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.
Hi James,
ReplyDeleteI can not see the question.
Sorry for quick publish, QUESTION;
ReplyDeleteThe steps above used to solve mathematics problem may not necessarily be followed in same sequence but teachers may use one or more approach while teaching mathematics problem solving concepts. How would curriculum implementer use or improve on the approach in a class room situation ?
MY RESEARCH INTEREST;
ReplyDeleteMy interest is why mathematics is poorly performed as compared to other disciplines by children of age ten to fourteen of primary schools in Kenya and why concentrated among less fortunate members of the society and more so the girl child.
Interesting question for your thesis, James! For your papers for this class, I would like you to choose one of the themes for our course that you see as the grounding or background for your question. The question you have raised seems possible to relate to at least two of our themes: social justice and equity in mathematics education, and gender and mathematics. (There might be other themes that relate to your question too!)
DeleteLook through the list of themes in our second draft course outline (posted on the blog on the first day of class) and then let me know which theme you will follow up on.
I think nowadays both teachers and scholars are involved in making and defining curriculum. It means, curriculum makers or implementers are aware of the most approaches that are in use in the classrooms. From my point of view, the mentioned methods equally are suitable and applicable. However, each might be applicable for some specific questions. For example, when teacher is asking a question that students already solved it’s similar one, she/he can ask one or some students to solve it on the chalk board. Otherwise, maybe it is better to talk about the question a little bit and explain variety aspect of its solution, then ask students to solve it. Sometime teacher can use a combination of both methods and while student is attempting to solve a question on the chalk board, teacher explain the question for all students. There is no doubt that teacher has an important role guiding students toward the solution and finding the answer. As a teacher, when I talk about a new question which is related to a new topic that my student did not see it yet, I start with helping student to understand the question and if it is possible bring some relevant examples. However, if the question is not completely new, I start asking questions to help student remembering the similar examples and solution. My experiences show me students mostly are not willing to solve a question on their own, they prefer having help and explanations. However, I think they need to learn how to solve a question when they do not have any help around. This ability help them to face the real life situations.
ReplyDeleteSharing problem posing in a classroom requires development of social and collaborative work skills for the students including creating a safe environment and risk taking. A philosophical community of inquiry approach with suspended judgement could be used. There would also need to be close attention to the individual needs of students, for support or challenge, that may be masked in a social context.
ReplyDeleteThe abstract and word based nature of problem posing can distract from practical, concrete applications or from visual-spatial mathematical thinking. However, links could be made to both of these. I am curious about opening up the possibility for mathematical problem posing using other than words.
I have found that when I develop problems in collaboration with students, narratives develop including jokes, creative segues, and emergent perspectives of mathematical thinking.
I think that looking at the learner, especially girls, helps to see what will work or not work. For instance, I was asking Ting about advice about teaching coding and he brought up the point that girls often do not want to disturb the peace. They have been socialized to agree and be nice. This is certainly something to consider as we are encouraging our students to critique or edit each other's work. (This was something I knew but it was a good reminder for me)
ReplyDeleteI really like the work of Ted Aoki. Some of his work is about the living curriculum and how we as teachers embrace the tension between what happens in 'real life' with students and what is in the curriculum. This in between space is where the possibilities are. The possibilities will look different depending on the learner and teacher and the tension or relationship between them as well.