Implementing the Assessment Standards for School Mathematics: Assessing Justification and Proof in Geometry Classes Taught Using Dynamic Software

1998 ◽  
Vol 91 (1) ◽  
pp. 76-82
Author(s):  
Enrique Galindo
Keyword(s):  
High School ◽  
High School Student ◽  
Dynamic Geometry ◽  
Dynamic Geometry Software ◽  
School Mathematics ◽  
Computer Mouse ◽  
Assessment Standards ◽  
Dynamic Software

Consider the midpoints of all the chords that can be drawn from a given point, say, A, on a circle (see fig. 1). Can anything special be found about these midpoints? Using dynamic geometry software, students can trace the locus of these midpoints by dragging the chord AB from point B. That is, they can use the computer mouse to select and hold point 8 as it is moved around the circle. The computer displays a dynamic chord with a fixed endpoint A and traces the path of the midpoints. The small blue dots shown in figure 2 represent the midpoints of the chords generated as point B is dragged around the circle. Figure 2 suggests that these midpoints lie on a circle. Is this observation true? How can we be sure? When presented with this task, a high school student answered, “It forms … it forms a circle! The midpoints … the midpoints when you move it around form a smaUer circle inside the big circle!” When the student was asked to justify his answer, he said, “I can see it before me, and it does form a circle. I have evidence for it.”

Radio and Airplane Distances

1929 ◽  
Vol 22 (2) ◽  
pp. 117-120
Author(s):  
P. H. Nygaard
Keyword(s):  
High School ◽  
High School Student ◽  
School Mathematics ◽  
High School Mathematics ◽  
Shortest Distance

With the recent development of the radio and the airplane considerable interest has arisen in the problem of determining the shortest distance between any two points on the earth's surface. The writer proposrs in the following discus. ion to treat the problem in a manner mathematically exact, and at the same time make the explanation simple enough to be understood by any high school student who has had experience with elementary problems involving sines and cosines. It is hoped that teachers may find the discussion helpful in providing supplementary work for high school mathematics classes, and for reference reading on the part of interested students.

Mathematical Lens: Making a Pitch for Slope

2010 ◽  
Vol 103 (8) ◽  
pp. 557-561
Author(s):  
Heidi Rudolph
Keyword(s):  
High School ◽  
School District ◽  
Dynamic Geometry ◽  
Dynamic Geometry Software ◽  
Geometer's Sketchpad ◽  
City School ◽  
City School District ◽  
District Administration ◽  
School District Administration

Heidi Rudolph teaches mathematics at Orange High School in Pepper Pike, Ohio, located across the street from the Orange City School District administration buildings (see photograph 1). The buildings' rooflines inspired her to develop questions related to the slopes of the roofs and to consider ways in which dynamic geometry software such as The Geometer's Sketchpad® (GSP) could be used to make measurements that would help answer her questions.

scholarly journals GEOGEBRA: TOWARDS REALIZING 21ST CENTURY LEARNING IN MATHEMATICS EDUCATION

2017 ◽  
Author(s):  
Khor Mui Kim ◽  
Ruzlan Md-Ali
Keyword(s):  
Mathematics Education ◽  
21St Century ◽  
Dynamic Geometry ◽  
21St Century Learning ◽  
Dynamic Geometry Software ◽  
Post Test ◽  
Geometry Problem ◽  
Dynamic Software ◽  
Geometry Problem Solving ◽  
Experimental Group

Purpose – This study examines the effect using GeoGebra dynamic geometry software on students’ ability to confront geometry problem solving, their achievement in spatial visualization skills, and their usage of cognitive skills in applying, analyzing, evaluating, creating and constructing ideas for geometry problem solving on the topic of Shape and Space towards supporting 21st century learning of Mathematics Education. Methodology – Quantitative and qualitative data were collected for this study. A total of 102 Form Two students participated in the study, which had employed the pre-test and post-test quasi-experimental research design. The research participants were divided into three groups, namely Experimental Group 1 (n=33), Experimental Group 2 (n=35) and Control Group (n=34). A guideline book on using GeoGebra dynamic geometry software in learning of Shape and Space, developed by the researchers and validated by a panel of experts, was used by the teachers and students in the experimental groups. The quantitative data, obtained via the Topical Test (TT) and Spatial Visualization Ability Test (SVAT), were analysed using MANOVA. The reliability coefficients of TT and SVAT were 0.972 and 0.953 respectively. The qualitative data, collected via interviews, teaching observations, video recordings and students’ works, was thematically analysed. Findings – The experimental groups’ TT and the SVAT post-test mean scores for both the experimental groups were significantly higher than the control group’s TT and the SVAT post-test mean scores. The learning of Shape and Space using GeoGebra dynamic geometry software had enabled students to produce works with evidence of critical, creative and innovative elements in their solutions. The experimental groups’ students agreed that using the dynamic software something new to them and was indeed as an attractive way to learn mathematics because they had the opportunity to experience hands-on learning of mathematics using ICT. They voiced their dessire to also use the GeoGebra dynamic geometry software when learning other mathematics topics. Significance – The use of GeoGebra dynamic geometry software to support the notion of integration of technology in the teaching and learning of mathematics in schools has the potential to promote active students involvement in mathematics learning. The active learning could provide students with meaningful learning experiences and opportunities to produce quality, creative and innovative works. The dynamic software has the capacity to support students’ logical and systematic approaches in solving geometry problems and also triggers multiple ways of interactions and collaborations in the mathematics classrooms. The stimulation of students’ creative and innovative thinking provide evidence for the potential support of the dynamic software towards realizing 21st century learning within Mathematics Education.

scholarly journals Enhancing the Skill of Geometric Prediction Using Dynamic Geometry

Mathematics ◽  
2021 ◽  
Vol 9 (8) ◽  
pp. 821
Author(s):  
Elisa Miragliotta ◽  
Anna E. Baccaglini-Frank
Keyword(s):  
High School ◽  
High School Student ◽  
Mathematical Reasoning ◽  
Dynamic Geometry ◽  
Dynamic Geometry Environment ◽  
Geometrical Figure ◽  
Fine Grained ◽  
Analytical Tools ◽  
Insight Into

This study concerns geometric prediction, a process of anticipation that has been identified as key in mathematical reasoning, and its possible constructive relationship with explorations within a Dynamic Geometry Environment (DGE). We frame this case study within Fischbein’s Theory of Figural Concepts and, to gain insight into a solver’s conceptual control over a geometrical figure, we introduce a set of analytical tools that include: the identification of the solver’s geometric predictions, theoretical and phenomenological evidence that s/he may seek for, and the dragging modalities s/he makes use of in the DGE. We present fine-grained analysis of data collected during a clinical interview as a high school student reasons about a geometrical task, first on paper-and-pencil, and then in a DGE. The results suggest that, indeed, the DGE exploration has the potential of strengthening the solver’s conceptual control, promoting its evolution toward theoretical control.

Survey of Ohio college opinions with reference to high school mathematics programs

1963 ◽  
Vol 56 (4) ◽  
pp. 245-247
Author(s):  
Robert S. Brown
Keyword(s):  
High School ◽  
Mathematics Teachers ◽  
High School Student ◽  
School Mathematics ◽  
High School Mathematics

From the time of the appearance of the Report of the Commision on Mathematics in 1959, the mathematics teachers in Marion, Ohio, have been concerned about the contents of our program for collrge-bound high school student.

scholarly journals Applying Dynamic Geometry Software In The Studying Process In High School

2018 ◽  
Vol 18 (4) ◽  
pp. 177-182
Author(s):  
Natalia Shapovalova ◽  
◽  
Svitlana Kuchmenko ◽  
Keyword(s):  
High School ◽  
Dynamic Geometry ◽  
Dynamic Geometry Software

Student Self-Assessment and Self-Evaluation

1996 ◽  
Vol 89 (7) ◽  
pp. 548-554 ◽  
Author(s):  
Virginia Stallings ◽  
Carol Tascione
Keyword(s):  
High School ◽  
Communication Skills ◽  
Alternative Assessment ◽  
Evaluation Process ◽  
School Mathematics ◽  
College Mathematics ◽  
Self Assessment ◽  
Self Evaluation ◽  
Mathematics Vocabulary ◽  
Assessment Standards

Current recommendations for alternative assessment call for more student involvement in the evaluation process. Although very little research on student self-evaluation has been carried out beyond determining how well students' perceptions of their achievement align with their teacher's perceptions, the Assessment Standards for School Mathematics (NCTM 1995) supports activities that involve students in evaluating their own progress. According to the Assessment Standards, student self-assessment can be used to improve students' confidence in their ability to do mathematics and allow them to become more independent in their learning of mathematics. We have employed student self-assessment and self-evaluation in our high school and college mathematics classes and have found that the processes engage students in evaluating their progress, aid in developing their communication skills, and increase their mathematics vocabulary. Most important, students reflect on their understanding of mathematics and on their ability to learn mathematics. Although our procedures differ somewhat, as we describe subsequently, our goal of involving students in the evaluation process is the same.

scholarly journals The Area of the Disk in Middle School Grade by GeoGebra.

2017 ◽  
Vol 12 (11) ◽  
pp. 28 ◽  
Author(s):  
David Lognoli
Keyword(s):  
Middle School ◽  
Sampling Methods ◽  
Teaching Strategy ◽  
Dynamic Geometry ◽  
Dynamic Geometry Software ◽  
Regular Polygons ◽  
School Grade ◽  
Level Of Knowledge ◽  
Multimedia Environments ◽  
Dynamic Software

The visualization and exploration of mathematical objects and concepts in multimedia environments can facilitate learning. Geometry is particularly involved with the growing use of software in teaching. GeoGebra is a dynamic geometry system that increases the level of knowledge and skills in mathematics. Use of GeoGebra permits to complete and extend a teaching strategy based on manipulative activities. The area of a disk in the Middle School, i.e. Grades 7-8 offers the opportunity to a large use of geometry dynamic software. This paper proposes, as example of combining between manipulative activating and dynamic geometry software, the use GeoGebra to permit the visualization of three different approaches to the area of a disk. First is based on the limit of the area of inscribed regular polygons, second on dynamical morphing of the disk in a triangle and third on sampling methods.

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