A teaching aid for signed numbers

1966 ◽  
Vol 13 (7) ◽  
pp. 589-591
Author(s):  
Edna M. Pratt
Keyword(s):  
Mathematical Proof ◽  
Number Line ◽  
Negative Numbers ◽  
Inductive Approach ◽  
Hard Time ◽  
Teaching Aid ◽  
Model Approach

Each year the time comes when it is necessary to illustrate the multiplication of signed numbers. There are many approaches to helping the student develop insight and skill. Some of the more common are multiplying two negative numbers using the number line, 1 * an inductive approach,2 the modern mathematical proof approach,3 the statement approach,4 or the model approach,5 but some young mathematicians still have a hard time understanding these ideas. The following is a very effective device which may be used to help students discover and then reinforce the operation of multiplication of signed numbers.

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.

Number line multiplication for negative numbers

1966 ◽  
Vol 13 (3) ◽  
pp. 213-217
Author(s):  
Lewis H. Coon
Keyword(s):  
Elementary School ◽  
School Child ◽  
Number Line ◽  
Elementary School Child ◽  
Intermediate Grades ◽  
Negative Numbers ◽  
Vector Representations

The number line, a traditional tool in arithmetic classes, continues to find greater acceptance in some of the new mathematics programs. The logic behind some of the applications of “cricket- Jumps,” vectors, or hops1 to and fro on the line seems to give an elementary school child a model suited to his learning level. Thus the jumps of the earlier grades are replaced by moves in the intermediate grades, which are replaced by vector representations in the upper grades. Figure 1 shows the addition of 3 to 2, written 2+3.

A Context for Integer Computation

2007 ◽  
Vol 13 (1) ◽  
pp. 46-50
Author(s):  
Jeff Gregg ◽  
Diana Underwood Gregg
Keyword(s):  
Research Council ◽  
Field Model ◽  
National Research Council ◽  
Number Line ◽  
Line Model ◽  
Negative Numbers ◽  
Hot Air ◽  
Positive Integers ◽  
Line P ◽  
Integer Computation

The National Research Council (2001) notes that a variety of metaphors have been used to introduce negative numbers in school, “including elevators, thermometers, debts and assets, losses and gains, hot air balloons, postman stories, pebbles in a bag, and directed arrows on a number line” (p. 245). In addition, standard textbooks have typically employed either a chip model, where positive integers are represented by black chips and negative integers by red chips; a charged-field model, showing +/−; or a number-line model. Some contexts or models are not really metaphors because, for example, negative numbers do occur in temperatures, in accounting, and in some sports scoring (e.g., scores under par in golf). However, these contexts become metaphorical when they are used to model arithmetical operations with integers. Each model or context must construct a scenario that makes it plausible to explain, for instance, why subtracting an integer is the same as adding its opposite or why a negative times a negative is a positive.

scholarly journals Student Magnitude Knowledge of Negative Numbers

2015 ◽  
Vol 1 (1) ◽  
pp. 38-55 ◽  
Author(s):  
Laura K. Young ◽  
Julie L. Booth
Keyword(s):  
Middle School ◽  
Middle School Students ◽  
Magnitude Estimation ◽  
Similar Pattern ◽  
Number Line ◽  
Negative Number ◽  
School Students ◽  
Negative Numbers ◽  
Number Magnitude ◽  
Linear Representations

Numerous studies have demonstrated the relevance of magnitude estimation skills for mathematical proficiency, but little research has explored magnitude estimation with negative numbers. In two experiments the current study examined middle school students’ magnitude knowledge of negative numbers with number line tasks. In Experiment 1, both 6th (n = 132) and 7th grade students (n = 218) produced linear representations on a -10,000 to 0 scale, but the 7th grade students’ estimates were more accurate and linear. In Experiment 2, the 7th grade students also completed a -1,000 to 1,000 number line task; these results also indicated that students are linear for both negative and positive estimates. When comparing the estimates of negative and positive numbers, analyses illustrated that estimates of negative numbers are less accurate than those of positive numbers, but using a midpoint strategy improved negative estimates. These findings suggest that negative number magnitude knowledge follows a similar pattern to positive numbers, but the estimation performance of negatives lags behind that of positives.

Zero

2020 ◽  
pp. 37-55
Author(s):  
Marcel Danesi
Keyword(s):  
Number Line ◽  
Negative Numbers ◽  
Place Holder ◽  
Over Time

Numerals are symbols that represent numbers. The most commonly used numerals, which are easy to read after one has learned to use them, are the decimal ones. The principle used to construct them is an efficient one—the position of each digit in the numeral indicates its value as a power of ten. But for such numerals to work this system requires a symbol as a place-holder for a position that has “nothing” in it. That symbol is 0, which makes it possible to differentiate between numbers such as “eleven” (= 11) “one hundred and one” (= 101), and “one thousand and one” (= 1001) without the need for additional numerals. The 0 tells us, simply, that the position is “empty.” This chapter looks at the origin of this extraordinary symbol, which over time became a number like any other, but with peculiar properties. It led to concepts such as negative numbers and the number line, which became crucial to the evolution of mathematics itself.

Cognitive Representation of Negative Numbers

2003 ◽  
Vol 14 (3) ◽  
pp. 278-282 ◽  
Author(s):  
Martin H. Fischer
Keyword(s):  
Number Line ◽  
Mental Number Line ◽  
Phylogenetic Hypothesis ◽  
Cognitive Representation ◽  
Negative Numbers ◽  
Number Representations

To understand negative numbers, must we refer to positive number representations (the phylogenetic hypothesis), or do we acquire a negative mental number line (the ontogenetic hypothesis)? In the experiment reported here, participants made lateralized button responses to indicate the larger of two digits from the range -9 to 9. Digit pairs were displayed spatially congruent or incongruent with either a phylogenetic or an ontogenetic mental number line. The pattern of decision latencies suggests that negative numbers become associated with left space, thus supporting the ontogenetic view.

Extending the Mental Number Line—How Do Negative Numbers Contribute?

Perception ◽  
10.1068/p7081 ◽  
2012 ◽  
Vol 41 (11) ◽  
pp. 1323-1335 ◽  
Author(s):  
Y u Zhang ◽  
Xuqun You
Keyword(s):  
Number Line ◽  
Mental Number Line ◽  
Holistic Processing ◽  
Negative Numbers ◽  
Absolute Value ◽  
Low Level ◽  
Task Requirements ◽  
Context Dependent ◽  
And Task

Previous studies suggest that there is an association between positive numbers and space; however, there is less agreement for negative numbers. The main purpose of the present study was to investigate the nature of the processing and representation of negative numbers, and the association between negative numbers and space. Results of the two experiments show that low-level processing (perception) of negative numbers can induce spatial shifts of attention. Whether this is caused by their numerical value or absolute value depends on the numerical context and task requirements, indicating that there are both components and holistic processing, and representation for negative numbers. The representation is automatically associated with leftward space; the coding and representation of the mental number line is adaptable to the specific numerical context and task requirements. The mental number line, therefore, can extend to the left side of zero, thus supporting the context-dependent view.

“Though this be madness,…”

1969 ◽  
Vol 16 (8) ◽  
pp. 606-608
Author(s):  
Wallace P. Havenhill
Keyword(s):  
Number Line ◽  
Negative Numbers

The number line is a powerful tool that can be used to illustrate the arithmetical operations and their relationships. Unfortunately, when the topic of multiplication and division involving two negative numbers occurs, there seems to be little or no information regarding how to represent these problems on the number line. With the use of two interpretations for the + and − signs, both multiplication and division involving negative numbers can be easily represented and their inverse nature illustrated.

The number line as a teaching aid

1985 ◽  
Vol 16 (4) ◽  
pp. 411-424 ◽  
Author(s):  
Paul Ernest
Keyword(s):  
Number Line ◽  
Teaching Aid
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