how a particular trait supports learning or experimentally compare a selected combination of the 45 pictorial, 45 written symbol, 10 tactile, 2 kinesthetic, and 1 auditory trait. Implications for practice include recognizing what representations are present or missing from books used in classrooms. The study also serves as an example of how the field of mathematics education would benefit from adopting structures from disciplinary science, such as field guides, to inform how we organize phenomena of mathematics learning. 

scholarly journals A Study of Errors and Misconceptions in the Learning of Addition and Subtraction of Directed Numbers in Grade 8

SAGE Open ◽  
2016 ◽  
Vol 6 (4) ◽  
pp. 215824401667137 ◽  
Author(s):  
Judah Paul Makonye ◽  
Josiah Fakude
Keyword(s):  
Conceptual Understanding ◽  
Teaching And Learning ◽  
Study Data ◽  
Negative Numbers ◽  
Teaching And Learning Mathematics ◽  
Learning Mathematics ◽  
Number Lines ◽  
Addition And Subtraction ◽  
Logical Errors ◽  
Grade 8

The study focused on the errors and misconceptions that learners manifest in the addition and subtraction of directed numbers. Skemp’s notions of relational and instrumental understanding of mathematics and Sfard’s participation and acquisition metaphors of learning mathematics informed the study. Data were collected from 35 Grade 8 learners’ exercise book responses to directed numbers tasks as well as through interviews. Content analysis was based on Kilpatrick et al.’s strands of mathematical proficiency. The findings were as follows: 83.3% of learners have misconceptions, 16.7% have procedural errors, 67% have strategic errors, and 28.6% have logical errors on addition and subtraction of directed numbers. The sources of the errors seemed to be lack of reference to mediating artifacts such as number lines or other real contextual situations when learning to deal with directed numbers. Learners seemed obsessed with positive numbers and addition operation frames—the first number ideas they encountered in school. They could not easily accommodate negative numbers or the subtraction operation involving negative integers. Another stumbling block seemed to be poor proficiency in English, which is the language of teaching and learning mathematics. The study recommends that building conceptual understanding on directed numbers and operations on them must be encouraged through use of multirepresentations and other contexts meaningful to learners. For that reason, we urge delayed use of calculators.

FOSTERING STUDENTS' INTEREST IN MATHEMATICS LEARNING WITH THE UTILIZATION OF ETHNOMATHEMATICS THROUGH MAKKUDENDENG TRADITIONAL GAME

MaPan ◽  
2021 ◽  
Vol 9 (1) ◽  
pp. 27
Author(s):  
Andi Aras ◽  
Fawziah Zahrawati
Keyword(s):  
Design Research ◽  
Mathematics Learning ◽  
Student Interest ◽  
Research Subjects ◽  
Whole Numbers ◽  
Learning Mathematics ◽  
Grade Ii ◽  
Learning Interest ◽  
Traditional Game ◽  
Is Design

Interest in learning is one important factor that determines student success in learning. Low student interest in learning is associated with their ability to master the concept of summing whole numbers. This study aims to foster students' interest in learning mathematics through makkudendeng traditional game. The research method is design research starting from the preliminary design, design experiment, and retrospective analysis. The research subjects were students in grade II primary school. The results of this study conclude that the makkudendeng traditional game, which is used as a learning resource in learning the addition of whole numbers, has relevance to the indicators of learning interest, which include: pleasure in learning, interest in learning, attention, and involvement in learning. It is because students learn while playing. So, the makkudendeng traditional game can be a solution to foster students' interest in learning mathematics.

A number pencil

1967 ◽  
Vol 14 (7) ◽  
pp. 557-559
Author(s):  
David M. Clarkson
Keyword(s):  
Elementary Teachers ◽  
Sixth Grade ◽  
Rational Numbers ◽  
Class Discussion ◽  
Irrational Numbers ◽  
Whole Numbers ◽  
Number Lines

So much use is being made of number lines these days that it may not occur to elementary teachers to represent numbers in other ways. There are, in fact, many ways to picture whole numbers geometrically as arrays of squares or triangles or other shapes. Often, important insights into, for example, oddness and evenness can be gained by such representations. The following account of a sixth-grade class discussion of fractions shows how a “number pencil” can be constructed to represent all the positive rational numbers, and, by a similar method, also the negative rationals. An extension of this could even be made to obtain a number pencil picturing certain irrational numbers.

New Challenges to the Research Community: Reflections of the Research Advisory Committee

1998 ◽  
Vol 29 (5) ◽  
pp. 499-502
Keyword(s):  
Teaching Practice ◽  
Mathematics Classroom ◽  
Mathematics Learning ◽  
Research Community ◽  
National Council ◽  
Mathematical Ideas ◽  
Education Community ◽  
Research Findings ◽  
New Challenges ◽  
Children’S Thinking

Drawing on several decades of research findings, the National Council of Teachers of Mathematics (NCTM) produced, between 1989 and 1995, three volumes of Standards in which members of the mathematics education community formulated new visions of mathematics learning, teaching, and assessment. These new visions comprise an ambitious agenda for the mathematics classroom—one that includes, but surpasses, mastery of facts and procedures, the mainstay of extant practice—designed to engage students in the exploration of mathematical ideas and their interrelationships. Students would now be invited to articulate their ideas, and teachers to identify and mobilize those elements in children's thinking upon which stronger conceptions can be built. Paralleling this ambitious departure in teaching practice, new means of assessment were proposed to capture progress toward these far-reaching goals.

scholarly journals Active Learning dalam Pembelajaran Matematika SD Melalui Permainan Engklek Mamun

2020 ◽  
Vol 5 (2) ◽  
pp. 233-238
Author(s):  
Ulfatun Khasanah
Keyword(s):  
Active Learning ◽  
Mathematics Learning ◽  
Number Line ◽  
Negative Number ◽  
Negative Numbers

The weak ability of the students on the summation material and reduction in the background of this research. Mathematics is abstract, so in mathematics learning the necessary medium/intermediary that serves to confine so that facts clearer and more easily accepted by students. Media used is the game usually Mamun, which is a game conducted in groups in the form of advanced crank if the number of positive and crank backward if the number is negative. Numbers is a row of students holding positive and negative number flags. Each student holds a number. Students who do not hold the number do the forward or backward crank according to the prescribed number. The method is qualitative. The result is that through the game Engklek Mamun students can do the counting operation summation and reduction on the number line.

scholarly journals Students' Mathematical Communication Ability through the Brain-Based Learning Approach using Autograph

2019 ◽  
Vol 4 (1) ◽  
pp. 1-10 ◽  
Author(s):  
Mailis Triana ◽  
Cut Morina Zubainur ◽  
Bahrun Bahrun
Keyword(s):  
Communication Skills ◽  
Mathematics Learning ◽  
Descriptive Analysis ◽  
Learning Approach ◽  
Observation Data ◽  
Mathematical Communication ◽  
Mathematical Ideas ◽  
Communication Ability ◽  
Brain Based Learning ◽  
The Brain

AStudents’ skills in expressing mathematical ideas in various ways have not met the expectation. Teachers need to apply the learning providing students’ opportunities to present their mathematical ideas. Utilizing the Brain-Based Learning (BBL) approach with Autograph can help students develop their mathematical communication skills. The purpose of this study was to analyze the development of students’ mathematical communication skills. Twenty-eight 10th grade students in one of the high schools in Banda Aceh participated in the study. The instruments used were a mathematical communication skills test and the activity observation. Data were analyzed using descriptive analysis. The study showed that mathematics learning applying BBL approach with Autograph contribute to developing students’ mathematical communication skills.

scholarly journals Ethnomathematics Exploration of The Masjid Raya Bandung Ornaments in Transformation Geometry Materials

2021 ◽  
Vol 5 (2) ◽  
pp. 235
Author(s):  
Tia Purniati ◽  
Turmudi Turmudi ◽  
Dadang Juandi ◽  
Didi Suhaedi
Keyword(s):  
Qualitative Research ◽  
Literature Review ◽  
Mathematics Learning ◽  
Research Data ◽  
Geometric Transformation ◽  
Data Display ◽  
Islamic Culture ◽  
Alternative Source ◽  
Mathematical Ideas ◽  
Transformation Geometry

The mosque is the result of acculturation between Islamic culture and local culture. Many mosque ornaments use geometric motifs.  This research is an ethnomathematics study that aims to explore the ethnomathematics aspects of mosque ornament, especially the material of geometric transformation Ethnomathematics research is part of qualitative research, so this research uses qualitative research. The purpose of ethnomathematics research is to study the mathematical ideas contained in a culture, so the method used is ethnographic. The research location is Masjid Raya Bandung which was selected by purposive sampling. The researcher acts as an instrument that collects data through observation, documentation, and literature review. The research data were analyzed through data condensation, data display, and concluding. The results showed that there are ethnomathematics aspects of Masjid Raya Bandung ornaments in the material of transformation geometry, namely translation, reflection, rotation, and dilation. The mosque ornaments can be used as an alternative source of learning in mathematics learning, especially transformation geometry material. Keywords: ethnomathematics, transformation geometry, mosque ornament.

scholarly journals Developmental Relations between Mathematics Anxiety, Symbolic Numerical Magnitude Processing, and Arithmetic Skills from First to Second Grade

2021 ◽  
Author(s):  
Riikka Mononen ◽  
Markku Niemivirta ◽  
Johan Korhonen ◽  
Marcus Lindskog ◽  
Anna Tapola
Keyword(s):  
Mathematics Anxiety ◽  
Performance Test ◽  
Longitudinal Research ◽  
Rank Order ◽  
Change Score ◽  
Mathematics Performance ◽  
Numerical Magnitude ◽  
Magnitude Processing ◽  
And Gender ◽  
Over Time

We investigated the levels and changes in mathematics anxiety (MA), symbolic numerical magnitude processing (SNMP) and arithmetic skills, and how those changes are linked to each other. Children’s (n = 264) MA, SNMP and arithmetic skills were measured in Grade 1, and again in Grade 2, including also a mathematics performance test. All three constructs correlated significantly within each time point, and the rank-order stability over time was high, particularly in SNMP and arithmetic skills. By means of latent change score modeling, we found overall increases in SNMP and arithmetic skills over time, but not in MA. Most interestingly, changes in arithmetic skills and MA were correlated (i.e., steeper increase in arithmetic skills was linked with less steep increase in MA), as were changes in SNMP and arithmetic skills (i.e., improvement in SNMP was associated with improvement in arithmetic skills). Only the initial level of arithmetic skills and change in it predicted mathematics performance. The only gender difference, in favour of boys, was found in SNMP skills. The differential effects associated with MA (developmentally only linked with arithmetic skills) and gender (predicting only changes in SNMP) call for further longitudinal research on the different domains of mathematical skills.

By Way of Introduction: Show Me the Mathematics!

2006 ◽  
Vol 13 (1) ◽  
pp. 4-5
Author(s):  
P. Mark Taylor
Keyword(s):  
Professional Development ◽  
Mission Statement ◽  
Mathematics Learning ◽  
Pedagogical Strategies ◽  
Mathematical Ideas ◽  
Link Type

The Editorial Panel of Teaching Children Mathematics (TCM) welcomes you to volume 13! We are committed to the goals and ideals summarized in TCM's mission statement, which can be found at the bottom of the masthead page of each issue. The mission statement embraces the NCTM ideal of more and better mathematics for all students through the exchange of mathematical ideas, activities, and pedagogical strategies and through sharing and interpreting research. In view of NCTM's professional development focus of the year—“Show Me the Mathematics: Learning through Representation” (www.nctm.org/focus/)—we would like to highlight the specific mathematics represented in this volume of Teaching Children Mathematics.

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