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    teaching statistics teaching statistics Presentation Transcript

    • 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.
    • Grade 8 competencies  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.
    • Grade 8 competencies  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
    • Grade 10 competencies  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.
    • Grade 10 competencies  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
    • Experiential and Situated 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?
    • Experiential and Situated 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?
    • Ask for 2 volunteers  Participants will provide their own example of 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?
    • Ask for 2 volunteers  Participants will provide their own example of 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.
    • Cooperative learning  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.
    • Cooperative learning  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.
    • Ask for 2 volunteers  Participants will provide their own example of 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
    • Ask for 2 volunteers  Participants will provide their own example of an activity for cooperative learning.
    • Insights