Mathematics teaching and learning and disadvantage in Kenya

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Embodiment in Mathematics

Response to a reading from Martha W. Alibali and Mitchell J. Nathan on Embodiment in Mathematics Teaching and Learning: Evidence From Learner's and  Teacher's Gestures.




The writer stated three ways in which embodiment mathematics assist in mathematics learning process in schools. This taking place consciously or unconsciously. The first method is pointing and as  Alibali and Nathan put it, is commonly in lower primary schools in Kenya. The second is representational in which assist in bringing any given situation into a classroom for natural knowledge acquisition. The third is metaphoric. Glenberg and Robertson [1999, 2000] are emphasizing the use of embodied mathematics as they argue that pointing links speech to associated mental process.Alibali and Nathan based information that embodied knowledge is an integral component of math thinking.
When I first stepped to teachers training college, our maths methodology tutor made us make sounds and movement with our fingers when writing numbers. The method was to teach us how to go and introduce numbers to class one pupils.  Practically there are several body movements conveying messages in a mathematics lesson. It's in the context that it require professional input so as for equipping curriculum implementors entirely.
Question
Teachers engage in embodiments mathematics frequently when discharging duties. How best should this be practice to make learning more enjoyable?

Response to a reading of Erna Yackel and Paul Cobb on Sociomathematical norms, argumentation and autonomy in Mathematics.

The normative understanding of what counts as Mathematically different, Mathematically sophisticated, Mathematically efficient and Mathematically elegant in a classroom are the socio-mathematical norm. The writer gives the difference between the socio-mathematical norm and a social norm as former to be what constitute the argument and later as the case or class discussion. What accounts as an acceptable Mathematical explanation and justifiable is the socio-mathematical norm. Class discussions are supposed to be supervised by the teacher so that it leads to proper learning and acquisition of mathematics concepts. Students given a chance for arguments may deviate and end up not having a healthy class discussion leading to achievement of the lesson objective,  professionalism should be displayed to provide direction when conducting class discussions.

The teacher is required to regulate mathematics argument so as to influence the learning opportunity. Students should be guided to argue their points at appropriate moment so that learning takes place. The writer gives a fascinating example of why students need to stick to their answers when they are sure of it or the need for learners to provide concrete answers. The student who changed the answer, but could not when asked her name remained same after asked more than once.

In my teaching experience, I could let group leaders choose members of the group alternatively, as they choose those who could help them in solving mathematics problems, give a task and then do the marking. Students from another group could name a member of a competing team, one they suspect may not handle the given task competently this will warrant named student perform the work on white board for all to witness steps involved. Each group is supposed to teach one another in how to do the task they got as a group well. Another one they would sit beside one a student choose to compete and argue how they reached to a conclusion of each mathematic problem. This method gave learners extensive experience on handling different questions.

The timed lessons may not urger well with this method since if not carefully monitored by teachers ,then students may end up discussing other experiences irrelevant to the lesson. It is demanding situation for teachers because they have to try make sense of the wide array of solutionsoffered by children [Carpenter, Ansell, Franke, Fennema, and Weisbeck 1993].This way of learning mathematics develops intellectual autonomy which is a major goal in current educational reform movement. The reform is in agrement with Piaget [1948-1973].
Question
Most teacher will agree with me that class discusion is an important laerning tool and if not supervised well may lead uneccesary argument and time consuming,  how do you captualise and give proffessional guidelines ?

Response to a reading on using two languages when learning mathematics by Judith Moschkovich.

The use of two or more languages while teaching mathematics is so common in Kenya. The practise started way back with  missionaries when they introduced western education to, by then "The east Africa British protectorate''. The missionaries themselves learnt the local languages in areas they established mission churches . Schools and hospitals were then built within and local languages used for communication. In urban areas i.e. city and municipal councils, the official medium of instructions in schools in lower classes is Swahili whereas rural or county council areas , is the local language. Kenya has forty two local different languages and thus why Swahili is used in the urban areas because children come from different communities. The schools situated in the high cost areas of Nairobi , capital city , the official medium of instruction is strictly English. This came after attainment independence [1963] . Before that , different races used to have different schools.
 
Its so interesting to see young children talk in their own language as they solve mathematics questions. The learners come up with another language better known to themselves when discussing a mathematics problem. This has brought up the introduction of a different language close to Swahili known as "shen'g". Its a mixture of all different local languages as children from different communities met in urban schools and had no idea how some other things are called in either Swahili or English.

 Mathematics is the only subject that is still taught using two or more different languages in Kenyan schools. The use of mathematics terms such as congruent,tessellate ,perpendicular and many others is a result to use of one or more languages when teaching the subject. Use of local teaching and learning aids or materials for demonstrations and experiments in mathematics lesson could also be the reason why bilingual approach to mathematics is embraced.

Reading these articles has made me realize that all educational class room experienced in Kenya, has once been experienced elsewhere and requires to be addressed by educational stake holders. This also encourage teachers and learners to one or more languages so long as the concept is understood by the recipient . Since upper primary schools in Kenya the medium of instruction  has been English, teachers have shied off to use any other language lest not be found by their immediate supervisors starting with head of that particular institution.


Question:

As a class room teacher, do you agree with the use of two or more language in a mathematics lesson ?  why ?

Response to a reading of Rochelle Gutierrez on The Sociopolitical Turn in Mathematics Education.

     The is very right to bring attention of sociopolitical turn in mathematics education since it has been there insignificantly with less attention put to it by education researchers .To my view, this is why most of African scholars are living abroad for fear of their lives in case of airing their views. Earlier they lived in exile , likes of professor Ngugi wa thiong'o of Kenya and Chinua Achebe of Nigeria . These people never lived in their countries most of their lives for fear of political persecution due to their divergent thoughts towards education. In some African countries even national examinations are tampered with to reward loyalists politically.

    Rochelle Gutierrez [2002] moved beyond sociocultural view to espouse on sociopolitical concept and theories highlighting identity and power at play. The writer considered race, ethnicity, equity,and diversity in bringing new possibility for relationship between people , mathematics and the globe. This in general should be embraced by all teachers taking into account on how to handle learners in war torn areas.  Africa, the political class live in denial never to accept defeat and would cling in power, send teachers in such volatile places. In Kenya , we have got mobile schools following nomadic tribes but of late it turned to be following cattle rustlers. Learners, especially ones in secondary schools are armed and would respond to a distress call any moment in the middle of a lesson from their kinsmen looking after cattle when attacked. Teachers are supposed to be in a position to handle such situations. In most African countries during election , school children and their teachers could be caught in stampedes when police with tear gas , at times live bullets trying to stop demonstrations and gatherings.

   Rochelle Gutierrez also pointed out that mathematical critical thinking approach enlighten sociopolitical ideologies when the learners are allowed to discover their political position in the society. She advises teachers to use problem posing approach to let students reflect and find their position.This leads them to political awareness as said by Frankenstein [1989,1990,1995,2009] , Powell and Brantlinger [2008], Skovsmose [1994,2004]. The knowledge shall equip teachers to develop conscientizacao  in their students, meaning critical thinking produced through ones ability to analyze society from a political point of view . The views incorporate ones identity and being able to identify injustices in the world.

   Sociopolitical in Mathematics, translate to making sense of data to help see the humanity behind numbers and use this to expose and analyze injustices in the society , therefore convince others to a particular view.The frequent rigging of election in most African countries should come to end with the coming generation if they continue in the direction of sociopolitical turn in mathematics education.


Question:

By use of examples , state situations as teacher you can bring to an end of social injustice in the learning environment .

   

Response to a reading of Gerd Brandell. Giles Leder . Peter Nystrom on Gender and Mathematics: recent development from a Swedish perspective.

The experience were very healthy for establishing the correct analytical statistics in the gender response to mathematics education. In my experience as a mathematics teacher , I realized that in lower grades , girls tend to perform better in mathematics as compared to boys . There are topics in upper classes which I discovered that girls could do better while good performers amongst the boys experienced difficulties . For example graph work and geometry , girls were neat in their working and performed better . Problem solving in calculus posed difficulties to the girl child more in the upper classes .
      I have learnt from the reading that the gender disparity experienced in mathematics teaching with low grades from female learners is as result of encouragement to assume gender stereotype roles and behaviour from birth as stated by Lipman Bitumen [1984]. Female learners have received a huge global support and encouragement from the government and none governmental organizations in their education .This practice for some period now , has left boys to drag behind as Connel [1995] proves the fact in his writing . In Kenya , through UNICEF in collaboration with the government , have gone as far as coming up with course books for grades 4 & 5 written on cover page  in  Kiswahili " wasichana wote wasome " meaning all girls to learn. These books are meant for all pupils in class regardless of gender. Some boys have taken it negatively and tend not to take content serious as would be expected. Boy child have been left out and many pass through horrifying ordeal such as sodomy and suffers a lot in silence. I realized this due to the fact that I was a principal to a slum school with children from less fortunate society being given free lunch by world food program [WFP].

   In the new constitution which was passed [2010] in Kenya, a third gender rule is practised with resistance from all corners even parliament was trying to bend it by sneaking in some amendment because in  every county , there is a woman representative in the national assembly.This is  affecting the economy of the state. The rule is slowly taking roots in the country even the private sector. It is the duty of a mathematics teacher to encourage all learners to have positive attitude towards mathematics education. Mathematics books should be sensitive to gender stereotype issues and the teacher in the classroom should avoid taking
 some roles as a one gender activity.


Question


All inclusiveness teaching is mandatory to the present society where child rights is practised and corrections be made to previous culturally affected learners, design appropriate measures and steps you would display for an effective mathematics lesson as a teacher ?  

RESPONSE TO A READING FROM STEPHEN BROWN AND MARION WALTER ON PROBLEM POSING IN MATHEMATICS

   I totally agree that if mathematics is viewed or to be viewed as an act of liberation , then mathematics sensitivity ought to be recurrent themes which should be incorporated into peoples formal and informal mathematics experiences.These experiences are practiced on daily basis and the implementer emphases on it should be encouraged hence learners. The authors came up with ways of identifying these sensitivities more on pedagogical issues than mathematics context.

   -An irresistible problem solving drive; In 1980 was mentioned as the year of problem solving in mathematics but in actual fact it had always been termed as a problem solving discipline. Third world countries, mathematics education was directly introduced as problem solving discipline and this results dismal performance hence interest withdrawal. Students should be free to discover why a given formula is used in solving the problem.

   -Problems and their educational potential; The concept of problem is followed by solution, once the learners understand as to why is important for solution , need shall be developed to come up with a solution. This eliminate rote memory and substitute with reasoning, discovery and development of interest. Students may be encouraged to take a problem and create another into a solution instead of creating a solution to neutralize the problem. By so doing, solutions for other unexpected are reached in advance.

   -The interconnections of posing and solving; Posing and solving  relate to each other as parent to child.This is the stage of coming up with a formula, that is how I understood it, because in any given mathematics problem , there should be a procedure to be followed in order to come up with a solution, teachers are required to train students on point of posing then solve.

   -Coming up with problems; The writer advises on two ways of generating the problems either by accepting the given or challenging. Its true that when given a mathematics problem one is to either solve it or notice its irrelevancy. In my experience teaching mathematics to Kenya certificate of primary education [KCPE] candidates who are 13 years , I realized  this stage of importance  where learners have to understand question clearly before the start for solution..It encompass dimension of problem posing and the process of analyzing the question. Gorge Bernard Shaw once wrote "you see things and you say why? but dream things that were never and say why not ?"

   -Social context of learning; This is  group discussion which practically assist in acquisition of mathematical concepts , once I grouped first learners with slow and went round monitoring learning procedure, was fascinated to the way learners were using  terms best known to them while explaining a concept ,In some cases letting a student to solve a problem on chalk board  and then analyze with all the learners in class following each step and the student readily give explanation enhances learning.

RESPONSE TO ' Learning Mathematics through Birch Bark biting' Affirming indigenous identity. By Lunney Borden.

   Birch bark biting involves folding thin pieces of bark and biting shapes into the bark to create designs. When folding the learners think of fractions, angles , symmetry and creating designs.  Lunney Borden focused his study on the Mi'kmaw community found in the Atlantic Canada who used to practise the tradition art of birch bark biting over many years. In 2010, He concluded that disconnect between school based mathematics and Mi'kmaw ways of reasoning mathematically can impact mathematics learning for their  students.
   The introduction of "Show Your Maths" [SYM] to the Mi'kmaw students was a very fascinating idea used to encourage  and improve mastery of mathematics concepts. It developed sense of wholeness which resist fragmentation and created quality mathematics experiences amongst the learners. This inspired Doolittle [2006] and said that it helps in considering how we might be able to pull mathematics into indigenous culture rather than mathematics to be pushed into culture or culture to be pulled into mathematics. This idea is quite encouraging and should be used by teachers especially in many parts of Africa where education is still treated as means of robbing culture. The Turkana of Kenya perceive educated members of their clans as people who do disappears to the major towns, marry from the other tribes, and men who are not able to carry on with traditions of raiding neighbouring tribes off livestock which they very much value and for the girls , cannot move further in search of education since they are married off at a very early age. This practise cut across many African tribes eg Masai,Borana, Samburu, Pokot of Kenya and Karamojong of uganda.When using this method one has to explore practises relevant to the community.
   Mathematics can be pulled in through identifying types of reasoning inherent in the community that can help students to make sense of school based mathematics. It also means creating learning experiences that helps learners realise that mathematical reasoning is part of their daily life experience and has been in existence for generations.
   

     QUESTION

Explain how mathematics can be pulled to indigenous culture in a multicultural class ?

MY RESPONSE TO READING FROM PAULUS GARDEN ON ''FROZEN MATHEMATICS'' AND GEOMETRY.

The article confronts a widespread prejudice about mathematical knowledge that mathematics is ''culture free''. This is proved by demonstrating alternative construction of geometrical shapes developed from traditional culture of human kind.
     In most cases in the third world countries ,post independence education has not succeed in appeasing thirst for knowledge of its people.Although there have been a drastic increase in the number of students population in schools,the current over crowded classes brought by millennium goal of free universal primary education,shortage of teachers and lack of teaching/learning materials have always contributed to the low level of concept attainment in mathematics education. The post colonial government practically planted mathematics curriculum from industrialised countries, thus ending up mathematics being taken as an entry point to the university education.
    Mathematics is therefore structured in the interest of the social elite, leaving out the indigenous mathematical skills which was rich in very many aspects.Mathematics education is so far referred to as the most effective filter as put by El Tom.
    Mathematics education is used as a barrier to social access, no any other subject in school serves so well this filtering purpose of reinforcement of power structure as does mathematics. In African culture, a girl child was taken as a source of acquiring wealth through payment of dowry by the suitor, to the few who managed to access education early days, were discouraged in performing well in mathematics and termed as a boy oriented subject.This trend is still visible in schools especially Kenya and Uganda where I have experienced.
    A case study in  Mozambique which is a replica to many of third world countries, mathematics is mainly taught by teachers who are a bully with harsh punishments and as a result most learners don't like the subject. The curriculum formulators have been forced to make mathematics a compulsory subject, the methods used is rote memory whereby learners are forced to recite mathemathecal tables and other formulae.
    Experiment showed that a native adult African Kpellen tribe in the remote part of Mozambique performed better than an adult North American when solving problems like approximation of number of rice fullcups in a container.This definetly belongs to indigenous mathematics,serious douts about the effectiveness of school mathematics teaching are also raised by Latin American researcher Eduado Luna of Dominican Republic, who posed a question if it is possible, but this happens frequently as shown by the Brasillian Carraher and Schlienmann,children,who knew before they went to school ,how to solve creatively arithmetical problems which they encountered in daily life eg at the market place, could later in the school, not solve the same problem ,they can not solve it with the method taught in the arithmetic class.This concludes that learned matheracy eliminates the so called spontaneous matheracy. An individual who manages perfectly well numbers, options, geometric forms, and notions, when facing completely new and formal approach to the same facts and needs, creates a psychological blockade which grows as a barrier  between the different modes of numerical and geometrical thought.How can this psychological blockade be avoided ?
   Gay and Cole became convinced that it is neccessary to investigate first the indigenous mathematics in order to build effective bridges from indigenous mathematics to the new mathematics to be introduced in schools.The teacher should begin with materials of the indigenous culture leading the learner to the use them in creative way and from there advance to the new school mathematics.
    The incoporation of ethnomathematics into the curriculum in order to avoid a psychological blockade should be embressed by teachers also elimination of related culture. Traditional form of education reflects accumulated experience and wisdom. It constitute not only biological and physical knowledge about the materials that are used, but also mathematical knowledge about properties and relation of circles, angles, rectangles, squares, polygons, cones, pyramids, cylinders and etc as displayed in WEAVING and BUILDING techniques.

QUESTION

How would you use ethnomathematic education as an introductory to a new mathematic lesson ?          

MY RESPONSE TO READING FROM WHEELER,WESHAR,BELL AND CALEB

Pearl defined research as a way of trying to solve a general problem by the use of many other specific questions to give partial answers to the general problem. Different people from different discipline work on quite different questions yet they are all aimed at progressing in the understanding of the general problem. This implies that answers collected from different people are analysed and compiled to give solution of solving certain mathematical concepts. This research method has prove to give significant positive results. Pearl also does not agree that solving mathematics problems require use of one particular mathematical research guideline, he encourages many researchers to come up with  genuine research program which will be accepted by many researchers and accumulated to gain continuity and progress. Mathematics has taken long since research was focused and directed towards its development. The last time was the period of new maths and then followed by the current back to basics,this express great disappointment to the public with the current situation in mathematics education.There is the growing need of people who can handle mathematics fluently and also mastering mathematics basic concepts as compared to mastering basic language skills.We are to ask ourselves, what could be the problem in learning mathematics as compared to the learning of natural language.In view of Pearl , the central problem of maths education is total ignorance about cognitive processes involved in acquisition of mathematics concepts.The effort put by curriculum innovators did not fulfil hopes that accompanied introduction of schools.Research for it to achieve good result and make learning mathematics simple, easy and enjoyable, it has to concentrate in understanding the process involved in acquisition of mathematics as is in acquisition of natural language and other human skills which seems to be example of a successful learning.They need to use psychological or sociological questions while carrying out research. A call to educators is also required for them to try discover why a child acquire knowledge about abstract objects in ordinary language and what could be the parallel to it mathematically,how does one reason in ordinary language and what part are transferable in mathematics.These questions should be answered by examining the events of learning probably computing it, of recent scientist have been using this method though they are more concerned with formal description of theories and not acquisition of competence to describe things formally by means of maths.Allan Bell said that its obvious that what is taught is not what is learnt, giving example how pupils are taught several decimal places but end up solving few number of decimal places.This is why mathematical tables and use of calculater come in use.The learning of integers also give learners a lot of difficulties, as a result he suggest use of experimental teaching which has successfully been used and performed in relation to Piagetian conservationists. Inhelder,Sinclair,and Boret 1974 taught conservation of quantities and length and class inclusion obtained permanent gain and a transfer to untaught concepts. Gelman 1969 taught numbers and length using experimental method and had a spectacular success by presenting situation of shortfall and giving immediate feedback of correctness.    QUESTION. Do you agree that there is no a particular rule in formulation of mathematics research questions  give reason