This document presents on personalized learning through inquiry-based learning and McRel's 6-phase model in mathematics. It discusses how personalized learning enhances the learning process through goal setting, working on curiosities, and thinking creatively. The presentation covers goal setting, sharing curiosities, brainstorming goals, and symbiotic learning. It demonstrates stages of the learning process including becoming interested, committing to learning, focusing on new knowledge, practicing and rehearsing, and extending and applying knowledge. Examples discussed include concept mapping, research, statistics such as standard deviation, z-scores, correlation, and linear regression. Reflection on the learning process is also emphasized.

1. -PERSONALIZED LEARNING @
ALAMANDA
P R E S E N T E D B Y W I L L

2. Personalized learning through
Inquiry - Mining Creativity and
Imagination through Research
Design & McRel’s 6-phase
model in mathematics

3. LEARNING INTENT / GOAL
• To understand how
personalized learning
enhances the learning
process through goal
setting, working on
curiosities and thinking
creatively.

4. SUCCESS CRITERIA
• To be confident working with
students in crafting their
personalized learning through
mining creativity and
imagination through research
design and McRel’s 6-Phase
learning model.

5. “The moving power of mathematical
invention is not reasoning but
imagination.”
Augustus De Morgan

7. GOAL SETTING
Goal setting is the process of establishing an outcome (a goal) to serve as
the aim of one's actions (Locke & Latham, 2020). Setting goals:
• makes the direction of learning clear to the student and the teacher
• increases students' motivation and achievement levels
• works best if they are specific and require a moderate amount of
challenge
• works best for high-ability students if they are co-constructed.
• Teachers need to help high-ability students set goals that are
appropriately challenging for them. This may mean that their goals are
quite different to the rest of the class.
•

8. SHARING MY GOAL SETTING
Goal 1
To take everyone on a journey through
personalized learning..
Goal 2:
To help everyone see the world differently after
this presentation..
Goal 3:
To learn through an encouraging symbiotic
process..

9. CURIOSITIES…
Factual:
• What enduring understandings or skills must students develop?
Conceptual:
• What should they learn when they’re 7 or 17 and still recall when
they’re 70?
• How will students demonstrate these understandings?
• What are the success criteria?
• How will you spark student interest, making these understandings
relevant and meaningful to students?
• What challenging learning tasks will I use to frame this unit?

10. SYMBIOTIC LEARNING
Symbiosis is a biological phenomenon in which two dissimilar organisms
coexist for mutual subsistence. The concept of symbiosis can be employed
to foster mutual learning. In this paper, the idea of symbiotic learning is
explored. To achieve this purpose, the concept of symbiosis is interpreted
from a philosophical perspective, which is primarily derived from ecological
philosophies such as Gestalt thinking and the philosophy of coevolution
(Wang, 2019).
Gestalt psychology is a school of thought that looks at the human mind and
behavior as a whole. When trying to make sense of the world around us,
Gestalt psychology suggests that we do not simply focus on every small
component.

11. BRAINSTORM – WHAT ARE YOUR GOALS
TODAY?

12. TASK 1
• In your table groups,
share your perceptions
and knowledge of
“Personalized Learning”
• Set your goals on what
you intend to learn
through this symbiotic
process
• Present your mindmap
on your discussion

13. PRESENTATION TIME

14. Personalized learning is a complex activity approach
that is the product of self-organization (Chatti, 2010;
Miliband, 2006) or learning and customized instruction
that considers individual needs and goals.

15. Personalized learning can be an efficient approach that
can increase motivation, engagement and
understanding (Pontual Falcão, e Peres, Sales de
Morais and da Silva Oliveira, 2018), maximizing learner
satisfaction, learning efficiency, and learning
effectiveness (Gómez, Zervas, Sampson and Fabregat,
2014).

21. MINI
LESSON

22. STAGE 1: BE INTERESTED

24. INTRODUCING THE OVERARCHING
INQUIRY STATEMENT

26. MINING CURIOSITIES

36. MINING CURIOSITIES: CHECKPOINT
ONE
Source: McRel Curiosity WorksTM (Rouleau, 2018)
Characteristics of quality questions
KCAASE
Knowledge (What are your goals in knowledge Acquisition, and your
assumptions)
Comprehension (Why do you think that is your assumption)
Application (Why did you pick that particular concept?)
Analysis (How do your questions answer your curiosities?)
Synthesis (How can we weave all our learning in a cohesive investigation)

37. MINING CURIOSITIES: CHECKPOINT
TWO
Source: McRel Curiosity WorksTM (Rouleau, 2018)
Characteristics of quality questions
Factual questions – Great checkpoint on their foundational understanding
and helps goal setting
Conceptual questions – Helps connects and manage relationships
Debatable (Metacognitive questions) –Help understand the students own
thinking, learning and how to approach a task, and think about implications.

38. TASK 2: STORY TELLING USING DATA
• SETUP:
FACTUAL QUESTIONS: What are the factors that influence skyrocketing
fuel prices?
• CONFLICT:
CONCEPTUAL QUESTIONS:
How can data or data structures can I use to analyze this phenomenon?
• RESOLUTION:
DEBATABLE QUESTIONS: Eliminating conflict can prevent further petrol
price increases in the future?

40. CRAFTING A PERSONALIZED INQUIRY
QUESTION
• Refer to the Overarching inquiry question.
• What triggers your curiosities?
• Look at your curiosities (Factual, Conceptual and Debatable
questions)
• How can we fuse these and create an engaging question that
opens up new grounds for discoveries?

42. STAGE 2: COMMIT TO LEARNING

43. WORKING ON THE
PERSONALIZED INQUIRY
AND START GOAL SETTING

44. MINING CURIOSITIES: CHECKPOINT
THREE
Source: McRel Curiosity WorksTM (Rouleau, 2018)
Designing Challenging Tasks
Providing students with choice
PCPE
Process: What are the different ways to demonstrate our learning? Correlates to how
students will learn.
Content: What are the problems that you may encounter and how can teachers
support them?
Product: What are the ways to demonstrate our mastery?
Environment: What are the different learning structures/conditions?

48. CONCEPT MAPPING (CREDITS: MANNY
MAHAL)
Will India match Australia in terms of
liveability in the next 20 years?
Numerical
Discrete
Categorical
Continuous Ordinal
Nominal

50. Rubrics

51. Checklist

57. STAGE 3 & 4: FOCUS ON NEW KNOWLEDGE & MAKE
SENSE OF LEARNING

58. RESEARCH COMPONENT - CASE STUDY
(MANNY MAHAL)

59. GOAL SETTING:
NEW KNOWLEDGE CONTENT &
ANALYSIS
• Biasedness of data – Describe what biasedness of data is in
mathematics.
• Bessel’s Correction – Describe what the concept is. Its relevance
to real-life applications
• Proof of Bessel ‘s Correction (n-1) – To append what we have done
in class as a group.
• Degrees of Freedom
• Pearson’s Product-Moment Correlational studies
• Linear Regression Calculation
• Kurtosis

60. STANDARD DEVIATION (SETUP, CONFLICT,
RESOLUTION-INDIA)
• Setup:
Investigation of the standard deviation of life expectancy in India between 2011-
2021. I would like to see how much the data deviates from the previous years for
life expectancy. This is because when I analyze this over a period of 10 years, it
would give me an accurate snapshot of the development in Healthcare over the
recent observable growth in India.
• Conflict: If the life expectancy hasn’t changed drastically, the data suggests that
the country is improving or the country has improved over the last 10 years in
healthcare. There may be possible cases of corruption that has affected the life
expectancy as these would take away resources from healthcare budgeting.
Possible conflicts or war would also impact the life expectancy. Huge income
divide could have an impact. It is a question of equity vs equality. Diseases or
pandemics could have a possible impact on life expectation. Overpopulation
could have a direct impact on this. Access to education could have a possible
correlation to life expectation.

61. RESOLUTION: WORKING OUT

62. GRAPH OF LIFE EXPECTANCY OF INDIA (TIME
SERIES)
67
67.5
68
68.5
69
69.5
70
70.5
71
71.5
72
2010 2012 2014 2016 2018 2020 2022
Age
Year
Life Expectancy of India
Series1 Linear (Series1)

63. PROOF OF BESSEL’S CORRECTION AND
DEGREES OF FREEDOM

65. INVESTIGATING Z-SCORES
Z-scores provide contextualized measurements of scores in relation to the average as
proportionate to the standard deviation.

66. INDIA: MY INVESTIGATION IN RELATION
TO Z-SCORES
• I am interested to investigate how India fared in 2021 in terms of
life expectancy over the last 10 years.
• Life expectancy for 2021 = 71.2 years old
• Average life expectancy = 69.7 years old
• Z Score =
71.2−69.7
1.188
• = 1.26

67. AUSTRALIA: MY INVESTIGATION IN
RELATION TO Z-SCORES
• I am interested to investigate how Australia fared in 2021 in terms of life
expectancy over the last 10 years.
• Life expectancy for 2021 = 83.1 years old
• Average life expectancy = 82.8 years old
• Z Score =
83.1−82.78
0.244
• = 1.31

68. Z-SCORE ANALYSIS
• In my opinion, Australia performed better in z-scores in life expectancy
because……..
• India has performed less favourably. The possible reasons are:…
• Every analysis has to connect to the inquiry statement.

69. LINEAR REGRESSION
& PEARSON'S
CORRELATION

70. Why are Correlational studies
important?
**Causation vs Correlation

71. P E A R S O N ’ S C O R R E L AT I O N – C O M PA R I S O N S O F H O W I N C O M E A N D L I F E
E X P E C TA N C Y C O R R E L AT E I N I N D I A

75. COMPARISONS OF HOW INCOME AND
LIFE EXPECTANCY CORRELATE TO
AUSTRALIA
y = 0.194x + 73.919
R² = 0.7838
81.6
81.8
82
82.2
82.4
82.6
82.8
83
41 41.5 42 42.5 43 43.5 44 44.5 45 45.5 46
Life
Expectancy
Average Income of Australia
Life Expectancy
Linear (Life Expectancy )

76. ANALYSIS
• What does the data suggest?
• Is there a correlation?
• Why do you think there is a correlation?
• Can you suggest why this correlation occurs?

77. LINEAR REGRESSION FORMULA AND
CALCULATIONS
• Work out the value of m
• Work out the value of the y-intercept
• Check if the calculations tally
• Extension** r=0.9, Sx = 2.3, Sy =1.9.

82. COEFFICIENT OF DETERMINATION
• What is the r2 value?
• How does it connect to probability?

83. FUTURE IMPLICATIONS -
EXTRAPOLATION
• Equation of the line.
• Predict the future using the equation

84. Further Curiosities

89. IMPLICATIONS OF KURTOSIS RISK
• XXXXXX

90. FUTURE IMPLICATIONS AND
CONNECTIONS TO INQUIRY STATEMENT
• Students are required to answer this portion

91. STAGE 5 & 6: PRACTISE AND REHEARSE, EXTEND
AND APPLY

92. REFLECTION

93. MINING CURIOSITIES: CHECKPOINT
FOUR
Source: McRel Curiosity WorksTM (Rouleau, 2018)
Feedback that motivates
Feedback that motivates
Formative: Self assess and correct
Show: Use models, research design, etc.
Self talk: Think about future implications.

94. LESH’S TRANSLATION MODEL IN
MATHEMATICS

95. Reflection(By using Lesh’sTranslation Model):
Real World Contexts/Situations What have I learnt about the real-world applications of the
concepts?
I learnt how data can help extrapolate the future and
reflect a changing world. I’ve learnt how correlation can
show what factors lead to certain events and how strong
a relationship between two events are. I’ve also learnt
how standard deviation can help to guide choices
financially, in how risky a choice is. It also shows how
variant a spread of data is.
Written Symbols What are the mathematical symbols or formulae that are
applicable in this research?
ℴ (sigma) is the sign for standard deviation and ℴ2
(sigma squared) is the variance, which is the standard
deviation squared. These symbols are used to show the
distance from points in a data set from it’s mean. r is the
Pearson’s correlation that shows how correlated two
events are. r
2
is Pearson’s correlation squared, and is
used to determine the percentage of x that determines y.
Pictures What are the graphical representations of the concepts? A Pie Graph was used to compare top 10 exports. A
Column Graph was used to compare life expectancy. A
Histogram and Box/Whisker Plot was used to compare
Income. A Line Graph was used to compare population.
A Scatter Plot was used to compare income and life
expectancy.
Verbal Symbols What are the important vocabulary related to this
mathematical concept?
“Correlation” This is used in Pearson’s correlation to
determine the strength of a relationship. “Standard
Deviation” The measure of how variant a spread of
values are. “Variance” The Standard Deviation squared,
which is used whilst calculating standard deviation to find
absolute values. “Sample” A small group taken from the
population. “Population” The whole group that is being
studied. “Numerical” A type of data that is represented by
numbers. “Categorical” A type of data that is represented
by categories.
Manipulatives/Concrete Models What are the digital tools used in this project? A Scientific Calculator was used for calculating standard
deviation, summary statistics & Pearson’s correlation.

96. REFERENCES (APA7)
Cooper, H., Hedges, L.V., & Valentine, J.C. (2009). The handbook of research synthesis and meta-
analysis (2nd ed.). Russell Sage Foundation.
Dewey, A., & Drahota, A. (2012). Designing a cardiology research project: research questions, study
designs and practical considerations. Journal of Clinical and Preventive Cardiology. 2. 37-47.
Ernest, P. (1994) ‘Social Constructivism and the Psychology of Mathematics Education’, in Ernest, P.
(Ed.) Constructing Mathematical Knowledge: Epistemology and Mathematical Education, London: The
Falmer Press, 62-72.
Ernest, P. (1998) Social Constructivism as a Philosophy of Mathematics, Albany, NY: SUNY Press.
O’Connor, M. C. (1998) ‘Can We Trace the "Efficacy of Social Constructivism"?’ Review of Research in
Education, Vol.23, 25-71.
Templier M., & Paré G. (2015). A framework for guiding and evaluating literature
reviews. Communications of the Association for Information Systems, 37(6),112–137.
Vygotsky, L.S. (1978) Mind in Society: The Development of Higher Psychological Processes,
Cambridge, MA: Harvard University Press.

97. BIBLIOGRAPHY & SOURCES:
• https://www.gapminder.org/
• https://www.who.int/emergencies/diseases/novel-coronavirus-
2019?gclid=CjwKCAjwhYOFBhBkEiwASF3KGbC4_l_7Cr6lDPj6LjM-T46iVA-
VeO8Io9yRzwZNcVDgCMwhcPfJChoCQSIQAvD_BwE
• https://www.cia.gov/
• https://www.abs.gov.au/
• https://www.imf.org/en/Data
• https://www.worldometers.info/coronavirus/?utm_campaign=homeAdUOA?Si
• https://www.imathas.com/stattools/histo.html
• https://www.populationpyramid.net/united-arab-emirates/2019/

98. RESEARCH PROCESS - CASE
STUDY (ASHLEE GRIGG)