1. Presenter; Jigmgup Dorji, Khanduchem Wangdi, Yeshitshok Gyeltshen Objectives; By the end of our lesson, trainee mates should able to: 1.Write definition of behaviorism and constructivist theory. 2.Tell what are vital role does Behaviorist theory and Constructivist theory in learning mathematics. 3.Differentiate between Behaviorist theory and Constructivist theory. 4.Identify at least two advantages of Behaviorism and constructivism.

2. Behaviorism Definition Behaviorism is a learning theory that only focuses on objectively observable behaviors and discounts any independent activities of the mind.

3. Behaviorism depends on two types of conditioning In learning process Classic conditioning ; Occurs when a natural reflex responds to a stimulus. example; students exhibit irrational fears and anxieties like fear of failure, fear of public speaking and general school phobia. Behavioral or operant conditioning occurs when a response to a stimulus is reinforced. For example, leading behaviorist B.F. Skinner used reinforcement techniques to teach pigeons to dance and bowl a ball in a mini-alley.

4. Behaviorist theories of learning mathematics "They make use of one or both of two principal classes of explanations for learning: 1. based on contiguity (simultaneity of stimulus and response events) 2. based on the effects of behavior (reinforcement and punishment)" (Lefrancois 1988:29).Lefrancois 1988:29

5. Principles from behaviorist theory to apply in teaching learning mathematics The following are valuable: – Repetition – Small, concrete, progressively sequenced tasks – Positive and negative reinforcement – Consistency in the use of reinforces during the teaching-learning process Habits and other undesirable responses can be broken by removing the positive rein forcers connected with them. Immediate, consistent, and positive reinforcement increases the speed of learning. Once an item is learned, intermittent reinforcement will promote retention.

6. Constructivist theory Formalization of the theory of constructivism is generally attributed to Jean Piaget, who articulated mechanisms by which knowledge is internalized by learners. He suggested that through processes of accommodation and assimilation, individuals construct new knowledge from their experiences.

7. Constructivism Constructivism is a process in which the learner actively constructs or builds new concepts and ideas based on past knowledge and experience. References Adams, J. W. (2007).

8. The features of a constructivist approach to mathematics In a constructivist approach to mathematics, emphasis is placed on the learner, rather than the teacher and learner autonomy is encouraged. Rather than students having to fit the curriculum, the curriculum is developed around the interests, needs and aspirations of students.

9. Herrara and Owens (2001, p.89) suggests that mathematic is enhanced through: active student involvement in discovering and constructing mathematical relationships, rather than merely memorising procedures and following them by rote; the use of concrete materials, calculator graphics, tables or other representations as a means of helping students to grasp abstract concepts; group work, including students sharing and justifying their ideas; student writing (including drawings, diagrams and charts) to encourage reflection on mathematical ideas, and oral presentation to promote communication of those ideas; the use of context, whether imaginary or real world, as a way of capturing student interest in problems; the teacher as the orchestrator of classroom discourse and facilitator of learning experiences.

10. The strategies promote constructivism in mathematics. using relevant learning contexts; increasing enjoyment and success through learning games; improving students' ability to work in teams and communicate ideas; using technology to allow students to pace their own learning; developing students' understanding of mathematical language and terms; using concrete materials to develop grounded mathematical understandings; developing group skills and collaboration;

11. engaging students in ongoing project work; identifying mathematics out of the classroom; negotiating with students about their learning; integrating mathematics with other learning areas; making mathematics in other learning areas explicit to students

12. Constructivist learning intervention The nature of the learner Social constructivism views each learner as a unique individual with unique needs and backgrounds. Social constructivism encourages, utilizes and rewards it as an integral part of the learning process (Wertsch 1997). The learner is also seen as complex and multidimensional

13. The importance of the background and culture of the learner Social constructivism encourages the learner to arrive at his or her version of the truth, influenced by his or her background, culture or embedded. Historical developments and symbol systems, such as language, logic, and mathematical systems, are inherited by the learner as a member of a particular culture and these are learned throughout the learner's life. as this background also helps to shape the knowledge and truth that the learner creates, discovers and attains in the learning process it is important that they have background and culture (Wertsch 1997).

14. The responsibility for learning Social constructivism thus emphasizes the importance of the learner being actively involved in the learning process than teacher. Learners look for meaning and will try to find regularity and order in the events of the world even in the absence of full or complete information.

15. The motivation for learning motivation to learn is strongly dependent on the learner’s confidence in his or her potential for learning. Von Glasersfeld (1989)

16. The teacher should be facilitator not instructor The role of the instructor -teacher gives an informative lecture that covers the subject matter, a facilitator helps the learner to get to his or her own understanding of the content.

17. Difference between the teacher and facilitator TeacherFacilitator Tells lectures from the front gives answers according to a set curriculum gives a monologue Asks Supports from the back provides guidelines and creates the environment for the learner to arrive at his or her own conclusions continuous dialogue with the learners

18. A few strategies for cooperative learning include Reciprocal Questioning: students work together to ask and answer questions Jigsaw Classroom: students become "experts" on one part of a group project and teach it to the others in their group Structured Controversies: Students work together to research a particular controversy (Woolfolk 2010)

19. Collaboration among learners Learners with different skills and backgrounds should collaborate in tasks and discussions to arrive at a shared understanding of the truth in a specific field (Duffy and Jonassen 1992)

21. Strength of Behaviorism the learner is focused on a clear goal and can respond automatically to the cues of that goal. Establishing and maintaining classroom management. Discipline is maintained in the class

22. Weakness of Behaviorism the learner may find themselves in a situation where the stimulus for the correct response does not occur, therefore the learner cannot respond. In terms of the concept of learning, the process tends to be passive with regard to the behaviorist theory. The learner uses low level processing skills to understand material and the material is often isolated from real-world contexts or situations.

23. Criticisms of behaviorism are; Behaviorism does not account for all kinds of learning, since it disregards the activities of the mind. Behaviorism does not explain some learning–such as the recognition of new language patterns by young children–for which there is no reinforcement mechanism. Research has shown that animals adapt their reinforced patterns to new information. For instance, a rat can shift its behavior to respond to changes in the layout of a maze it had previously mastered through reinforcements.

24. Strength of constructivism. The learner will learn to apply their knowledge under appropriate conditions. Use of scaffolding, provided by teacher or group, for individual problem solving (Wilson & Cole, 1991). Learners will be able to develop meta-cognitive skills (Savery & Duffy, 1995). Learners will get support via cognitive apprenticeship in the complex environment rather than simplifying the environment for the learner (Savery & Duffy, 1995).

25. Weakness of constructivism. One of the biggest disadvantages of constructivism is that the learner may be hampered by contextualizing learning in that, at least initially, they may not be able to form abstractions and transfer knowledge and skills in new situations (Merrill, 1991) In other words, there is often, during the initial stage, confusion. and even frustration. Learners will enjoy this new approach of discovering learning, but do not always actively construct meaning and building an appropriate knowledge structure (Merrill, 1991) [they simply copy what the better students do]..

26. Criticism of educational constructivism  focus more on learning as memorization rather than learning as behavior change or action  Learners do not possess the underlying mental models, necessary for "learning by doing" (e.g. Sweller, 1988)  Lacks practicality for teaching and learning.  Kirschner, et al. (2006) describe these methods as "unguided methods of instruction."

27. Group Activity Debate, Fore the motion: “punishment is must for effective mathematics learning”, support behaviorism theory of learning mathematics. Against the motion; “punishment is nuisance to learning mathematics", support constructivist theory of learning mathematics. Procedure, Divide the class in to two groups. From each group there should have three participants. Each participant should speak not more than three minutes.

29. Be well prepared for the next debate session.