teaching and learning framework in mathematics

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Teaching and Learning Framework in Mathematics Carlo Magno, PhD De La Salle University, Manila

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Page 1: Teaching and learning framework in mathematics

Teaching and Learning Framework in MathematicsCarlo Magno, PhDDe La Salle University, Manila

Page 2: Teaching and learning framework in mathematics

•What do you think are the important skills that students needs to learn in mathematics?

Page 3: Teaching and learning framework in mathematics

Goals of Mathematics education in the K to 12

Critical Thinking

Problem Solving

Page 4: Teaching and learning framework in mathematics

Critical Thinking

•Intellectually disciplined process of actively and skillfully conceptualizing, applying, analyzing, synthesizing, and/or evaluating information gathered from, or generated by, observation, experience, reflection, reasoning, or communication, as a guide to belief and action (Scriven & Paul, 1987).

Page 5: Teaching and learning framework in mathematics

Problem solving

•Finding a way around a difficulty, around an obstacle, and finding a solution to a problem that is unknown (Polya, 1945 & 1962).

Page 6: Teaching and learning framework in mathematics

Content areas in the curriculum•Numbers and Number Sense •Measurement •Geometry •Patterns and Algebra •Probability and Statistics

Page 7: Teaching and learning framework in mathematics

Skills and processes to be developed

•Knowing and Understanding •Estimating •Computing and Solving •Visualizing and Modelling •Representing and Communicating •Conjecturing •Reasoning •Proving and Decision-making •Applying and Connecting

Page 8: Teaching and learning framework in mathematics

values and attitudes

•Accuracy •Creativity •Objectivity •Perseverance •Productivity

Page 9: Teaching and learning framework in mathematics

Tools in teaching mathematics

•manipulative objects •measuring devices •calculators and computers •Smartphones and tablet PCs •Internet

Page 10: Teaching and learning framework in mathematics
Page 11: Teaching and learning framework in mathematics

Teaching Principles in Mathematics •Principle 1: While the ability to explain

and solve a problem is evidence in good understanding of mathematical ideas, teaching mathematics requires more than this.

•Principle 2: Mathematics must be real to students and therefore, mathematics teachers should be mindful of students contexts an when teaching mathematics.

Page 12: Teaching and learning framework in mathematics

Teaching Principles in Mathematics • Principle 3: Mathematics is best learned

when students are actively engaged. • Principle 4: Mathematics can never be learned

in an instant, but rather requires lots of work and the right attitude.

 • Principle 5: All students regardless of gender,

culture, socio0economic status, religion, and educational background have the right and be taught good and correct mathematics.

Page 13: Teaching and learning framework in mathematics

Teaching Principles in Mathematics •Principle 6: Assessment must be an

integral part of the mathematics instruction.

 •Principle 7: Mathematics as a field

continues to develop and evolve. Therefore, the teaching if it must keep up with development in the field.

Page 14: Teaching and learning framework in mathematics

Teaching Principles in Mathematics •Principle 8: Technology plays an

important role in the teaching and learning of mathematics. Mathematics teachers must learn to use and manage technological tools and resources well.

•Principle 9: Mathematics teachers must never stop learning.

Page 15: Teaching and learning framework in mathematics

Learning Principles in Mathematics •Principle 1: Being mathematically

competent means more than having the ability to compute and perform algorithms and mathematical procedures.

•Principle 2: The physical and social dimension of a mathematical environment contribute to one’s success in learning mathematics.

Page 16: Teaching and learning framework in mathematics

Learning Principles in Mathematics •Principle 3: Mathematics is best learned

when students are actively engaged.•  •Principle 4: A deep understanding of

mathematics requires a variety of tools for learning.

Page 17: Teaching and learning framework in mathematics

Learning Principles in Mathematics •Principle 5: Assessment in mathematics must

be valued for the sake of knowing what and how students learn or fail to learn mathematics.

 •Principle 6: Students’ attitudes and beliefs

about mathematics affect their learning.

•Principle 7: Mathematics learning needs the support of both parents and other community groups.

Page 18: Teaching and learning framework in mathematics

Learning Principles and Theories•Experiential and Situated Learning •Reflective Learning •Constructivism •Cooperative Learning •Discovery and Inquiry-based Learning

Page 19: Teaching and learning framework in mathematics

Experiential and Situated Learning•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).

Page 20: Teaching and learning framework in mathematics

Experiential and Situated Learning•Situated learning, theorized by Lave and

Wenger, is learning in the same context on which concepts and theories are applied.

Page 21: Teaching and learning framework in mathematics

Reflective Learning

•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.

Page 22: Teaching and learning framework in mathematics

Constructivism

•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.

Page 23: Teaching and learning framework in mathematics

Cooperative Learning

•Cooperative Learning puts premium on active learning achieved by working with fellow learners as they all engage in a shared task.

Page 24: Teaching and learning framework in mathematics

Discovery and Inquiry-based learning•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.

Page 25: Teaching and learning framework in mathematics

Experiential and Situated learning• Ask students to record the time it takes them to

travel from home to school in minutes for one week.• Tabulate the results• Ask students to make interpretation

▫Which days took the longest time? Why is this so?▫Which days took the shortest time? Why is this so?

• Open google maps and see how many kilometers is the distance from your house to school.

• What is the average time required to get to school?• How many minutes per kilometer does it take you to

travel?

Page 26: Teaching and learning framework in mathematics

Experiential and Situated learning• Watch your favorite cartoons.

▫Count all the words being said in the cartoons.▫How long is the cartoon in minutes?▫ If the time of the cartoon is doubled, can you

predict the number of words that can be mentioned?

• If you talk in the telephone for a 10 minutes, what is the estimated number if words you can use?

• If you need to tell your friend an important message with 50 words, how much time will it require you to tell him/her?

Page 27: Teaching and learning framework in mathematics

Experiential and Situated learning•Measure how much volume can your bathroom

pail contain water.•Determine the time it takes you to fill the pail.• If you double the size of your pail, how much

time will you fill it?•Take the time in consuming the one pail of

water when taking a bath. How many pails do you consume?

•Given the pails of water you consume, estimate how long you take a bath.

Page 28: Teaching and learning framework in mathematics

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 households 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

Page 29: Teaching and learning framework in mathematics

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?

Page 30: Teaching and learning framework in mathematics

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.

Page 31: Teaching and learning framework in mathematics

Experiential and Situated learning•Participants will give their own example

Page 32: Teaching and learning framework in mathematics

Reflective Learning

•Use google maps and estimate the kilometers from your house to where your father is working.

•Ask for the total amount spent when commuting.

•Ask for the total amount spent when driving your won car.

•Show your data to your father and recommend which mode of transportation is better.

Page 33: Teaching and learning framework in mathematics

Reflective Learning

•Get the weight of each of your family members.

•Determine their ages and check who is underweight and overweight.

•Given your data make recommendations on the following:▫Money spent on food▫Menu for the week▫Exercise activities for the family

Page 34: Teaching and learning framework in mathematics

Reflective Learning

•Keep a journal and take note of all your travels via plane.

•Jot down in the journal the time you spent in the plane and the places you went.

•Summarize the following:▫What places took the longest plane ride?

Why?▫What places took the shorted plane

ride? Why?▫What is the relationship between time

and distance?

Page 35: Teaching and learning framework in mathematics

Reflective Learning • Get the square meter of your land area.• How much does your land cost?• Get the square meter of other land areas.• How much do they cost?• Get the square meter of residential lands in the

city. How much do they cost.• Compare the cost of equal land areas in the city

and in the province? • Is there a difference? Why is this so? • What do you need to do if you want to live in

the city?

Page 36: Teaching and learning framework in mathematics

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.

Page 37: Teaching and learning framework in mathematics

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?

Page 38: Teaching and learning framework in mathematics

Reflective Learning

•Participants will give their own example

Page 39: Teaching and learning framework in mathematics

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)

Page 40: Teaching and learning framework in mathematics

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)

Page 41: Teaching and learning framework in mathematics

Constructivism

•Measure the temperature for the months of April and May.

•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 for each day and the temperature?

•What does the temperature got to do with the type of clothes sold?

Page 42: Teaching and learning framework in mathematics

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)

Page 43: Teaching and learning framework in mathematics

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.

Page 44: Teaching and learning framework in mathematics

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?

Page 45: Teaching and learning framework in mathematics

Constructivism

•Participants will provide their own example.

Page 46: Teaching and learning framework in mathematics

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.

Page 47: Teaching and learning framework in mathematics

Cooperative Learning

•Students form three groups and are assigned to measure the floor area of the classroom.

•One group will only use a one inch paper clip.

•One group will use an 8 inches pencil.•One group will use a 15 inches long stick.•Which group do you think will measure

the floor area the fastest? Why?

Page 48: Teaching and learning framework in mathematics

Cooperative Learning

•Participants will provide their own example

Page 49: Teaching and learning framework in mathematics

Discovery and Inquiry-based

•Students will ask their parents at home the different tools they use to measure length of objects.

•The students will bring this material and demonstrate to their classmates how the tools are used.

Page 50: Teaching and learning framework in mathematics

Discovery and Inquiry-based•Self-study on the procedure to convert oC

to oF.•Show how it is done in class

Page 51: Teaching and learning framework in mathematics

Discovery and Inquiry-based•Self-study on the procedure to compute

for the mean, median and mode.•Show how it is done in class

Page 52: Teaching and learning framework in mathematics

Discovery and Inquiry-based•Participants will provide their own

example

Page 53: Teaching and learning framework in mathematics

Insights