Literature Review on Discovery Based Learning and Student Centred Learning with a Focus in Mathematics at a High School Level
Abstract
Mathematics is a logical form of reasoning which involves making of judgments and justifying conclusions. Mathematical behaviour therefore is expressed when we can describe and recognise patterns, manipulate, represent and reflect on ideas while solving problems through the invention of procedures (Battista, 1999). Mathematics, as a subject has never been mentioned as one of the easier subjects – if anything, it is to the contrary as students are more prone to fail mathematics than many other subjects. Many critics have blamed the methods applied in the teaching of mathematics as the reason behind unsatisfactory performance. This essay will look into the discovery based learning and student centred learning as two methods applied in the teaching of mathematics in the high school level.
The teaching and learning of mathematics is changing every day to enable students accomplish what they should from the study of mathematics. These forms of learning make use of various assumptions that have been made about teaching of mathematics
- Changes in technology have changed the importance of some mathematical concepts
- Technological tools are now able to create new instructional environments
- Purposeful engagement based on prior experience is necessary for mathematics learning to take place (Romberg, 2000).
One of the major problems with the teaching and application of mathematics is the fact that many people believe that they will be unable to apply mathematical solutions in the real world. It has however been proven that mathematics can be used to solve authentic life problems. Most students study mathematics to pass an assessment or an exam and once this is over they forget what they were taught. The major reason behind this problem is the fact that most students just sit through a lecture going through the moments as the teacher traditionally teaches mathematics. Such students are bound to forget whatever it was that they may have taught in class the day before. This goes on to become a vicious cycle. However there are methods of instruction that would ensure that students not only participate in class, but that they are involved with the lessons and in so doing having that topic or subject of the day being ingrained in them for life. This method also provides them with instances where they see that their daily life problems can be solved with the math they have learnt in class.
Traditional mathematics is basically just a process of regurgitation where the teacher provides the students with the information they need to pass the test or assessment and then the assessment is given. So the better students tend to be those who can remember what was taught to them in class. This kind of teaching see students playing math as they never learn mathematics to the level where they can use the problem solving strategies they acquired to solve real life problems. For a student to really learn maths they must be able to internalise the information as they apply it to previous experiences and situations outside the classroom. The student-centred learning says that students need to be actively involved in their own learning.
Mathematics is synonymous with problem solving as this is an essential part of the subject. Using the study of fractions as an example, when the study of fractions is applied to other contexts in real life students tends to have a richer understanding of the subject. This way they learn to use the subject topic in new settings and math finally comes alive to them. Once this can be accomplished the students are more willing to study mathematics as they have seen a correlation between the subject and the real world.
This now leads to communication and how it plays in the mathematics classroom. Communication is so important in the classroom generally and the National Council of Teachers of Mathematics has emphasized the importance it plays with regards the subject.
- Communication helps consolidate mathematical thinking
- Communication helps students articulate clearly their mathematical thoughts to their peers and to others.
- It helps in the expression of mathematical ideas.
In 2001 Pugalee claimed that the opportunity afforded students in communicating about mathematics open doors in the engaging of their thinking skills (p 296). Communication builds a balanced and effective mathematics program he added.
Discovery Centred Learning
The tides on the global terrain are turning as employers of labour are more interested in people who can solve problems. Books are being written and lectures are being held in a bid to find that employee of choice that can identify trends as he adapts to changes. Employees with the ability to hit the ground running are preferred to those who would require a sizeable amount of training irrespective of what Ivy League school they graduated from. The traditional teaching and learning methods can no longer fill those required gaps as learning approaches have to be able to create greater success.
Discovery learning is facilitated through teaching methods that apply guided learning strategies. It includes the individual, the teaching and instructional strategies that ensure learning takes place and this strategy is created by the teacher and the environment created through the use of the required strategies. Traditional learning on the other hand is the learning that takes place in the teacher-led classroom which involves drill and practice. Improved classroom technology has made it mandatory to utilize technology based discovery learning as this is more effective.
What then is discovery learning? It includes an instructional model and strategies that focus on active, hands on learning opportunities for students (Dewey, 1916/1997; Piaget, 1954, 1973). Its main attributes have been said to be
- Problem solving and exploring as tools to integrate, create and generalize knowledge
- The ability of the student to determine the sequence and frequency of learning through interest based and student driven activities
- The integration of new knowledge into the learner’s existing knowledge base.
Exploring and problem solving give students an active role in the creation, integration and generalization of knowledge. They are no longer passively receiving information but are now establishing applications for skills with the help of activities that encourage the examination of unique experiences and problem solving (Bicknell-Holmes & Hoffman, 2000). This form of learning puts the focus on the student and not the teacher as the student is the one driving the lesson. A degree of flexibility can be achieved in frequency and sequencing when mathematics is taught using the discovery learning because the lesson is no longer tackled as a static progression of activities and learning. Discovery learning has some fundamental differences from traditional learning and these are the fact that
- Learning is no longer passive but active
- Learning is now process oriented and not content oriented
- Failure plays an important role in this learning process
- Feedback no longer takes a back seat but is very necessary
- It deepens understanding (Papert, 2000)
Because students are more inclined to find the answers they eventually learn more as a result and this learning is applicable to their lives outside the classroom as the learning content is no longer the end result but now the focus has been shifted to the process through which the content was learnt. Discovery learning has latched onto the Thomas Edison’s lesson where he was said to have tried 1,200 designs for the light bulb before he eventually got the one that worked (Love, 1996). While many people would have felt like a failure to trying it 1,199 times Edison only claimed that now he had learnt over a thousand different ways not to make a light bulb and one way to make it.
Discovery learning does not stress on getting the right answer to be the all-important result. Studies have shown that students can actually learn from getting it wrong as well as getting it right. People are born curious and this bodes well for discovery learning as this very curiosity propels them to learn. There are five architectures that can be categorised as propelling discovery learning. These are learning that is case based, learning by reflection, learning through incidents and simulation based learning. However there are teachers who do not teach using this method of discovery learning and they have given varied reasons from their belief that such a form of instruction may not cover the entire course content to the fact that they believe their classes are too big to successfully benefit from such a strategy.
While it is true that the time required for preparation of discovery learning is high, it should be noted that the activities and exercises that have been created can be used again and again with just minor alterations and adjustments (Bonwell, 1988). Class size is indeed a hamper with regards successful discovery learning as this strategy flourishes when there is adequate one on one interaction and the time allocated for teaching in school is not adequate. Technology today has made it even easier for students to explore and this is a vital ingredient in the success of discovery learning.
SCL was coined as a phrase that is used to denote a paradigm shift in the purpose and achievement of higher education. Barr and Tagg in 1995 said this shift saw a move from knowledge being transferred to students from the faculty to knowledge acquired via student discovery. These learning-centred instructions moved the focus away from teaching to learning. SCI therefore is an approach to passing instruction whereby it is students that drive the pace, activities and content. Students are the centre of this instruction as teachers provide the students with different opportunities that enable them learn independently from one another as they are provided with the skills needed to achieve such learning. Active learning experiences is being substituted for lectures and open ended questions that cannot be solved by using text book examples are some of the techniques that are used to accomplish this learning style. This style of learning is believed to increase student’s desire to acquire knowledge as it provides a more positive approach to the subject being taught (Collins & O’Brien, 2003).
John Dewey said, “True learning is based on discovery guided by mentoring rather than the transmission of knowledge”. Studies have proven that when students learn collaboratively with studies focussed on student groups, skills are developed that are beneficial to students lives after the leave the school gates. This collaborative learning according to Johnson & Smith results in not only academic success but also attitude effects. This therefore shows that when our learning is focussed on the students through collaborative learning they tend to achieve the desirable goals that have been listed above. When mathematics courses are prepared the traditional way, the people that are actually getting the most learning are the teachers preparing the lesson. This is true because in the course of preparing the topic, research and instruction and pulling information from previous experiences are some of the things taking place and this is in itself learning. Student centred learning provides students with the opportunities for them to learn.
This kind of learning is very successful in the teaching of mathematics as students are taught to ask the right questions and try various methods to getting the answer. Being right is not the most common ingredient of such a strategy and as such students could solve problems on calculus and will not feel inadequate if they were to get it wrong after a couple of tries. If I were to teach integration for instance with the student based learning, I will present the students with a problem and they determine the pace and structure the problem solving will take. Usually working in groups they gather their ideas and the previous knowledge they have on the problem as they try to use the available resources they have to solve the problem. They begin to form ‘learning issues’ as they pose questions. Because of the way the curricula in mathematics is structured the students would have learnt about differentiation before they are taught integration. And once they have been told that integration is the inverse of differentiation or vice versa they will then be able to ask leading questions that will help them in the solving of the integration problem. Their “learning issues” could very well be on their bringing to mind how they were able to handle the problems of differentiation. Now previous knowledge and experience comes into play and they begin to try to get the result they are looking for. It may take them more than one try to get their required result but all the wrong tries add up to the correct solution to form their learning experience.
While the instructor is there to support the initiatives of the students, they in turn begin to see the students view learning as an ongoing process. Now mathematics which is viewed as one of the most dreaded subjects for high school students begins to come alive in their sight and their interest to learn more about it begins to grow. Student centered learning provides skills for life.
Although research has shown that there is a lot of benefits in applying the discovery based and student centered learning in the classrooms a couple of teachers are not so comfortable with relinquishing their autonomy with regards how the class is run.
Mathematics has been studied for thousands of years as a discipline. While it may not be one of the more popular subjects with high school students a large chunk of their adult life require some knowledge in mathematics. For a subject that seems to be so important one would expect that students are readily shown in their classes how this subject could benefit them in later life. What we see instead are instructors trying to feed students this discipline the traditional way where students sit and listen and take notes and the teachers speaks and give notes. This kind of instruction makes mathematics more abstract than it actually is.
The computer and recent technology has made it possible for mathematics to be studied in such a way as now the student does not have to rely solely on the teacher or available text books but now they too can find out this knowledge by themselves and watch in essence as that knowledge stays with them for life.
The teacher could write out the mathematics lesson plan but instead of writing it out for their own personal use they should write it out for the students to use. Now the students are the ones asking the questions instead of me instructing them to listen and learn. This turn of events makes learning motivating to students and they are more interested now to get to the solution to the problem no matter how many tries they take. Tests are no longer given just for the student to pass the assessment but they now are a learning experience and they now can be graded based on what they have learned. The classroom will always be for learning no matter how we reconstruct them and learning will always be a key to success. We just have to find the right keys.
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