Emphasize that one of the factors is psychology of learning mathematics
making it difficult for children to grasp the meaning of new concept in the classroom. and so everyday experience interferes with classroom learning. everyday experience of learners.
because although insightful performance is a more ambitious aim, it actually has a better chance of success. It yields faster and permanent results. The same mathematics should be taught to all students because no one can know in advance which students will eventually use mathematics professionally.
Piaget described two processes used by the individual in its attempt to adapt: assimilation and accommodation. Both of these processes are used throughout life as the person increasingly adapts to the environment in a more complex manner.
Sensorimotor stage (Infancy). Knowledge of the world is limited (but developing) because its based on physical interactions / experiences. Pre-operational stage (Toddler and Early Childhood). intelligence is demonstrated through the use of symbols, language use matures, and memory and imagination are developed, but thinking is done in a non-logical, non-reversible manner.Concrete operational stage (Elementary and early adolescence). intelligence is demonstrated through logical and systematic manipulation of symbols related to concrete objects. Formal operational stage (Adolescence and adulthood). In this stage, intelligence is demonstrated through the logical use of symbols related to abstract concepts.
Itlm topic 7_8
SOME BASIC LEARNING THEORIES FORTEACHING SECONDARY MATHEMATICSITLM Topic 7-8
LEARNING OBJECTIVES Be aware of and understand some basicpsychological learning theories advocated by Piagetand Bruner that can be applied to the teaching andlearning of secondary mathematics Be aware of the difference between Piaget stages ofdevelopmental theories and his learning theoriesapplied to the teaching and learning of secondarymath Use the learning theories to show examples howmathematics are taught Make students more independent to read texts onlearning theories
PROBLEM SOLVING PROCESS Recent problem solving researches agreethat children actively construct theories at alltimes, including conceptions about themanipulation of quantity and how thephysical world works. This leads to notions that children’sdifficulties in school are due to the absenceof relevant everyday experiences or to theirfaulty conceptualization in non-schoolsetting.
ROUND ROBIN Give a list of possible factors that studentshave problem in learning and solvingmathematical problems. Explain all possible factors that studentshave problem in learning and solvingmathematical problems.
THREE COMMON LEARNING DIFFICULTIES Everyday life provides too little relevantexperience, Everyday life provides erroneous experience,or children actively construct erroneousconcepts of it, Too little and too weak a connection betweenwhat is being taught and the intuitive.
STRENGTHENING MATH LEARNING IN SCHOOL According to Polya, a major aim of education isthe development of intelligence to teach youngpeople to think. In primary school, children should be taught todo their arithmetic insightfully rather thanmechanically In secondary school, mathematics should offersomething to those who will, and those who willnot, use mathematics in their later studies orcareers.
PIAGETS THEORY OF COGNITIVE DEVELOPMENT Process of Cognitive Development: theprocess of coming to know. Stages of Cognitive Development: the stageswe move through as we gradually acquirethis ability
PROCESS OF COGNITIVE DEVELOPMENT Assimilation is the process of using ortransforming the environment so that it canbe placed in preexisting cognitive structures. Accommodation is the process of changingcognitive structures in order to acceptsomething from the environment.
TEACHING STUDENTS BEGINNING TO USEFORMAL OPERATIONS (ADOLESCENCE)Continue to use many of the teachingstrategies and materials appropriate forstudents at the concrete operational stage: Use visual aids such as charts andillustrations, as well a simple but somewhatmore sophisticated graphs and diagrams. Use well-organized materials that offer stepby step explanations.
TEACHING STUDENTS BEGINNING TO USEFORMAL OPERATIONS (ADOLESCENCE)Give students an opportunity to explore manyhypothetical questions: Provide students opportunities to discusssocial issues. Provide consideration of hypothetical "otherworlds."
TEACHING STUDENTS BEGINNING TO USEFORMAL OPERATIONS (ADOLESCENCE)Encourage students to explain how they solveproblems: Ask students to work in pairs with one student actingas the problem solver, thinking aloud while tackling aproblem, with the other student acting as the listener,checking to see that all steps are mentioned and thateverything seems logical. Make sure that at least some of the tests you giveask for more than rote memory or one final answer;essay questions, for example, might ask students tojustify two different positions on an issue.
TEACHING STUDENTS BEGINNING TO USEFORMAL OPERATIONS (ADOLESCENCE)Whenever possible, teach broad concepts, notjust facts, using materials and ideas relevant tothe students: While discussing a topic such as the CivilWar, consider what other issues have dividedthe country since then. Use lyrics from popular music to teach poeticdevices, to reflect on social problems, and soon.
ASSIGNMENT Browse internet and find other learningtheories such as Bruner, Ausubel, Vygotsky,or others (in pairs). Make a summary and an example ofsecondary mathematics that could be taughtby the learning theory you chose.