Development and validation of a Learning Progression of basic astronomy phenomena

NYS Geometry [Common Core] January 2016 Regents Exam || Part 1 #’s 13-24 ANSWERS
NYS Geometry [Common Core] January 2016 Regents Exam || Part 1 #’s 13-24 ANSWERS

Development and validation of a Learning Progression of basic astronomy phenomena

Development and validation of a
Learning Progression of basic
astronomy phenomena
Silvia Galano
Physics Division, School of Science and Technology, University of Camerino, Italy
Supervisors:
Prof. Irene Marzoli
Physics Division, School of Science and Technology, University of Camerino Italy
Dr. Italo Testa
Department of Physics “E. Pancini”, University of Naples “Federico II”, Italy

Aim of this study
In last years learning progressions (LPs) have been
increasingly used by researchers in science education to
describe how students develop their understanding of a
given concept across school levels.
(Duncan & Hmelo-Silver., 2009; Smith, Wiser, Anderson, & Krajcik, 2006; Stevens, Delgado &
Krajcik, 2010; Wilson & Bertenthal, 2006).

Aim of this study
LPs can be useful means to improve teaching practices at
different school levels. They can play a key role in order to
reform and build coherent curricula and to develop
instructional educational materials.

Aim of this study
LPs are usually built around “big ideas” in science, i. e. “core”
concepts.
Corcoran, Mosher & Rogat, 2009)
“Big ideas” help students connect different phenomena,
empirical laws, and explanatory models.
(Duschl, Maeng & Sezen, 2011)
Despite increasing attention, up to now, few are the big ideas in
astronomy for which LPs have been developed and validated.
(Plummer et al., 2015; Plummer & Maynard, 2014)

Astronomical phenomena: Why?
Astronomy increase student’s interest towards science.
Data on 2014/2015. MIUR (Italian Ministry for Education) – Ufficio di Statistica”; “Fonte: elaborazione su dati
MIUR – Ufficio di Statistica”

Astronomical phenomena:Why?
Astronomy is one of the most fascinating and charming matter.
Just think about how many astronomical elements you can find in
books, TV series, manga, games etc.
The Starry Night, Vincent
van Gogh 1888

Astronomical phenomena: Why?
Previously studies have proved that astronomical topic are
difficult to understand for the students
Why do seasons change?
Because when it’s
summer we are
closer to the Sun
while in winter we
are faraway from
the Sun. It’s simple! Which is the
cause of solar
eclipses?
There is a planet
between the
Earth and the
Sun so that it is
not possible to
see the Sun.
Which is the
cause of Moon
phases?
Something,
maybe an
asteroid, casts
his shade on the
Moon.

RESEARCH QUESTIONS
RQ1: how do students develop their understanding about change of seasons,
Moon phases and solar/lunar eclipses from middle school to graduate level?
RQ2: drawing on RQ1 findings, which learning progression that describes
students’ cognitive levels about the addressed astronomical phenomena can be
hypothesized?
RQ3: how well does the hypothesized learning progression actually describe
students’ understanding of the addressed astronomical phenomena across
different educational levels? How can it be optimized?
RQ4: to what extent a teaching- learning sequence (TLS) based on the
optimized learning progression is effective in addressing students’
misconceptions about the addressed astronomical phenomena?

Learning Progression
Learning Progression (LP) can be defined as “descriptions of the
successively more sophisticated ways of thinking about a topic that can
follow one another as children learn about and investigate a topic over a
broad span of time” (NRC, 2007).
LPs are based on a developmental view of learning: the students learn a
given science content starting from their intuitive ideas (lower anchor) and
progress through subsequent levels of more sophisticated understanding of
the topic towards the scientifically correct idea (upper anchor).
(Driver, 1994; Posner et al., 1982)

Developing and validating LP
If the
alignment is
satisfying
Previously research results, students’ answers to
questionnaire or interviews, well known
misconceptions are used to hypothesise a first version
of the LP (HLP)
Design a measurement instrument (usually a questionnaire or an interview)
Test the alignment between LP and actual students’ achievements
Validate/reviserd
version of LP (RLP)
Yes
No
Revise HLP

Developing and validating LP
To test the alignment between students’ achievements and LP
two methods are used:
Qualitative approach data from interviews and open tasks
(e,g Krajicik et al., 2010; Shea & Duncan, 2013).
Quantitative approach scoring students’ answers to a multiple-
choice questionnaire
(e,g, Hadelfedt et al., 2016; Neumann, Viering, Boone & Fischer, 2013)

LP and big ideas
Researchers have developed many LPs around big ideas from
different scientific area:
Energy (Neumann, Viering, Boone & Fischer, 2013)
Matter (Stevens, Delgado & Krajcik, 2010; Hadenfeldt, et al. 2016)
Force and motion (Alonzo & Steedle, 2009)
Water (Gunckel, Covitt, Salinas, & Anderson, 2012)
Modern genetics (Todd & Romine, 2016)

LPs and astronomical topics
Recently, there has been an increasing interest of science education
research community towards students’ difficulties in understanding
astronomical topics and there have been some attempts to extend LPs
approach to astronomical core concepts:
(Plummer, 2014; Plummer 2009; Sneider, Bar & Cavanagh, 2011)
Solar System formation (Plummer et al. 2015)
Celestial motion (Plummer & Maynard, 2014; Plummer & Krajcik 2010)
It has to be noted that no LP has yet been validated across all school
levels from, middle school up to post graduate.

Misconceptions on changes of seasons
Tilt of Earth’s axis:
“The seasons are caused by the tilting of the earth’s axis
toward and away from the sun. While it is winter here, we are
farther away from the sun, but some places on earth are closer
to the sun so it is summer there”.
(Atwood & Atwood, 1996)
Earth-Sun distance:
Changes in Earth-Sun distance cause changes in seasons. It is
summer when the Earth is closer to the Sun.
(Baxter, 1989; Nazé & Fontaine, 2014)

Misconceptions on Moon phases
Students often confuse lunar eclipses with Moon phases, in
particular they are unable to articulate the difference between a full
moon and a lunar eclipse and how the role the Earth plays in the
occurrence of a lunar eclipse.
(Trumper, 2000; Barnett, 2002; Barnett & Morran J., 2002).
Moon phases are due to the Sun periodically blocking the view of
the moon from earth (‘‘Sun blocking’’).
(Trundle, Atwood, Christopher, 2007)
Moon phases are explained only in terms of the shadows of other
planets.
(Baxter, 1989)

Misconceptions on lunar/solar eclipses
Many students thought that the Moon must be in its Full phase
for there to be a total solar eclipse.
(Trumper, 2001)
Many students think that during lunar eclipses the Sun is
between the Earth and the Moon so that it is not possible to see
the Moon.
(Testa et al., 2013)
Students are not able to justify period of eclipses.
(Testa et al., 2013)

Spatial reasoning
Spatial reasoning skills may help students in
understanding astronomical phenomena.
Motion in three-dimensional reasoning: “3D computational modelling
supported students in developing scientifically sound understandings of
dynamical astronomical phenomena”.
(Hansen et al. 2004; Parker & Heywood, 1998)
Changing frames of reference and perspective: there are many difficulties
in visualization of three-dimensional position in space and two-
dimensional representation of three-dimensional objects.
(Parker & Heywood, 1998)

Physics and Astronomy
Many difficulties in understanding astronomical topic can be due
to difficulties in understanding physics related topics (e.g. light’s
property and propagation, Gauss’s law for flux, energy transfer
etc.)
Causes of season strictly depend on Gauss’s flux law and energy
transfers
Light propagation is the main cause of shades that determine
eclipses and Moon phases
Understanding reference systems and relative motion is
fundamental in order to develop a scientifically correct knowledge
of Moon phases and eclipses

RQ1 and RQ2
We developed an open questionnaire, based on previous studies
Students’ answers were categorized through a content-based
iterative categorization in three levels of understanding:
Informed
Partial
Naïve
The emerging categories informed initial LP levels (HLP).

RQ3
To empirically validate the hypothesized LPs, a 48-items mixed true/false,
multiple-choice questionnaire was developed. The questionnaire featured
12 two-tier items, for a total of 12 multiple choice questions and 36 true or
false statements.
4 items for each phenomenon.
Two versions of the questionnaire were developed, one for the middle
school level (q2), the other for secondary school and graduate students
(q1).

RQ3
To design q1 questions, we used a modified Ordered Multiple Choice (OMC)
model, where each item corresponds to a LP level
“OMC items feature a constrained set of response options that can be scored
objectively; the potential qualitative richness comes because OMC response
options are both designed to correspond to what students might answer in
response to an open-ended question and explicitly linked to a discrete level of
an underlying learning progression”.
(Alonzo, & Wenk Gotwal, 2012).

RQ3
Example of items for q1 questionnaire
Indicate, for each of the following statements, if it is true or false
Q13 Earth’s motion around the Sun is a periodic motion on a closed orbit
Q14 Earth’ s orbit around the Sun is a very eccentric ellipse
Q15 Season periodicity is due to the revolution of the Earth around the Sun
Q16 Which of the following statements best explains the phenomenon of the different seasons? (please
indicate the correct one)
(i) During the revolution, the distance between the Earth and the Sun changes so, in a certain places of the
Earth, solar rays do not always have the same incidence on the surface
(ii) During the revolution, the direction of the Earth’s axis changes so, in a certain place of the Earth, solar
rays do not always have the same incidence on the surface
(iii) During the revolution, Earth’s axis remains parallel to itself so, in a certain place of the Earth,
solar rays do not always have the same incidence on the surface
(iv) During revolution, Earth’s axis is always perpendicular to the orbit plane so, in a certain place of the
Earth, solar rays do not always have the same incidence on the surface

RQ3
The total score for q1 was 48.
Students’ answers to q1 were analysed using a dychotomous model Rasch
analysis.
Using Rasch analysis, it will be possible to lump together the two different
forms of the questionnaire.
Comparing difficulties of the items allowed us to compare also levels of
the HLP and to revise them according to actual students’ achievements.

RQ4
A TLS focused on change of season and based
on the validated version of the LP was
designed and validated through cycles of
school implementations with students of
secondary school (14-18 ys).
Questions of q1 targeting change of seasons
have been used as pre- and post- test to test
the efficacy of the TLS.
(Testa et al., 2015; Galano, 2016)

Development of the TLS
From the RLP for seasons, it emerged that the role
of the Earth’s axis on the change of seasons was
the most difficult to understand for the students.
From the analysis of students’ answers to q1 it
emerged that students often know “facts” related to
astronomical phenomena but find difficult to
connect them in order give a scientifically correct
explanation of changes of seasons. This may be
due to misconceptions in the physics related topics.

Development of the TLS
We chose to focus on the relationships between the
energy received by the Earth and the different
conditions under which Solar light hits the Earth’s
surface.
We choose to explicitly deal with physics topic
related to changes of season: Gauss’ flux law,
energy transfer etc.

Development of the TLS
The main aim is to guide students to understand the
mathematical relationships between the flow across
a surface and:
the angle between the normal to the surface and the
direction of the incident radiation (cosine law)
the distance between the surface and a point-like
source (inverse square distance law)

Sample
Preliminary study (RQ1 and RQ2):
189 students at the beginning (13-14 years old) and the end (18-19
years old)
10 university students
Main study (RQ3):
10 Prospective secondary physics teachers
10 Prospective primary teachers
80 Prospective middle school science teachers
140 Secondary school students (18-19 years old)
114 Secondary school students (13-14 years old)
Main study (RQ4):
45 Secondary school students (17-18 years old)

First Learning Progressions on basic astronomical phenomena
Phenomenon Level q1 items Progress indicator: The students know that
Seasons (1) Lower anchor Q5 – Q8 Student know that season are due to inclination of solar
rays that changes during the year
2 Q1 – Q4 Level 1 + the revolution of Earth around the Sun
3 Q9 – Q12 Level 2 + tilt of Earth’s axis
(4) Upper anchor Q13 – Q16 Level 3 + Earth’s axis constant direction in space
Eclipses (1) Lower anchor Q33 – Q36 Sun and Moon eclipses are due to alignment between the
Sun, Moon, and Earth
2 Q41 – Q48 Level 1 + alignment happens in a 3D space
(3) Upper anchor Q36 – Q40 Level 2 + relative inclination of Moon and Earth orbits’
planes
Moon phases (1) Lower anchor Q17 – Q20 Moon phases are due to revolution of the Moon around
Earth
2 Q25 – Q28 Level 1 + periodicity of the phases
3 Q21 – Q24 Level 2 + Sun illumination
(4) Upper anchor Q29 – Q32 Level 3 +relative positions of Earth, Moon, and the Sun

Rasch statistics
Item Statistics
Mean INFIT MNSQ 1,00
Mean OUTFIT MNSQ 0,97
MODEL RMSE 0,13
SEPARATION 7,12
ITEM RELIABILITY 0,98
Person Statistics
Mean INFIT MNSQ 1,00
Mean OUTFIT MNSQ 0,97
MODEL RMSE 0,34
SEPARATION 1,90
PERSON
RELIABILITY .
0,78
CRONBACH ALPHA 0,78

RQ3: q1 Wright map
As expected multiple choice
questions resulted to be more
difficult than true/false
questions.
Knowledge of astronomical
facts is not sufficient to build
up a coherent scientific
explanation for astronomical
phenomena

Position of Earth, Sun and
Moon during eclipses,
eccentricity of Earth’s orbit
RQ3: q1 Wright map
Moon’s orbit period, Moon
phases’ shape
Tilt of Earth’s axis, Earth’s
revolution, relative inclination of
orbit plans
Relationship
between the tilt
of Earth’s axis
and the
inclination of
sun rays;
consequences
of Earth, Sun
and Moon
relative motion
Earth’s axis remains parallel to
itself, three body motion in 3D
space
Causal
reasoning
Basic
facts
Spatial
reasoning

RQ3: q1 Wright map
On average,
prospective
teachers have a
more informed
knowledge of
astronomical
phenomena than
students
Prospective
primary
teachers have
the same ability
of secondary
school students
From the distribution of the sample
on the Wright map, we can identify
two different Gaussian distributions,
one centred at about 0,5 and one at
1,6. This reflects an important feature
of our sample: teachers are on
average at an upper stage of our LP

RQ3: revision of LP on seasons
Level Seasons: first version of
LP
Seasons: revised LP
(4) Upper
anchor
Level 3 + Earth’s axis constant
direction in space
Level 3 + revolution of Earth around
the Sun and constant tilt of Earth’s
axis w.r.t. orbit’s plane
3 Level 2 + tilt of Earth’s axis Level 2 + constant direction in space
of the Earth’s axis
2 Level 1 + the revolution of
Earth around the Sun
Level 1 + the inclination of solar
rays changes during the year
(1) Lower
anchor
Student know that season are
due to inclination of solar rays
that changes during the year
Seasons are due to Earth’s axis
inclination w.r.t. the orbit’s plane

RQ3: revision of LP on Moon phases
Level Moon phases: first
version of LP
Moon phases: revised LP
(4) Upper anchor Level 3 + relative positions
of Earth, Moon, and the Sun
Level 3 + the same phase is visible from
every Earth locations that can see the
Moon (which is a consequence of
illumination conditions of the Moon
Surface).
3 Level 2 + Sun illumination Level 2 + Sun illumination
2 Level 1 + periodicity of the
phases
Level 1 + periodicity of the phases
(1) Lower anchor Moon phases are due to
revolution of the Moon
around Earth
Moon phases are due to relative positions
of Earth, Moon, and the Sun

RQ3: revision of LP on eclipses
Level Solar/lunar eclipses:
first version of LP
Solar/lunar eclipses: revised
LP
(3) Upper anchor Level 2 + relative inclination of
Moon and Earth orbits’ planes
Level 2 + frequency of eclipses and
the fact that they are visible only from
a small portion of Earth’s surface as
consequence of relative inclination of
Moon and Earth orbits’ plan and scale
of the Sun-Moon-Earth system.
2 Level 1 + alignment happens in
a 3D space
Level 1 + alignment happens in a 3D
space
(1) Lower anchor Sun and Moon eclipses are due
to alignment between the Sun,
Moon, and Earth
Sun and Moon eclipses are due to
alignment between the Sun, Moon,
and Earth

RQ3: RLPs
Level Seasons Solar/Lunar eclipses Moon Phases
Upper anchor
(4)
Level 3 + revolution of Earth
around the Sun and constant
tilt of Earth’s axis w.r.t. orbit’s
plane
Level 2 + frequency of
eclipses and the fact that they
are visible only from a small
portion of Earth’s surface as
consequence of relative
inclination of Moon and Earth
orbits’ plan and scale of the
Sun-Moon-Earth system.
Level 3 + the same phase is visible
from every Earth locations that can
see the Moon (which is a
consequence of illumination
conditions of the Moon Surface).
3 Level 2 + constant direction in
space of the Earth’s axis
Level 2 + Sun illumination
2 Level 1 + the inclination of
solar rays changes during the
year
Level 1 + alignment happens
in a 3D space
Level 1 + periodicity of the
phases
Lower anchor
(1)
Seasons are due to Earth’s axis
inclination w.r.t. the orbit’s
plane
Sun and Moon eclipses are
due to alignment between the
Sun, Moon, and Earth
Moon phases are due to relative
positions of Earth, Moon, and the
Sun
Upper anchor of the
three LP have in
common that students
need to master skill of
spatial reasoning
Students’
explanation of
astronomical
phenomena are
based on causal
reasoning

RQ3: LP on Celestial Motion
Revised Learning Progression on Celestial Motion
Level Progressor Indicator
(4)
Upper
Anchor
Explanations showing more complex reasoning: Knowledge of 3D geometrical
features of the Sun, Moon, and Earth motion, and of how change of the
observer’s perspective may change the description of the phenomena.
3 Explanations with simple implications from basic facts: Knowledge of Earth’s
surface illumination conditions, and of the frequency of Moon phases and
eclipses phenomena.
2 Explanations from basic facts: Knowledge of plane geometry conditions, and of
E-S-Mpositions and motion.
(1)
Lower
Anchor
Explanations based on naïve ideas: Lack or insufficient knowledge about Earth-
Sun distance, and about the motion of the Moon around the Earth and the Sun.

RQ4
RLP level q1 item q1 questions Progress indicator: the
students know that
(4)
Upper anchor
I2 Q1 – Q4 Level 3 + revolution of Earth around
the Sun and constant tilt of Earth’s
axis w.r.t. orbit’s plane
3 I4 Q13 – Q16 Level 2 + constant direction in space
of the Earth’s axis
2 I1 Q5 – Q8 Level 1 + the inclination of solar
rays changes during the year
(1)
Lower anchor
I3 Q9 – Q12 Seasons are due to Earth’s axis
inclination w.r.t. the orbit’s plane

Validation of the LP
We submitted the questionnaire q2 to 173 students of middle
school and we are going to analyse their answers and drawing.
We will lump together the two different forms of the
questionnaire q1 and q2 to validate LP for students from 13
years old to post graduate students
We will extend our sample to in-service teachers and university
students.
We will include in our sample lay people without a scientific
degree and students of the last year of elementary school.

RQ3
Example of items for q2 questionnaire
Q4: Explain why it is colder in winter than in summer. You can answer making a draw.
Q5: The main reason for change of seasons is:
i. changes of the distance between the Earth and the Sun
ii. the Earth’s rotation
iii. change in the duration of day
iv. changes in the inclination of solar rays on the Earth surface during the year

Overview of the teaching module “Causes of seasons”
Activity What students do Intended objectives
1 Discuss about the possible factors underlying
the cause of seasons. Design an experiment to
show the relevance of the identified factors.
To elicit students’ ideas about the change
of seasons. To reinforce students’ skills in
selecting control variables in
experiments.
2 Measure the output power of a photovoltaic
panel illuminated by an incandescent lamp
when changing the source – panel distance and
the inclination of the panel with respect to the
direction of the incoming radiation.
To introduce the cosine and inverse
square laws of the incident radiation flow
on a surface. To reinforce students’ skills
in dealing with analysis and fitting
methods.
3 Estimate the solar radiation flow at different
locations of the Earth at a fixed time of the
year and at a fixed location of the Earth over
the year using the models constructed in the
previous activity. Estimate the radiation flow
at perihelion and aphelion.
To exploit mathematical models to
describe experimental evidences.
4 Measure the specific heat of the sand. Discuss
about the role of the environment on the
temperature of a given location on Earth’s
surface.
To relate the temperature of a location to
the heat transfers between radiation and
the environment.

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Editor’s Notes

KR-20 (Cronbach Alpha) is an index of the repeatability of raw scores, misinterpreted as linear measures. KR-20 overstates the reliability of the test-independent, generalizable measures the test is intended to imply. For inference beyond the test, Rasch reliability is more conservative and less misleading.
Separation is the signal-to-noise ratio in the data. Specifically, the separation coefficient gives us the square root value of the ratio between the true person variance and the error variance in the data (Linacre, 2012 ). Separation can range from 0 to infinity; thus, there is no ceiling to this index. For purposes of an introductory analysis, a higher value is “better” than a lower value.
Reasonable Mean-Square Fit Values”. In general, a range between 0.5 and 1.5 suggests a reasonable fit of the data to the model.
Fit describes how well data conform to the Rasch model. Person fit looks at how a person answered all the items on a survey or test, but those answers are reviewed in light of the person’s measure, which is computed using all of the respondent’s answers compared to the difficulty level of the items. Person Infit is a statistic that gives more weight to responses on items near a person’s measure. Person Outfit is a statistic that gives more weight to responses on items far away from a person’s measure.
Model RMSE
Errore medio sulle difficoltà degli item
Errore medio sulle abilità (ovviamente la distribuzione è più ampia)

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