Authors:Testa I.(1), Colantonio A. (2), Galano S. (1)
1 Department of Physics “E. Pancini”, University Federico II, Naples (Italy)
2 School of Advanced Studies, University of Camerino (Italy)
Sinopsi: INVESTIGANTING THE ROLE OF TEXTBOOK IMAGES ON CHILDREN’S MODELS OF S...Silvia Galano
This study investigated how textbook images influence 373 middle and high school students' drawings about seasonal change. Students were taught about seasons and then assigned to treatment and control groups. The treatment group viewed a textbook image before drawing. Factor analysis identified models in the drawings. While knowledge about seasons did not differ between groups, the image significantly impacted the treatment group's drawings. Over 40% of treatment drawings matched the image's distance-based orbital model, rather than the correct axis tilt explanation. The results suggest textbook images can mislead students and more emphasis is needed on image design and instruction to correctly interpret them.
Investiganting the role of textbook images on children's models of seasonal c...Silvia Galano
Oral Presentation at the ESERA Conference 2017 in Dublin.
Abstract: In this study, we investigated the influence of textbook images on first year high school and middle school students' drawings about change of seasons. Participating students were first taught with a short curriculum sequence about change of seasons. Then, after three months, students were randomly assigned to a treatment and control group and asked to make a drawing and write an explanation of the phenomenon. Students of the treatment group were shown a typical textbook image before completing the task. Overall, 373 students (treatment group=193; control group=180) completed the task. Drawings were analyzed using factor analysis to identify emerging models. Results indicate that, while treatment and control groups students did not differ in knowledge about change of seasons, the image significantly influenced drawings of the treatment group students. This work suggests that iconic features of textbook images may play an essential role in students' understanding of the underlying concepts
A Two-Tier questionnaire on basic astronomical topicsSilvia Galano
The document describes a three-tier astronomy questionnaire developed to assess student misconceptions about seasonal changes, eclipses, and moon phases. The questionnaire contains 15 two-tier multiple choice items with a content question and justification question for each topic. It was administered to 197 Italian secondary students. Analysis of responses found common misconceptions among students related to the causes of seasons and moon phases. The most frequent misconceptions were about the role of an observer's position and shadows in moon phases. The questionnaire showed potential to reliably identify student misconceptions, informing teaching strategies to address conceptual difficulties.
Students' understanding of astronomy concepts was compared when taught with traditional textbook images versus specially designed visual representations (VRs). Students who learned with the specially designed VRs performed better, producing more scientifically accurate drawings and explanations and scoring higher on a baseline test. The specially designed VRs were more effective at addressing student misconceptions. Future work will explore combining specially designed VRs with laboratory activities.
This document outlines an interdisciplinary unit plan about patterns of time for a second grade class. The unit will last two weeks and cover science, geography, language arts, math, and technology topics related to how the sun, moon, and earth affect each other and patterns of day and night. Students will engage in hands-on activities and complete assessments to help answer the essential questions of how patterns of time affect them and the world.
Kathryne J. Daniel is a PhD candidate in Physics and Astronomy at Johns Hopkins University. Her research focuses on constraints on radial migration in disk galaxies using analytic and numerical modeling techniques. She has extensive experience using programming languages like C++ and Python for simulations and data analysis. Daniel has received several prestigious fellowships including an NSF Graduate Research Fellowship and an AAUW American Dissertation Fellowship. She has published papers in ApJ and MNRAS and presented her work at numerous international conferences.
Development and validation of a Learning Progression of basic astronomy pheno...Silvia Galano
The document describes the development and validation of a learning progression for basic astronomy phenomena. It discusses:
1) The aims of developing learning progressions to improve science education and describe how student understanding develops over time.
2) Research questions about characterizing student understanding of astronomical concepts like seasons and eclipses, and developing and validating a learning progression.
3) Methods used including open response questionnaires to develop initial levels of understanding, and a multiple choice assessment to empirically validate the hypothesized learning progression levels.
The document provides resources and lesson planning information for teaching 8th grade students about the life cycle of stars. It includes state standards, student expectations, activities to emphasize key points, components of a good lesson plan, examples of lessons, and strategies for differentiation and assessment. The purpose is to support teachers in planning units on the life cycle of stars through providing relevant content, instructional materials, and recommendations for instruction.
Sinopsi: INVESTIGANTING THE ROLE OF TEXTBOOK IMAGES ON CHILDREN’S MODELS OF S...Silvia Galano
This study investigated how textbook images influence 373 middle and high school students' drawings about seasonal change. Students were taught about seasons and then assigned to treatment and control groups. The treatment group viewed a textbook image before drawing. Factor analysis identified models in the drawings. While knowledge about seasons did not differ between groups, the image significantly impacted the treatment group's drawings. Over 40% of treatment drawings matched the image's distance-based orbital model, rather than the correct axis tilt explanation. The results suggest textbook images can mislead students and more emphasis is needed on image design and instruction to correctly interpret them.
Investiganting the role of textbook images on children's models of seasonal c...Silvia Galano
Oral Presentation at the ESERA Conference 2017 in Dublin.
Abstract: In this study, we investigated the influence of textbook images on first year high school and middle school students' drawings about change of seasons. Participating students were first taught with a short curriculum sequence about change of seasons. Then, after three months, students were randomly assigned to a treatment and control group and asked to make a drawing and write an explanation of the phenomenon. Students of the treatment group were shown a typical textbook image before completing the task. Overall, 373 students (treatment group=193; control group=180) completed the task. Drawings were analyzed using factor analysis to identify emerging models. Results indicate that, while treatment and control groups students did not differ in knowledge about change of seasons, the image significantly influenced drawings of the treatment group students. This work suggests that iconic features of textbook images may play an essential role in students' understanding of the underlying concepts
A Two-Tier questionnaire on basic astronomical topicsSilvia Galano
The document describes a three-tier astronomy questionnaire developed to assess student misconceptions about seasonal changes, eclipses, and moon phases. The questionnaire contains 15 two-tier multiple choice items with a content question and justification question for each topic. It was administered to 197 Italian secondary students. Analysis of responses found common misconceptions among students related to the causes of seasons and moon phases. The most frequent misconceptions were about the role of an observer's position and shadows in moon phases. The questionnaire showed potential to reliably identify student misconceptions, informing teaching strategies to address conceptual difficulties.
Students' understanding of astronomy concepts was compared when taught with traditional textbook images versus specially designed visual representations (VRs). Students who learned with the specially designed VRs performed better, producing more scientifically accurate drawings and explanations and scoring higher on a baseline test. The specially designed VRs were more effective at addressing student misconceptions. Future work will explore combining specially designed VRs with laboratory activities.
This document outlines an interdisciplinary unit plan about patterns of time for a second grade class. The unit will last two weeks and cover science, geography, language arts, math, and technology topics related to how the sun, moon, and earth affect each other and patterns of day and night. Students will engage in hands-on activities and complete assessments to help answer the essential questions of how patterns of time affect them and the world.
Kathryne J. Daniel is a PhD candidate in Physics and Astronomy at Johns Hopkins University. Her research focuses on constraints on radial migration in disk galaxies using analytic and numerical modeling techniques. She has extensive experience using programming languages like C++ and Python for simulations and data analysis. Daniel has received several prestigious fellowships including an NSF Graduate Research Fellowship and an AAUW American Dissertation Fellowship. She has published papers in ApJ and MNRAS and presented her work at numerous international conferences.
Development and validation of a Learning Progression of basic astronomy pheno...Silvia Galano
The document describes the development and validation of a learning progression for basic astronomy phenomena. It discusses:
1) The aims of developing learning progressions to improve science education and describe how student understanding develops over time.
2) Research questions about characterizing student understanding of astronomical concepts like seasons and eclipses, and developing and validating a learning progression.
3) Methods used including open response questionnaires to develop initial levels of understanding, and a multiple choice assessment to empirically validate the hypothesized learning progression levels.
The document provides resources and lesson planning information for teaching 8th grade students about the life cycle of stars. It includes state standards, student expectations, activities to emphasize key points, components of a good lesson plan, examples of lessons, and strategies for differentiation and assessment. The purpose is to support teachers in planning units on the life cycle of stars through providing relevant content, instructional materials, and recommendations for instruction.
The document discusses research on teaching and learning astronomy. It finds that students struggle with spatial visualization, mental modeling, and conceptual change. Effective teaching strategies engage students in challenging prior beliefs through activities that incorporate historical discoveries and modeling. Further research is needed to evaluate strategies for developing students' spatial thinking and orientation frameworks for understanding celestial phenomena. The document concludes by recommending exemplar areas for further research, such as investigating students' thinking processes for celestial motion problems.
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The document provides an overview of a physical sciences presentation template. It includes sections for fonts, graphics, credits, colors, icons, editable slides, a table of contents, sample slides on topics like energy forms and the solar system, and suggestions for group activities, experiments, and assessments involving physical science concepts.
The document provides an overview of a physical sciences presentation template, including sections on energy forms, states of matter, chemical changes, and more. It outlines the contents, fonts, colors, icons, and other editable elements that can be used to create the presentation. Instructions are provided for adding text, images, graphs, and other media to each slide.
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This document provides an editable presentation template for a science project. It includes sections for an introduction, table of contents, topics like energy forms and states of matter, examples, diagrams, images, and resources. Instructions are provided for customizing colors, fonts, images and using the templates slides and elements. Credits are given to the template designers.
A three-dimensional map of the Milky Way using 66,000 Mira variable starsSérgio Sacani
We study the three-dimensional structure of the Milky Way using 65,981 Mira variable stars discovered
by the Optical Gravitational Lensing Experiment (OGLE) survey. The spatial distribution of the Mira
stars is analyzed with a model containing three barred components that include the X-shaped boxy
component in the Galactic center (GC), and an axisymmetric disk. We take into account the distance
uncertainties by implementing the Bayesian hierarchical inference method. The distance to the GC is
R0 = 7.66 ± 0.01(stat.) ± 0.39(sys.) kpc, while the inclination of the major axis of the bulge to the
Sun-GC line-of-sight is θ = 20.2
◦ ± 0.6
◦
(stat.) ± 0.7
◦
(sys.). We present, for the first time, a detailed
three-dimensional map of the Milky Way composed of young and intermediate-age stellar populations.
Our analysis provides independent evidence for both the X-shaped bulge component and the flaring
disk (being plausibly warped). We provide the complete dataset of properties of Miras that were used
for calculations in this work. The table includes: mean brightness and amplitudes in nine photometric
bands (covering a range of wavelength from 0.5 to 12 µm), photometric chemical type, estimated
extinction, and calculated distance with its uncertainty for each Mira variable. The median distance
accuracy to a Mira star is at the level of 6.6%.
The pillars of_creation_revisited_with_muse_gas_kinematics_and_high_mass_stel...Sérgio Sacani
The document discusses observations of the Pillars of Creation in the Eagle Nebula using integral field spectroscopy from the MUSE instrument on the VLT. For the first time, the study maps physical parameters like extinction, density, temperature, and velocity across the pillars. The data show that the pillar tips have high densities and are being photoevaporated by the massive stars in NGC 6611. The kinematics indicate a blueshifted photoevaporative flow, consistent with simulations. The 3D geometry of the pillars is inferred, with some in front of and some behind the ionizing stars. A previously unknown outflow is detected from the middle pillar, suggesting an embedded protostar.
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The document discusses theoretical and conceptual frameworks for research. It defines a theoretical framework as using established theories to relate study findings to relevant knowledge theories. A conceptual framework refers to the ideas and theories that specifically support the study. Guidelines are provided for developing theoretical frameworks, including understanding study variables and relationships, reviewing literature, and selecting relevant theories. Variables such as independent, dependent, moderating, and mediating are also defined. Common examples of conceptual frameworks are also discussed.
The document discusses a study investigating whether superflare behavior observed on G dwarf stars by the Kepler mission can be attributed to unseen, low-mass companion stars. The study uses a population synthesis model to recreate the Kepler sample and add simulated flaring companion stars. It also surveys stars observed to superflare to search for companions. Preliminary results suggest that 70% of superflares observed could be from companions, and over 60% of stars surveyed have at least one companion. The results support the hypothesis that many observed G dwarf superflares may actually be caused by companion stars.
This document provides instructions and contents for a lesson presentation template from Slidesgo. It includes 10 slides with:
1) An overview of the template contents which includes illustrations, credits slide, and customizable elements.
2) A table of contents for customizing the lesson sections.
3) Sample content slides on planets that can be modified with descriptive text, images, and diagrams.
4) Instructions for customizing and using the template for a lesson presentation.
This document provides instructions for using a lesson presentation template from Slidesgo. It contains 10 slides with an overview of the template contents, instructions for use, credits that must be kept, and premium resources available for customization. Users are allowed to modify and use the template for personal or commercial projects but cannot redistribute or sell the template. Premium users can use the template without attribution to Slidesgo.
This document outlines an Earth science curriculum for grades 1-5. It includes 9 units of study for each grade level with performance expectations aligned to disciplinary core ideas and science practices. The units cover topics like Earth's place in the universe and solar system, plate tectonics, weather and climate, and natural resources. Appendices provide templates for proficiency scales and curriculum refinement.
This document provides instructions and contents for a lesson presentation template from Slidesgo. It includes 10 slides with:
1) An overview of the template contents which includes illustrations, credits slide, and customizable elements.
2) A table of contents for editing the presentation.
3) Sample slides for topics, definitions, features, and concepts that can be customized for a lesson.
This document provides instructions for using a lesson presentation template from Slidesgo. It includes 10 slides with information on the template contents, fonts and colors used, illustrations and icons available, and instructions for premium users. Users can modify and reuse the template for personal or commercial purposes while attributing Slidesgo.
This document provides instructions and contents for a lesson presentation template from Slidesgo. It includes 10 slides with:
1) An overview of the template contents which includes illustrations, credits slide, and customizable elements.
2) A table of contents for editing the presentation.
3) Sample slides for different lesson sections like overview, features, activities.
The template provides sample slides, layouts, and elements to build out a lesson presentation with topics, definitions, activities and assessments.
Sean D. Johnson is a PhD candidate in astronomy and astrophysics at the University of Chicago. His research focuses on galaxy evolution and the intergalactic medium using observations from telescopes including Hubble, Magellan, and ARC. He has received fellowships from the NSF and Sigma Xi and has published 7 papers. Johnson teaches astronomy to high school students and serves on department committees.
Deja vu all_over_again_the_reapperance_of_supernova_refsdalSérgio Sacani
O Telescópio Espacial Hubble das agências NASA e ESA registrou a imagem pela primeira vez da explosão prevista de uma supernova. O reaparecimento da supernova Refsdal foi calculado a partir de diferentes modelos de aglomerados de galáxias, cuja imensa gravidade está entortando a luz da supernova.
Muitas estrelas terminam a sua vida com uma explosão, mas somente poucas dessas explosões estelares têm sido registradas no ato que acontecem. Quando isso acontece, é pura sorte, pelo menos até agora. No dia 11 de Dezembro de 2015, os astrônomos não somente fizeram a imagem de uma supernova em ação, como também observaram quando e onde ela estava prevista para acontecer.
A supernova, apelidada de Refsdal, foi registrada no aglomerado de galáxias, conhecido como MACS J1149.5+2223. Enquanto que a luz do aglomerado gasta cerca de cinco bilhões de anos para chegar até nós, a supernova explodiu muito tempo antes, a aproximadamente 10 bilhões de anos atrás.
A história da Refsdal começou em Novembro de 2014, quando os cientistas registraram quatro imagens separadas da supernova num raro arranjo conhecido como Cruz de Einstein, ao redor de uma galáxia dentro do MACS J1149.5+2223. A ilusão de óptica cósmica ocorreu devido ao fato da massa de uma única galáxia dentro do aglomerado estar entortando e ampliando a luz da distante explosão estelar, num processo conhecido como lente gravitacional.
This document provides an introduction to solar geometry. It discusses the Earth-sun relationship from a heliocentric perspective, including the Earth's elliptical orbit around the sun and the 23.5 degree tilt of its axis of rotation. This results in seasonal variation of the solar declination angle. The document also defines key terms like geographical latitude and discusses methods for graphically representing the sun's path and calculating solar angles, which are important for designing shading devices and assessing overshadowing.
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(sys.). We present, for the first time, a detailed
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extinction, and calculated distance with its uncertainty for each Mira variable. The median distance
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This document provides instructions and contents for a lesson presentation template from Slidesgo. It includes 10 slides with:
1) An overview of the template contents which includes illustrations, credits slide, and customizable elements.
2) A table of contents for editing the presentation.
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Chapter 2
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PRINCIPAL COMPONENT ANALYSIS OF LEARNER-GENERATED DRAWINGS AS A STRATEGY TO INVESTIGATE STUDENTS’ MENTAL MODELS: EXAMPLES FROM ASTRONOMY EDUCATION
1. PRINCIPAL COMPONENT ANALYSIS OF
LEARNER-GENERATED DRAWINGS AS A
STRATEGY TO INVESTIGATE STUDENTS’
MENTAL MODELS: EXAMPLES FROM
ASTRONOMY EDUCATION
ITALO TESTA,ARTURO COLANTONIO, & SILVIA GALANO
2. Overview of the talk
• Literature review
• Theoretical Framework
• Research Questions
• Methods
• Results
• Discussion and Implications
• Conclusions
italo.testa@unina.it;
@italo_testa
More information can be found in:
I. Testa, S. Leccia, and E. Puddu, Astronomy textbook
images: do they really help students? Phys. Ed. 49, 332 2198
(2014)
S. Galano, A. Colantonio, S. Leccia, I. Marzoli, E. PudduI & I.
Testa, Developing the use of visual representations to
explain basic astronomy phenomena Phys. Rev. ST Phys.
Educ. Res. Focused Collection on Astronomy Education
Research (2018)
Contacts:
3. Review of literature
To involve students in generating drawing may:
• promote memory, observation, and imagination (Neu & Berglund, 1991; Stein & Power, 1996)
• be beneficial for explanation (Adoniou, 2013)
• help construct patterns by selecting real world features (Cox, 2005)
• promote science learning (Britton & Wandersee, 1997; Quillin & Thomas, 2015)
• assess learning (White & Gunstone, 2000)
• help in uncovering reasoning strategies, attitudes and mental models (Vosniadou & Brewer,
1992; Waldrip et al. 2010; Hsieh & Tsai, 2017)
Renewed emphasis in science education research on the use of drawings as effective tool to access
students’ reasoning strategies and mental models (Ainsworth, Prain, & Tytler, 2011).
4. Review of literature
It is of essential then to:
Address methodological issues in analyzing students’ drawings to push further the field
The case of Draw-A-Scientist test (Symington & Spurling, 1990; Losh et al., 2008; Reinisch et al., 2017)
• One or more scientist?
• Appearance
• Activity
• Symbolic representations
• Context in which the scientist is drew
How reliable is the Draw-A-Scientist test to elicit students’ mental models about a scientist?
Literature results are often inconsistent (Van Meter & Garner, 2005)
5. Theoretical Framework
Paivio (1991) graphical modalities encompass first the construction of an internal representation of the
concept and then the effort to externalize it in conventional form through referential links
Van Meter and Garner (2005) drawing involves constructive learning processes that engage nonverbal
representational modalities and requires integration
Ehrlén (2008) drawings are products of pictorial conventions in cultural contexts and, therefore, the
conception that is represented in a drawing depends on the convention chosen by the student for the
representation.
6. Research questions
RQ1. To what extent drawings may reliably uncover students’ mental
models about a given phenomenon?
RQ2. What is the relationship between drawings and knowledge about the
target phenomenon?
RQ3. To what extent do textbook visualizations and curriculum instruction
influence students’ drawings?
7. Content area
• ASTRONOMY
• astronomy education and popularization are historically based on visualizations
• planetariums and science centers regularly offer to visitors realistic simulations of space travels
and explorations based on computer elaboration of photographs
• multimedia visual representations support students in conceptualizing and representing complex
phenomena that cannot be experienced by first-hand
• Images are fundamental tools for astronomers and professional researchers in astrophysics
• Few studies focused on students’ difficulty with the interpretation of diagrams and iconic
representations in astronomy (Kikas, 1998; Barab et al., 2000; Hansen et al., 2004)
• Astronomical representations require formal knowledge and are not necessarily linked to real
life experience (Vosniadou, 2010)
9. Methods – Analysis of students’ drawings
• Typical textbook images about seasonal changes feature iconic elements difficult to
intepret
• may lead students to interpret incorrectly the mechanism underlying the represented phenomenon
• Pre-existing scoring schemes focused on
• accuracy and fidelity
• number or types of iconic elements that are present in the drawings
cannot be used to analyze the students’ drawings
• highly prescriptive notion of what should be considered as a “successful drawing”
• better fit to pre-determined “expert” instances
• do not allow to cluster emerging students’ models according to visual features
10. Methods – Exploratory Factor Analysis (EFA)
Applying PCA to drawings:
Identify initial variables grounded list of all the iconic elements in the drawings
Reduce initial variables redundant or “constant” iconic elements were eliminated
Score of the variables 1 or 0 according to the presence or absence of each element in the
drawing
Two main approaches: Principal Component Analysis (PCA) and Factor Analysis (FA)
Main aim of FA uncover structures underlying the set of original variables
Main aim of PCA to reduce the dimensionality of a data set consisting of a large number of interrelated
variables, while retaining as much as possible of the variation present in the data set
11. Methods – Principal Component Analysis (PCA)
Example of initial identified variables - Seasonal changes
Label Element Description
S1 Orbit Presence of the Earth’s orbit
S2 Elliptical orbit Presence of Earth’s orbit represented as elliptical
S3 Earth Presence of the Earth
S4 One Earth Presence of only one Earth
S5 Multiple Earth Presence of more than one Earth
S6 Multiple Earth and orbit Presence of the Earth’s orbit and of more Earths along this orbit
S7 Multiple Earth and no orbit Presence of more Earths but of no orbit
S8 Sun Presence of the Sun
S9 Sun and orbit Presence of the Sun and the Earth’s orbit
S10 Sun and no orbit Presence of the Sun but of no Earth’s orbit
S11 Rays Presence of some kind of rays
S12 Rays hitting the Earth Presence of some kind of rays hitting the Earth’s surface. It should be possible that the source of the rays is not represented
S13 Converging rays Presence of rays drawn as convergent. It is not important who is the source of the rays
S14 Converging and inclined rays Presence of convergent rays and of their inclination with respect to the hit surface. It is not important who is the source of the rays
S15 Distance Presence of elements (segments, arrows ec.) representing the distance between the Earth and the Sun
S16 Axis Presence of the Earth’s axis
S17 Moon Presence of the Moon
S18 Weather Presence of elements related to clime and weather (rain, cloud, snow etc.)
S19 N/S Presence of cardinal points
S20 Angle Presence of the angle between the Earth's axis and its orbit or between solar rays and the Earth’s surface.
S21 INT Presence of two or more conceptually related images
S22 VER Presence of verbal elements to be read as an important part of the image, such as captions
S23 SEL Presence of elements selected or conceptually highlighted in relation to textual/graphical features, which do or do not make them salient
S24 SYM Presence of elements that require appropriate readings of symbols
12. Methods – Principal Component Analysis (PCA)
Example of selection of variables - Seasonal changes
Label Element Description
S1 Orbit Presence of the Earth’s orbit
S2 Elliptical orbit Presence of Earth’s orbit represented as elliptical
S3 Earth Presence of the Earth
S4 One Earth Presence of only one Earth
S5 Multiple Earth Presence of more than one Earth
S6 Multiple Earth and orbit Presence of the Earth’s orbit and of more Earths along this orbit
S7 Multiple Earth and no orbit Presence of more Earths but of no orbit
S8 Sun Presence of the Sun
S9 Sun and orbit Presence of the Sun and the Earth’s orbit
S10 Sun and no orbit Presence of the Sun but of no Earth’s orbit
S11 Rays Presence of some kind of rays
S12 Rays hitting the Earth Presence of some kind of rays hitting the Earth’s surface. It is possible that the source of the rays is not represented
S13 Converging rays Presence of rays drawn as convergent. It is not important which or where is the source of the rays
S14 Converging and inclined rays Presence of convergent rays and of their inclination with respect to the hit surface. It is not important which or where is the source of the rays
S15 Distance Presence of elements (segments, arrows ec.) representing the distance between the Earth and the Sun
S16 Axis Presence of the Earth’s axis
S17 Moon Presence of the Moon
S18 Weather Presence of elements related to climate and weather (rain, cloud, snow etc.)
S19 N/S Presence of cardinal points
S20 Angle Presence of the angle between the Earth's axis and its orbit or between solar rays and the Earth’s surface.
S21 INT Presence of two or more conceptually related images
S22 VER Presence of verbal elements to be read as an important part of the image, such as captions
S23 SEL Presence of elements selected or conceptually highlighted in relation to textual/graphical features, which do or do not make them salient
S24 SYM Presence of elements that require appropriate readings of symbols, and that contain examples of synonymy, homonymy and/or polysemy of
symbols
13. PCAVS. FACTOR ANALYSIS OF DRAWING
MODELS of
SEASONAL
CHANGES
Presence of the Earth’s orbit
Presence of the Earth
Presence of more than one Earth
Presence of the Sun
Presence of rays
Presence of Rays hitting the Earth’s surface
Presence of Convergent Rays hitting the Earth’s surface
Presence of Convergent and Inclined Rays hitting the Earth’s surface
Presence of Convergent Rays hitting the Earth’s surface
Presence of elements representing the distance between the Earth and the Sun
Presence of the Earth’s axis
Presence of elements related to clime and weather
Presence of cardinal points
Presence of an angle between the Earth's axis and its orbit
Models are not
known in
advance
We «measure»
the presence of
iconic elements
Variability in the
iconic elements
causes the
variance of the
models
14. PCAVS. FACTOR ANALYSIS OF DRAWING
MODELS of
SEASONAL
CHANGES
Presence of the Earth’s orbit
Presence of the Earth
Presence of more than one Earth
Presence of the Sun
Presence of rays
Presence of Rays hitting the Earth’s surface
Presence of Convergent Rays hitting the Earth’s surface
Presence of Convergent and Inclined Rays hitting the Earth’s surface
Presence of Convergent Rays hitting the Earth’s surface
Presence of elements representing the distance between the Earth and the Sun
Presence of the Earth’s axis
Presence of elements related to clime and weather
Presence of cardinal points
Presence of an angle between the Earth's axis and its orbit
Models are
considered as a
latent variable
We «measure»
the presence of
iconic elements
Variability in the
iconic elements
is caused by
existence of
different models
15. JUSTIFICATION FORTHE USE OF PCA OF DRAWINGS
Models emerge from the “data” (the iconic elements) and can be interpreted
ex-post
Possibility of introducing models from factor scores and not only from
eigenvalue-based criteria
While similar, PCA is not a technique to perform FA, which assumes the
existence of a “latent trait”, in our case, a “latent” model
While models precede drawings, they cannot be limited a-priori to those
foreseen by literature emerging models could be not “stable” enough
As such, mental models cannot be considered technically as a “latent trait”
16. METHODS - RELIABILITY
Using the models obtained from PCA, a researcher again classified the
students’ drawings
Inter-rater reliability between the categorization based on factors scores
and the classification of the researcher
17. METHODS - RELATIONSHIPS BETWEEN DRAWINGS & KNOWLEDGE
Written task in two modalities: with/without a side textbook picture
Written questionnaire with 6 T/F and 2 multiple choice questions
18. METHODS – RUBRICS
WRITTEN TASK ABOUT SEASONAL CHANGES
0 points: Unclear answer;
1 point: incorrect answer (e.g., distance
misconception)
2 point: partial answer (e.g., reasoning is
incomplete)
3 point: correct answer
T/F and MULTIPLE CHOICE QUESTIONS
0,5 points: for each correct T/F
1 point: partial answer choice in the M/C
2 point: correct answer choice in the M/C
Max score: 7 0-1 incorrect knowledge (0);
2-3 naïve (1); 4-5 partial (2); 6-7 correct (3)
19. METHODS - RELATIONSHIPS BETWEEN DRAWINGS AND (I) TEXTBOOK
VISUALIZATIONS AND (II) CURRICULUM INSTRUCTION
Textbook image shown/not shown before drawing
Curriculum vs. no formal instruction about astronomy
20. SAMPLE
736 students
339 6th - 8th grade (no curricular instruction about astronomy)
151 9th – 10th grade (curricular instruction about astronomy)
108 9th – 10th grade (textbook image shown before drawing)
138 9th – 10th grade (drawing first)
6th - 8th grade middle school (compulsory)
9th – 10th grade first two years high school (compulsory)
Average age: 13.0±0.1
Contents taught in curriculum instruction (6-10 hs): Earth motions around the Sun,
solar system
22. RQ1. To what extent drawings may reliably uncover students’
mental models about a given phenomena?
PCA of drawings is effective in identifying students’ mental models
from iconic elements
Few «more relevant» iconic elements explain about 60% of the variance
in the original drawings
Sufficient agreement (60%) between factor scores and researcher’s
rating
23. RQ2. What is the relationship between drawings and knowledge
about the target phenomenon?
Students who produced naïve and distance-based drawings were more
likely to give unclear explanations and choose incorrect answers to
aggregate T/F and MC questions
Students who produced a distance-based drawing were more likely to
choose a distance-based answer choice and to give incorrect
explanations
Naïve drawings correspond incorrect accounts about sun emission of
energy
24. RQ2. What is the relationship between drawings and knowledge
about the target phenomenon?
Students who produced an inclination-based drawing were more likely
to
choose correct answer choices
give correct explanations
Inclined-based drawings more likely correspond to correct notions
about the Earth’s axis
25. RQ3. To what extent do textbook visualizations and curriculum
instruction influence students’ drawings?
Textbook images lead to more “detailed” student generated drawings
• Inclination-based drawing less frequent in “textbook images” group
More correct drawings were generated by students exposed to
curriculum teaching about astronomy
• Distance-based drawing more common in “no instruction” group
27. PCA OF STUDENTS’ DRAWINGS - STATISTICS
KMO (Keiser Meyer Olkin) 0,759
Bartlett's test of
sphericity
χ2 2310,023
df 120
p-value 0,000
Total variance explained: 57.3%
28. PCA OF STUDENTS’ DRAWINGS – FACTOR LOADINGS
Principal Component
1 2 3 4
Presence of the Earth’s orbit ,467
Presence of the Earth ,788
Presence of more than one Earth ,643
Presence of the Sun ,834
Presence of some kind of rays -,629
Presence of some kind of rays hitting the Earth’s surface ,837
Presence of rays drawn as convergent. ,916
Presence of convergent rays and of their inclination with
respect to the hit surface.
,804
Presence of elements representing the distance
between the Earth and the Sun
,454 ,353
Presence of the Earth’s axis ,778
Presence of elements related to climate and weather -,855
Presence of cardinal points ,588
Presence of the angle between the Earth's axis and its
orbit
,748
Presence of two or more related images -,701
Presence of verbal elements ,815
Presence of elements that require appropriate readings
of symbols
,343
29. PCA OF STUDENTS’ DRAWINGS - MODELS
Principal Component
1
Presence of the Earth ,788
Presence of the Sun ,834
Presence of elements that require appropriate readings
of symbols
,343
Distance 1
30. PCA OF STUDENTS’ DRAWINGS - MODELS
Principal Component
1 2 3 4
Presence of some kind of rays hitting the Earth’s surface ,837
Presence of rays drawn as convergent. ,916
Presence of convergent rays and of their inclination with
respect to the hit surface.
,804
Rays
31. PCA OF STUDENTS’ DRAWINGS - MODELS
Principal Component
1 2 3 4
Presence of the Earth’s orbit ,467
Presence of more than one Earth ,643
Presence of elements representing the distance
between the Earth and the Sun
,454
Presence of verbal elements ,815
Distance 1I
32. PCA OF STUDENTS’ DRAWINGS - MODELS
Principal Component
1 2 3 4
Presence of the Earth’s axis ,778
Presence of cardinal points ,588
Presence of the angle between the Earth's axis and its
orbit
,748
Tilt
41. CORRELATION BETWEEN MODELS AND MC QUESTIONS
(N = 438)
The change of seasons is
mainly due to:
a) Earth-Sun changing distance 35 49 8 20
b) The Earth rotating around itself 15 15 15 17
c) The changing duration of the day 12 5 6 0
d)The changing inclination of
the sunrays hitting the Earth*
38 31 71 63
χ2 = 56,228; df = 9; p<10-4
42. CORRELATION BETWEEN MODELS AND MC QUESTIONS
(N = 455)
Why in summer it is hotter
than in winter
a) Because the Sun emits more
energy
27 9 4 8
b) Because how the Earth is hit
by sunlight changes*
44 34 83 56
c) Because we are farther from the
Sun and the Earth slows down
3 8 2 6
d) Because the Earth is closer to
the Sun
26 49 11 29
43. CORRELATION BETWEEN MODELS ANDT/F QUESTIONS
(N = 401)
During Summer the Sun emits
more energy
False 79 48 36 49
True 21 52 64 51
χ2 = 9,198; df = 3; p = 0.027
44. CORRELATION BETWEEN MODELS ANDT/F QUESTIONS
(N = 394)
Energy absorbed by a surface is
maximum when light hits
normally the surface
False 50 36 20 38
True 50 64 80 62
χ2 = 6,580; df = 3; p = 0.087
45. CORRELATION BETWEEN MODELS ANDT/F QUESTIONS
(N = 396)
Sunrays incidence on Earth
changes during the year
False 22 23 27 22
True 78 77 73 78
χ2 = 0,350; df = 3; p = 0.950
46. CORRELATION BETWEEN MODELS ANDT/F QUESTIONS
(N = 395)
Earth surface asorbs energy
from the Sun
False 33 24 18 27
True 67 76 82 73
χ2 = 2,070; df = 3; p = 0.558
47. CORRELATION BETWEEN MODELS ANDT/F QUESTIONS
(N = 387)
The Earth axis is inclined w.r.t.
the orbit’s plane
False 25 26 2 18
True 75 74 98 82
χ2 = 13,684; df = 3; p = 0.003
48. CORRELATION BETWEEN MODELS ANDT/F QUESTIONS
(N = 380)
The Earth axis remains parallel
to itself during the year
False 53 52 56 51
True 47 48 44 49
χ2 = 0,204; df = 3; p = 0.977
49. CORRELATION BETWEEN MODELS ANDTEXTBOOK IMAGES
(N = 194)
GROUP
Textbook image before drawing 0 48,6 13,0 82,6
Drawing first 100 51,4 87,0 17,4
χ2 = 27.825; df = 3; p < 10-4
50. CORRELATION BETWEEN MODELS AND INSTRUCTION
(N = 276)
GROUP
No instruction 100 60,1 69,7 44,0
Instruction 0 39,9 30,3 56,0
χ2 = 22.952; df = 3; p < 10-4
52. Discussion
Drawing were good predictors for explanations in open questions
Drawings were good predictors for answers to MC questions
Drawings were good predictors for answers to some T/F questions
53. Discussion
Using Paivio’s theory of representations:
PCA can help clarify the relationships between students’ drawings and their
conceptions of the represented phenomenon
Trough PCA, the internal representation of the concept can be “reconstructed”
from the referential links used
54. Implications
Use of PCA helps investigate
which iconic elements students are more often used in visual representations
(Van Meter and Garner, 2005)
how such models correlate to explanation categories of increasing complexity
the influence of conventional representations used in instructions (Ehrlén,
2008)
55. Implications
Main advantages of PCA with respect to typical indexing schemes and self-
made rubrics (Stieff, 2011; Lundin & Jakobson, 2014; Bowker, 2007)
to identify common patterns from the data
to focus on the conception expressed in the drawing rather than on superfluous
or difficult to represent symbols
56. CONCLUSIONS
Findings suggest that drawings are effective tools to elicit mental models
and to negotiate evidence-based accounts of familiar astronomical
phenomena
PCA could be extended to drawing analysis in other areas
However, more research is needed to investigate relationships wirth:
written explanations and questionnaire
curricular instruction