Alamanda Workshops

1. PERSONALIZED LEARNING @ ALAMANDA
Personalized learning through Inquiry - Mining Creativity and
Imagination through Research Design & McRel’s 6-phase model in
mathematics
PRESENTED BY WILL

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

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 GOALS
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).

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

37. 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?

39. 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?

41. STAGE 2: COMMIT TO LEARNING

42. WORKING ON THE
PERSONALIZED INQUIRY AND
START GOAL SETTING

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

48. Rubrics

49. Checklist

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

56. RESEARCH COMPONENT - CASE STUDY
(MANNY MAHAL)

57. 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

58. 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.

59. RESOLUTION: WORKING OUT

60. 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)

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

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

64. INDIA: MY INVESTIGATION IN RELATION TO
Z-SCORES
•

65. AUSTRALIA: MY INVESTIGATION IN RELATION
TO Z-SCORES
•

66. 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.

67. LINEAR REGRESSION &
PEARSON'S
CORRELATION

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

69. PEARSON’S CORRELATION – COMPARISONS OF HOW INCOME AND LIFE EXPECTANCY
CORRELATE IN INDIA

73. 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 )

74. 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?

75. 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.

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

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

82. Further Curiosities

87. IMPLICATIONS OF KURTOSIS RISK
• XXXXXX

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

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

90. REFLECTION

91. LESH’S TRANSLATION MODEL IN
MATHEMATICS

92. Reflection (By using Lesh’s Translation 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?
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.

93. 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.

94. 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/

95. RESEARCH PROCESS - CASE STUDY (ASHLEE
GRIGG)