7/31/2019 Teaching Strategies in Mathematics
1/75
INNOVATIVE TEACHING
STRATEGIESIN MATHEMATICS
By:
JOCELYN G. TAMARES
Maruhat national High School
Gapan City Division
MERCY LEGASPI
Mayapyap National High School
Cabanatuan City Division
7/31/2019 Teaching Strategies in Mathematics
2/75
A teachers primary job is touncover the important ideas
in subjects, not cover atextbook.
-Anonymous
7/31/2019 Teaching Strategies in Mathematics
3/75
Challenges in Teaching
Engaging the learners;
Empowering the teachers;
and
Enabling research.
7/31/2019 Teaching Strategies in Mathematics
4/75
7/31/2019 Teaching Strategies in Mathematics
5/75
Promoting Inquiry
Inquiry Question Openers
7/31/2019 Teaching Strategies in Mathematics
6/75
What is an inquiry-based classroom?
It is a classroom which allows a student to play the
role of an experienced co-researcher rather than
of someone with all the answers.
Here, the teacher:
gives enough hints and poses probing questions;
offers encouragement for good thinking, not
just for right answers. treat answers, right and wrong, as discussion
topics until the class the research team - reaches
a consensus.
7/31/2019 Teaching Strategies in Mathematics
7/75
An inquiry-based classroom demands flexibility
in responding to students ideas.
Here, the goal is for students to experience mathematics as a
process of finding and connecting ideas so that
justifying ideas and problem solving become moreimportant than the actual solutions;
the teacher spends time in planning and thinkingof how students might address the problem under
investigation; and
the teacher leads students to know that thethinking and problem-solving skills they develop
can serve them in all aspects of their lives.
7/31/2019 Teaching Strategies in Mathematics
8/75
Some Effective Mathematics
Teaching Methods
7/31/2019 Teaching Strategies in Mathematics
9/75
Indicators of Effectiveness of a
Teaching Strategy/Method
Students ability to
perform the desired competencies;
transfer learning and use whateverconcepts and skills learned to solve a similaror related problem;
accomplish tasks that require higher orderthinking skills; and
appreciate the application of the concept
or principle to real-life situations.
7/31/2019 Teaching Strategies in Mathematics
10/75
7/31/2019 Teaching Strategies in Mathematics
11/75
CONCEPT MAPPING
A concept map
is a diagram or network indicating
interrelationships among concepts and
representing conceptual frameworks within aspecific domain of knowledge (Novak, 1990).
Here, the nodes represent concepts, the lines
linking the nodes represent relationships, andthe labels on the lines represent the nature of
the relationships.
7/31/2019 Teaching Strategies in Mathematics
12/75
generates and communicates ideas which can
aid collaborative projects (brainstorming, etc.);
aids learning by explicitly integrating new and
old knowledge;
helps in assessing understanding or diagnosing
misunderstanding;
enhances the problem-solving phases of
generating alternative solutions and options; encourages positive self-concept.
(Seaman, 1990; Gaines and Shaw, 1995;
Plotnick, 1997; Williams,1997
7/31/2019 Teaching Strategies in Mathematics
13/75
Sample Concept Map
7/31/2019 Teaching Strategies in Mathematics
14/75
FLOW CHARTING
an outline of the sequence of processes indiagram form
7/31/2019 Teaching Strategies in Mathematics
15/75
MINDS-ON HANDS-ON
, focusing on the core conceptsand critical thinking processes needed for
students to create and re-create
mathematical concepts and relationships intheir own minds.
, experimenting first-hand with
physical objects in the environment and
having concrete experience before learning
abstract mathematical concepts.
7/31/2019 Teaching Strategies in Mathematics
16/75
PROBLEM-BASED LEARNING
This is a curriculum delivery system that
recognizes the need to develop problem
solving skills.
The teachers act as facilitators of learning.
The students are given guidelines on how to
approach the problem.
(Here, students act as professionals andconfront problems as they occur with fuzzy
edges, insufficient information - to determine
the best solution.)
7/31/2019 Teaching Strategies in Mathematics
17/75
Problem-based Learning
EVALUATION
EXPLANATION
ELABORATION
ENGAGEMENT
EXPLORATION
7/31/2019 Teaching Strategies in Mathematics
18/75
Sample Problem
(Systems of Linear Equation)
You have decided to purchase a cell phone and areconsidering which company offers the mostaffordable plan for you.
Talk-a-lot charges P199.90 per month and
P15 per minute
Motor mouth charges P399.90 per month
and P5 per minute
1. Write an equation that represents each phonecompany.
2. Is there ever a time when both would charge the
same amount? When? How much?
7/31/2019 Teaching Strategies in Mathematics
19/75
COOPERATIVE LEARNING Think-Pair-Share- a strategy designed to
provide students with food for thought ona given topic enabling them to formulateindividual ideas and share these ideas with
another student. Uses: Note check, vocabulary review, quiz
review, concept review, lecture check,
Management Ideas: Assign partners, changepartners, give think time, monitor discussion,timed-pair-share, randomly select students
7/31/2019 Teaching Strategies in Mathematics
20/75
CONSTRUCTIVIST TEACHING METHOD
Orientation Students are given the opportunity
to develop a sense of purpose and motivation forlearning the topic.
Elicitation Students are provided with questions
or problems for them to think about. Their initialideas about the concepts covered in the lessonare solicited as well as their answers to the givenquestions.
Discussion This includes (a) clarification andexchange of ideas; (b) construction of new ideas;and (c) evaluation of new ideas.
7/31/2019 Teaching Strategies in Mathematics
21/75
Constructivist
Application Students are given the opportunity
to use their developed ideas in a variety ofsituations. In cooperative groups, they solve,
explain and justify the solution of practical and
textbook exercises. Summary and Reflection Students are asked to
summarize the principles learned and write their
reflections on how they learned the concepts andprinciples and how the method helped them in
dealing with mathematical activities.
7/31/2019 Teaching Strategies in Mathematics
22/75
MATHEMATICAL INVESTIGATIONS
7/31/2019 Teaching Strategies in Mathematics
23/75
7/31/2019 Teaching Strategies in Mathematics
24/75
Profitable Activities in Teaching Mathematics
1. Use of Music2. Visualization
3. Games and Puzzles
4. Math Lab5. Arts and Aesthetics
6. Journal Writing
7. Mathematics in
Context: Story
Mathematics
8. MathematicalConnections
9. Using News Items and
Clippings10. Research Reports
and Projects
11. Integratingtechnology
12. Use of manipulatives
7/31/2019 Teaching Strategies in Mathematics
25/75
To make the students relaxed, entertained,and eager to learn, especially when they aretired of routine work in mathematics.
This technique works very well as long as thevolume remains low enough for the studentsnot to compete against but loud enough to be
heard and to eliminate squeaks and other littledistractions.
7/31/2019 Teaching Strategies in Mathematics
26/75
2. Visualization
Provide projects and hands-on materials
and draw three-dimensional figures from
real models.
7/31/2019 Teaching Strategies in Mathematics
27/75
Some manipulatives in the form of
mathematical games and puzzles aretangrams, Rubiks cube and Soma cubes,
and problems which can be solved
through logical reasoning.
7/31/2019 Teaching Strategies in Mathematics
28/75
3. Games and Puzzles
useful in improving problem solving andvisualization skills;
promote high-level skills such as analysis
and synthesis; reinforce concepts and skills;
improve students attitude toward learning
math;
add variety to the instructional program.
7/31/2019 Teaching Strategies in Mathematics
29/75
4. Math Lab
offers opportunity for math to come aliveand for students to get involved and see the
positive relationship between mathematics
and everyday life; provides opportunity for encouraging
creativity and social skills development.
7/31/2019 Teaching Strategies in Mathematics
30/75
Sample Math Lab Activities
A. Assume that you have Php10,000 whichyou can spend for a party.
1. Using the ads of a certain restaurant,
plan your expenses.2. Draw up a budget that will include all
party expenses.
7/31/2019 Teaching Strategies in Mathematics
31/75
B. Clip a recipe for cooking your favorite
dish and make a new recipe for 20 servings.
1 lb spaghetti
cup heavy cream
4 eggs
lb bacon, cut into-inch dice
1 tsp extra virgin
olive oil
2 Tbsp chopped
Italian parsley
Kosher salt and
freshly ground black
pepper, to taste
cup freshly grated
pecorino-romano
cheese (parmesan
may be substituted)
Serving: 4
7/31/2019 Teaching Strategies in Mathematics
32/75
Fill a large soup pot with cold water and add a
handful or so of Kosher salt. Stir and taste; it should
taste like seawater. Cover the pot and heat the
water until it boils.
Add the diced bacon to a cold saut pan and cook
slowly over a low heat for 10 to 15 minutes or until
crisp. Remove bacon from pan and drain on papertowels.
7/31/2019 Teaching Strategies in Mathematics
33/75
Drop the spaghetti into the boiling salted
water and cook according to package
instructions, about 6 to 9 minutes or until aldente, or tender but still firm to the bite.
While the pasta cooks, combine the eggs,
cheese, cream and olive oil in a bowl and beatwith a whisk until completely mixed.
Drain pasta, toss with the egg and cream
mixture, then add the cooked bacon andchopped parsley. Serve right away, with
additional grated cheese if desired.
http://culinaryarts.about.com/od/glossary/g/Al-Dente.htmhttp://culinaryarts.about.com/od/glossary/g/Al-Dente.htmhttp://culinaryarts.about.com/od/glossary/g/Al-Dente.htmhttp://culinaryarts.about.com/od/glossary/g/Al-Dente.htm7/31/2019 Teaching Strategies in Mathematics
34/75
C. Turn to the Computers for Sale section
of the classified ads.
1. Figure out the average cost per
computer in four different outlets.
2. Draw a bar graph which shows theaverage cost per computer in the four
outlets.
7/31/2019 Teaching Strategies in Mathematics
35/75
D. Have everyone in the class select a stock
and follow it up for a week.1. Each student follows the progress of his
chosen stock and draws a line graph
depicting its behavior.
2. Ask students to describe the behavior of
the said stock.
7/31/2019 Teaching Strategies in Mathematics
36/75
E. Turn to the sports page of any newspaper
and find the standings of any professionalsport.
1. Add up the total number of wins and losses
for each division.2. Which division appears to be the
strongest? the weakest?
3. By how much do their average winnings
differ?
F Mathematical Magic
7/31/2019 Teaching Strategies in Mathematics
37/75
F. Mathematical Magic1. Ask a student volunteer to write down any
three- digit number whose first and last digitsdiffer by more than one.
2. Then form another three-digit number by
reversing the digits of the first number(i.e., 235 becomes 532).
3. Subtract the smaller number from the larger
number, reverse the digits of the answer, and
add this to the result of subtraction.
4. What is the sum? Justify your answer.
7/31/2019 Teaching Strategies in Mathematics
38/75
5. Arts and Aesthetics
The use of art as teaching aid can lead studentstowards better understanding of, andappreciation for mathematics.
Tessellations, modular art, and
curve stitching may be done in
the classroom.
7/31/2019 Teaching Strategies in Mathematics
39/75
6. Writing Math/Journal Writing
Give students the opportunity to create andcommunicate mathematics problems of their
own.
Write
- an algorithm, a definition, a problem;
- generalizing a concept/relationship;
- reporting a project;
- accomplishments, reactions
7/31/2019 Teaching Strategies in Mathematics
40/75
7. Mathematics in Context: Story
MathematicsPlace a mathematical topic in the context
of a brief story to further explain it and
motivate students to carry out problem-solving activities.
7/31/2019 Teaching Strategies in Mathematics
41/75
Sample of Mathematics in Context
Suppose that a classical concert ticket
costs twice as much as a rock concert
ticket.
Is it cheaper, more expensive, or equally
expensive for you to take 100 friends to a
rock concert or two friends, 25 timeseach, to a classical music concert?
7/31/2019 Teaching Strategies in Mathematics
42/75
-Which of the regions in the Philippines is thelargest in land area?
-Which is the smallest?
-How many times greater is the largest?
Which region has the largest population?
-What is the population density (number of personsper square mile)of a particular region?
-What is the population density in persons per
hectare of the region in which you live?
7/31/2019 Teaching Strategies in Mathematics
43/75
-What change in the area occurs in a leaf of a fast-
growing plant as the growing season advances?-What is the rate of the change based on a simple
graph of area versus time?
-How does the rate of change in the area comparewith the rate of change in the length of the leaf?
Ifthe distributed electric current through a metalstrip of uniform but irregular cross section is one
ampere, what is the current density per square
centimeter across the cross section?
9 News Items that Provide Real
7/31/2019 Teaching Strategies in Mathematics
44/75
9. News Items that Provide Real
Mathematical Experiences
Decimals can be computed from batting orshooting averages and percentage of passcompletions for a favorite sports activity.
Common fractions are found in recipes. Find arecipe serving six persons and have studentsconvert the quantities so the recipe will serve15 persons.
Metric system can be introduced or reviewedby reading and interpreting articles,especially from foreign news services.
7/31/2019 Teaching Strategies in Mathematics
45/75
7/31/2019 Teaching Strategies in Mathematics
46/75
Graphs are common in most newspapers,
and students can draw their own from data
they find in articles.
Bar graphs may be constructed from sports
statistics such as baskets scored by each of
the baseball or basketball teams.
Election results can be depicted through a
circle graph in which sectors indicate thepercentages of vote received by each
candidate.
7/31/2019 Teaching Strategies in Mathematics
47/75
Line or bar graphs can record daily
temperatures of hours of daylight (from a
certain date to another), height of annualrainfall or the rise and fall of tide in the
locality, or the households monthly water
and energy consumption.
10 Use of Research Reports
7/31/2019 Teaching Strategies in Mathematics
48/75
10. Use of Research, Reports,
and Projects
Encourage students to pursue individual areas of
interest and open up new dimensions of study for
them.
This provides teachers excellent opportunities to
know their students better and work with themon an individual basis.
Sample of Use of Research Reports
7/31/2019 Teaching Strategies in Mathematics
49/75
Sample of Use of Research, Reports
and Projects
Finding the common fraction or decimal
approximation of a given number to correct to
the given number of decimal places
The Pythagorean Theorem has over 300 proofs
(see, for example, Loomis 1968).
The intriguing secret order of the Pythagoreans
may be of interest to some students.
7/31/2019 Teaching Strategies in Mathematics
50/75
The mathematics of the honeycomb was studiedby Pappus, a fourth-century Alexandrian
mathematician. No other shape of cell is aseconomical of space and materials as is thehexagonal structure of the honeycomb.
Mathematics and postage stamps will interestsome students as a project. Mathematics inmeasurement, computation, cartography
(mapmaking), and design is an interestingresearch topic.
Other Mathematical Activities
7/31/2019 Teaching Strategies in Mathematics
51/75
Other Mathematical Activities Gas Station Map mathematics which uses road
maps can be a nice source of mathematical
activities.Some of these are:
1. Tracing a highway across a region an countingthe towns it passes through.
2. Measuring the distance between two citiesshown on the map, then computing how farapart these cities are in kilometers.
3. Using the mileage chart on the map to finddistances between cities and using yarn orstring to find distances through the mapsconversion scale. Why are these distances not
the same?
4 I f M l Il l h h l
7/31/2019 Teaching Strategies in Mathematics
52/75
4. In a trip from Manila to Iloilo, how much lesstime does the airplane have to cover than aferry boat?
5. Find the areas of some cities and compare resultswith figures found in official records.
Kite building can lead to the study of geometricshapes (such as Graham Bells famoustetrahedral kites), to methods of heights (such
as using the hypsometer), and to studies of thephysics of flight.
7/31/2019 Teaching Strategies in Mathematics
53/75
Graphing pictures through point plotting is
instructive and entertaining. Students find
solution sets for equations and plot them bygiving pictures of a variety of objects or pictures.
On top of the lesson on trigonometry of triangles,
students may be asked to investigate thetrigonometry of squares.
Probability and statistics provide a rich source of
interesting, real-life problems. Initially, chanceoutcomes can be shown using coins, dice, a
table of random digits or a deck of cards
7/31/2019 Teaching Strategies in Mathematics
54/75
11. Use technology
Using internet sources
Blended e-learning
Use powerpoint presentations
12 U f M l
7/31/2019 Teaching Strategies in Mathematics
55/75
12.Use of Manipulatives
to represent mathematical concepts,numbers and operations
Algebra tiles
Geometric figures
Other mathematical gadgets
T hi P bl S l i
7/31/2019 Teaching Strategies in Mathematics
56/75
Teaching Problem Solving
Provide opportunities for students toactively contribute to the formulation of the
problem, to write the problems themselves,
and to change conditions in the problemsand to critique a given solution.
Problem Solving
7/31/2019 Teaching Strategies in Mathematics
57/75
Problem Solving
(Mathematics and Science
Education Center)
EliminatePossibilities
Break itdown intosubordinateproblems
Draw apicture ordiagram,or make amodel
Solve a simpler
related problem
Look for Patterns
Workbackwardsfrom whereyou want toend up
Make atable,chart ororganizedlist
Guess,estimate,checkand revise
Cl f f P bl
7/31/2019 Teaching Strategies in Mathematics
58/75
Classification of Problems
1. Problems without numbers
2. Problem situation without questions
3. Problems with insufficient or
extraneous data4. Problems that can be solved by drawing
a diagram
5. Problems whose are also
problems
6. Open-search Problems
7/31/2019 Teaching Strategies in Mathematics
59/75
2 Problem situation without
7/31/2019 Teaching Strategies in Mathematics
60/75
2. Problem situation without
questions
Joy and Sally go to the store. Joy hasPhp580 and Sally has Php620. They want
to buy a gift that costs Php920.
7/31/2019 Teaching Strategies in Mathematics
61/75
3. Problem with Insufficient or
Extraneous Data
Two sides of a triangle have lengths 4cm
and 6cm. Find the perimeter of thetriangle.
4 P bl h
7/31/2019 Teaching Strategies in Mathematics
62/75
4. Problems whose are
also problems
Examples:
1. a) 337 + 456 = ?
b) 3_7 + _ _6 = 533
2. a) What are the prime factors of 90?
b) List the 12 smallest numbers the prime
factors of which are 2, 3, and 5.
7/31/2019 Teaching Strategies in Mathematics
63/75
3. a) Round off 5.77 to the nearest tenth.
b) What numbers when rounded off to
the nearest tenth give 5.8?
4. a) What is the surface area of a box withdimensions 2 cm x 6 cm x 10 cm?
b) Design a box with a surface area of
128 sq cm.
5 Problems that can be solved by
7/31/2019 Teaching Strategies in Mathematics
64/75
5. Problems that can be solved by
drawing a diagram
Activity: Ask the students to prepare a sketch
that illustrates a given problem and solve the
problem based on the figure.
1. John, Alex, and May live on the same road.
John lives 10 km from Alex. May lives 2km
from Alex. How far does John live from May?
2. Ninety-six students are to be placed in rows,
with eight students in each row. How many
rows will there be?
6 O h P bl
7/31/2019 Teaching Strategies in Mathematics
65/75
6. Open-search Problems1. Find all primes that are one less than a
fourth power.
2. Draw plane figures with equal areas.
3. Design a basketball court, given the size ofthe lot.
7/31/2019 Teaching Strategies in Mathematics
66/75
Conduct problem-solving activities
Activity: The students may be asked tocollect problems: textbook problems, media
problems, non-routine problems, puzzles,
and strategy games.
Some of these strategy games are Tic- Tac-Toe and
the Tower of Hanoi.
T lk b t th ti l li ti f
7/31/2019 Teaching Strategies in Mathematics
67/75
Talk about the practical applications of
mathematics.
Activity: Ask students to interpret graphsand charts, cause and effects of certain
day to day happenings, estimate and
evaluate responses.
Elements of a Thoughtful Learning
7/31/2019 Teaching Strategies in Mathematics
68/75
Elements of a Thoughtful Learning
Environment
A classroom layout that invites thinking, i.e. a
seating arrangement where students face
each other in groups or clusters, or around a
hollow square, which makes possible
student-to-student interchanges, provides
opportunities for active student learning and
thinking
Classroom interactions that involve
7/31/2019 Teaching Strategies in Mathematics
69/75
Classroom interactions that involve
information processing rather than information
receiving and repeating students in posing problems, comparing,
analyzing, formulating hypotheses, judging the
worth of arguments, and in asking and answeringquestions.
In a thinking classroom, students dissect, reflect on,
and add to what they read, hear, see, or feel togive new meaning to it, rather than simply
remember the meanings provided by authorities in
the field.
The Emerging Role
7/31/2019 Teaching Strategies in Mathematics
70/75
The Emerging Role
of the Mathematics
Teacher
Creator of a thoughtful learning environment
that promotes and support higher-order thinking
and a classroom climate that nurtures thinking
beyond the levels of recall and translation, as well
as an environment in which more complex thinkingcan occur
Originator of precise thoughtful
7/31/2019 Teaching Strategies in Mathematics
71/75
Originator of precise, thoughtful
language rather than vague terminology
or generalizationsPromoter of higher order thinking skills
through questioning, structuring,
responding and modeling
Organizer of classroom study and courses
around thoughtful questions
Makes innovative changes and focuses on
something other than memorization of
contents;
7/31/2019 Teaching Strategies in Mathematics
72/75
Realistic and relevant applications of
the topic under considerationEncourages independent thinking
through the use of divergent strategies
in solving problems;Makes the teaching-learning process
more credible, convincing, meaningful,
and interesting.
7/31/2019 Teaching Strategies in Mathematics
73/75
Use of manipulatives to provide
experiences in actual problem-solvingsituations and analyzing sensory data
Have field trips since educational
excursions can be used fruitfully to enrichinstruction in mathematics
7/31/2019 Teaching Strategies in Mathematics
74/75
Life is good for only two things,discovering mathematics and
teaching mathematics."
Simon Poisson
7/31/2019 Teaching Strategies in Mathematics
75/75
THANK YOU!