Using Puzzles to Teach the Pythagorean Theorem

1989 ◽  
Vol 82 (5) ◽  
pp. 336-339 ◽  
Author(s):  
James E. Beamer
Keyword(s):  
High School ◽  
High School Students ◽  
Careful Analysis ◽  
Pythagorean Theorem ◽  
Alternative Proof ◽  
School Students ◽  
High School Geometry ◽  
School Geometry ◽  
Starting Point ◽  
Senior High School Students

One of the aims of a mathematics prog- gram is to familiarize the students with the Pythagorean theorem. The result, stated algebraically, is c2 = a2 + b2. Stated geometrically, the Pythagorean theorem refers to squares drawn on the three sides of a right triangle. The theorem states that the square drawn on the longest side has exactly the same area as that of the other two squares combined. Is it possible systematically to dissect the two smaller squares into pieces that will cover the larger square? The answer to this question is the focus of this article, which offers sugges-tions about how the Pythagorean theorem can be introduced to students in the middle school years. Enrichment challenges in the form of proofs suitable for high school geometry students are also included. Finally, three proofs of the Pythagorean theorem based on careful analysis of the puzzles are discussed. Senior high school students can be asked to prove that the pieces actually fit and to use this tessellation as a starting point to provide an alternative proof of the theorem.

The Incorporation of Geometer’s Sketchpad in a High School Geometry Curriculum

2013 ◽  
pp. 639-646
Author(s):  
Lisa Ames ◽  
Heejung An ◽  
Sandra Alon
Keyword(s):  
High School ◽  
High School Students ◽  
Conceptual Knowledge ◽  
Inductive Reasoning ◽  
Thinking Skills ◽  
Geometer's Sketchpad ◽  
School Students ◽  
Mathematics Standards ◽  
High School Geometry ◽  
School Geometry

The Common Core State Mathematics Standards (CCSSM) recommend that technology should be integrated into teaching and learning Mathematics. This chapter addresses how the Geometer’s Sketchpad computer program can support students’ thinking skills and learning outcomes in a high school geometry class, in particular for more effectively addressing the High School Geometry Standards (CCSSM: G.CO.10, G.CO. 11, and G.CO. 12). The findings from the study presented in this chapter indicate that this tool can help high school students increase their learning of geometry in terms of inductive reasoning and conceptual knowledge, but may not help improve students’ motivation to learn geometry.

scholarly journals High school students interpretations and use of diagrams in geometry proofs

2017 ◽  
Author(s):  
◽  
Ruveyda Karaman
Keyword(s):  
High School ◽  
High School Students ◽  
School Students ◽  
Clinical Interviews ◽  
High School Geometry ◽  
Geometrical Reasoning ◽  
School Geometry ◽  
Study Participants ◽  
Reasoning Study

In high school geometry, proving theorems and applying them to geometry problems is an expectation from high school students (CCSSI, 2010). Diagrams are considered as an essential part of the geometry proofs because diagrams are included in a typical geometric statement such as a claim or problem (Manders, 2008; Shin et al., 2001). This interview-based study investigated how high school students interpret and use diagrams during the process of proving geometric claims. Particular attention is given to the semiotic resources such as symbols, visuals, and gestures that students draw from the diagrams to develop their proving activities. Hence, the goal of the current study is to contribute to the mathematics education field by providing insights into the details of semiotic aspects of diagrammatic reasoning. Study participants were grade 10-12 high school students and data was collected through one-on-one task- based clinical interviews. In general, students focused on the figural properties of the diagrams more frequently than the conceptual properties of the diagrams in their proofs even when they produced a new diagram or multiple diagrams. Regarding the semiotic structure of students' proving process, gesture resources were prominent in the semiotic structure of students' proving process in diagram-given tasks. The findings also suggested that, in general, some visual resources such as drawing a new figure or multiple figures occurred regularly in particular tasks such as diagram-free tasks with non- diagrammatic register or truth-unknown features. Overall, the frameworks used in this study showed how important it is to consider the mathematics as multi semiotic, understanding the role of gestures in students' geometrical reasoning.

The Incorporation of Geometer’s Sketchpad in a High School Geometry Curriculum

2013 ◽  
pp. 102-109
Author(s):  
Lisa Ames ◽  
Heejung An ◽  
Sandra Alon
Keyword(s):  
High School ◽  
High School Students ◽  
Conceptual Knowledge ◽  
Inductive Reasoning ◽  
Thinking Skills ◽  
Geometer's Sketchpad ◽  
School Students ◽  
Mathematics Standards ◽  
High School Geometry ◽  
School Geometry

The Common Core State Mathematics Standards (CCSSM) recommend that technology should be integrated into teaching and learning Mathematics. This chapter addresses how the Geometer’s Sketchpad computer program can support students’ thinking skills and learning outcomes in a high school geometry class, in particular for more effectively addressing the High School Geometry Standards (CCSSM: G.CO.10, G.CO. 11, and G.CO. 12). The findings from the study presented in this chapter indicate that this tool can help high school students increase their learning of geometry in terms of inductive reasoning and conceptual knowledge, but may not help improve students’ motivation to learn geometry.

Families Ask: Geometry: More than Just Shapes

2006 ◽  
Vol 12 (2) ◽  
pp. 100-101
Author(s):  
David Allen
Keyword(s):  
High School ◽  
Elementary School ◽  
High School Students ◽  
School Experiences ◽  
Complex Relationship ◽  
Abstract Reasoning ◽  
Thought Processes ◽  
School Students ◽  
High School Geometry ◽  
School Geometry

Think back to the geometry you experienced as an elementary school student. Now recall a problem from high school geometry. Often, geometry tasks at the younger grades are limited to identifying shapes or labeling properties; in high school, students are expected to use abstract reasoning to prove a complex relationship. Instruction in geometry has traditionally been overlooked during middle school, which causes a gap between elementary school experiences and the thought processes required in high school.

DEVELOPING INTERACTIVE MEDIA TO TEACH SPEAKING SKILL FOR GRADE 11 STUDENTS

2016 ◽  
Vol 5 (2) ◽  
Author(s):  
Anggi Yulihar And Nora Ronita Dewi
Keyword(s):  
High School ◽  
High School Students ◽  
Research And Development ◽  
Interactive Media ◽  
Senior High School ◽  
School Students ◽  
Need Analysis ◽  
Speaking Skill ◽  
The Subject ◽  
Senior High School Students

The study deals with the developing interactive media for senior high school students. The objective of this study is to find out how to develop interactive media for better speaking skill of senior high school students. The research was conducted by using Research and Development (R&D). The subject of this research was 2016/2017 students of the eleventh grade of Class XI IPA4 in SMAN 1 Batang Kuis. The number of the students was 30 students. The data of this study was collected by using need analysis questionnaire and experts’ judgment. Need analysis questionnaire was calculated by using percentage to get the information of students’ need before developing interactive media. Experts’ judgment was calculated by using likert data, mean and criteria interval of expert judgment to know the validity of interactive media which has been developed. After the data analyzed, it was found that the experts’ judgment result was 4.80 which had a very good criteria interval. The result of the research find that interactive media is a very good to be used in teaching speaking skill.

LEXICAL AMBIGUITY IN READING ANALYTICAL EXPOSITION TEXTS FOR SENIOR HIGH SCHOOL STUDENTS

2017 ◽  
Vol 6 (4) ◽  
Author(s):  
Putri Sembiring And Sortha Silitonga
Keyword(s):  
High School ◽  
High School Students ◽  
Qualitative Method ◽  
Lexical Ambiguity ◽  
School Students ◽  
Dominant Type ◽  
Ambiguous Words ◽  
Reading Materials ◽  
English Textbooks ◽  
Senior High School Students

The objectives of this study were to find out the types of lexical ambiguity and the most dominant type of lexical ambiguity used in analytical exposition texts in English Today 2 and Advanced Learning English 2 textbooks. This study was conducted by using descriptive qualitative method. The research was mainly focused on the four types of lexical ambiguity proposed by Saeed, such as homonymy, polysemy, synonymy and antonymy. In carrying out this study, the data were taken from analytical exposition texts in reading materials and exercise material from the two English textbooks which contained of ambiguous words. The result of the study indicated the numbers of lexical ambiguity were 46 words within homonymy (34,8%), polysemy (28,2%), synonymy (19,6%), and antonymy (17,4%).

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