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. 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.

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.

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.

scholarly journals An Emerging Problem of Shisha Smoking among High School Students in Ethiopia

2021 ◽  
Vol 18 (13) ◽  
pp. 7023
Author(s):  
Selamawit Hirpa ◽  
Andrew Fogarty ◽  
Adamu Addissie ◽  
Linda Bauld ◽  
Thomas Frese ◽  
...  
Keyword(s):  
High School ◽  
High School Students ◽  
Smokeless Tobacco ◽  
Addis Ababa ◽  
Capital City ◽  
School Level ◽  
Cluster Sampling ◽  
High Concentration ◽  
School Students ◽  
Study Participants

Shisha smoking is also known as hookah, water pipe, goza, and nargile. Shisha use among the young is increasing globally. Shisha smoke results in a high concentration of carbon monoxide, tar, nicotine, and heavy metals which can be toxic to humans, especially with chronic exposure. This study aims to determine the prevalence and risk factors of shisha smoking among in-school adolescents in Ethiopia. Four regional states in Ethiopia (Oromia, Amhara, Southern Nations, Nationalities, and Peoples’ Region, Tigray) and the capital city (Addis Ababa) were the study areas. A two-stage cluster sampling approach was employed to produce a representative sample. From the sampling frames in the study areas, 36 high schools were selected randomly. A multi-level logistic regression analysis was used to account for cluster-specific random effects, the effect of individuals’, and school-level variables for ever-use of shisha. A total of 3355 secondary school grade 9 and 10 students aged between 13 and 22 years took part in this study. A total of 86 (2.6%) and 20 (0.6%) of the study participants, reported that they had ever smoked or were current smokers of shisha, respectively. Of all study participants, 38.6% perceived shisha as less harmful than cigarettes and 48.5% reported that they do not know which was more harmful to health. Students were more likely to ever use shisha if they had friend/s who smoke shisha (AOR = 16.8, 95% CI: 6.4–44.3), ever smoked cigarettes (AOR = 8.2, 95% CI: 3.4–19.8), ever used khat (AOR = 4.2, 95% CI: 1.9–10.4), ever used marijuana (AOR = 3.9, 95% CI: 1.4–11.1), ever used smokeless tobacco (AOR = 3.1 95% CI: 1.1–8.4), and students had received income from their parents (AOR = 3.1 CI: 1.1–8.8). Prevalence of ever and current use of shisha among high school students is low in Ethiopia compared to many countries in Africa. The majority of adolescents perceived shisha as less harmful to health than cigarette smoking. Health education about the harmful effects of shisha should be delivered to adolescents, along with information on other substances like khat, cigarettes, marijuana, and smokeless tobacco to prevent initiation of substance use.

scholarly journals Teacher Orchestration of Language and Gesture in Explaining Science Concepts in Images

2021 ◽  
Author(s):  
Thu Ngo ◽  
Len Unsworth ◽  
Michele Herrington
Keyword(s):  
High School ◽  
High School Students ◽  
Senior High School ◽  
School Students ◽  
Symbolic Representations ◽  
Different Types ◽  
Cell Components ◽  
Diagram Comprehension ◽  
Senior High School Students

AbstractStudents’ difficulties interpreting diagrams remain a concern in science education. Research about improving diagram comprehension has included few studies of teachers’ orchestration of language and gesture in explaining diagrams—and very few in senior high schools. Research with younger students and studies of research scientists’ practice indicate the significance of the interaction of teachers’ gesture and language in explaining visualisations. The strategic deployment of such teacher-focussed authoritative explanations has been observed in facilitating progression to more complex and symbolic representations in classroom work. However, the paucity of such research in senior high school leaves open the question of how these teachers use gesture and language in managing the challenges of explaining the intricate sub-microscopic and abstract visualisations senior high school students need to negotiate. In this paper, we outline existing studies of teachers’ use of gesture and language to explain complex images in senior high school and investigate how it is managed by two biology teachers with images of different types and complexity representing the activity of certain cell components in the early phase of cell duplication. Implications are drawn for foci of further research including the role of a metalanguage describing different types of visualisations and their affordances.

Risk as Value: A Switch of Set Hypothesis

1976 ◽  
Vol 38 (2) ◽  
pp. 655-658 ◽  
Author(s):  
George W. Kelling ◽  
Rhea Zirkes ◽  
Deena Myerowitz
Keyword(s):  
High School ◽  
Sex Differences ◽  
High School Students ◽  
General Tendency ◽  
Age Group ◽  
School Students ◽  
Risky Shift

Advisers are expected to be cautious. Typical instructions in research on risky shift induce the adviser role. However, subjects may take the role of the story's hero when they can identify with the hero. It is acceptable for people to be daring when acting for themselves. This hypothesis of a switch of set predicts that subjects should consider themselves more risky than the majority of their peers, a way of expressing the value of risk, when they are similar to the story's hero. High school students rated themselves and the majority on stories dealing with situations common to their age group and on stories dealing with adult problems. Sex of hero was also manipulated. Results supported the hypothesis of a switch of set. Subjects displaced themselves more when the situation was similar to those they might face; in addition, subjects displaced themselves more when the story's hero was of their sex. No sex differences in general tendency to risky displacement were found.

scholarly journals The Relationship Between Social Support and Student Academic Involvement: The Mediating Role of School Belonging

2021 ◽  
pp. 082957352110347
Author(s):  
Luis Francisco Vargas-Madriz ◽  
Chiaki Konishi
Keyword(s):  
Social Support ◽  
High School ◽  
High School Students ◽  
Parental Support ◽  
Critical Role ◽  
School Belonging ◽  
School Students ◽  
Academic Involvement ◽  
The Relationship

Canada’s high school graduation rates are still low when compared to other members of the OECD. Previous studies have found academic involvement is associated with positive trajectories toward graduation, that social support promotes student engagement, and that school belonging could mediate this relationship. Still, little is known about the specificity of such mediation, especially in Québec. Therefore, this study examined the role of belonging as mediator of the relationship between social support and academic involvement. Participants ( N = 238) were high-school students from the Greater Montréal Area. All variables were measured by the School-Climate Questionnaire. Results from hierarchical multiple regressions indicated parental support had a direct relationship, whereas peer and teacher support had a mediated relationship by school belonging with academic involvement. Results highlight the critical role of school belonging in promoting academic involvement in relation to social support.

Trauma and self-harming behaviors in high school students: The mediating role of identity formation

2021 ◽  
Vol 92 ◽  
pp. 20-29
Author(s):  
Leni Raemen ◽  
Koen Luyckx ◽  
Nina Palmeroni ◽  
Margaux Verschueren ◽  
Amarendra Gandhi ◽  
...  
Keyword(s):  
High School ◽  
High School Students ◽  
Identity Formation ◽  
School Students ◽  
Mediating Role
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