The Role of Learning Theories in Effective Mathematics Education

mathematics is one subject that pervades life at any age and in any circumstance thus its value

goes beyond the classroom and the school mathematics is a school subject therefore must be learned

comprehensively and with much there to succeed in teaching mathematics

teachers need to enhance their understanding of the students learning abilities experiences reasoning

and logical abilities learning theories and teaching methods on the other hand have

been used in different educational systems around the world teaching methods involve the use of

learning theories and each theory has different outcomes in mathematics education as

experienced teachers we believe that all teachers operate according to theories

our practice is driven by our theories about what will work for our students some of these theories are explicit and

are learned in school some are implicit and are the products of years of experience in schools

as teachers parents and students the conceptual framework of mathematics education

in the philippines is supported by the following underlying learning principles and

theories one we have experiential and situated learning

constructivism cooperative learning and discovery and inquiry based learning however in our

presentation later on we've added the cognitivism so the mathematics curriculum is

grounded on these theories now let's go to the learning theories

number one we have here cognitivism psja one of the cognitive theorists promoted the concept that the mind has an

important role in learning and so to focus on what happens in between the appearance of environmental

stimulus and student response as a reaction benjamin bloom created a taxonomy for cognitive skills

and the six stages are further elaborated and revised in study by anderson and grothwall as remembering

understanding applying analyzing evaluating and creating cognitivism can be

applied by teachers through memorization of basic facts and fundamental formulas in measurement

conversion and geometry the use of window cards for speed and accuracy

in the four basic facts and helping students find different solutions and formulas to solve the problem

other key concepts and skills involving numbers and number sense whole numbers number

theory fractions decimals ratio and proportion percent and integers are some of the

topics in elementary mathematics where incognitivism can be applied

let's go to constructivism constructivism is the theory that argues that knowledge is constructed when the

learner can draw ideas from his or her own experiences and connect them to new ideas

john dewey is often cited as the philosophical founder of this approach bruner and piaget are considered the

chief theorists among cognitive constructivists while wigatsky

is a major theorist among the social constructivists the constructivist theory is a

learner-centered approach that emphasizes the importance of individuals

actively constructing their knowledge and understanding through the guidance of their teacher

constructivism emphasizes the importance of knowledge beliefs and skills

in an individual brings to the experience of learning it recognizes the construction

of new understanding as a combination of prior learning

new information and readiness to learn individuals make choices about what new ideas to accept

and how to fit them into the established views of the world the class uses raw data primary sources

manipulatives physical and interactive materials constructivism implies that learners are born with innate

ability to deal with small integers such as 0 1 2 3 4 and so on

and to make comparative estimates of larger numbers teachers aid the students when

it comes to their own understanding and instead of telling the teacher begins

asking teachers role can be a mentor a consultant and a coach and challenge the student by

making them effective critical thinkers also constructivist teacher

challenges students to reach beyond the simple factual response connect and summarize concepts by

analyzing predicting justifying and defending their ideas

constructivist teachers teach math using cpa approach concrete which includes using real objects or manipulatives

pictorial which includes pictures and illustrations and abstract which includes symbols and variables

the use of self-assessment is an important reflection tool for students to manage what they learned

their progress and the goals they would like to have for work they would have to do

in the future constructivist reduce the load of algorithms in the classroom it is not about the

number of items solved by the learners but how depth the learning is the focus its quality other than quantity

also practical simulations using pupils and or materials to describe or represent mathematical knowledge or

processes the constructivist approach involves students in

real world possibilities numbers and number sense which includes whole numbers number

theory fractions decimals ratio and proportion percent and integers

measurement which includes the time speed perimeter circumference and area of

plane figures volume and surface area of solid figures temperature and meter reading

and statistics and probability are some of the topics in elementary mathematics where constructivism can be applied

moving on to discovery learning bruner as the lead proponent points to learning that occurs one

students are required to find out something by themselves discovery learning and inquiry based

learning support the idea that students learn when they make

use of personal experiences to discover facts relationships and concepts learners

acknowledge the challenge of realizing something for themselves rather than requiring the teacher to

provide for them answers some of the topics in elementary mathematics where

discovery learning can be applied include finding the circumference of circle

and area of plane features volume and surface area of solid or space figures and repeating patterns and simple

experiment and experimental probability in statistics another theory that can be associated

with teaching elementary mathematics is a situated learning theory by jin lav and nichian wenger

situated learning is an instructional approach developed by jean lave and ichian wenger in the early 1990s

and follows the work of dewey vygotsky and others who claim that students are more inclined to learn by actively

participating in the learning experience learning best occur in an authentic situation

or learning context learning for them takes place in social situations with other people

[Music] in teaching mathematics since not all schools can let the learners conduct

classes in actual places or areas like stores for example

in teaching basic math facts like additions and multiplication and kitchens for example in teaching

them the knowledge and measurement teachers should create learning space for learners to act

as if they are in the actual scenario [Music] it is also important to consider the

accessibility of these contacts to the learners their needs what they want to learn as

to provide them with a more meaningful learning experience

[Music] here are the topics in elementary mathematics where situated learning can

be applied basic mathematical operations involving money

standard measures of length weight capacity area and the like the knowledge of time

interpreting and representing data through graphs and tables and recognizing patterns and sequencing

because these competencies can always be used and applied by the learners in daily lives

[Applause] [Music] in situated learning teachers must

provide authentic context that reflect the way the knowledge will be used in real life

provide authentic mathematical activities provide access to expert performances

and modeling of processes solutions and solving problems they should also provide multiple roles in

perspective for the learners and support collaborative construction

of knowledge for every one of them in this case teacher turns from transmitter to facilitator of learning

by tracking progress assessing products produced by learners building collaborative learning

environments and encouraging reflection and learners will be assessed

through discussion reflection evaluation and validation in the community's perspective

what are the implications to childhood mathematics education of situated learning

situated learning involves students in cooperative activities where they are challenged to use their

critical thinking and kinesthetic abilities these activities could be applicable and

transferable to students homes communities and workplaces another theory that could be related

to situated learning is david gold's experiential learning theory [Music]

as advocated by david cold it is the 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

this theory focuses on the use of concrete manipulatives and direct experience in learning

experiential learning can be used in teaching basic mathematical operations involving

money standard measures of length weight capacity

area and the like and knowledge of solid and plain figures wherein they can manipulate things

[Music] in this case teachers must provide meaningful tasks

in context which will encourage learners to try various strategies in solving problems

use appropriate tools such as concrete manipulatives which are really

accessible for learners and are countered by them in daily life the tool should not just be limited to

localized materials but teachers must also let them explore modern tools

which can enhance their 21st century skills in solving problems and arriving in solutions

and they should also introduce play and games in learning this type of learning can elevate

students cognition levels increase the use of critical thinking skills

and learners can acquire knowledge to concrete tangible felt qualities of the world relying to

their senses in concrete reality and results to active participation [Music]

another one is the cooperative learning theory cooperative learning is a teaching

strategy that encourages students to assist each other in a small group to achieve common goal

through cooperative learning methods each student in a group responsible to share opinion

and work together to solve the mathematical problem [Music]

these topics could be taught using cooperative learning basic mathematical operations knowledge

and measurement and teaching through problem solving [Music]

in this case teachers must group learners considering certain factors to have a fair combination of them and

provide a learning space enough for the learners to work together especially explain the whole process

[Music] with that learners will be able to have the opportunity to collaborate and share

ideas with fellow learners as they all together create solutions

and solve problems and teachers can use cooperative learning activities to help students make

connections between the concrete and abstract level of instruction through peer interactions and carefully

designed activities [Music] no one size fits all there is no best

learning theory that can make our learners competent in grasping mathematics however some

learning theories might not be effective in teaching mathematics but can give bountiful learning

experiences to other learning contents our role as curricularist is to understand each learning theory

so that we can design effective lessons that are appropriate for our students cognitive levels