Exploring Individual Differences in Children's Mathematical Skills: A Correlational and Dimensional Approach

2013 ◽  
Vol 113 (1) ◽  
pp. 23-30 ◽  
Author(s):  
H. Sigmundsson ◽  
R. C. J. Polman ◽  
H. Lorås
Keyword(s):  
Individual Differences ◽  
High Specificity ◽  
General Assumption ◽  
Basic Knowledge ◽  
Mathematical Tasks ◽  
Mathematical Skills ◽  
Task Specificity ◽  
Mathematics Tasks ◽  
Mathematics Test ◽  
Mathematical Skill

Individual differences in mathematical skills are typically explained by an innate capability to solve mathematical tasks. At the behavioural level, this implies a consistent level of mathematical achievement that can be captured by strong relationships between tasks, as well as by a single statistical dimension that underlies performance on all mathematical tasks. To investigate this general assumption, the present study explored interrelations and dimensions of mathematical skills. For this purpose, 68 ten-year-old children from two schools were tested using nine mathematics tasks from the Basic Knowledge in Mathematics Test. Relatively low-to-moderate correlations between the mathematics tasks indicated most tasks shared less than 25% of their variance. There were four principal components, accounting for 70% of the variance in mathematical skill across tasks and participants. The high specificity in mathematical skills was discussed in relation to the principle of task specificity of learning.

Sneaking in Some Drill

1979 ◽  
Vol 26 (8) ◽  
pp. 14
Author(s):  
Lloyd I. Richardson
Keyword(s):  
The Other ◽  
Mathematical Activity ◽  
Mathematical Skills ◽  
Other Hand ◽  
Mathematics Games ◽  
Mathematical Skill

Classroom situations that help students strengthen a mathematical skill while they are enjoying a mathematical activity should be an objective of all teachers. And yet, quite often, classroom periods devoted to maintaining mathematical skills become days devoted to dull drill. On the other hand, the mathematics lessons that students enjoy most seem to be those involving mathematics games with limited overt computations. What is needed then are games that covertly require computation.

Brief Reports: The Effects of Two Strategies for Teaching Two Mathematical Skills

1981 ◽  
Vol 12 (3) ◽  
pp. 220-225
Author(s):  
Thomas J. Cooney ◽  
Edward J. Davis ◽  
James J. Hirstein
Keyword(s):  
Relative Importance ◽  
Mathematical Skills ◽  
Mathematical Skill

In recent years there has been a concern over the acquisition of basic mathematical skills by students. The phrase “back to basics” has been coined in reference to this concern. One of the underlying issues of the back-to-basics emphasis is the relative importance of understanding a mathematical skill versus performance of that skill.

Applications of Neuroscience to Mathematics Education

2014 ◽  
Author(s):  
Bert De Smedt ◽  
Roland H. Grabner
Keyword(s):  
Mathematics Education ◽  
Skill Acquisition ◽  
Mathematics Learning ◽  
Educational Interventions ◽  
Imaging Data ◽  
Mathematical Skills ◽  
Neuroimaging Data ◽  
Brain Imaging Data ◽  
Atypical Development ◽  
Mathematical Skill

In this chapter, we explore three types of applications of neuroscience to mathematics education: neurounderstanding, neuroprediction, and neurointervention.Neurounderstandingrefers to the idea that neuroscience is generating knowledge on how people acquire mathematical skills and how this learning is reflected at the biological level. Such knowledge might yield a better understanding of the typical and atypical development of school-taught mathematical competencies.Neuropredictiondeals with the potential of neuroimaging data to predict future mathematical skill acquisition and response to educational interventions. Inneurointervention, we discuss how brain imaging data have been used to ground interventions targeted at mathematics learning and how education shapes the neural circuitry that underlies school-taught mathematics. We additionally elaborate on recently developed neurophysiological interventions that have been shown to affect mathematical learning. While these applications offer exciting opportunities for mathematics education, some potential caveats should be considered, which are discussed at the end of this chapter.

Investigating How to Support Principals as Instructional Leaders in Mathematics

2016 ◽  
Vol 12 (3) ◽  
pp. 183-214 ◽  
Author(s):  
Melissa D. Boston ◽  
Erin C. Henrick ◽  
Lynsey K. Gibbons ◽  
Dan Berebitsky ◽  
Glenn T. Colby
Keyword(s):  
Mathematics Teachers ◽  
Design Research ◽  
Necessary Conditions ◽  
Instructional Leaders ◽  
Mathematical Tasks ◽  
High Quality ◽  
Specific Content ◽  
Content Areas ◽  
Quality Instruction ◽  
Mathematics Tasks

We present a framework for considering principals’ knowledge and actions to support high-quality instruction in a specific content area (mathematics). Using design research, we engaged principals in professional development and assessed principals’ ability to identify aspects of high-quality mathematical tasks and instruction through pre–post task sort analyses and classroom video analyses. Significant differences occurred in principals’ identification of high-quality mathematics tasks and instruction, students’ thinking, and teachers’ actions. Subsequent data identified changes in principals’ feedback to mathematics teachers; however, this change was not sustained in following years. We hypothesize necessary conditions for supporting principals as instructional leaders in specific content areas.

scholarly journals MATHEMATICAL ABILITY ANALYSIS BASED ON ASSIST SCALE WITH A DIFFERENT LEARNING APPROACH TO PREPARE A PROFESSIONAL TEACHER CANDIDATE IN DEALING WITH ASEAN ECONOMIC COMUNITY (AEC)

2017 ◽  
Vol 1 (2) ◽  
Author(s):  
Dame Ifa Sihombing ◽  
Agusmanto Hutauruk ◽  
Ismail Husein
Keyword(s):  
Study Skills ◽  
Information Criterion ◽  
Analysis Method ◽  
Mathematical Skills ◽  
Critical Thinking Ability ◽  
Thinking Ability ◽  
Professional Teacher ◽  
Cluster Analysis Method ◽  
Mathematical Skill ◽  
One Way Anova

This paper aimed to basic mathematical skills based to the studying approach. To this subject pre detection is a need. One way ANOVA analyzing will show the significant of basic mathematical skill of students by giving different studying approach. Hence, there is correlation within basic mathematical skill to studying approach. Teachers should be able measure basic mathematical by designing model supporting understanding level, critical thinking ability made concept. The sample consisted of all the second semester of mathematical students by random sampling. Approaches and Study Skills Inventory for Students (ASSIST) is used to studying approach, Bayesian Information Criterion (BIC) is used to create group classification. Two Step Cluster Analysis Method divided into three approaches (Strategies, Surface, Deep)

scholarly journals Programming as a mathematical activity

2020 ◽  
Vol 18 (2) ◽  
pp. 13-17
Author(s):  
Peter Rowlett
Keyword(s):  
Mathematical Thinking ◽  
Mathematical Activity ◽  
Undergraduate Mathematics ◽  
Mathematical Skills ◽  
Second Year ◽  
Mathematical Skill ◽  
Mathematical Applications ◽  
Mathematical Activities

Programming in undergraduate mathematics is an opportunity to develop various mathematical skills. This paper outlines some topics covered in a second year, optional module ‘Programming with Mathematical Applications’ that develop mathematical thinking and involve mathematical activities, showing that practical programming can be taught to mathematicians as a mathematical skill.

scholarly journals Knowledge of mathematical symbols goes beyond numbers

2020 ◽  
Vol 6 (3) ◽  
pp. 322-354
Author(s):  
Heather Douglas ◽  
Marcia Gail Headley ◽  
Stephanie Hadden ◽  
Jo-Anne LeFevre
Keyword(s):  
Individual Differences ◽  
Written Language ◽  
Orthographic Knowledge ◽  
Decision Task ◽  
Mathematical Skills ◽  
Word Problem Solving ◽  
Post Secondary ◽  
Mathematical Symbols ◽  
Whole Number Arithmetic

The written language of mathematics is dense with symbols and with conventions for combining those symbols to express mathematical ideas. For example, reading a factored polynomial function such as f(x) = x²(2x + 15) requires the knowledge that parenthesis can be used to signify function notation in one context and multiplication in another. Mathematical orthography is defined as orthographic knowledge of symbolic mathematics. It entails both knowledge of discrete mathematical symbols and the conventions for combining those symbols into expressions and equations. The ability to read text written in the base-ten system, comprised of digits and conventions for combining digits to express whole and rational quantities, is an important aspect of mathematical orthography. However, success in secondary and post-secondary programs requires more advanced mathematical orthography. The goal of this research was to determine if a simple and novel measure of mathematical orthography captures individual differences in adults’ mathematical skills. Mathematical orthography was measured with a timed dichotomous symbol decision task. Adults (N = 58) discriminated between conventional and non-conventional combinations of mathematical symbols (e.g., x² vs. ²x; |y| vs. ||y). The mathematical symbol decision task uniquely predicted individual differences in whole-number arithmetic, fraction/algebra procedures, and word problem solving. These findings suggest that the symbol decision task is a useful index of symbol associations in mathematical development and, thus, provides a tool for understanding the role of mathematical orthography in individual differences in adults’ mathematical skills.

scholarly journals KEMAMPUAN MAHASISWA PGMI DALAM MEMECAHKAN MASALAH GEOMETRI DITINJAU DARI PERBEDAAN KEMAMPUAN MATEMATIKA

2019 ◽  
Vol 2 (2) ◽  
pp. 152
Author(s):  
Nida Jarmita
Keyword(s):  
School Teacher ◽  
Research Process ◽  
Primary School Teacher ◽  
Math Skills ◽  
Mathematical Skills ◽  
Explorative Study ◽  
The Subject ◽  
Primary School Teacher Education ◽  
Mathematical Skill ◽  
And Task

This research is an explorative study using qualitative approach that aims to describe the ability of students in solving geometry problems in terms of differences in mathematical skills. Students' problem-solving capabilities were reviewed based on Polya's troubleshooting techniques, namely: understanding the problem, devising a plan, carrying out the plan, and looking back to review the results obtained. The subjects of the study are three students from Department of Primary School Teacher Education (PGMI) of Faculty of Tarbiyah and Teacher Training, Universitas Islam Negeri Ar-Raniry Banda Aceh. The research process begins by giving a mathematics competency test to the student from a class unit, followed by selecting one student from each group, respectively from high math skills, medium math skills, and low math skills. These three selected subjects were assigned geometry-solving tasks and task-based interviews. The validity of data were checked using time triangulation. The results showed that the subject of high mathematical skill was able to use all 4 steps to solve the problem and provide correct answer. The subject of medium mathematical skill was capable of using the 4 steps of Polya's technique but also was less accurate in giving answers. Subjects of low math skill are able to use only 3 steps but are not correct in giving answers.

One Point of View: Basic Mathematical Skills or School Survival Skills?

1987 ◽  
Vol 35 (1) ◽  
pp. 2
Author(s):  
Eugene A. Maier
Keyword(s):  
Everyday Life ◽  
Graduate Student ◽  
Point Of View ◽  
Mathematical Skills ◽  
Half Century ◽  
Survival Skills ◽  
Paper And Pencil ◽  
Mathematical Skill

Some lists of “basic mathematical skills” lead me to wonder why certain topics are included. To me the designation of a mathematical skill as “basic” implies the need for that skill in life beyond school. But I see topics on such lists that have nothing to do with pre paring students to function mathematically in the nonschool world. For example, consider paper-and-pencil procedures for computing problems like 136.7 × 56.8 or 7584 ÷ 354. In a half-century of doing mathematics—as a schoolboy, as a college and graduate student, in any number of odd jobs that paid my way through college, as an industrial mathematician, as a university teacher and reearcher, in everyday life, and just for fun—nothing I have done, apart from schoolwork, requires uch procedures today.

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