Quick Reads: Another Good Idea: The Zero Box

Paul Friedmann

doi:10.5951/mtms.14.4.0222

Quick Reads: Another Good Idea: The Zero Box

Mathematics Teaching in the Middle School ◽

10.5951/mtms.14.4.0222 ◽

2008 ◽

Vol 14 (4) ◽

pp. 222-223

Author(s):

Paul Friedmann

Keyword(s):

Middle School ◽

Middle School Students ◽

Symbolic Representation ◽

School Students ◽

Negative Numbers

The concept of adding and subtracting positive and negative numbers is not easy for middle school students to grasp. An effective bridge from the use of manipulatives and pictures to the use of traditional symbolic representation (number sentences) and mathematical rules is needed so that students can internalize the process. The zero box is just such a bridge.

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The Integer Test of Primary Operations: A Practical and Validated Assessment of Middle School Students’ Calculations with Negative Numbers

International Electronic Journal of Mathematics Education ◽

10.29333/iejme/11471 ◽

2022 ◽

Vol 17 (1) ◽

pp. em0667

Author(s):

Julie Nurnberger-Haag ◽

Joseph Kratky ◽

Aryn C. Karpinski

Keyword(s):

Middle School ◽

Middle School Students ◽

School Students ◽

Negative Numbers

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Children's Learning in a Computer Microworld for Transformation Geometry

Journal for Research in Mathematics Education ◽

10.5951/jresematheduc.22.2.0122 ◽

1991 ◽

Vol 22 (2) ◽

pp. 122-137

Author(s):

Laurie D. Edwards

Keyword(s):

Middle School ◽

Middle School Students ◽

Visual Feedback ◽

Visual Display ◽

Symbolic Representation ◽

School Students ◽

Children’S Learning ◽

Computer Microworld ◽

Transformation Geometry ◽

Children's Learning

Twelve middle school students working in pairs used a computer microworld to explore an introductory curriculum in transformation geometry. The microworld linked a symbolic representation (a set of simple Logo commands) with a visual display that showed the effects of each transformation. Worksheets were designed with the objective of encouraging the students to find and express mathematical patterns in the domain. The students were successful in constructing an accurate working understanding of the transformations. There was a tendency for symbolic overgeneralization in some activities, but the students were able to use visual feedback from the microworld and discussions with their partners to correct their own errors.

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Student Magnitude Knowledge of Negative Numbers

Journal of Numerical Cognition ◽

10.5964/jnc.v1i1.7 ◽

2015 ◽

Vol 1 (1) ◽

pp. 38-55 ◽

Cited By ~ 8

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.

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