Unit 2: Teaching Mathematics to Culturally Diverse Learners PDF

Unit 2 MFM 22EF Chapter 2 Teaching mathematics to culturally diverse learners In the Foundation Phase Compiled by Mrs. H. Claassens Welkom Campus Outcomes  Define the concepts of diversity  Understand the influence culture has on education  Describe what Africanisation in education entail...

Unit 2 MFM 22EF Chapter 2 Teaching mathematics to culturally diverse learners In the Foundation Phase Compiled by Mrs. H. Claassens Welkom Campus Outcomes  Define the concepts of diversity  Understand the influence culture has on education  Describe what Africanisation in education entails  Discuss the influence of language on teaching and learning  Indicate the importance of positive teacher expectations in the mathematics classroom  Describe how learners can use the theory of multiple intelligence to learn best in the mathematics classroom  Introduction (p.32)  Teachers in South African school are faced with the challenge of teaching more culturally diverse classes  Providing learners with the skills, attitudes and knowledge they need to function within their community culture and mainstream culture  As well as within and across other cultures  Teachers have to be culturally responsive Every society is characterized by diversity (p.32)  Diversity – more than one of different kind or variety  Colonization, migration, immigration - brought demographic shifts all over the world  Diversity not only constitutes groups - ethnic, race, language and religious groups.  Individuals within every group differ from one another in important ways  Within any group – different viewpoints develop due to factors – geographic origins, socioeconomic class and gender  Personal qualities – personality, aptitude and appearance make a difference  The influence of culture on Education Working with diversity in the mathematics What is ethno classroom mathematics? Africanization of education Diverse funds of knowledge: macro and micro (sub) cultures   Culture – complex human phenomenon  Often associated with food and dress of particular group  Culture is more complex  Culture is a learnt, socially transmitted heritage of artefacts, knowledge, beliefs and normative expectations that provides members of particular society with tools of coping with recurrent problems The influence of culture in education (p.  Diverse funds of knowledge: macro- and micro (sub) cultures (p. 33)  Multicultural education focuses – equal educational opportunities – different groups within national culture  Two concepts: macro culture and micro (sub) cultures  Macro cultures - embodied by country’s overarching symbols (e.g. flag, national anthem) and values (justice, equality, human dignity) shared to some degree by all citizens  Microcultures – smaller groups: religious groups, language groups, sport groups, classroom or office groups  Member of microcultures share – rules, roles, values, behaviors  Teacher should transmit and interpret the knowledge of  both dominant culture (macro culture) and microcultures –  Provide education that is multicultural  NB if learners are to acquire appropriate knowledge, attitudes and skills required to function within macro and micro cultures  Diverse funds of knowledge: macro- and micro (sub) cultures (p. 33)  Teachers are the key figures in the process – need to have understanding and knowledge of own culture  Be aware of cultures of learners  Know which cultural factors may influence the teaching- learning process Africanization of education (p.33)  “People’s education” after 1994– an education system decided upon by the people  Laid a foundation for education reform in years to come  Official policy on an indigenous knowledge system – adopted by cabinet in 2004  Policy provided an enabling framework to stimulate and strengthen the contributions of indigenous knowledge for social and economic development  CAPS includes guidelines on the inclusion of indigenous knowledge in teaching and learning experience  Ethnomathematics (p.34)  A branch of mathematics that specifically studies how the study field relates to culture Attempts to make a shift from formal academic setting to mathematics made up of surrounding practices and indigenous cultures – inform us – use mathematics to make sense of their world  Children bring ideas and experiences about mathematics concepts from their home environments  Construction of knowledge is dependent on what learner already know (existing knowledge)  Incorporation of two discourses (mathematics and context) enables more effective acquisition of mathematical skills rking with diversity in the mathematical classro (p.34) o Classroom – is a microculture, different cultures of learners and teacher meet to form one complex and unique classroom culture o Learners and teacher bring into classroom a set of beliefs, values, experiences which influence attitudes, behaviours and perception o For culturally diverse learners to feel acceptance – teaching and learning process must concretely demonstrate respect for cultural differences and knowledge about learners’ cultural backgrounds  Cultural factors influencing the teaching and learning process in the mathematics classroom (p.35)  Socialization: the process(SCLSW) whereby individual attains knowledge, values, language and social skills. Enable him to become integrated in society. Way in which children are brought up – linked to particular culture.  Communication: Different cultural groups speak different languages. Learning through foreign language will influence learning success  Learning preference: The way in which individual learns – closely associated with culture. Teachers must plan teaching to accommodate different learning styles  Social values: beliefs or ideas on how individual ought or ought not behave. Values acquired form social system. Sometimes value differ from culture to culture – conflict  Cultural factors influencing the teaching and learning process in the mathematics  World view:classroom (p.35) the way in which cultural group perceive people and events. People share similar beliefs, social values, experiences – more likely to view reality in same way. Inclined to develop similar ways of learning, conceiving, recognizing, interpreting and reasoning The best way to curb social and cultural Conflict is by positive communication ositive cross-cultural communication (p.36)  Teacher must choose words carefully and convey them appropriately  Consider learners’ needs – design message learners interpret them as intended  Learners my receive teacher’s message but interpretation may differ from teacher’s intention  Effective cross-cultural communication depends upon understanding both the language and other person’s cultural priorities  We communicate in terms of our perception of the environment  Cultural background includes symbols, manners, dress code, gestures and even silence. ositive cross-cultural communication (p.36)  Non-verbal behaviour plays an important role in communication  The message is not conveyed by words alone  70-90 % of our message is conveyed by non-verbal means  Much of non-verbal behaviour is also determined by our cultural background  Teachers who aim to reach all learners must consider the ways their language might be difficult for some learners delines for effective communication in the cultur diverse classroom Effective cross-cultural communication between learner and teacher requires careful planning and considerable skill Suggestions to guide teachers to reduce barriers to effective communication: (LCSRD)  Listen – Not only listen for words – but for meaning. Avoid jumping to conclusions. Verbal and non-verbal messages must be listened to  Check perceptions – Ask learners – if you have correctly grasped what they have said. Clarify perceptions from the other person’s point of view  Seek feedback – Was message received as intended? Teacher must clarify feedback – what has been said is mutually understood  Resist judgemental reactions – Avoid premature or emotional malion effect: the influence on achievement in mathem Pygmalion effect – when teachers let learners know that they believe in them and expect them to do well, learners begin to believe in themselves and do their best to achieve success Teacher communicate expectations and attitude towards learners through actions and words Expectations teachers have of learners – strong effect on learners’ motivation, self-concept and performance  Teachers form expectations early on in contact with learners Expectations are formed on the basis o  Initial impression on meeting a learner  Quality of schoolwork  Gender  Home language  Socioeconomic background  Discussions with previous teachers and parents  School records  Previous contact with brothers or sisters of a learner  Physical appearance  Social class Teachers’ expectations in classroom illustrated in the following way: (p.38) Phase 1 – Teacher forms expectations about each learner in terms of his classroom academic work performance and behaviour. Other characteristics of learners also shape the expectations formed by teacher Phase 2 – As result of these expectations – teacher interacts differently with each learner – those expect to succeed are praised, given opportunities to success Phase 3 – Each learner is sensitive to different ways teacher behaves towards him/her in class.  Phase 4 – Over time, each learner’s performance comes to the teacher’s expectations ect of negative teacher expectations on learners (p.38 o Teacher expectations affect the classroom climate o High-expectations learners receive more positive non-verbal communication – smiles, nod and eye contact o High-expectations learners are given more hints or clues by teacher when attempting to answer a question o Teacher more likely to repeat or rephrase a question for benefit of these learners o Teacher will spend more time teaching or explaining to these learners  Teachers show expectations of different learners in following ways: (p39)  Seat low-expectations learners further back in class – put together in group  Pay less attention – verbal and non-verbal interactions  Call less on them to answer questions  Spend shorter periods of time waiting for learners to answer questions  Give fewer clues or hints – when they fail to answer questions  Criticize learners more often  praise learners less frequently  Praise learners more frequently when they give marginal responses or inferior answers in classroom  Give less accurate and detailed feedback  Requires less work form learners and interrupt the responses Strategies for valuing learners (p.39-41) (PECUBE)  Every learner can succeed  Praise learners  Be inclusive  Establish trust  Use language carefully  Cooperation  Every learner can succeed (p.39)  Characteristic of effective teacher – belief that all learners can and will succeed  Teacher sends out clear, positive messages – increase feelings of self-worth  Essential that teachers become aware of their own expectations of learners – consequently sensitive to their own behaviour in the classroom  Effective teacher will work at giving all learners feeling of success in classroom  Praise learners (p.40)  Teacher can use praise to motivate all learners  Primary school learners are motivated by teacher praise  Secondary school learner – too much praise can have a negative effect Guidelines for the effective use of praise:  Genuine progress or actually accomplished something  Accompanied by explanation of why learner’s performance deserves praise  Be spontaneous and draw attention to learner  Attribute success to effort and ability – not luck  Specific rather than general  Private more often than public – older learners will be embarrassed by public praise  Be communicated to parent who has interest in learner’s successes  Be communicated verbally and non-verbally – with smile, pat, nod  Be linked to learners’ past performance – that they can assess their own improvement  Be inclusive (p.40)  Teachers should consider learners of gender, religion, language, ethnicity, or deprived background as possible advantages that could assist them in school  Teachers need to be proactive  Creating situations that offer meaningful entry into an area where a learner is not familiar  Establish trust (p.40) classroom – place where learners can trust it is safe – express feelings When learners express feelings to another - gather data about those feelings and how others respond to them Takes time for learners to be comfortable and skilled at sharing feelings Teachers’ role – give trust and support Learners need clear message – acceptable to ask questions - including questions about sensitive issues Teacher may want to put limits on the times and places for such questions Message should be to reassure learners that differences are valued, are cared for because of their uniqueness  Use language carefully (p.41) Careful language use tool in building classroom environment – learners and adults respect each other Words can and do hurt Focus on using language carefully – set classroom standard of “no put downs” “Put-down – any statement that gives a negative value to someone  Cooperation (p.41) Learners must first believe that they are valued – before they can value others and learn from them Classroom where they feel – competing for attention, materials, space, or friends – not place where they can begin to appreciate others Defensive learners see world as win-lose situation Their outlook “I can only get mine by making sure you don’t get yours” This attitude does not allow learners to appreciate differences If differences are appreciated and they feel accepted and welcome – will open up to learning  Empowering learners who experience barriers to learning (p.41-43)  Barriers to learning – physical, mental, emotional and social areas of learner development  Language of teaching as barrier to learning – children’s language ability may differ, not only in language background but also in their communicative needs, levels of proficiency, attitudes toward it and cognitive styles  Basic interpersonal communication skills – visible aspect of language – pronunciation, basic vocabulary, grammar BICS alone not sufficient for academic success  Cognitive academic language proficiency – proficiency needed to understand academic concepts and to perform higher cognitive operations necessary to achieve in school  Empowering learners who experience barriers to learning (p.41-43)  Learners who need to acquire language of learning and teaching (LoLT) may need 5 to 7 years to obtain sufficiently (CALP)cognitive academic language proficiency to perform well at academic tasks.  Acquisition of (BICS) basic interpersonal communication skills – takes about 2 years  Low proficiency in language of instruction may hamper learners’ initial comprehension of the steps needed to carry out mathematical processes involved in solving problems  Teachers have to adapt classroom practice to meet needs of learners who are learning in second language  Use lots of visual displays, demonstrations, dual language text, bilingual software programs, hands-on activities, group work and cooperative learning  Communicate through gestures, pictures, and word they know from learners’ home language  Other barriers to learning (p.43)  Learners 'intellectual abilities, socioeconomic needs, developmental level and behaviour  These barriers requires teacher to modify instructional delivery and classroom tasks to address the needs of all learners  FP learners: express themselves through multiple signs sytems, pictures, numbers, hands-on manipulatives to demonstrate mathematical concepts  Lesson modifications – modified worksheets, individualized instructions, modified assignment, peer tutors and oral exam nning guidelines for working with learners who exper barriers to learning(p.43)  Gather information – exceptional learners’ differences – how it might affect teaching and learning process  Seek assistance from other teachers and specialists in the field  Use specialized equipment – print enlarger, computers and DVD – allow learners to function at an optimal level  Individualise the curriculum – adapting materials and teaching strategies to better meet the needs of exceptional learners  Remove physical barriers and psychological barriers tha may limit learners’ ability to succeed in classroom. Promote an empathetic learning environment  Example of classroom modification plan p.43- 44 How learners will learn best in the mathematics Classroom (p.44 – 48) o Instruction should be provided to help learners make connection between classroom activities and real-world problem solving o Strong emphasis on activity-oriented problem solving and deep levels of conceptual understanding o Interacting with variety of materials that represent mathematical ideas and processes in different ways and sharing knowledge with one another ward Gardner – theory of multiple intelligence (p.45 – 6 different intelligence  Verbal-linguistic intelligence  Musical intelligence  Logico-mathematical intelligence  Spatial intelligence  Body-kinaesthetic intelligence  Personal intelligence Provide different ways to access learning. Multiple intelligence theory provides teachers with famework for creating different opportunities for learning – focusing on wide spectrum of abilities Multiple intelligence practise in classroom – regcognise diversity  Verbal-linguistic intelligence Learners have a natural tendency to talk and read Explore the logical-mathematical domain by asking and discussing “how” and “why” questions verbally Like to read and think out loud Teachers will create an environment that is conducive to the development of mathematical knowledge through use of reading, writing and speaking  Musical intelligence Music forms a close relation to mathematical performance There is strong relationship between musical patterns and mathematical concepts such geometrical concepts, symmetry as well as expansions Fraction – strong relationship between algebraic fractions and rhythmic patterns – musical measure consists of several beats, whole consist of several fractional parts Learning to make music contributes to spatial development – NB component of mathematical development Teachers can teach multiplication tables by exposing them to easy songs People showing a positive reaction to music are more likely to be creative and curious – active imagination If teachers need learners to think innovatively / solve problems creatively – music may create background for better performance  Logico-mathematical intelligence The ability to analyse and solve problems Carry out mathematical operations Conduct scientific investigations through manipulating objects in the environment Learners who display a natural ability for logical-mathematical intelligence display a strength in reasoning, thinking logically and engaging in problem-solving activities Find it easy to work with numbers and patterns Teachers should create opportunities where learners can explore science materials, reason about things, manipulate objects in the environment and be engaged in field trips to science museums  Spatial intelligence Closely linked with our visual world Spatial ability helps us to link a map with a specific terrain Helps us to determine depth, discriminate among parts that form a whole Help us to visualize the rotation of an object Teachers needs to be aware that learners prefer learning through full engagement in activities Ample opportunities need to be created where learners can execute experiments and engage in various kinds of hands-on activities  Bodily kinaesthetic intelligence Closely linked with spatial intelligence – manipulation of our bodies as well as the adaptation of our actions in reaction to the world around us The activity in the brain to judge the timing, force and execution of movement as well as the adjustment of this to the environment Learning mathematics not only require knowledge and skills in steps and procedures – also requires displaying clear understanding of the problem and making sense of it Teacher can use finger counting techniques to enhance mathematical learning in classroom Children demonstrate understanding through the use of fingers, drawings or objects such as cubes Finger counting has been proven to increase children’s numerical performance Calculations 2 + 3 – show 2 and 3 fingers This help children to become competent in processing mathematical  Personal Intelligence The capacity to reason about personality – use personality and personal information to enhance one’s thoughts, plans and life experiences Children between 6 and 8 years become more aware of capabilities and the degree if success reaches when exhibiting what knowledge and skills they possess. Group work – strategy where personal intelligence can be used to enhance learning Children can use intrapersonal knowledge to verbalise their feelings and ideas – improving their understanding of concept under investigation Apply interpersonal knowledge during group work when realizing own strengths and weaknesses When teachers support and accommodate all kinds of intelligence and learners’ preferences in this regard, academic achievement, attitudes  Guidelines for effective classroom practice (p.48) The Teacher should: o Recognise and accommodate learners’ diverse multiple intelligence and learning styles o Become aware of their own learning and teaching style o Become flexible in their choice of teaching strategies – introducing new learning content o Use multisensory approach to teaching o Use cooperative as well as competitive teaching strategies tural games in the mathematics classroom (p. 48 – 50  Playing games – much more that a fun activity  Most of cultural games transmit important mathematical concepts – counting, adding, subtracting or problem solving  Mathematical games – use their own internally constructed knowledge of mathematics – to gain physical and social knowledge of a mathematical concept in a relaxed and “fun” way. Need to tap into problem-solving skills to understand the rules of the game and plan a strategy to beat the opponent  Problem-solving are linked with mathematical concepts such as  identifying shapes,  symmetry in squares,  understanding the similarities and differences between the different squares,  counting of the tokens,  adding and subtracting of the token to establish the winner (use the board game Morabaraba) Can be played outside on playground – board can be drawn in the sand and stones can be used as tokens Important links are made between the physical knowledge gained (moving forwards/backwards on the board or counting tokens) Social knowledge – vocabulary or new vocabulary – rules of the games – support learner in forming a ow different cultures show the meaning of number wo  All learners need to have mastered the verbal and notational representation system of the specific culture  Children must be able to recognise the number word of the mathematical system  Know how to represent the number words in that system symbolically  Each culture has a different way of using finger in order to make sense of quantity  Examples: p. 50-51 (Indian culture, Chinese, Zulu)  This is the physical knowledge of numbers that the learners have internalized  Teachers should use different ways of showing numbers as opportunities for mathematical discussion  Social knowledge shared – help learners to form new ideas and concepts, conceptual knowledge of numbers will deepen  Grade 3 teacher using technology to demonstrate different intelligence field - to teach the 4 times table  Spatial and visual – PowerPoint -teach the correct number pattern of 4 times table. Learners count aloud  Kinaesthetic – using smartphones, video cameras or laptops – teach a dance each movement is associated with a number on the 4 times table. Can be recorded and used to teach others in the future. Moving while counting activates more centres of the brain and learning takes place more effectively  Verbal-linguistic – Songs and rhymes come to life through animation – video software is freely available – teacher can animate characters  Interpersonal – Create opportunities for peer teaching in classroom. Interviews can be recorded on smartphones. Homework – recorded mathematical methods, solutions and content for learning gave proven to be excellent resources  Intrapersonal – Checking whether one can do task by oneself – CAMI  Grade 3 teacher using technology to demonstrate different intelligence field - to teach the 4 times table  Musical – number patterns using specific rhymes. SongSmith – free educational tool. Used to record songs and provides list of options to choose from. While music plays – learners repeat the number sequence  Logico-mathematical – Number-explore by visnos.com – effective online resource to show how different number patterns are formed (https://www.visnos.com/) When planning lessons and learning activities – it is recommended to keep these intelligence fields in mind. It will enhance the storage of new information