Two-Dimensional Goal Description

Part of the Mathematics Education Library book series (MELI, volume 3)


The previous chapter described the permanent goals of mathematics education that are pursued by Wiskobas.


Mathematics Instruction Process Goal General Goal Counting Sequence Goal Approach 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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    However, the terms are often not interpreted in the same way. This can be demonstrated by the term “specific”. A large number of Dutch speaking authors (De Corte, Stroomberg, Huber, Pilot and others) use the term “specific” as a synonym for “concrete”. But sometimes the term is reserved for less concrete objectives (Westrhenen), or in reference to a different dimension and taken as the opposite of general objectives, similarly to abstractconcrete: Corte, E. de: Onderwijsdoelstellingen. Bijdrage tot de didaxologische theorievorming en aanzetten voor het empirisch onderzoek over onderwijsdoelen, Leuven 1973, p. 17. Stroomberg, H. P.: `Onderwijsdoelstellingen en doelstellingenonderzoek’, Pedagogische Studien 50(1973), p. 512.Google Scholar
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    It is quite a problem to discover what is the relationship between an objective and the set of tests by which it can be represented. Roughly speaking, if a formulated objective is taken as the starting point, the problem arises as to how this objective can be unfolded in sub-objectives that together cover the total objective, and how to refine these sub-objectives so that they become susceptible to measuring such that the envisaged thing is covered by what is actually measured. De Groot refers to this as the coverage problem, which in his opinion has not been solved by the common methods of measurement. He draws attention to the importance of students’ reporting and to formulations of objectives like “I have learned that”. This learning can apply to oneself as well as to the world around one. De Groot gives an important addition to common methods of measurement, which can also be applied to mathematics. Groot, A. D. de: `Over fundamentele ervaringen: Prolegomena tot een analyse van gesprekken met schakers’, Pedagogische Studien 51(1974), 329–349.Google Scholar
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    This interpretation of process goals is in accordance with what is often encountered in literature on the subject. However, a few other meanings are attributed to the term process goals.Google Scholar
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    Many of the authors quoted agree on this point: Klauer, McAshan, De Corte and De Groot. See also Note 49.Google Scholar
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    Taxonomies that show agreement with Wood’s are: “Educational Testing Service” (USA), “The Indian National Council of Educational Research Classification” (India), the classification of “The Schools Mathematics Study Group” and “The International Study of Achievements in Mathematics” (Husn, Sweden). Here is a short explanation of Wood’s classification:Google Scholar
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    For this terminology see Rasche, H.: De functie van doelstellingen in een leerplan’, Pedagogische Studin 50 (1973), p. 530.Google Scholar
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    See Notes 39 and 43 and also: Philp, H.: `Mathematical education in developing countries; some problems of teaching and learning’, in Howson, A. G. (ed.), Developments in mathematical education, Cambridge 1973, pp. 154–181.Google Scholar
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    For such a strict approach to product goals see: Corte, E. de, and Janssens, A.: Praktische leidraad voor het formuleren van leerdoelen, Leuven 1974.Google Scholar
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    The inadequacy of this strict approach is most clearly evident in Klauer. See the remarks in Note 27.Google Scholar
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    See for example: Greenberg, H. J.: `The objectives in mathematics education’, The Mathematics Teacher 67 (1974), 639–644. Steiner, H. G.: `Mathematics curriculum development in the USA. A look at the past twenty years’, Zentralblatt fiir Didaktik der Mathematik 8 (1976), 136–141.Google Scholar
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    This source of misunderstanding is also found in the above mentioned work by Wilson: placing certain test items under certain categories is, disregarding the actual instruction given, very arbitrary. Sullivan has also referred to this. See Sullivan, H. J.: `Objectives, evaluation, and improved learner achievement’, in Popham, W. J. (ed.), Instructional objectives, Chicago 1969, p. 94.Google Scholar
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    Wijdeveld, E.: Vierkubers, IOWO curriculum development publication 5, Utrecht 1977. Goffree, F.: `Kijk op kans. Proefwerk nieuwe stijl’, Wiskobas Bulletin2 (1973), 907–919. b0 Popham, W. J., E.sner, E. W. et al.: Instructional Objectives, Chicago 1969, p. 35.Google Scholar
  56. 60.
    De Block on “expressive objectives”: It is clear that we are concerned here with a description of the learning process, not the learning objectives. Of course this does not exclude that sometimes we do not know what the actual result of certain intended objectives will be. Nor does this mean that the learning process (subject matter, methods and media) is of no importance. Eisner does not make sufficient distinction between the learning objectives and the learning process and thus comes to his highly disputable theses. (Block, A. de: Taxonomie van leerdoelen, Antwerp 1975, p. 157.)Google Scholar
  57. 61.
    De Groot does not use the term process goals, but what he says about the subjective aspect of objectives, the pursuit of general objectives and the fact that the affective domain is no separate domain, but is of a cognitive nature, fits within the terms of process and product goals. His ideas on evaluation can therefore well be applied to the evaluation of process and product goals. We have in mind especially his “student reporting” in the form of “I have learned that See: Groot, A. D”. de: Hoe stelt men eindtermen op? Universiteit en Hogeschool 20 (1974), 213–233.Google Scholar
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Copyright information

© D. Reidel Publishing Company 1987

Authors and Affiliations

  1. 1.Mathematics Education Research Group (OW & OC)State University of UtrechtThe Netherlands

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