Non-symbolic and symbolic number lines are dissociated

Where and under what conditions do spatial and numerical skills converge and diverge in the brain? To address this question, we conducted a meta-analysis of brain regions associated with basic symbolic number processing, arithmetic, and mental rotation. We used Activation Likelihood Estimation (ALE) to construct quantitative meta-analytic maps synthesizing results from 86 neuroimaging papers (~ 30 studies/cognitive process). All three cognitive processes were found to activate bilateral parietal regions in and around the intraparietal sulcus (IPS); a finding consistent with shared processing accounts. Numerical and arithmetic processing were associated with overlap in the left angular gyrus, whereas mental rotation and arithmetic both showed activity in the middle frontal gyri. These patterns suggest regions of cortex potentially more specialized for symbolic number representation and domain-general mental manipulation, respectively. Additionally, arithmetic was associated with unique activity throughout the fronto-parietal network and mental rotation was associated with unique activity in the right superior parietal lobe. Overall, these results provide new insights into the intersection of numerical and spatial thought in the human brain.

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

SAGE Open ◽

10.1177/2158244016671375 ◽

2016 ◽

Vol 6 (4) ◽

pp. 215824401667137 ◽

Cited By ~ 6

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.

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Facilitating Mathematical Practices through Visual Representations

Teaching Children Mathematics ◽

10.5951/teacchilmath.23.7.0404 ◽

2017 ◽

Vol 23 (7) ◽

pp. 404-412

Author(s):

Aki Murata ◽

Chana Stewart

Keyword(s):

First Graders ◽

Visual Representations ◽

Place Value ◽

Mathematical Practices ◽

Number Lines ◽

Practice Standards

This set of lesson examples demonstrates effective uses of magnets, number lines, and ten-frames to implement practice standards as first graders use place value to solve addition problems.

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An Economical Way to Number Lines, Plots, and Quadrats

Journal of Wildlife Management ◽

10.2307/3797308 ◽

1958 ◽

Vol 22 (1) ◽

pp. 99

Author(s):

P. F. English

Keyword(s):

Number Lines

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The Time Equation Explaining Equations in Physics and Economics

International Journal of Engineering and Advanced Technology - Regular Issue ◽

10.35940/ijeat.f1027.0986s319 ◽

2019 ◽

Vol 8 (6S3) ◽

pp. 165-168

Keyword(s):

Social Science ◽

Three Dimensional ◽

Value Of Time ◽

Time Value ◽

A Value ◽

Principal Axes ◽

Number Lines ◽

Exact Position ◽

Consumption And Saving ◽

The Relationship

Researchers know a little about time. If they could not find where time was, they could not study it. The objective of this study was to find where time was. Any numbers in three principal axes were used to be data. Galileo’s concept of the relationship among distance, speed, and time was used to find a position of a value of time in any number lines in a three-dimensional body. Mathematical derivative was used to prove the positions of the values of time. The investigation found that time is in all number lines including three principal axes. Also, the time equation can be used to calculate the exact position of any values of time in the line. The equation can be used to explain equations in science such as equations of Newton, Einstein, and Plank, and social science such as equations of consumption and saving in macroeconomics. If researchers use the time equation to explain N equations, then a time value can get at least N variables of N equations. The speed of calculation will increase. The equation will be used to open new characteristics about time and others because mathematicians use numbers to represent everything in nature

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