Assignment Teaching and Learning of School Mathematics

8/2/2019 Assignment Teaching and Learning of School Mathematics

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ACE MATHEMATICS

CURRICULUM B

ASSIGNMENT

Student: Faiq SalieStudent no.: SLXMOG013Lecturer: Derek Gripper


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FAILING BY EXAMPLE: INITIAL REMARKS ON THE CONSTITUTION OFSCHOOL MATHEMATICS, WITH SPECIAL REFERENCE TO THETEACHING AND LEARNING OF MATHEMATICS IN FIVE SECONDARYSCHOOLS

In their 2007 research paper Davis and Johnson have formulated what theycall a methodological framework to develop analytical descriptions for theteaching of mathematics. This serves as an attempt to describe what can betermed as mathematics in schools today.

According to Davis and Johnson:

Mathematics teaching and learning mainly happens throughthe use of worked examples to demonstrate the applicationof standard procedures.

Students struggled to reproduce the application of the

standard procedures they were expected to learn. Teachers and students worked at a slow pace.

The following hypotheses are presented by Davis and Johnson which sumsup their findings in the mathematics classes that they observed.

ContrastingIn contrasting we find some positives emerging from Davis and Johnsonsresearch exploring the fact that we might not be giving the proper basics.

The goalSystematically defines the research problem and the production of researchhypotheses.

The revelationWith their observations they reveal that the pace of teaching and learning isslow but that students fail to learn the content adequately.

The problemThe problem centres on the absence of explicit operation of mathematicalgrounds to support the elaboration of standard procedures.

The findingsAccording to the researchers these hypotheses open up a series of lines ofinvestigation that are being pursued currently.

These hypotheses formulate The constitution of mathematics in the teachingand learningof high school mathematics.


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Designing Intervention Strategies by raising questions based on theirobservations.With this they aim to generate a general description of mathematics teachingto inform the design of intervention strategies aimed at improving the qualityof mathematics teaching in the schools.

They consider as interrelated questions:(1) What is constituted as mathematics in the five schools?(2) How is it constituted?

Mathematics lessons were observed to generate analytical descriptions of theteaching of mathematics in each school. With findings such as that, teachingand learning was happening almost exclusively through the elaboration ofworked examples to demonstrate the application of standard procedures;students struggled to reproduce the application of these standard proceduresthey were expected to learn; and both teachers and students generally

worked at a slow pace.

Poor exposition of principles and little explicit ideas, being rehearsed.

Examples that were used are sited in this regard are:(1) Exposition by teachers demonstrating the worked examples.(2) By students working at a slow pace.(3) Classroom time spent on activity not related to the topic of a lesson.

What became apparent was that the bulk of classroom lessons were spent onthe elaboration of mathematics through worked examples.Distinctions made between individual classes as well as between individualteachers, revealed that the time spent on worked examples and time spentexplicitly on the elaboration of ideas, principles and definitions, from which itbecame apparent that the way in which time is used in the different gradesacross the schools is very similar.

The question that arose in response to their observation of the use of time inschools was: Why should it be the case that students struggle withmathematics? To them a disturbing trend in average time spent per problemin schools where the average time increases might be indicating that the

deficiencies in the students knowledge of mathematics becomes moreapparent at grade 12 level where they start working on typical problems foundin school leaving examination papers. According to Davis and Johnson theaverage time per worked example per grade for each school in terms of theuse of time, does not enable them to understand what is happening in theteaching and learning of mathematics or explain why students struggle eventhough they apparently have sufficient time to learn the content.


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The reflection.Their reflection on the question as a result of the research has enabled themto comment on the relation between teaching and learning time and studentfailure in the context of the education of working class children.A number of research studies that attempt to reveal the pedagogic conditions

contributing to successful learning outcomes for working class studentsindicate that a slowing of pacing is a commonly occurring theme.One conclusion derived from the extensive body of research produced by theESSA group is that the control of pacing should be weakened so that studentscan slow pacing when they need to do so.

According to Davis Johnson a weak pacing and coherence that limitsstudents opportunities to learn persistently characterize many of the systemshigh-poverty schools (Smith, Smith & Bryk, 1998: 27).Therefore strictly speaking, weakly framed pacing allows pace to speed upand slow down as dictated by students needs. This however, indicates that a

slowing of pace is essential for working class students. Davis paraphrases,Morais Bernsteinian language, the first part of her statement asserts that it isessential that students are able to vary the pace when they need to, approachteachers when they need assistance, shift between academic and non-academic (everyday and metaphorical) expressions of knowledge, and beable to interact with others, including the teacher, freely.

They conclude that reflection arrives at a point indicating that the furtherpursuit of their study demands a focus on investigating the relations betweenevaluative criteria and pacing. In order to do so, they need to develop the useof the notion of evaluative criteria. Stating that mathematics is constitutedthrough the operation of evaluative criteria, as is the particular specialisationof consciousness that might be vaguely referred to as mathematical thinking?

Evaluative criteria are productive of what comes to be mathematics in apedagogic context as well as productive of the particular manner of thinkingmathematics in that context. They also suspect that the absence of explicitattention to mathematical grounds in evaluative criteria will produce a seriesof negative effects that slow pacing because the mathematics constitutedwill be generally inconsistent and hence unstable.

In presenting the effects Davis and Johnson expects to find as hypothesesthat:

(1) Procedures will tend to constitute mathematical notions as effectsrather than being grounded by such notions, resulting in inconsistentnotions that, therefore, cannot be generalised successfully;

(2) The imageof the various solution procedures students are exposed towill function as the chief supporting ground for student work onproblems, because what step to do next according to worked

examples.


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(3) The lack of stability of the notionsconstituted as mathematical notionscombined with the use of worked examples as the chief ground supportfor the production of solutions, will produce mathematics as highlycontextualised, making it difficult for students to transfer knowledgegained in the context elaboration of one class of solution.

Kallaways findings on the failing of OBE

Kallaway makes a good argument against the current educational system. Hisanalyses of the current state of education are insightful in terms of OBEconstructivist knowledge (knowledge crafted in your own back yard) which inmy opinion have now become back yard knowledge. In his analyses of theproblem Kallaway very skilfully takes the reader through the changes of theold apartheid CNE educational system to our current OBE system of

education. He shows a good understanding of the motivation behind theabandoning of the old system albeit throwing the baby out with the bathwater in desperation of changing what was thought to be a mind suppressing and oppressive system of education. His analyses of not only the difficulty ofeducators coping with a system that like the youth of today feeds onresources but also lack of understanding and training to coping with largeclasses and unruly learners while corporal punishment have been abolished isvery well crafted. I like that he mentions the fact that educators are no longerrulers of their domain but facilitators facilitating learners who have a wealth ofrights but remain irresponsible and unmotivated. My problem with hisreasoning on what is to be done is that he assumes that the government isunaware of the fact that Rome is burning!If educators are aware of this fact and by virtue of being in the employ of theDepartment of Education and very rarely are able to affect policy, what then isto be done if an educator has to follow DOE policy and practice?

CAPS (CURRICULUM AND ASSESSMENT POLICY STATEMENT)

The CAPS document essentially does not propose to change the currentcurriculum by a very large degree and therefore cannot be taken seriously in

light of the shortcomings of the current curriculum. The CAPS do not addressmathematics as a field on its own but tries to integrate it with the learnerssocial environmental, cultural an economic relations, recognising mathematicsis a creative part of human activity. This idea of integrated mathematics hasseriously damaged the subject as a science and has confused learners andeducators alike. The document tries to improve the content understandingand delivery by reintroducing the laws of mathematics eg. axioms, formulatingconjectures and definitions.


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Conclusion

The findings of Davis and Johnson make for good research and are helpful inidentifying the problems experienced in teaching mathematics specifically and

teaching in general. Their research however do not offer much in solving thecurrent crises in mathematics teaching and learning. In reply to Mr. Kallawaywho still has faith in changing the system via change in policy. My theory isthat education falls in line with any governments macroeconomic policy; it istherefore motivated and ruled by economic practices. South Africa havebecome part of the western capitalist global economy and the trend most ofthe major western countries i.e. The U.S. and Britain are following, is to cutdown on health and education. No capitalist country can survive without aviable and reliable labour force. The curriculum (that) was (therefore)manipulated in ways which intended to promote apartheid ideology1 is nowbeing used to create a viable and reliable workforce for our new capitalist

masters.

My challenge to educators is this. Given the fact that we moan and cry oftenthat what we see and experience is detrimental to education as a whole andlearning in general, what are we prepared to do? If our assessment of theproblem compels us to work outside the DOEs framework are we prepared todo so openly or secretly and as a united front?

Bibliography

Zain Davis, Yusuf Johnson , School of Education, University of CapeTown,

Peter Kallaway, Emeritus Professor of Education, UWC, ResearchAssociate, UCT, This is no this is no time to fiddle as education isburning; Cape Times 7 Sept. 2009

CAPS (CURRICULUM AND ASSESSMENT POLICY STATEMENT)- Mathematics Senior Phase

1. Peter Kallaway: This is no this is no time to fiddle as education isburning; Cape Times 7 Sept. 2009

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Assignment Teaching and Learning of School Mathematics