teaching statistics

TEACHING AND LEARNING
STATISTICS
Carlo Magno, PhD
De La Salle University, Manila

K to 12 Mathematics Content
Areas
 Numbers and Number Sense
 Measurement
 Geometry
 Patterns and Algebra
 Probability and Statistics

Question:
 List down one application of statistics in the
following areas:
 Grades of students
 Public and private school teachers salary

Grade 7 Competencies
 Explains the basic concepts, uses and importance of
Statistics.
 Poses questions and problems that may be answered using
Statistics.
 Collects or gathers statistical data and organizes the data in
a frequency table according to some systematic
considerations.
 Uses appropriate graphs to represent organized data: pie
chart, bar graph, line graph and a histogram.
 Finds the mean, median and mode of statistical data.
 Describes the data using information from the mean,
median and mode.
 Analyzes, interprets accurately and draws conclusions from
graphic and tabular presentations of statistical data.

Grade 8 competencies
 Recalls the meaning and interpretation of the
mean, median and mode of ungrouped data
and extend them to grouped data.
 Discusses the meaning of variability.
 Calculates the different measures of
variability of a given set of data: (a) range; (b)
average deviation; (c) standard deviation.
 Describes a set of data using measures of
central tendency and measures of variability.

 Defines an experiment, outcome, sample
space and event.
 Defines and discusses the probability of an
event.
 Interprets the meaning of the probability of
an event.
 Differentiates between an experimental
probability and a theoretical probability.

 Counts the number of occurrences of an
outcome in an experiment and organize them
using a table, tree diagram, systematic listing
and the fundamental counting principle.
 Solves simple problems involving
probabilities of events.

Grade 9
 No topics on statistics

 Defines and describes the following measures
of position: quartiles, deciles and percentiles.
 Explains and interprets quartiles, deciles and
percentiles.
 Calculates specified percentiles (e.g. 90th
percentile) of a set of data.
 Uses measures of position to describe a set of
data and infer some information about the
data.

 Solves problems involving quartiles, deciles and
percentiles.
 Constructs box plot from a set of data.
 Counts the number of occurrences of an event
using: (a) a grid table; (b) a tree diagram; (c)
systematic listing.
 Derives and uses the formula for finding the
permutation of n objects taken r at a time.
 Defines a combination of n objects taken r at a
time as a subset.

K to 12 Mathematics
 The framework is supported by the following
underlying learning principles and theories:
 Experiential and Situated Learning
 Reflective Learning
 Constructivism
 Cooperative Learning
 Discovery and Inquiry-based Learning

K to 12 Mathematics
 Experiential learning as advocated by David
Kolb is learning that occurs by making sense
of direct everyday experiences.
 Experiential learning theory defines learning
as "the process whereby knowledge is created
through the transformation of experience. “
 Knowledge results from the combination of
grasping and transforming experience" (Kolb,
1984, p. 41).

K to 12 Mathematics
 Situated learning, theorized by Lave and
Wenger, is learning in the same context on
which concepts and theories are applied.

K to 12 Mathematics
 Reflective learning refers to learning that is
facilitated by reflective thinking.
 It is not enough that learners encounter real-
life situations.
 Deeper learning occurs when learners are
able to think about their experiences and
process these allowing them the opportunity
to make sense and meaning of their
experiences.

K to 12 Mathematics
 Constructivism is the theory that argues that
knowledge is constructed when the learner is
able to draw ideas from his own experiences
and connects them to new ideas that are
encountered.

K to 12 Mathematics
 Cooperative Learning puts premium on
active learning achieved by working with fellow
learners as they all engage in a shared task.

K to 12 Mathematics
 The mathematics curriculum allows for
students to learn by asking relevant questions
and discovering new ideas.
 Discovery and Inquiry-based learning
(Bruner, 1961) support the idea that students
learn when they make use of personal
experiences to discover facts, relationships
and concepts.

Experiential and Situated
Learning
 Ask students to collect their own data such as:
 weight of children in their barangay,
 number of people working in the community
 Students who had fever over the last month
 Number of house holds where things are stolen
 Summarize the data by reporting the:
 Histogram, line graph
 Mean, Median, mode
 Standard deviation, range, quartile deviation
 Ask students to make interpretation

Learning
 Count the number of people who joined
“hueteng” in your community.
 Compute the chance of winning for each person.
 Judge whether there is a big chance of winning.
 Estimate the number of people who joins the
lotto each day.
 Compute the chance of winning for each person.
 Which game will give you a greater chance of
winning?

Learning
 Count the set of pants and set of shirts you have
at home.
 Compute the number of combinations that you
can make each?
 Report how many days can you wear each
combination.
 Take a picture of each combination and put it in a
portfolio. Plan when you will wear each pair.
 When you ran out of combination how many
pairs do you still need to buy for the rest of the
occasion you need to wear a new set.

Ask for 2 volunteers
 Participants will provide their own example of
an activity for experiential and situational
learning.

Reflective learning
 Count the total number of days your parents
played for the lotto. Compute how much
money did they spend for it?
 If they have not won anything, how much
could they have saved if they had not joined?
 Where could this money be spent?
 Provide a set of recommendations for your
parents given your predictions.

Reflective learning
 Get a graph of the Philippine’s GDP from 2000
until 2013.
 What years is the GDP high?Years it is low?
 What inferences can you make about the present
situation compared to the past years?
 What events made the GDP high in those years?
 What events made the GDP low in those years?
 What projects should be engaged in order to
increase the GDP again?

Reflective thinking
 Keep a journal.
 Jot down in the journal each day all the
money you spent.
 After a month summarize the following:
 What days did you spend the most?
 What days you spent less?
 What is your average daily expense?
 What items did you spend the most money?
 What do you need to cut down in order to save?

Reflective thinking
 Make a pie chart of your family expenditures
in a month.
 Convert them into a percentage.
 What other items would like to spend for?
 What can you do to help your family increase
funds in order to allocate more for the things
you want?

an activity for reflective learning.

Constructivism
 Students will identify a problem in their community
in the following areas:
 Waste management
 Overcrowding
 Increased air temperature
 Collect data to serve as evidence to these problems
by:
 Measure the weight of garbage produced by each
household each day for 4 weeks
 Count the number of people living in each household and
the floor area of their house. Report the ratio.
 Get the temperature each day and tabulate it.
 Provide recommendations given the severity of the
problem (reflective learning)

Constructivism
 What type of body pains did you experience as
the most painful? Why did you had such pain?
 List them down.
 For each pain indicate how painful it is using a
scale from 0 (no pain) to 10 (very painful)
 Ask your classmates to rate the list of pain you
have.
 Get the average of the rating for each pain.
 Report the standard deviation.
 Given the SD are you all having a similar feeling
for each pain? (reflective learning)

Constructivism
 Make your own portfolio of the clothes you
will wear this summer.
 Which of these clothes is your favorite?
 Go to the malls and ask some sales person
which types of clothes are bought and the
quantity.
 Tabulate the number of purchases for each
type of clothes. Report into percentage.
 Make a pie chart.

Constructivism
 Which model of cell phone do you have?
 What do you think is the best cell phone
model?
 List down different cell phone models and
count the number of people in your
community who has it.
 Make a bar graph for each model of cell
phone?
 Which one is the most in demand?

an activity for constructivist learning.

Cooperative learning
 Form a group and each one will be assigned
to a place to take the air temperature for 7
days.
 Compare the temperature for each person.
 Why is there variation in the temperature?
 Report the findings.

 Students in a group are assigned to different
school to survey about the attitude of school
administrators about Br.Armin Luistro being
the secretary of education.
 Students combine the results of their survey
and present it in class.

 A memory experiment will be assigned to be
replicated by each group in class.
 The students will plan the conduct of the
experiment.
 They will use t-test for 2 independent
samples using a software.
 The will present the results in class.

an activity for cooperative learning.

Discovery
 Students will conduct an interview with
DENR officials in their region about the
pressing problems in the environment in their
community.
 Ask the affected people in the community if
they experience the problem.
 Count the incidents that was affected by the
problem?

Discovery
 Self-study on the procedure to compute for
the mean, median and mode.
 Show how it is done in class

teaching statistics

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