JGS Exam Notes - Family Law - PDF

lOMoARcPSD|43165940 JGS Exam notes Family law (University of Pretoria) Scan to open on Studocu Studocu is not sponsored or endorsed by any college or university Downloaded by Abigail Govender ([email protected]) ...

lOMoARcPSD|43165940 JGS Exam notes Family law (University of Pretoria) Scan to open on Studocu Studocu is not sponsored or endorsed by any college or university Downloaded by Abigail Govender ([email protected])  lOMoARcPSD|43165940 JGS 121 – Teaching foundation phase mathematics. [Exam notes] Chapter #1: [Pg. 1 – 29] Concepts/definitions: Notes:  Adaptive Reasoning: “Neglect of mathematics works injury to all knowledge, since he who is ignorant of it cannot know the other sciences or the things of the world” – Roger Bacon.  The ability to adjust/adapt your reasoning depending  Mathematics can be said to provide us with the essential on circumstances/outcom knowledge/laws of natural sciences by which we navigate our es to be able to physical world, thus the existence of humans and our understanding explain a specific of how earth ultimately works largely depends on our understanding situation/fact and use of mathematics in our everyday lives.  Conceptual Knowledge: 1. What is mathematics?  A type of knowledge  It can be said that mathematics is the explanation/story of how you acquire when you reflect on what you we organise our everyday lives to make sense of what is going on already know. around us.  E.g., you May be able  It often explains the actions of other and translates our thoughts to verbalise own to those around us.  These stories are shared through a ‘universal language’ that can mathematical thinking and tell others how they know what they be understood using numbers, symbols, and images. know.  See definition for numerate person.  Constructivism: 2. Where did it all start?  The concept of new knowledge that is  [Mathema – Greek for “subject of instruction”] being created by relying on existing  Mathematics as a concept is as old as the world itself. knowledge from  Ancient times – up to 7 different number systems were used to previous experiences help civilisations communicate their understanding of the world. to try and find a  Most of us today use the “Hindu-Arabic number system” solution to a new and/or unfamiliar problem. 3. Mathematics is for everyone and in everything:  Numerate person:  Inborn mathematical abilities:  Someone who can perform basic  Studies have shown that some animals exhibit basic mathematical mathematical skills to navigate their environments. procedures and apply  When we use mathematical abilities different parts of the them to daily activities. brain act together to help us make sense of the world.  E.g., Add, subtract,  As a foundation phase teacher our focus in teaching multiply and divide. mathematics is to assist learners to become numerate – to understand the way the world operates and how they can use  Physical knowledge: mathematics to be productive.  Type of knowledge you acquire by touching, using, playing with, or acting Mathematics is adaptable/flexible. on concrete/physical objects.  Procedural fluency: 1|Page Downloaded by Abigail Govender ([email protected])  lOMoARcPSD|43165940 JGS 121 – Teaching foundation phase mathematics. [Exam notes]  Acquired mathematical skills (lived experiences):  Type of mathematical skill acquired when you carry out mathematical Children construct or build their own knowledge of procedures accurately, efficiently, and mathematics through lived experiences. flexibly, whilst being able to adapt according to different problems and/or  For them to construct this knowledge they need hands-on contexts. experience (physical knowledge) to give meaning to or understand the things they think about when they; touch,  Productive smell, look, listen, kick, run, climb, and use objects to disposition: discover what they can do or how they can solve real-world  The belief that problems. mathematics is a  Working memory and long-term memory. sensible activity and that you can use your acquired mathematical 4. How does the mind think when solving problems skills appropriately. mathematically?  Semiotics:  The study of various  The memory systems and mathematical problem types of signs/symbols and solving: what they mean and how they relate to  The role of long-term memory in solving mathematical certain things (concrete) or ideas problems: (abstract).  Long-term memory system stores various kinds of  Social knowledge: information/concepts.  Long-term memory works in tandem with working  Type of knowledge acquired through memory. social context.  [figure 1.2 – pg. 6]  E.g., being told (knowledge delivered  The role of working memory in solving mathematical through oral tradition) and remembered problems: throughout a period.  The working memory holds information for a very short  Strategic competence: time (3-8 seconds) and if anything interferes working memory while attempting to workout an answer, the  The ability to apply a variety of solutions to information will be lost. a problem and gain  Long-term memory sends information to the working consequent memory so that a problem can be solved – if this makes knowledge from the sense it will be transferred to the long-term memory. problem solving.  Automaticity = The aim of mathematics education is  Labelling: to help learners make sense of their environment so that detailed concepts can be formed while information  Occurs when learners can also be retrieved and used within split seconds. who struggle to do  Constructivism is important to our understanding of the classwork are unfairly/unreasonably how we make sense of the world around us. labelled as lazy, slow, or unmotivated.  How we construct schemas of concepts and ideas about our environment: 2|Page Downloaded by Abigail Govender ([email protected])  lOMoARcPSD|43165940 JGS 121 – Teaching foundation phase mathematics. [Exam notes] Constructivism/constructivist theory is mainly concerned with “how we come to know” what we know. – proposes that our sensations, perceptions, and knowledge form part of who we are.  Constructivists believe gaining some knowledge is not something that teachers “teach” but rather an act where learners gain knowledge and form concepts from within themselves – knowledge is constructed internally.  Learners should engage in mathematics through concrete experiences.  Curiosity and discovery should be the basis of mathematical experiences in the classroom – will lead learners to form their own ideas and deepen formulation of concepts in long- term memories.  Montessori - The constructivist approach:  Maria Montessori – explained constructivist approach through her work with children who experienced barriers to learning.  She noted that children experience episodes of deep attention and concentration when engaged in certain activities and that multiple repetitions of the activities are necessary for effective learning as well as a well-organised learning environment is conductive to experiential learning.  Based on 7 principles: 1. Free exploration of concepts. 2. Repetition of activities and skills. 3. Learning through manipulation of materials. 4. Logical reasoning and deduction. 5. One-on-one communication. 6. Freedom of movement. 7. Non-traditional grading systems. (No testing)  Critiques against Montessori method: 1. Method can be overly rigid in its approach to teaching and learning. 2. Too little room for imagination, social interaction, and play. 3. Training of teachers needs to be specific. 4. Production and use of some materials may be too expensive in certain contexts. 5. Can be seen as too “loose” – many learners might not function well. 6. Varying ages of learners in one classroom can be impractical. 3|Page Downloaded by Abigail Govender ([email protected])  lOMoARcPSD|43165940 JGS 121 – Teaching foundation phase mathematics. [Exam notes] Montessori approach explains how learners need practical, hands-on experiences with concrete material for them to formulate deep concepts in their minds.  Vygotsky – The zone of proximal development:  Lev Vygotsky – Theories centre around the importance of social interaction in cognitive development and takes a central role in our efforts to make sense of our environments.  Takes places on 3 Levels: 1. Learning occurs when learners interact with other in their environment to learn about a phenomenon. 2. Learning takes place when they interact with a more knowledgeable person (teacher or older siblings) and/or another entity (computer). 3. Learning occurs between two borders: (the distance between the 2 borders = zone of proximal development.) - Ability of learner when they solve a problem with support and guidance. - Individual ability of student when they solve a problem without input from others. - See figure 1.3 [pg. 10]  Knowledge acquisitions doesn’t happen in isolation but rather an act of sharing knowledge between learners and teachers.  Critiques against Vygotsky’s theories: 1. The role of the individual is often neglected and focus on collective social learning. 2. The zone of proximal development doesn’t recognise motivation as a factor that may influence learning. 3. The ability to adhere to rules during play is the key capacity for school preparedness. (Imagination is a greater key to cognitive development.)  Piaget – The theory of cognitive development: 4|Page Downloaded by Abigail Govender ([email protected])  lOMoARcPSD|43165940 JGS 121 – Teaching foundation phase mathematics. [Exam notes]  Jean Piaget – notably one of the most influential educationalists of modern times.  Children can be grouped according to the different stages of their cognitive development: 1. Sensorimotor stage (birth – 2 years):  Children interact with their environment through physical actions. (Rolling, crawling, sucking, grabbing, shaking etc.)  Through these actions they build “cognitive structures” about their environment and how it functions and/or responds. 2. Preoperational stage (2 – 7 years):  Learners can’t form abstract ideas about things yet. (Numbers in the mind.)  They also can’t yet draw basic conclusions from hands-on experiences and visual representations.  Repeated experiences are essential for development during this stage. 3. Concrete operations (7 – 11 years):  Learners acquire an abundance of knowledge and skills from their physical experiences.  Sophisticated conclusions and predictions are made from their knowledge and skills.  Learners still understand educational material and activities best when it refers to real-world (concrete) situations. 4. Formal operations (11 – 15 years):  Learners’ knowledge base and cognitive structures start resembling those of an adult.  Ability to form abstract thoughts increases significantly.  Critiques against Piaget’s theories: 1. The cognitive development theory might not fully encapsulate or define children’s development and further research might reveal more detailed nuances. 2. Piaget may have underestimated some aspects of the development of young children as it has since been found that they can reach some of these stages earlier than projected. 3. Claims that actual physical manipulation of objects is essential for normal cognitive development are now rejected to a certain extent. 4. Many of his theories only accommodated a western worldview of learning and development. 5|Page Downloaded by Abigail Govender ([email protected])  lOMoARcPSD|43165940 JGS 121 – Teaching foundation phase mathematics. [Exam notes]  The 3 kinds of knowledge required for developing mathematical skills:  All 3 are essential for learning mathematics but don’t necessarily follow a sequential path, it is considered more of an interchangeable process in acquiring knowledge.  Physical knowledge:  Consists of a combination of various kinds of information that learners discover and explore through their senses and manipulation of objects.  Social Knowledge:  Refers to the world of personal experiences and is learnt from others.  Gained when students observe others.  Should be taught.  Vygotsky.  Logico-mathematical knowledge – own pace and time.  Conceptual knowledge:  Piaget – constructed internally.  Not static, adapts and grows as learners gain more experience of concepts.  Teacher should provide learning opportunities that will enable them to construct their own knowledge. – Need to be encouraged to reflect on what they are doing, to verbalise their thoughts and to interpret and understand the ideas of others.  Applying the kinds of knowledge in mathematics:  The following milestones should be reached: 1. Learners will understand mathematical concepts, operations, and relations. - Count, recognise numbers and symbols, understand how different numbers link to each other and how we use these concepts to understand quantity. 2. Learners will be skilled in carrying out procedures accurately, efficiently, and flexibly, while being able to adapt in various situations. 3. Learners will be able to formulate, represent and solve mathematical problems. 4. Learners will be able to think logically and to reflect to explain and justify their thoughts. 5. Learners will see mathematics as being sensible, useful, and worthwhile, and believe in diligence and their own efficacy. 6|Page Downloaded by Abigail Govender ([email protected])  lOMoARcPSD|43165940 JGS 121 – Teaching foundation phase mathematics. [Exam notes]  Teachers can support learners to become numerate so that they can: 1. Understand what they are doing. 2. Apply what they have learnt. 3. Reason about what they have learnt. 4. Realise that they need to engage actively with a problem. 5. Be confident in doing calculations.  How the kinds of knowledge help learners become numerate:  5 components of becoming proficient in mathematics is also called the ‘five strands of mathematical proficiency.’  Strand #1: [conceptual understanding] Concept – general idea we form in our mind of things in our environment based on how we group ideas.  Learners can recognise the concept and can name it.  A cube and square are both shapes.  They know the facts about the concept and can apply the facts correctly.  A cube has sides, angles, and faces that are all the same, no matter how you look at it.  They use symbols, signs, and words to explain the concept.  A cube is a 3-D shape that is related to a 2-D square; the volume of a cube is measured by multiplying the length, breadth, and height.  They can use manipulatives or models that represent the concept.  Making a drawing of a cube.  Learners can make sense of mathematical concepts when they have ample opportunity to explore and engage in hands-on activities that lead them to better understand and remember important ideas about a concept.  Strand #2: [strategic competence] 7|Page Downloaded by Abigail Govender ([email protected])  lOMoARcPSD|43165940 JGS 121 – Teaching foundation phase mathematics. [Exam notes]  Conceptual understanding leads to strategic competence when learners can think of and use a variety of problem-solving techniques.  Strand #3: [procedural fluency]  To become strategically competent in mathematics, learners also need to be procedurally fluent.  Doesn’t only refer to numbers, also includes measuring and calculating distances, calculating the area inside spaces, and predicting the next pattern in a series.  Procedural fluency and conceptual understanding are interdependent.  Teachers need to ensure that during activities, procedural fluency is accompanied by conceptual understanding, and taught in a way that learners can apply them interchangeably.  Strand #4: [Adaptive reasoning]  Sometimes learners only focus on semiotics and can manipulate mathematical symbols through algorithms without understanding the concept of the algorithm.  Happens when teachers give too much attention to teaching procedural Fluency without emphasising critical thinking and reasoning.  Can’t explain answers = learners haven’t acquired conceptual knowledge.  When a learner can solve a problem and explain it, they demonstrate adaptive reasoning and strategic learning abilities.  Strand #5: [productive disposition]  Learners need to see mathematics as a sensible and useful skill while being confident in their abilities = productive disposition/self-efficacy.  Self-efficacy is important in mathematics because when they succeed in solving a problem, they gain confidence which develops into a tendency to be more productive.  Tendency to be more productive is achieved when a learner engages with the mathematical problems knowing that they may need to try different strategies to get the answer.  With the 5 strands in mind, teaching and learning in the classroom should be structures in a way that learners can acquire Piaget’s 3 kinds of knowledge in a variety of ways to help them to: 1. Apply different solutions to problems. 2. Become procedurally fluent and competent in executing mathematical tasks. 3. Be able to reason to explain mathematical facts. 4. Become proficient in mathematics. 8|Page Downloaded by Abigail Govender ([email protected])  lOMoARcPSD|43165940 JGS 121 – Teaching foundation phase mathematics. [Exam notes] 5. Planning mathematical learning experiences:  Why a child-centred approach?  When mathematics is taught according to a child-centred approach in the foundation phase, it implies the teaching of mathematics through the solving of problems.  This approach suggests that learning occurs by focusing on what learners must learn and how.  An environment that is conductive to effective learning must be set-up before child-centred teaching and learning can take place.  Effective learning through problem solving take place in a classroom where learners: 1. Feel safe and secure. 2. Can feel free to make mistakes without judgement – mistakes are seen as learning opportunities. 3. Are supported by fellow learners. 4. Can feel free to express their own ideas. Teacher-centred approach Child-centred approach  Teacher decides what learners  Learners plan with teacher to need to know and how they acquire the type of knowledge should learn it. they need and how they’ll learn it best.  Teacher designs activities which  Learners work collaboratively to learners must do to achieve solve problems guided by open- certain goals. ended questions that can be set up by teacher.  Teacher demonstrates step-by-  Learners use their own step how to solve problems. strengths and prior knowledge of concepts to solve a problem.  Learners receive information  Learns actively participate in passively from teacher. constructing their own knowledge.  Only teacher evaluates learner’s  Learns can monitor their own work. learning and make decisions around future learning.  How to organise the classroom:  Learners need to be able to communicate; discuss, reason and reflect their ideas and share their thoughts and findings on mathematical issues – Vygotskian perspective. This can only be achieved if teachers support this kind of learning. 1. Seating arrangements:  A flexible design is the most effective as it allows teachers to adapt the teaching and learning environment according to needs of learners.  E.g., when learners need to collaborate on a problem the best would be for them to be seated around a cluster of tables. 9|Page Downloaded by Abigail Govender ([email protected])  lOMoARcPSD|43165940 JGS 121 – Teaching foundation phase mathematics. [Exam notes]  E.g., if individual learning needs to be done the best would be two seated at a table or specially planned workstations can be set up.  E.g., whole-class teaching it is suggested that seats are arranged in a U-shape – maximum visibility of teacher.  If you group learners based on abilities, it may lead to labelling of learners – Mixed ability grouping is preferred. (Learners who struggle to master concepts may learn faster in social structures where they can learn from their peers.)  NB!!! Learners shouldn’t ever be seated with backs to the blackboard/presentation wall.  Carpets can be very useful when small groups can be called for individual attention. 2. Whole-class teaching:  Whole class teaching approach is beneficial for the teaching and learning experience depending on the kind of mathematical knowledge learners need to gain.  NB!!! Learners must still have the opportunity to work at their own pace even in a large group.  Can be effective as part of the introduction to a mathematical lesson (counting as a group or reciting/singing a song) or during mental computation instructions when a sum is given to the class and learners need to do rapid calculations.  Whole-class discussions should be considered as a kind of follow-up to problem solving activities.  Whole-class discussion can also be an effective strategy for teachers to determine whether learners acquired the necessary conceptual knowledge or to identify whether any misconceptions exist. – also gives teachers an opportunity to identify areas or concepts that still need to be explored more or to know which areas learners have already mastered.  Preferable to keep this method to a minimum due to possible exclusions of some learners who may feel inhibited by the large group. Advantages Disadvantages  Teachers can use the time  Learners can find Lessons to be available to teach efficiently. boring or tedious.  Teachers have better control  Learners tend to forget over the behaviour of the entire information easily. group.  Teachers ensure correct  Learners don’t have to really methods and strategies are think for themselves. applied.  Teachers ensure lesson  Learners can demonstrate a lack outcomes are met. of understanding. 10 | P a g e Downloaded by Abigail Govender ([email protected])  lOMoARcPSD|43165940 JGS 121 – Teaching foundation phase mathematics. [Exam notes] 3. Small-group teaching:  Often preferred in mathematics teaching – because it can be challenging for learners whose mother tongue differs to the language of teaching and instruction. – Happens so that these learners can cope with learning mathematical concepts and deal with language barriers.  Often considered the most beneficial strategy because communication is supported in a safe and non-threatening environment.  Learners who have learning barriers (struggling to cope with basic work) also benefit from small group teaching because the pace can be adapted to their specific needs.  No more than 6-8 learners can sit with the teacher on the carpet/seated at desks clustered in small groups and engage in activities that encourage discovery at a more suitable level for the individuals.  Avoid labelling – arrange learners in small groups of mixed abilities.  Ensures that all learners understand the work and each of their progress can be observed effectively.  The following should be taken into consideration when using small-group teaching: 1. Always create an atmosphere of tolerance and acceptance. 2. Let learners know that mistakes are okay because that’s how you learn. 3. Choose tasks that will challenge learners. 4. Always support learners in all their endeavours. 5. Let learns work individually on specific tasks and follow-up with whole-class discussions (works well at the end of a lesson) 6. Give clear instructions to the group as a whole and set clear expectations for each learner – emphasise group goals and accountability.  Learners not involved in the small group teaching activities can be seated at their desks in separate groups.  Hints for planning activities for learners not involved in small- group activities: 1. Learners can be placed in their own small groups at their desks, with no more than 4 learners per group. (Prevents behavioural problems that might arise if the group is too large.) 2. Groups should be arranged according to the mathematical exercise that learners are engaged in. Different activities can be given each group or each learner within a group (prevents copying of work.) 3. Groups shouldn’t be static but rather change from time to time. (Prevents labelling) 4. Appropriate activities should be provided based on each learners’ ability level. (Impacts on behaviour) 5. Enrichment activities can be provided to engage in when initial work is complete. 6. Well-defined boundaries should be put in place for behaviour. 7. Learners should be taught to take responsibility of their own learning (not just copy others work.) 11 | P a g e Downloaded by Abigail Govender ([email protected])  lOMoARcPSD|43165940 JGS 121 – Teaching foundation phase mathematics. [Exam notes] Advantages: Disadvantages:  Learners are usually very  Teaching can take up a lot of motivated. time.  Information is retained much  Maintaining discipline may easier. prove to be difficult.  Learners are encouraged to be  Lessons and activities require creative. detailed planning.  Learners use cultural knowledge  Interruptions can’t be to make sense of mathematics. accommodated during lessons.  Learners develop a sense of  Teachers need to be aware of autonomy in mathematics. learners’ different ability levels.  The learning environment allows for efficient distribution of resources.  Assessments can be done effectively.  How to plan a lesson:  The more prepared the teacher is the better the lesson will be, this implies that the teacher:  Has a clear understanding of the outcomes of the lesson.  Understands their learners preferred learning styles.  Plans learning experiences that engages the multiple intelligences of learners.  Has a definite plan of how they will guide learners to gain new knowledge.  Knows what possible models and manipulatives their learners might need to construct their own knowledge.  Understands how assessment promotes learning.  Reflects on their lesson presentation to adapt it for future lesson planning.  The 3-part lesson design:  This lesson plan can be employed to plan for successful mathematical experiences and also be adapted accordingly to suit the needs of learners.  NB!!! Teachers should always ensure that lessons are planned in a way that learners have ample opportunity to acquire the requisite kinds of knowledge (physical, social, and conceptual.)  The goal of teaching mathematics in the foundation phase is to cultivate proficient users of mathematics that can go on to become numerate members of society. 1. Before/Introductory phase:  Prepares learners mentally by revising work they have done previously.  Posing a mathematical problem where learners need to use prior knowledge (physical) to come to a solution.  Learners typically explore a concept under investigation by interacting with teacher and peers through hands-on 12 | P a g e Downloaded by Abigail Govender ([email protected])  lOMoARcPSD|43165940 JGS 121 – Teaching foundation phase mathematics. [Exam notes] activities, thereby acquiring and displaying social knowledge. 2. During:  Engages learners in using their prior knowledge to investigate a new mathematical concept.  Usually structured around small-group activities where learners integrate 3 kinds of knowledge interchangeably to form new mathematical ideas. 3. After:  Learners have the opportunity to display conceptual knowledge by explaining their strategies, methods or models they have used to solve the problem.  Usually takes place in the form of whole-class discussions. 6. Technology in the classroom and teaching mathematics:  [READ 1.7 pg. 23 -27]  Technology and the skills to use different kinds of technology have become an inevitable requirement in most South African schools.  Access to computers/technology contributes to a perception that learners are learning how to use them.  Basic concepts such as clicking, digital drawing and digital storage gives colour to the most ordinary of school activities. (As early as grade 1)  Training in basic computer skills and software packages such as Microsoft Office remain in high demand, and technology contributes to effective school administration as well as staff, learner and parent communication. In South African schools a paradigm shift or change of perspective is required before technology can be fully implemented for the purpose of effective teaching and learning.  5 skills that would equip the next generation to be able to function more effectively after school: 1. Real-world problem solving and innovation. 2. Knowledge building. 3. Collaboration. 4. Self-regulation. 5. Practical use of technology.  This generation is defined as visual learners who react t external stimuli. 7. Looking towards the future of mathematics education:  Increased need for mathematics education:  The key to education for all societies around the globe – and increasingly so in modern times – is the preparation of citizens 13 | P a g e Downloaded by Abigail Govender ([email protected])  lOMoARcPSD|43165940 JGS 121 – Teaching foundation phase mathematics. [Exam notes] to become dynamic participants in economic activities, both locally and internationally. -UNESCO  Research has found that early intervention by governments, societies, and parents in the education of their children, ultimately leads to more effective schooling and an enhanced workforce that can shape the economy for the better.  Evidence from research shows that a lack of mathematical skills creates an ever-widening gap that must be filled to gain even a reasonable chance to achieve economic prosperity that will eventually benefit an entire country.  Importance of mathematics for sustainability:  Mathematics can offer us a way to make certain recommendations for managing our ecosystems in a more sustainable manner.  Mathematics impacts sustainable development in all aspects of our being – whether on a social, environmental, or economic level – and as such, our quest in understanding and using mathematics continues.  Summary on pg. 28  Activity on pg. 29 Chapter #2: [Pg. 31 – 55] Concepts/definitions: Notes:  Africanisation of  Teachers in south African schools are faced with the challenge of education: teaching progressively more culturally diverse classes so the needs of all learners are met. – includes inter alia, providing learners with  Educational reform that tries to bring concepts the skills, attitudes, and knowledge they need to function within of African culture into their community culture and mainstream culture, as well as within formal teaching and and across other cultures – Teachers must be culturally responsive. learning experiences across the education system. 1. Every society is characterised by diversity:  Culture:  For centuries, factors such as colonisation, migration,  Is a learnt, socially immigration, and war have brought about demographic shifts transmitted heritage of all over the world. artefacts, knowledge,  People from varying backgrounds have settled in specific beliefs, and normative geographic areas, thus over time diversity became typical of expectations; it provides the members all societies. of a particular society  Diversity doesn’t only constitute groups such as ethnic, race, with tools of coping language, and religious groups. – individuals within each with recurrent group differ from one another (different viewpoints develop problems. due to geographic origins, socioeconomic class and gender  Diversity: and personal qualities like personality, aptitude and appearance make a difference.)  Originates from Latin  Diversity also includes sexual orientation, disabilities, learning “diversus” preferences, educational level, age, marital status, parental status, etc. 14 | P a g e Downloaded by Abigail Govender ([email protected])  lOMoARcPSD|43165940 JGS 121 – Teaching foundation phase mathematics. [Exam notes]  Means more than one/ Different kinds/ A variety. 2. The influence of culture on education:  Culture is a very complex human phenomenon and is often  Ethnomathematics: associated with material goods and artefacts, or with obvious  The examination of visual aspects such as food and dress of a particular group. how both mathematical  Often defined as in terms of a particular group’s art, music, ideas and mathematical and literature – but according to Goodman and Marx culture is practices are processed defined as “a learnt, socially transmitted heritage of artefacts, and used by different cultures in everyday knowledge, beliefs and normative expectations that provide activities. the members with tools of coping with recurrent problems.  Multiple intelligence  Diverse funds of knowledge: macro and micro cultures: theory:  Provides teachers with  NB!!! Consider cultural variation within the broad south a framework for African culture, because multicultural education focuses on creating different equal opportunities for different groups within the national opportunities for learning by focusing on culture. a wide spectrum of  2 concepts that can be used to appreciate cultural variations abilities. are: macro culture and micro/subcultures.  Teachers should therefore transmit and interpret the  Prejudice: knowledge of both cultures and hence provide education that  A judgement or is multicultural. – Important if learners are to acquire the opinion, against, or in appropriate knowledge, attitudes and skills required to favour of, a person or function in the cultures in society. thing, which is formed  Teachers are key figures and must have an understanding beforehand and without the and knowledge of their own culture, be aware of learners’ examination of facts. cultures and know which cultural factors may influence the teaching-learning process.  Pygmalion effect:  When teachers let Macro culture Micro/subculture learners know that they  Embodied by a country’s  Smaller groups such as believe un them and overarching symbols (flag, religious, language, sports expect them to do well, national anthem) and values groups or even a classroom or learners begin to (justice, equality, human office. believe in themselves dignity) which are shared to  Members share a belief in and do their best to some degree amongst all certain rules, roles, values, and achieve success. citizens. behaviours.  When teachers let learners know that they  May perceive/experience the believe in them and overarching national values and expect them to do well, ideals differently. learners begin to  Not necessarily isolated entities. believe in themselves and do their best to achieve success.  Africanisation of education:  Racism:  A call for an African renaissance in terms of education reform has been voiced since post-apartheid.  The belief that one’s  “Peoples education” – NECC suggested this where own race is superior to another. education is decided upon by the people to legitimise the education system and replace education practices  Stereotyping: used under apartheid regime. – never became a blueprint but did lay a foundation for education reform  Happens when mental in years to come. categories are created to place people, items,  Official IKS was adopted by cabinet in 2004 – marking or events in the first milestone for the recognition, affirmation, conceptually specified development, promotion, and protection of indigenous groups. knowledge. It provided an enabling framework to 15 | P a g e Downloaded by Abigail Govender ([email protected])  lOMoARcPSD|43165940 JGS 121 – Teaching foundation phase mathematics. [Exam notes]  Xenophobia: stimulate and strengthen the contribution of indigenous knowledge for social and economic  A hatred or fear of development. foreigners.  CAPS includes guidelines on the inclusion of  NECC: indigenous knowledge in the teaching and learning experience and makes special reference to the rich  The National Education and diverse history and heritage that contribute to and Coordinating nurture the values contained in constitution. Committee.  Teachers need to specifically consider and integrate ethnomathematical studies into the curriculum.  IKS:  Indigenous knowledge  What is ethnomathematics: system  According to Dlamini and Machaba, ethnomathematics  “No put-downs”: is considered too be a branch of mathematics that specifically studies how the study field relates to  Broadly defined as culture. any statement that  Rosa and Orey state that it attempts to make a gives a negative value to something or meaningful shift from a formal academic setting to a someone. type of mathematics that’s made up of the surrounding practices and indigenous cultures that inform us how people use mathematics to make sense  Defensive learner: of their world.  Practising ethnomathematics refers to formal  See the world as a academic mathematics as Eurocentric/western- win-lose situation, from a standard of European mathematics and maintains that the scarcity. western way of approaching mathematics is alien to  Outlook is “I can only many Africans. – they believe that to learn get mine by making mathematics optimally, content needs to be culturally sure you don’t get yours.” and contextually familiar to learners.  Doesn’t allow learners  In accordance with Piaget and Vygotsky’s theories – to appreciate learners bring ideas and experiences about differences. mathematical concepts from their home environments.  Learners don’t come into the classroom with “black  LoLT: minds” but rather that the construction of knowledge is dependent on what a learner already knows and  Language of learning and teaching. what they must know going forward.  The incorporation of the two discourses (mathematics  BICS: and context) therefore enables more effective acquisition of mathematical skills.  basic interpersonal communication skills.  CALP: For culturally diverse learners to feel genuine acceptance, the teaching and learning process must  Cognitive academic concretely demonstrate respect for cultural differences language proficiency. and knowledge about the learners’ cultural backgrounds.  SASC:  South African Sports  Working with diversity in the classroom: Commission.  The classroom is a microculture where different cultures of  Morabaraba: learners and teachers meet to form one complex and unique classroom culture.  Also known as  Every teacher and learner are a unique individual and mlabalaba, mmela. cultural being who brings a distinct set of beliefs, values and experiences into the classroom which influences 16 | P a g e Downloaded by Abigail Govender ([email protected])  lOMoARcPSD|43165940 JGS 121 – Teaching foundation phase mathematics. [Exam notes]  In Setswana: attitudes, behaviours, and perceptions – according to muravava and Banks. umlabalaba.  In Lesotho: mororova.  The classroom is a setting in which cultural transmission  An example of an takes place and in which learners become socialised. indigenous game  Learners who come from different cultural backgrounds played by many then the classroom which is an extension of the school cultures in south Africa. culture and mainstream dominant culture may experience cultural alienation and cultural discontinuity. – this can  Isithupa: lead to learners failing or dropping out of school.  Teaching and learning processes must concretely  Zulu for six and demonstrate respect for cultural differences and means “thumb” knowledge about learners’ backgrounds.  Isikhombisa:  Cultural factors influencing the teaching and learning  Zulu for 7 means “the process: one that points out”  Isishiyagalombili:  Teachers need to be knowledgeable about the various cultural factors which might influence the way in which  Zulu for 8 means “two they teach and respond to learners, and the way in which remain” learners learn and behave in class.  Social conflicts can be generated by racism, prejudice,  Isishiyagalolunye: stereotyping and xenophobia – efforts need to be made to reduce these – positive communication is the best was to  Zulu for 9 means “one remains” curb this conflict.  Some factors: 1. Socialisation:  Generally, refers to the process whereby an individual attains the knowledge, values, language, and social skills that enable them to become integrated into society. 2. Communication:  Non-verbal communication is largely culturally determined and can have a profound effect on the communication and understanding between teachers and learners. 3. Learning preference:  Teachers need to plan their teaching to accommodate different learning styles because research suggests the way in which an individual learns is associated with their culture. 4. Social values:  Values are abstract constructs which are beliefs/ideals about how individuals behave.  Acquired from social system and culture in which the individual grows up.  Core values are commonly held by all.  Differ from one culture to the next – conflict could arise if it’s not understood which can have a detrimental effect on teaching and learning. 17 | P a g e Downloaded by Abigail Govender ([email protected])  lOMoARcPSD|43165940 JGS 121 – Teaching foundation phase mathematics. [Exam notes] 5. World view:  Refers to way in which cultural groups perceive people and events.  Those who share similar beliefs, social values and experiences are more likely to view reality the same way.  They are also inclined to develop similar ways of learning, conceiving, recognising, interpreting, and reasoning.  Positive cross-cultural communication:  Communication process is complex.  To communicate effectively, teachers should do more than plan what they want to say – they must choose their words carefully and convey them appropriately.  Teachers need to consider learners needs and design their messages so that learners will interpret them as intended.  Effective cross-cultural communication depends on understanding the language and the other persons cultural priorities.  We communicate in terms of our perception of the environment which is largely based on our experience of culture.  70-90% of our messages is conveyed by non-verbal means.  Guidelines for effective communication in the culturally diverse classroom: 1. Listen:  Listen for meaning not just words.  Verbal and non-verbal messages should be listened to. 2. Check perceptions:  Ask learners whether you understand them correctly. 3. Seek feedback:  Ask whether you have been understood.  Clarify so that what has been said is mutually understood. 4. Resist judgemental reactions:  Avoid premature or emotional judgements. 5. Develop self-awareness: 18 | P a g e Downloaded by Abigail Govender ([email protected])  lOMoARcPSD|43165940 JGS 121 – Teaching foundation phase mathematics. [Exam notes]  Examine your own communication style and become conscious of how you’re communicating. 3. Teachers’ expectations in the diverse classroom:  Our expectations of others behaviour is based on what we know objectively and also on what we know or think we know about them as individuals and as members of a group.  What we think of them is influenced by a set of generalisations about the relevant groups. – a.k.a: we stereotype people.  There are many factors that determine our perceptions (gender, socioeconomic status, appearance, race, and cultural background.)  The Pygmalion effect: (the influence on achievement in mathematics):  Teachers communicate their expectation and attitudes towards learners through actions and words.  According to research, the expectations that teachers have of learners exercise a complex, strong, and significant effect on learner motivation, self-concept, and performance.  Rosenthal and Jacobson (1968) illustrated the powerful effect of teacher attitudes on learners’ ability and their actual performance within the classroom. – conducted a study known as the Pygmalion effect or self-fulfilling prophecy.  Teachers usually form expectations early and are based on: 1. The initial meeting of a learner. 2. The quality of schoolwork. 3. Gender. 4. Home language. 5. Socioeconomic background. 6. Discussions with previous teachers and parents. 7. School records. 8. Previous contact with brothers or sisters. 9. Physical appearance. 10. Social class.  Brophy and Good (1973) state teacher expectations set off a chain of events in the classroom: 1. Phase #1:  Teacher forms expectations about each learner based on work performance and other behaviour (as well as other characteristics.) 2. Phase #2:  From these expectations teachers interact differently with each learner. 19 | P a g e Downloaded by Abigail Govender ([email protected])  lOMoARcPSD|43165940 JGS 121 – Teaching foundation phase mathematics. [Exam notes]  Expected to succeed are praised and given several opportunities.  Not expected to succeed are called upon less and given less time to answer. 3. Phase #3:  Each learner is sensitive to way the teacher behaves towards them which results in them labelling themselves and affects their social and academic behaviour and self-esteem. 4. Phase #4:  Each learner’s performance conforms to the teacher’s expectations.  The effect of negative teacher expectations on learners:  According to Cooper and Tom (1984) teacher expectations affect the classroom climate.  High-expectation learners receive more positive non- verbal communication from the teacher and receive more opportunities to master new and challenging learning content and are also given more hints or clues and teacher is more likely to repeat or rephrase questions whilst praising learners and giving less criticism than low- expectation learners.  Teachers show their expectations in the following ways: 1. Low-expectation learners are seated in the back of the class or put together in a group. 2. Less attention is given to them in verbal and non-verbal interactions. 3. Low-expectation learners are called on less often. 4. Less time is given for low-expectation learners to answer. 5. Fewer hints or clues are given to low-expectation learners. 6. Low-expectation learners are criticised more often. 7. Low-expectation learners are praised more when giving marginal responses or inferior answers. 8. Less accurate and detailed feedback is given to low- expectation learners. 9. Less work is required from low-expectation learners. 10. Low-expectation learners are interrupted more often.  Negative expectation detracts from learners’ sense of identity or how they see themselves and their place in the world.  The effects last long and are difficult to reverse or erase.  Strategies for valuing learners:  Learners feel valued when they are in a supportive environment and teachers can create such an environment by:  Every learner can succeed: 20 | P a g e Downloaded by Abigail Govender ([email protected])  lOMoARcPSD|43165940 JGS 121 – Teaching foundation phase mathematics. [Exam notes]  A characteristic of an effective teacher is the belief that all learners can and will succeed. – send out clear, positive messages to all learners that increase their feelings of self- worth.  Teachers thus need to become aware of their own expectations of learners and are consequently sensitive to their own behaviour in the classroom.  An effective teacher works at giving all learners a feeling of success in the classroom.  Praise learners:  Effective praise should: - Be given when a learner has made genuine progress or accomplished something. - Be accompanied by an explanation of why it deserves praise. - Be spontaneous and draw attention to the learner. - Attribute the success to effort and ability (not to luck) - Be specific rather than general. - Be private rather than public – older learners may be embarrassed. - Be communicated to a parent or significant other person who has an interest in the learner’s success. - Be communicated verbally and non-verbally. - Be linked to learners past performance.  Be inclusive:  Teachers should consider learners who represent subcultures attributes as possible advantages that could assist them in school and need to be proactive about creating situations which offer meaningful entry into an area where a learner is not familiar. (Girls day on a soccer field or boys day pretending and fantasising.)  Establish trust:  Learners should feel safe to express feelings in a classroom.  Teachers’ role is to give trust and support – clear message should be given to learners that differences are valued, and they are cared for because they are unique.  Use language carefully:  Words can and do hurt.  Set a classroom standard of “no put-downs”  Learners and adults should respect each other.  Cooperation:  Learners must first believe they are valued before they can value others and learn from the,  Learners shouldn’t feel that they are competing for attention, materials, space, or friends otherwise they will keep up defences. 4. Empowering learners who experience barriers to learning: 21 | P a g e Downloaded by Abigail Govender ([email protected])  lOMoARcPSD|43165940 JGS 121 – Teaching foundation phase mathematics. [Exam notes]  Barriers to learning includes many conditions that may or may not be noticeable and may include physical, mental, emotional, and social areas of learner development.  Language of teaching as a barrier to learning:  Mathematics is generally viewed as a universal language that doesn’t involve much use of language – but teachers need to recognise that mathematics is highly dependent on language for making meaning.  A primary challenge in a multicultural school is to meet the needs of learners from linguistically diverse backgrounds who have limited proficiency in the language of learning and teaching.  The LoLT of most south African schools is English. – there is often a mismatch between learners and teachers who don’t share the same linguistic background and who have little knowledge of the language communities from which the learners come.  Learners who aren’t proficient in the LoLT may have a language deficit since their home language may require only informal, colloquial language or basic interpersonal communication skills according to Cummins (2000)  Schools use formal language, so these learners consequently lack more sophisticated commands of language or the cognitive academic language proficiency necessary for success in the school system.  The distinction between BICS and CALP can be described as according to Cummins: - Basic interpersonal communication skills consist of “visible” aspects of language (pronunciation, basic vocabulary, and grammar) which allow learners to converse fluently in undemanding everyday situations. BICS alone aren’t sufficient for academic success. - Cognitive academic language proficiency is the proficiency needed to understand academic concepts and to perform higher cognitive operations necessary to achieve in school. (Learners learning a new language often have trouble with academic concepts and terminology because these terms and ideas are more abstract and are less easily understood and experienced than ideas and terms used in everyday social interactions.)  Teachers have a responsibility to adapt their classroom practice to meet the needs of learners who are learning through the medium of a second language. [pg. 42.] - Simplify the linguistic structure used to express mathematical problems. - Use lots of visual displays, demonstrations, dual language text, bilingual software programs, hands-on activities, group work and cooperative learning. 22 | P a g e Downloaded by Abigail Govender ([email protected])  lOMoARcPSD|43165940 JGS 121 – Teaching foundation phase mathematics. [Exam notes] - Teachers should try to communicate through gestures, pictures, and any words they know from the learns home language. - Take time to teach learners some keywords, phrases, or gestures so they can build peer relationships. - Encourage other learners to include them in activities. - Teachers should maintain a positive attitude. - Research suggests that acquiring LoLT may need 5 – 7 years to obtain sufficient CALP to perform well at academic tasks. - Acquisition of BICS takes about 2 years.  For second language learners one of the greatest barriers to learning is mastering the language of instruction.  Other barriers to learning:  Intellectual abilities, socioeconomic needs, developmental level, and behaviour can also be barriers.  See examples on pg.43.  Require the teacher to modify instructional delivery and classroom tasks to address the needs of all learners. (Teachers can create outlines, concept maps and other visual aids for learners who have difficulty processing complex concepts.)  Foundation phase learners should be encouraged to express themselves through multiple sign systems such as pictures, numbers, and hands-on manipulatives to demonstrate mathematical concepts. (Modified worksheets, individualised instruction, modified assignments, peer tutors and oral exams)  Moore and Hansens guidelines for working with learners with barriers: 1. Gather information about the nature of the exceptional learners’ differences and how that might affect the teaching and learning process. 2. Seek assistance from other teachers and specialists in the field. 3. Use specialised equipment to allow learners to function at an optimal level. (Print enlarger, computers, and DVD players) 4. Individualise the curriculum by adapting materials and teaching strategies to better meet the needs of the exceptional learners. 5. Remove physical (schoolbags) and psychological barriers that may limit exceptional learners’ ability to succeed in the classroom. – promote and empathetic learning environment. 5. Talented and gifted learners:  Every classroom has talented and gifted learners.  Teachers should plan their teaching with the same dedication to challenge these learners as they plan their lessons for learners with barriers to learning. 23 | P a g e Downloaded by Abigail Govender ([email protected])  lOMoARcPSD|43165940 JGS 121 – Teaching foundation phase mathematics. [Exam notes] 6. How learners will learn best in the classroom:  The best way for learners to learn in the mathematical classroom is to organise and plan appropriate experiences so that learners will individually construct mathematical meaning.  Instruction should be provided to help learners make connections between classroom activities and real-world problem solving.  Learners need to spend time interacting with a variety of materials that represent mathematical ideas and processes in different ways and sharing their knowledge with one another.  All children access information and demonstrate knowledge through distinctive symbols that are specific to a specific culture. – the human brain and nervous system are structured in such a way that each member within a culture are able to construct meaning, to understand, interpret, examine, evaluate or transform the messages conveyed by the unique symbols of each specific culture.  The theory of multiple intelligences:  Gardner identified 7 different intelligences (domains) which can all be distinguished in different combinations unique to every person and provide different ways to access learning.  Provides teachers with a framework for creating different opportunities for learning by focusing on a wide spectrum of abilities.  Multiple intelligence practices in classrooms recognise diversity through the creation of a range of opportunities that respond to a variety of strengths and learning styles because no two learners learn in the same way nor express their knowledge in the same way.  Verbal-linguistic intelligence:  Learners have a natural tendency to talk and read and explore the logical mathematical domain by asking and discussing “how” and “why” questions verbally.  They like to read and think out loud.  Teachers are expected to create an environment that is conductive to the development of mathematical knowledge by reading, writing, and speaking.  Musical intelligence: