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