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\fs20\lang2057\langfe1033\cgrid\langnp2057\langfenp1033 {\b\fs28 A \lquote Real World\rquote  example of Probability: An Investigation into Students\rquote  Constructs of Relevance.}{\fs28 
\par David Kay Harris.
\par University of Bristol Graduate School of Education.
\par }\pard \ql \li0\ri0\sa120\sl-320\slmult1\widctlpar\faauto\adjustright\rin0\lin0\itap0 {\i\fs24 This paper reports on a qualitative study that investigated the constructs of relevance that students in an International School had during a \lquote real-world
\rquote  application. The study, initially intended to illuminate relationships between relevance and involvem
ent, widened to include interesting values revealed by students during interviews. The findings suggest that properties of relevance are highly individual and that similar attempts to offer \lquote relevant\rquote 
 activities would be enhanced by understanding students\rquote  values and how they relate to the types of activities they participate in.}{\fs28 
\par This paper focuses on an attempt to make the study of probability relevant by situating it in a \lquote real world\rquote  context. The author was motivated by a feeling that his teaching of thi
s topic was mechanistic; producing students skilled in applying techniques, but possessing neither interest in nor awareness of wider issues about this topic.The themes of utility and reality in mathematics education are familiar: 
\par {\pntext\pard\plain\f3\lang2057\langfe1033\langnp2057 \loch\af3\dbch\af0\hich\f3 \'b7\tab}}\pard \ql \fi567\li0\ri0\sa120\sl-320\slmult1\widctlpar{\*\pn \pnlvlblt\ilvl0\ls1\pnrnot0\pnf3\pnstart1\pnindent-851 {\pntxtb \'b7}}
\faauto\ls1\adjustright\rin0\lin0\itap0 {\fs24 A submission to the Cockcroft Report (1982) included \'93Mathematics lessons in \tab \tab \tab secondary schools are very often not about anything. You collect like terms, or learn the laws \tab 
of indices, with no perceptions of why anyone needs to do such things.\'94 (paragraph 462)
\par {\pntext\pard\plain\f3\lang2057\langfe1033\langnp2057 \loch\af3\dbch\af0\hich\f3 \'b7\tab}}\pard \ql \fi567\li0\ri0\sa120\sl-320\slmult1\widctlpar{\*\pn \pnlvlblt\ilvl0\ls1\pnrnot0\pnf3\pnstart1\pnindent-851 {\pntxtb \'b7}}
\faauto\ls1\adjustright\rin0\lin0\itap0 {\fs24 \'93Learning Mathematics is enhanced when content is placed in context.\'94 NCTM (1998)}{\fs28 
\par }\pard \ql \li0\ri0\sa120\sl-320\slmult1\widctlpar\faauto\adjustright\rin0\lin0\itap0 {\fs28 
Fruedenthal (1973) invokes an image of a teacher who is keen to address the concerns in the Cockcroft report, but nevertheless falls back to familiar patterns of teaching: \'93..in many t
extbooks on probability, the world of non-mathematical creatures is only a figleaf to cover the nakedness of pure mathematics. After a realistic motivation, one flies as fast as one can into the safe harbour of mathematical formalism and relegates reality
 into the quarantine of examples and problems\'94 (p583). There are familiar causes for this which come to mind, perhaps the most likely being curriculum pressures: \'93Coverage is the killer of curriculum inquiry.\'94
 (Jacobs 1998) (p28). In this study, an attempt is made to cross this rubicon.
\par INVOLVEMENT AND RELEVANCE:
\par Dealing with \lquote real-world\rquote  tasks presents problems for both teacher and student. Authentic problems in the \lquote real world\rquote  can include other factors related to their context -or \lquote noise\rquote  - and are rarely
 clear-cut. Cooper (1994) has written of students having to ignore such noise in order successfully to complete \lquote real-world\rquote  tasks, and Vershaffe (1996) has written of student teachers\rquote  \'93
strong tendency to exclude real-world knowledge from their own spontaneous solutions of school word problems as well as from their appreciations of the pupil answers\'94
 (p 387). These findings perhaps suggest subliminal messages in mathematics education that it at best has a loose fit with reality; as Ainley (1997) counsels, the terms \lquote real\rquote , \lquote reality\rquote  and \lquote real-life\rquote 
 are problematic. One may na\'efvely hold that importing a \lquote real-world\rquote  problem to the classroom may result in \lquote relevance\rquote  but this does not necessarily follow for Mason (1988:202): 
\par }\pard \ql \li510\ri0\sa120\sl-320\slmult1\widctlpar\faauto\adjustright\rin0\lin510\itap0 {\fs24 \'93When pupils ask \lquote Why are we doing this?\rquote  they are rarely satisfied by a reply of the form \lquote It is important in the steel industry
\rquote  In fact, they are usually not asking a question at all, but rather making a plea for help, because they have lost contact with the content of the class. It is not \lquote relevance\rquote 
 in the utilitarian sense that is sought, but rather a statement that they are no longer coping. I claim that most attempts to \lquote make mathematics relevant to pupils\rquote  are misconceived and doomed to failure, because relevance is not a property
 of mathematics, nor of its application to a particular physical context. Relevance is a property of an appropriate correspondence between qualities of some mathematical topic and qualities of the perceiver. Relevance is a relative notion: it describes a 
\lquote ratio\rquote 
 between aspects of the content and the pupil..... I suggest that if pupils become involved in some topic or question, then they see that what they are doing is relevant to them at the time, and conversely, if something seems relevant, then the way i
s open for involvement.\tab \tab }{\fs28 
\par }\pard \ql \li0\ri0\sa120\sl-320\slmult1\widctlpar\faauto\adjustright\rin0\lin0\itap0 {\fs28 Mason\rquote s two implications are as follows:}{\b\fs28 
\par }{\fs28 (Implication One)\tab \tab }{\b\i\fs28 If\tab }{\b\fs28 RELEVANCE\tab   }{\b\i\fs28 then\tab }{\b\fs28 INVOLVEMENT\tab 
\par }{\fs28 (Implication Two)\tab }{\b\i\fs28 If\tab }{\b\fs28 INVOLVEMENT }{\b\i\fs28 then}{\b\fs28 \tab RELEVANCE\tab \tab }{\i\fs28 
\par }{\fs28 It is suggested in this study that the apparent symmetry of these implications can be expanded - that they associate with different }{\b\fs28 relevance constructs}{\fs28 
. These are hypothetical models which, it is proposed, enable us to understand what characterises relevance for students. 
\par Relevance associated with Implication one will be called }{\i\fs28 Primary Relevance }{\fs28 and with the other }{\i\fs28 Secondary Relevance. }{\fs28 
The focus of the study now widens to include an investigation of different constructs for relevance in each Implication. The following list of constructs is proposed: 
\par }\pard \ql \fi-1530\li1530\ri0\sl-320\slmult1\widctlpar\faauto\adjustright\rin0\lin1530\itap0 {\fs28 Primary: \tab }{\fs28\ul Arousal}{\fs28 , }{\fs28\ul Control}{\fs28  and }{\fs28\ul Interest}{\fs28   
(The latter category includes the degree to which students }{\i\fs28 liked}{\fs28  the activity, found it }{\i\fs28 important}{\fs28  and their }{\i\fs28 ability}{\fs28  to perform it.) after Middleton and Spanias  (1999) ;
\par }\pard \ql \li0\ri0\sa120\sl-320\slmult1\widctlpar\faauto\adjustright\rin0\lin0\itap0 {\fs28 \tab \tab \tab }{\fs28\ul Needs}{\fs28  of }{\i\fs28 Self-Actualisation}{\fs28  or }{\i\fs28 Esteem}{\fs28  after Maslow (1954) 
\par \tab together with the author\rquote s own proposals:
\par }\pard \ql \li1530\ri0\sl-320\slmult1\widctlpar\faauto\adjustright\rin0\lin1530\itap0 {\fs28\ul Desire to Know:}{\fs28  a subset of }{\fs28\ul Curiosity,}{\fs28  which supplements the latter with active inquisitiveness; 
\par }\pard \ql \li1530\ri0\sa120\sl-320\slmult1\widctlpar\faauto\adjustright\rin0\lin1530\itap0 {\fs28\ul Duty}{\fs28 : a passive construct - each task \lquote has to be done\rquote , is therefore briefly to the \tab fore of the student\rquote 
s experience and so is relevant; }{\fs28\ul Situation}{\fs28 : direct positive contribution to relevance from the task context,
\par }\pard \ql \li0\ri0\sa120\sl-320\slmult1\widctlpar\faauto\adjustright\rin0\lin0\itap0 {\fs28 \tab and:\tab 
\par }\pard \ql \li0\ri0\sl-320\slmult1\widctlpar\faauto\adjustright\rin0\lin0\itap0 {\fs28 Secondary:}{\b\i\fs28  \tab }{\fs28\ul Ownership}{\i\fs28\ul :}{\i\fs28  }{\fs28 eg. students arguing about an activity as they enter class; \tab \tab \tab }{\fs28\ul 
Willingness to Communicate:}{\fs28  Eg. prolific writing in coursework; \tab \tab \tab \tab }{\fs28\ul (Resolved) Desire to Know:}{\fs28  Eg. satisfaction from solving a problem, \tab \tab \tab which may contribute to an 
\par }\pard \ql \li0\ri0\sa120\sl-320\slmult0\widctlpar\faauto\adjustright\rin0\lin0\itap0 {\fs28 \tab \tab \tab }{\fs28\ul Appreciation}{\fs28  of wider issues relating to mathematics.
\par }\pard \ql \li0\ri0\sa120\sl-320\slmult1\widctlpar\faauto\adjustright\rin0\lin0\itap0 {\fs28 THE CASE STUDY: \'93BE A GENETIC COUNSELLOR\'94
\par The class consisted of 13 grade eleven students from 9 dif
ferent nationalities at an international school in London study for the International Baccalaureate Diploma, in which mathematics is compulsory for all years. One of the aims of their Mathematical Methods course is to \lquote 
apply skills and knowledge acquired in mathematics to other subject areas\rquote  (IBO, 1998). Most of the students had a strong background in Biology.
\par An application of probability theory to the laws of genetic inheritance was chosen because of its potential for dovetailing with probabilistic devices such as trees and tables. The activity, \lquote Be a Genetic Counsellor\rquote 
 (Kotelawala, 1997) involved students working in small groups to process a fictitious case file of a couple with a family history of a disease by calculating probabilities of simple, compo
und and conditional events. The author provided all necessary biological skills in Lesson One.
\par }\pard \ql \li0\ri0\sl-320\slmult1\widctlpar\faauto\adjustright\rin0\lin0\itap0 {\fs24 Lesson One:\tab Lecture on Mendel\rquote s laws of inheritance [20 mins], Introductory activity to practice \tab \tab \tab these laws\tab 
[20 mins], Video of the work of a Genetic Counsellor [20 mins]
\par }\pard \ql \li0\ri0\sa120\sl-320\slmult1\widctlpar\faauto\adjustright\rin0\lin0\itap0 {\fs24 Lesson Two:\tab \lquote Be a Genetic Counsellor\rquote \tab [60 mins]}{\fs28 
\par Conducting these lessons challenged the researcher, an experienced mathematics teacher with little biological knowledge. Preparation required collaboration with the Biology teacher and much reading in order to gain the level of competence necessary.

\par THE METHODOLOGY:
\par Since the first lesson comprised mostly of preparatory work, the main focus of the study was the second lesson. Triangulation of fieldnotes}{\b\fs28  }{\fs28 
written by the researcher, the teacher observer, and a student observer, formed a preliminary account. Taped group discussions were transcribed to reveal the nature of the discourse that students were involved in. A semi-structured interview schedule foll
owed up, for each interviewee, any emergent patterns in the above data and \lquote probed\rquote  for relevance constructs using a clinical interview method. At the start of each interview, students were exposed to the quotes: \'93
Mathematics lessons in secondary schools are very often not about anything\'94 and \'93When pupils ask \lquote Why are we doing this?\rquote  they are rarely satisfied by a reply of the form \lquote It is important in the steel industry\rquote \'94
. The interview guide \lquote funnelled\rquote  students into describing their perceptions of the acti
vity in relation to relevance. Scope was given for the interviewee to talk about what was important to him/her. Students were not exposed to the proposed list of relevance constructs. A thematic analysis of the interview transcripts was made using the pro
posed list, coding for primary and secondary relevance. The value statements required their own thematic analysis.
\par \lquote Be a Genetic Counsellor\rquote  was introduced with minimal input other than distribution of the case file and reference materials. The author wrote in his field notes: \'93Pleased with my behaviour...ideas in solutions }{\fs28\ul are}{\fs28 
 those of the students\'94 A \lquote hands-off\rquote  behaviour was maintained to avoid interference in students\rquote  experiences of relevance constructs. The teacher observer wrote \'93All groups continued 
to question their initial assumptions well after the 1/2 hour had passed\'94 and the researcher wrote \'93Involved in Bio noise at 11.35\'94 in his triangulation document. Even from a distance, \'93a level of sophistication which is pre-expertise\'94
 was observed in the probabilistic discourse, as was \'93Involvement! Lots of it!\'94
 Discussions occasionally crossed group boundaries, or took place at the whiteboard. All three triangulation observers reported task-related arguments amongst students. Students\rquote  work was collected 
and examined. The groups scored 2, 2, 2 and 3 correct responses from a possible 6. These groups used tree diagrams in 1, 2, 1 and 3 instances from a possible 3 questions whose successful completion could have been so aided. Every group turned in responses
 to all questions. Biology skills had been mastered - even amongst the non-biologists - as successful individual work handed in after the introductory activity in Lesson One demonstrated.
\par }{\fs24 Analysis of the interview transcripts revealed these values}{\fs28 :
\par }\trowd \trgaph108\trbrdrt\brdrs\brdrw15 \trbrdrl\brdrs\brdrw15 \trbrdrb\brdrs\brdrw15 \trbrdrr\brdrs\brdrw15 \trbrdrh\brdrs\brdrw15 \trbrdrv\brdrs\brdrw15 \trftsWidth1\trpaddl108\trpaddr108\trpaddfl3\trpaddfr3 \clvertalt\clbrdrt\brdrs\brdrw15 \clbrdrl
\brdrs\brdrw15 \clbrdrb\brdrs\brdrw15 \clbrdrr\brdrs\brdrw15 \cltxlrtb\clftsWidth3\clwWidth1418 \cellx1418\clvertalt\clbrdrt\brdrs\brdrw15 \clbrdrl\brdrs\brdrw15 \clbrdrb\brdrs\brdrw15 \clbrdrr\brdrs\brdrw15 \cltxlrtb\clftsWidth3\clwWidth3402 \cellx4820
\clvertalt\clbrdrt\brdrs\brdrw15 \clbrdrl\brdrs\brdrw15 \clbrdrb\brdrs\brdrw15 \clbrdrr\brdrs\brdrw15 \cltxlrtb\clftsWidth3\clwWidth4261 \cellx9081\clvertalt\clbrdrt\brdrs\brdrw15 \clbrdrl\brdrs\brdrw15 \clbrdrb\brdrs\brdrw15 \clbrdrr\brdrs\brdrw15 
\cltxlrtb\clftsWidth3\clwWidth557 \cellx9638\pard \ql \li0\ri0\sa120\sl-320\slmult1\widctlpar\intbl\faauto\adjustright\rin0\lin0 {\b\fs24 Value}{\fs24 \cell }{\b\fs24 Defined}{\fs24  as a statement that;\cell An }{\b\fs24 observed example}{\fs24 
 of which is;\cell }\pard \qc \li0\ri0\sa120\sl-320\slmult1\widctlpar\intbl\faauto\adjustright\rin0\lin0 {\fs24 Fq.\cell }\pard \ql \li0\ri0\widctlpar\intbl\aspalpha\aspnum\faauto\adjustright\rin0\lin0 {\fs24 \trowd \trgaph108\trbrdrt\brdrs\brdrw15 
\trbrdrl\brdrs\brdrw15 \trbrdrb\brdrs\brdrw15 \trbrdrr\brdrs\brdrw15 \trbrdrh\brdrs\brdrw15 \trbrdrv\brdrs\brdrw15 \trftsWidth1\trpaddl108\trpaddr108\trpaddfl3\trpaddfr3 \clvertalt\clbrdrt\brdrs\brdrw15 \clbrdrl\brdrs\brdrw15 \clbrdrb\brdrs\brdrw15 
\clbrdrr\brdrs\brdrw15 \cltxlrtb\clftsWidth3\clwWidth1418 \cellx1418\clvertalt\clbrdrt\brdrs\brdrw15 \clbrdrl\brdrs\brdrw15 \clbrdrb\brdrs\brdrw15 \clbrdrr\brdrs\brdrw15 \cltxlrtb\clftsWidth3\clwWidth3402 \cellx4820\clvertalt\clbrdrt\brdrs\brdrw15 
\clbrdrl\brdrs\brdrw15 \clbrdrb\brdrs\brdrw15 \clbrdrr\brdrs\brdrw15 \cltxlrtb\clftsWidth3\clwWidth4261 \cellx9081\clvertalt\clbrdrt\brdrs\brdrw15 \clbrdrl\brdrs\brdrw15 \clbrdrb\brdrs\brdrw15 \clbrdrr\brdrs\brdrw15 \cltxlrtb\clftsWidth3\clwWidth557 
\cellx9638\row }\trowd \trgaph108\trbrdrt\brdrs\brdrw15 \trbrdrl\brdrs\brdrw15 \trbrdrb\brdrs\brdrw15 \trbrdrr\brdrs\brdrw15 \trbrdrh\brdrs\brdrw15 \trbrdrv\brdrs\brdrw15 \trftsWidth1\trpaddl108\trpaddr108\trpaddfl3\trpaddfr3 \clvertalt\clbrdrt
\brdrs\brdrw15 \clbrdrl\brdrs\brdrw15 \clbrdrb\brdrs\brdrw15 \clbrdrr\brdrs\brdrw15 \cltxlrtb\clftsWidth3\clwWidth1418 \cellx1418\clvertalt\clbrdrt\brdrs\brdrw15 \clbrdrl\brdrs\brdrw15 \clbrdrb\brdrs\brdrw15 \clbrdrr\brdrs\brdrw15 
\cltxlrtb\clftsWidth3\clwWidth3402 \cellx4820\clvertalt\clbrdrt\brdrs\brdrw15 \clbrdrl\brdrs\brdrw15 \clbrdrb\brdrs\brdrw15 \clbrdrr\brdrs\brdrw15 \cltxlrtb\clftsWidth3\clwWidth4261 \cellx9081\clvertalt\clbrdrt\brdrs\brdrw15 \clbrdrl\brdrs\brdrw15 
\clbrdrb\brdrs\brdrw15 \clbrdrr\brdrs\brdrw15 \cltxlrtb\clftsWidth3\clwWidth557 \cellx9638\pard \ql \li0\ri0\sa120\sl-320\slmult1\widctlpar\intbl\faauto\adjustright\rin0\lin0 {\fs24 \lquote Relate\rquote \cell relating maths to real life is desirable
\cell \'93The good thing about it was that we related it to real life\'94\cell }\pard \qc \li0\ri0\sa120\sl-320\slmult1\widctlpar\intbl\faauto\adjustright\rin0\lin0 {\fs24 5\cell }\pard 
\ql \li0\ri0\widctlpar\intbl\aspalpha\aspnum\faauto\adjustright\rin0\lin0 {\fs24 \trowd \trgaph108\trbrdrt\brdrs\brdrw15 \trbrdrl\brdrs\brdrw15 \trbrdrb\brdrs\brdrw15 \trbrdrr\brdrs\brdrw15 \trbrdrh\brdrs\brdrw15 \trbrdrv\brdrs\brdrw15 
\trftsWidth1\trpaddl108\trpaddr108\trpaddfl3\trpaddfr3 \clvertalt\clbrdrt\brdrs\brdrw15 \clbrdrl\brdrs\brdrw15 \clbrdrb\brdrs\brdrw15 \clbrdrr\brdrs\brdrw15 \cltxlrtb\clftsWidth3\clwWidth1418 \cellx1418\clvertalt\clbrdrt\brdrs\brdrw15 \clbrdrl
\brdrs\brdrw15 \clbrdrb\brdrs\brdrw15 \clbrdrr\brdrs\brdrw15 \cltxlrtb\clftsWidth3\clwWidth3402 \cellx4820\clvertalt\clbrdrt\brdrs\brdrw15 \clbrdrl\brdrs\brdrw15 \clbrdrb\brdrs\brdrw15 \clbrdrr\brdrs\brdrw15 \cltxlrtb\clftsWidth3\clwWidth4261 \cellx9081
\clvertalt\clbrdrt\brdrs\brdrw15 \clbrdrl\brdrs\brdrw15 \clbrdrb\brdrs\brdrw15 \clbrdrr\brdrs\brdrw15 \cltxlrtb\clftsWidth3\clwWidth557 \cellx9638\row }\pard \ql \li0\ri0\sa120\sl-320\slmult1\widctlpar\intbl\faauto\adjustright\rin0\lin0 {\fs24 \lquote 
Formalist\rquote \cell claims maths is relevant in any case since it encourages the rigorous structuring of one\rquote s thoughts\cell \'93Even if you\rquote re not going to use it, it\rquote s still very important because it shapes your mind\'94\cell 
}\pard \qc \li0\ri0\sa120\sl-320\slmult1\widctlpar\intbl\faauto\adjustright\rin0\lin0 {\fs24 5\cell }\pard \ql \li0\ri0\widctlpar\intbl\aspalpha\aspnum\faauto\adjustright\rin0\lin0 {\fs24 \trowd \trgaph108\trbrdrt\brdrs\brdrw15 \trbrdrl\brdrs\brdrw15 
\trbrdrb\brdrs\brdrw15 \trbrdrr\brdrs\brdrw15 \trbrdrh\brdrs\brdrw15 \trbrdrv\brdrs\brdrw15 \trftsWidth1\trpaddl108\trpaddr108\trpaddfl3\trpaddfr3 \clvertalt\clbrdrt\brdrs\brdrw15 \clbrdrl\brdrs\brdrw15 \clbrdrb\brdrs\brdrw15 \clbrdrr\brdrs\brdrw15 
\cltxlrtb\clftsWidth3\clwWidth1418 \cellx1418\clvertalt\clbrdrt\brdrs\brdrw15 \clbrdrl\brdrs\brdrw15 \clbrdrb\brdrs\brdrw15 \clbrdrr\brdrs\brdrw15 \cltxlrtb\clftsWidth3\clwWidth3402 \cellx4820\clvertalt\clbrdrt\brdrs\brdrw15 \clbrdrl\brdrs\brdrw15 
\clbrdrb\brdrs\brdrw15 \clbrdrr\brdrs\brdrw15 \cltxlrtb\clftsWidth3\clwWidth4261 \cellx9081\clvertalt\clbrdrt\brdrs\brdrw15 \clbrdrl\brdrs\brdrw15 \clbrdrb\brdrs\brdrw15 \clbrdrr\brdrs\brdrw15 \cltxlrtb\clftsWidth3\clwWidth557 \cellx9638\row }\pard 
\ql \li0\ri0\sa120\sl-320\slmult1\widctlpar\intbl\faauto\adjustright\rin0\lin0 {\fs24 \lquote Future\rquote \cell exhibits concern about the future usefulness of the content of maths lessons in one\rquote s life.\cell \'93
Like, Sine, Cosine and that..I don\rquote t think I\rquote m going to need it because I\rquote m not going into a field like architecture\'94\cell }\pard \qc \li0\ri0\sa120\sl-320\slmult1\widctlpar\intbl\faauto\adjustright\rin0\lin0 {\fs24 9\cell }\pard 
\ql \li0\ri0\widctlpar\intbl\aspalpha\aspnum\faauto\adjustright\rin0\lin0 {\fs24 \trowd \trgaph108\trbrdrt\brdrs\brdrw15 \trbrdrl\brdrs\brdrw15 \trbrdrb\brdrs\brdrw15 \trbrdrr\brdrs\brdrw15 \trbrdrh\brdrs\brdrw15 \trbrdrv\brdrs\brdrw15 
\trftsWidth1\trpaddl108\trpaddr108\trpaddfl3\trpaddfr3 \clvertalt\clbrdrt\brdrs\brdrw15 \clbrdrl\brdrs\brdrw15 \clbrdrb\brdrs\brdrw15 \clbrdrr\brdrs\brdrw15 \cltxlrtb\clftsWidth3\clwWidth1418 \cellx1418\clvertalt\clbrdrt\brdrs\brdrw15 \clbrdrl
\brdrs\brdrw15 \clbrdrb\brdrs\brdrw15 \clbrdrr\brdrs\brdrw15 \cltxlrtb\clftsWidth3\clwWidth3402 \cellx4820\clvertalt\clbrdrt\brdrs\brdrw15 \clbrdrl\brdrs\brdrw15 \clbrdrb\brdrs\brdrw15 \clbrdrr\brdrs\brdrw15 \cltxlrtb\clftsWidth3\clwWidth4261 \cellx9081
\clvertalt\clbrdrt\brdrs\brdrw15 \clbrdrl\brdrs\brdrw15 \clbrdrb\brdrs\brdrw15 \clbrdrr\brdrs\brdrw15 \cltxlrtb\clftsWidth3\clwWidth557 \cellx9638\row }\pard \ql \li0\ri0\sa120\sl-320\slmult1\widctlpar\intbl\faauto\adjustright\rin0\lin0 {\fs24 \lquote 
Utilitarian\rquote \cell Middle school mathematics is more useful than high school.\cell \'93The most important part of math is in middle school...in high school it\rquote s going too deep\'94\cell }\pard \qc \li0\ri0\sa120\sl-320\slmult1
\widctlpar\intbl\faauto\adjustright\rin0\lin0 {\fs24 2\cell }\pard \ql \li0\ri0\widctlpar\intbl\aspalpha\aspnum\faauto\adjustright\rin0\lin0 {\fs24 \trowd \trgaph108\trbrdrt\brdrs\brdrw15 \trbrdrl\brdrs\brdrw15 \trbrdrb\brdrs\brdrw15 \trbrdrr
\brdrs\brdrw15 \trbrdrh\brdrs\brdrw15 \trbrdrv\brdrs\brdrw15 \trftsWidth1\trpaddl108\trpaddr108\trpaddfl3\trpaddfr3 \clvertalt\clbrdrt\brdrs\brdrw15 \clbrdrl\brdrs\brdrw15 \clbrdrb\brdrs\brdrw15 \clbrdrr\brdrs\brdrw15 \cltxlrtb\clftsWidth3\clwWidth1418 
\cellx1418\clvertalt\clbrdrt\brdrs\brdrw15 \clbrdrl\brdrs\brdrw15 \clbrdrb\brdrs\brdrw15 \clbrdrr\brdrs\brdrw15 \cltxlrtb\clftsWidth3\clwWidth3402 \cellx4820\clvertalt\clbrdrt\brdrs\brdrw15 \clbrdrl\brdrs\brdrw15 \clbrdrb\brdrs\brdrw15 \clbrdrr
\brdrs\brdrw15 \cltxlrtb\clftsWidth3\clwWidth4261 \cellx9081\clvertalt\clbrdrt\brdrs\brdrw15 \clbrdrl\brdrs\brdrw15 \clbrdrb\brdrs\brdrw15 \clbrdrr\brdrs\brdrw15 \cltxlrtb\clftsWidth3\clwWidth557 \cellx9638\row }\trowd \trgaph108\trbrdrt\brdrs\brdrw15 
\trbrdrl\brdrs\brdrw15 \trbrdrb\brdrs\brdrw15 \trbrdrr\brdrs\brdrw15 \trbrdrh\brdrs\brdrw15 \trbrdrv\brdrs\brdrw15 \trftsWidth1\trpaddl108\trpaddr108\trpaddfl3\trpaddfr3 \clvertalt\clbrdrt\brdrs\brdrw15 \clbrdrl\brdrs\brdrw15 \clbrdrb\brdrs\brdrw15 
\clbrdrr\brdrs\brdrw15 \cltxlrtb\clftsWidth3\clwWidth1418 \cellx1418\clvertalt\clbrdrt\brdrs\brdrw15 \clbrdrl\brdrs\brdrw15 \clbrdrb\brdrs\brdrw15 \clbrdrr\brdrs\brdrw15 \cltxlrtb\clftsWidth3\clwWidth3402 \cellx4820\clvertalt\clbrdrt\brdrs\brdrw15 
\clbrdrl\brdrs\brdrw15 \clbrdrb\brdrs\brdrw15 \clbrdrr\brdrs\brdrw15 \cltxlrtb\clftsWidth3\clwWidth4261 \cellx9081\clvertalt\clbrdrt\brdrs\brdrw15 \clbrdrl\brdrs\brdrw15 \clbrdrb\brdrs\brdrw15 \clbrdrr\brdrs\brdrw15 \cltxlrtb\clftsWidth3\clwWidth557 
\cellx9638\pard \ql \li0\ri0\sa120\sl-320\slmult1\widctlpar\intbl\faauto\adjustright\rin0\lin0 {\fs32 \lquote real}{\fs24 /}{real}{\fs24 \rquote \cell discerns between qualities of \lquote real-life\rquote  tasks\cell \'93
I found it interesting..more than just solving a problem with just facts in and you have to solve it...rather than an actual situation\'94\cell }\pard \qc \li0\ri0\sa120\sl-320\slmult1\widctlpar\intbl\faauto\adjustright\rin0\lin0 {\fs24 5\cell }\pard 
\ql \li0\ri0\widctlpar\intbl\aspalpha\aspnum\faauto\adjustright\rin0\lin0 {\fs24 \trowd \trgaph108\trbrdrt\brdrs\brdrw15 \trbrdrl\brdrs\brdrw15 \trbrdrb\brdrs\brdrw15 \trbrdrr\brdrs\brdrw15 \trbrdrh\brdrs\brdrw15 \trbrdrv\brdrs\brdrw15 
\trftsWidth1\trpaddl108\trpaddr108\trpaddfl3\trpaddfr3 \clvertalt\clbrdrt\brdrs\brdrw15 \clbrdrl\brdrs\brdrw15 \clbrdrb\brdrs\brdrw15 \clbrdrr\brdrs\brdrw15 \cltxlrtb\clftsWidth3\clwWidth1418 \cellx1418\clvertalt\clbrdrt\brdrs\brdrw15 \clbrdrl
\brdrs\brdrw15 \clbrdrb\brdrs\brdrw15 \clbrdrr\brdrs\brdrw15 \cltxlrtb\clftsWidth3\clwWidth3402 \cellx4820\clvertalt\clbrdrt\brdrs\brdrw15 \clbrdrl\brdrs\brdrw15 \clbrdrb\brdrs\brdrw15 \clbrdrr\brdrs\brdrw15 \cltxlrtb\clftsWidth3\clwWidth4261 \cellx9081
\clvertalt\clbrdrt\brdrs\brdrw15 \clbrdrl\brdrs\brdrw15 \clbrdrb\brdrs\brdrw15 \clbrdrr\brdrs\brdrw15 \cltxlrtb\clftsWidth3\clwWidth557 \cellx9638\row }\pard \ql \li0\ri0\sa120\sl-320\slmult1\widctlpar\faauto\adjustright\rin0\lin0\itap0 {\fs24 
\par 
\par 
\par 
\par Analysis of the interview transcripts revealed the following evidence of primary relevance:}{\fs28 
\par }\trowd \trgaph108\trbrdrt\brdrs\brdrw15 \trbrdrl\brdrs\brdrw15 \trbrdrb\brdrs\brdrw15 \trbrdrr\brdrs\brdrw15 \trbrdrh\brdrs\brdrw15 \trbrdrv\brdrs\brdrw15 \trftsWidth1\trpaddl108\trpaddr108\trpaddfl3\trpaddfr3 \clvertalt\clbrdrt\brdrs\brdrw15 \clbrdrl
\brdrs\brdrw15 \clbrdrb\brdrs\brdrw15 \clbrdrr\brdrs\brdrw15 \cltxlrtb\clftsWidth3\clwWidth1134 \cellx1134\clvertalt\clbrdrt\brdrs\brdrw15 \clbrdrl\brdrs\brdrw15 \clbrdrb\brdrs\brdrw15 \clbrdrr\brdrs\brdrw15 \cltxlrtb\clftsWidth3\clwWidth7938 \cellx9072
\clvertalt\clbrdrt\brdrs\brdrw15 \clbrdrl\brdrs\brdrw15 \clbrdrb\brdrs\brdrw15 \clbrdrr\brdrs\brdrw15 \cltxlrtb\clftsWidth3\clwWidth567 \cellx9639\pard \ql \li0\ri0\sa120\sl-320\slmult1\widctlpar\intbl\faauto\adjustright\rin0\lin0 {\b\fs24 Type}{\fs24 
\cell An }{\b\fs24 observed example}{\fs24  of which is;\cell }\pard \qc \li0\ri0\sa120\sl-320\slmult1\widctlpar\intbl\faauto\adjustright\rin0\lin0 {\fs24 Fq.\cell }\pard \ql \li0\ri0\widctlpar\intbl\aspalpha\aspnum\faauto\adjustright\rin0\lin0 {\fs24 
\trowd \trgaph108\trbrdrt\brdrs\brdrw15 \trbrdrl\brdrs\brdrw15 \trbrdrb\brdrs\brdrw15 \trbrdrr\brdrs\brdrw15 \trbrdrh\brdrs\brdrw15 \trbrdrv\brdrs\brdrw15 \trftsWidth1\trpaddl108\trpaddr108\trpaddfl3\trpaddfr3 \clvertalt\clbrdrt\brdrs\brdrw15 \clbrdrl
\brdrs\brdrw15 \clbrdrb\brdrs\brdrw15 \clbrdrr\brdrs\brdrw15 \cltxlrtb\clftsWidth3\clwWidth1134 \cellx1134\clvertalt\clbrdrt\brdrs\brdrw15 \clbrdrl\brdrs\brdrw15 \clbrdrb\brdrs\brdrw15 \clbrdrr\brdrs\brdrw15 \cltxlrtb\clftsWidth3\clwWidth7938 \cellx9072
\clvertalt\clbrdrt\brdrs\brdrw15 \clbrdrl\brdrs\brdrw15 \clbrdrb\brdrs\brdrw15 \clbrdrr\brdrs\brdrw15 \cltxlrtb\clftsWidth3\clwWidth567 \cellx9639\row }\trowd \trgaph108\trbrdrt\brdrs\brdrw15 \trbrdrl\brdrs\brdrw15 \trbrdrb\brdrs\brdrw15 \trbrdrr
\brdrs\brdrw15 \trbrdrh\brdrs\brdrw15 \trbrdrv\brdrs\brdrw15 \trftsWidth1\trpaddl108\trpaddr108\trpaddfl3\trpaddfr3 \clvertalt\clbrdrt\brdrs\brdrw15 \clbrdrl\brdrs\brdrw15 \clbrdrb\brdrs\brdrw15 \clbrdrr\brdrs\brdrw15 \cltxlrtb\clftsWidth3\clwWidth1134 
\cellx1134\clvertalt\clbrdrt\brdrs\brdrw15 \clbrdrl\brdrs\brdrw15 \clbrdrb\brdrs\brdrw15 \clbrdrr\brdrs\brdrw15 \cltxlrtb\clftsWidth3\clwWidth7938 \cellx9072\clvertalt\clbrdrt\brdrs\brdrw15 \clbrdrl\brdrs\brdrw15 \clbrdrb\brdrs\brdrw15 \clbrdrr
\brdrs\brdrw15 \cltxlrtb\clftsWidth3\clwWidth567 \cellx9639\pard \ql \li0\ri0\sa120\sl-320\slmult1\widctlpar\intbl\faauto\adjustright\rin0\lin0 {\fs24 Desire to know\cell \'93
Maybe it was really simple but our group found it really complicated..I quite enjoyed that.\'94\cell }\pard \qc \li0\ri0\sa120\sl-320\slmult1\widctlpar\intbl\faauto\adjustright\rin0\lin0 {\fs24 3\cell }\pard 
\ql \li0\ri0\widctlpar\intbl\aspalpha\aspnum\faauto\adjustright\rin0\lin0 {\fs24 \trowd \trgaph108\trbrdrt\brdrs\brdrw15 \trbrdrl\brdrs\brdrw15 \trbrdrb\brdrs\brdrw15 \trbrdrr\brdrs\brdrw15 \trbrdrh\brdrs\brdrw15 \trbrdrv\brdrs\brdrw15 
\trftsWidth1\trpaddl108\trpaddr108\trpaddfl3\trpaddfr3 \clvertalt\clbrdrt\brdrs\brdrw15 \clbrdrl\brdrs\brdrw15 \clbrdrb\brdrs\brdrw15 \clbrdrr\brdrs\brdrw15 \cltxlrtb\clftsWidth3\clwWidth1134 \cellx1134\clvertalt\clbrdrt\brdrs\brdrw15 \clbrdrl
\brdrs\brdrw15 \clbrdrb\brdrs\brdrw15 \clbrdrr\brdrs\brdrw15 \cltxlrtb\clftsWidth3\clwWidth7938 \cellx9072\clvertalt\clbrdrt\brdrs\brdrw15 \clbrdrl\brdrs\brdrw15 \clbrdrb\brdrs\brdrw15 \clbrdrr\brdrs\brdrw15 \cltxlrtb\clftsWidth3\clwWidth567 \cellx9639
\row }\pard \ql \li0\ri0\sa120\sl-320\slmult1\widctlpar\intbl\faauto\adjustright\rin0\lin0 {\fs24 Control\cell \'93There were no constraints, you just handed it out and said try thinking about this..I like that system.\'94\cell }\pard 
\qc \li0\ri0\sa120\sl-320\slmult1\widctlpar\intbl\faauto\adjustright\rin0\lin0 {\fs24 2\cell }\pard \ql \li0\ri0\widctlpar\intbl\aspalpha\aspnum\faauto\adjustright\rin0\lin0 {\fs24 \trowd \trgaph108\trbrdrt\brdrs\brdrw15 \trbrdrl\brdrs\brdrw15 \trbrdrb
\brdrs\brdrw15 \trbrdrr\brdrs\brdrw15 \trbrdrh\brdrs\brdrw15 \trbrdrv\brdrs\brdrw15 \trftsWidth1\trpaddl108\trpaddr108\trpaddfl3\trpaddfr3 \clvertalt\clbrdrt\brdrs\brdrw15 \clbrdrl\brdrs\brdrw15 \clbrdrb\brdrs\brdrw15 \clbrdrr\brdrs\brdrw15 
\cltxlrtb\clftsWidth3\clwWidth1134 \cellx1134\clvertalt\clbrdrt\brdrs\brdrw15 \clbrdrl\brdrs\brdrw15 \clbrdrb\brdrs\brdrw15 \clbrdrr\brdrs\brdrw15 \cltxlrtb\clftsWidth3\clwWidth7938 \cellx9072\clvertalt\clbrdrt\brdrs\brdrw15 \clbrdrl\brdrs\brdrw15 
\clbrdrb\brdrs\brdrw15 \clbrdrr\brdrs\brdrw15 \cltxlrtb\clftsWidth3\clwWidth567 \cellx9639\row }\pard \ql \li0\ri0\sa120\sl-320\slmult1\widctlpar\intbl\faauto\adjustright\rin0\lin0 {\fs24 Duty\cell Well I don\rquote 
t want to be a Genetic Counsellor, but I knew I was helping your experiment so I tried to put some effort in.\cell }\pard \qc \li0\ri0\sa120\sl-320\slmult1\widctlpar\intbl\faauto\adjustright\rin0\lin0 {\fs24 2\cell }\pard 
\ql \li0\ri0\widctlpar\intbl\aspalpha\aspnum\faauto\adjustright\rin0\lin0 {\fs24 \trowd \trgaph108\trbrdrt\brdrs\brdrw15 \trbrdrl\brdrs\brdrw15 \trbrdrb\brdrs\brdrw15 \trbrdrr\brdrs\brdrw15 \trbrdrh\brdrs\brdrw15 \trbrdrv\brdrs\brdrw15 
\trftsWidth1\trpaddl108\trpaddr108\trpaddfl3\trpaddfr3 \clvertalt\clbrdrt\brdrs\brdrw15 \clbrdrl\brdrs\brdrw15 \clbrdrb\brdrs\brdrw15 \clbrdrr\brdrs\brdrw15 \cltxlrtb\clftsWidth3\clwWidth1134 \cellx1134\clvertalt\clbrdrt\brdrs\brdrw15 \clbrdrl
\brdrs\brdrw15 \clbrdrb\brdrs\brdrw15 \clbrdrr\brdrs\brdrw15 \cltxlrtb\clftsWidth3\clwWidth7938 \cellx9072\clvertalt\clbrdrt\brdrs\brdrw15 \clbrdrl\brdrs\brdrw15 \clbrdrb\brdrs\brdrw15 \clbrdrr\brdrs\brdrw15 \cltxlrtb\clftsWidth3\clwWidth567 \cellx9639
\row }\pard \ql \li0\ri0\sa120\sl-320\slmult1\widctlpar\intbl\faauto\adjustright\rin0\lin0 {\fs24 Situation\cell \'93It was a question with a meaning and so by answering it, you had a }{\b\fs24 reason}{\fs24  to do it.\'94\cell }\pard 
\qc \li0\ri0\sa120\sl-320\slmult1\widctlpar\intbl\faauto\adjustright\rin0\lin0 {\fs24 7\cell }\pard \ql \li0\ri0\widctlpar\intbl\aspalpha\aspnum\faauto\adjustright\rin0\lin0 {\fs24 \trowd \trgaph108\trbrdrt\brdrs\brdrw15 \trbrdrl\brdrs\brdrw15 \trbrdrb
\brdrs\brdrw15 \trbrdrr\brdrs\brdrw15 \trbrdrh\brdrs\brdrw15 \trbrdrv\brdrs\brdrw15 \trftsWidth1\trpaddl108\trpaddr108\trpaddfl3\trpaddfr3 \clvertalt\clbrdrt\brdrs\brdrw15 \clbrdrl\brdrs\brdrw15 \clbrdrb\brdrs\brdrw15 \clbrdrr\brdrs\brdrw15 
\cltxlrtb\clftsWidth3\clwWidth1134 \cellx1134\clvertalt\clbrdrt\brdrs\brdrw15 \clbrdrl\brdrs\brdrw15 \clbrdrb\brdrs\brdrw15 \clbrdrr\brdrs\brdrw15 \cltxlrtb\clftsWidth3\clwWidth7938 \cellx9072\clvertalt\clbrdrt\brdrs\brdrw15 \clbrdrl\brdrs\brdrw15 
\clbrdrb\brdrs\brdrw15 \clbrdrr\brdrs\brdrw15 \cltxlrtb\clftsWidth3\clwWidth567 \cellx9639\row }\pard \ql \li0\ri0\sa120\sl-320\slmult1\widctlpar\intbl\faauto\adjustright\rin0\lin0 {\fs24 Interest\cell \'93I never knew about \lquote Genetic Counsellor
\rquote  so that was really interesting.\'94\cell }\pard \qc \li0\ri0\sa120\sl-320\slmult1\widctlpar\intbl\faauto\adjustright\rin0\lin0 {\fs24 6\cell }\pard \ql \li0\ri0\widctlpar\intbl\aspalpha\aspnum\faauto\adjustright\rin0\lin0 {\fs24 \trowd \trgaph108
\trbrdrt\brdrs\brdrw15 \trbrdrl\brdrs\brdrw15 \trbrdrb\brdrs\brdrw15 \trbrdrr\brdrs\brdrw15 \trbrdrh\brdrs\brdrw15 \trbrdrv\brdrs\brdrw15 \trftsWidth1\trpaddl108\trpaddr108\trpaddfl3\trpaddfr3 \clvertalt\clbrdrt\brdrs\brdrw15 \clbrdrl\brdrs\brdrw15 
\clbrdrb\brdrs\brdrw15 \clbrdrr\brdrs\brdrw15 \cltxlrtb\clftsWidth3\clwWidth1134 \cellx1134\clvertalt\clbrdrt\brdrs\brdrw15 \clbrdrl\brdrs\brdrw15 \clbrdrb\brdrs\brdrw15 \clbrdrr\brdrs\brdrw15 \cltxlrtb\clftsWidth3\clwWidth7938 \cellx9072\clvertalt
\clbrdrt\brdrs\brdrw15 \clbrdrl\brdrs\brdrw15 \clbrdrb\brdrs\brdrw15 \clbrdrr\brdrs\brdrw15 \cltxlrtb\clftsWidth3\clwWidth567 \cellx9639\row }\trowd \trgaph108\trbrdrt\brdrs\brdrw15 \trbrdrl\brdrs\brdrw15 \trbrdrb\brdrs\brdrw15 \trbrdrr\brdrs\brdrw15 
\trbrdrh\brdrs\brdrw15 \trbrdrv\brdrs\brdrw15 \trftsWidth1\trpaddl108\trpaddr108\trpaddfl3\trpaddfr3 \clvertalt\clbrdrt\brdrs\brdrw15 \clbrdrl\brdrs\brdrw15 \clbrdrb\brdrs\brdrw15 \clbrdrr\brdrs\brdrw15 \cltxlrtb\clftsWidth3\clwWidth1134 \cellx1134
\clvertalt\clbrdrt\brdrs\brdrw15 \clbrdrl\brdrs\brdrw15 \clbrdrb\brdrs\brdrw15 \clbrdrr\brdrs\brdrw15 \cltxlrtb\clftsWidth3\clwWidth7938 \cellx9072\clvertalt\clbrdrt\brdrs\brdrw15 \clbrdrl\brdrs\brdrw15 \clbrdrb\brdrs\brdrw15 \clbrdrr\brdrs\brdrw15 
\cltxlrtb\clftsWidth3\clwWidth567 \cellx9639\pard \ql \li0\ri0\sa120\sl-320\slmult1\widctlpar\intbl\faauto\adjustright\rin0\lin0 {\fs24 Arousal\cell \'93Why are we talking about all this Biology?\'94\cell }\pard \qc \li0\ri0\sa120\sl-320\slmult1
\widctlpar\intbl\faauto\adjustright\rin0\lin0 {\fs24 2\cell }\pard \ql \li0\ri0\widctlpar\intbl\aspalpha\aspnum\faauto\adjustright\rin0\lin0 {\fs24 \trowd \trgaph108\trbrdrt\brdrs\brdrw15 \trbrdrl\brdrs\brdrw15 \trbrdrb\brdrs\brdrw15 \trbrdrr
\brdrs\brdrw15 \trbrdrh\brdrs\brdrw15 \trbrdrv\brdrs\brdrw15 \trftsWidth1\trpaddl108\trpaddr108\trpaddfl3\trpaddfr3 \clvertalt\clbrdrt\brdrs\brdrw15 \clbrdrl\brdrs\brdrw15 \clbrdrb\brdrs\brdrw15 \clbrdrr\brdrs\brdrw15 \cltxlrtb\clftsWidth3\clwWidth1134 
\cellx1134\clvertalt\clbrdrt\brdrs\brdrw15 \clbrdrl\brdrs\brdrw15 \clbrdrb\brdrs\brdrw15 \clbrdrr\brdrs\brdrw15 \cltxlrtb\clftsWidth3\clwWidth7938 \cellx9072\clvertalt\clbrdrt\brdrs\brdrw15 \clbrdrl\brdrs\brdrw15 \clbrdrb\brdrs\brdrw15 \clbrdrr
\brdrs\brdrw15 \cltxlrtb\clftsWidth3\clwWidth567 \cellx9639\row }\pard \ql \li0\ri0\sa120\sl-320\slmult1\widctlpar\faauto\adjustright\rin0\lin0\itap0 {\fs24 Analysis of the interview transcripts revealed the following evidence of secondary relevance:}{
\fs28 
\par }\trowd \trgaph108\trbrdrt\brdrs\brdrw15 \trbrdrl\brdrs\brdrw15 \trbrdrb\brdrs\brdrw15 \trbrdrr\brdrs\brdrw15 \trbrdrh\brdrs\brdrw15 \trbrdrv\brdrs\brdrw15 \trftsWidth1\trpaddl108\trpaddr108\trpaddfl3\trpaddfr3 \clvertalt\clbrdrt\brdrs\brdrw15 \clbrdrl
\brdrs\brdrw15 \clbrdrb\brdrs\brdrw15 \clbrdrr\brdrs\brdrw15 \cltxlrtb\clftsWidth3\clwWidth1701 \cellx1701\clvertalt\clbrdrt\brdrs\brdrw15 \clbrdrl\brdrs\brdrw15 \clbrdrb\brdrs\brdrw15 \clbrdrr\brdrs\brdrw15 \cltxlrtb\clftsWidth3\clwWidth7371 \cellx9072
\clvertalt\clbrdrt\brdrs\brdrw15 \clbrdrl\brdrs\brdrw15 \clbrdrb\brdrs\brdrw15 \clbrdrr\brdrs\brdrw15 \cltxlrtb\clftsWidth3\clwWidth567 \cellx9639\pard \ql \li0\ri0\sa120\sl-320\slmult1\widctlpar\intbl\faauto\adjustright\rin0\lin0 {\b\fs24 Type}{\fs24 
\cell An }{\b\fs24 observed example}{\fs24  of which is;\cell }\pard \qc \li0\ri0\sa120\sl-320\slmult1\widctlpar\intbl\faauto\adjustright\rin0\lin0 {\fs24 Fq.\cell }\pard \ql \li0\ri0\widctlpar\intbl\aspalpha\aspnum\faauto\adjustright\rin0\lin0 {\fs24 
\trowd \trgaph108\trbrdrt\brdrs\brdrw15 \trbrdrl\brdrs\brdrw15 \trbrdrb\brdrs\brdrw15 \trbrdrr\brdrs\brdrw15 \trbrdrh\brdrs\brdrw15 \trbrdrv\brdrs\brdrw15 \trftsWidth1\trpaddl108\trpaddr108\trpaddfl3\trpaddfr3 \clvertalt\clbrdrt\brdrs\brdrw15 \clbrdrl
\brdrs\brdrw15 \clbrdrb\brdrs\brdrw15 \clbrdrr\brdrs\brdrw15 \cltxlrtb\clftsWidth3\clwWidth1701 \cellx1701\clvertalt\clbrdrt\brdrs\brdrw15 \clbrdrl\brdrs\brdrw15 \clbrdrb\brdrs\brdrw15 \clbrdrr\brdrs\brdrw15 \cltxlrtb\clftsWidth3\clwWidth7371 \cellx9072
\clvertalt\clbrdrt\brdrs\brdrw15 \clbrdrl\brdrs\brdrw15 \clbrdrb\brdrs\brdrw15 \clbrdrr\brdrs\brdrw15 \cltxlrtb\clftsWidth3\clwWidth567 \cellx9639\row }\trowd \trgaph108\trbrdrt\brdrs\brdrw15 \trbrdrl\brdrs\brdrw15 \trbrdrb\brdrs\brdrw15 \trbrdrr
\brdrs\brdrw15 \trbrdrh\brdrs\brdrw15 \trbrdrv\brdrs\brdrw15 \trftsWidth1\trpaddl108\trpaddr108\trpaddfl3\trpaddfr3 \clvertalt\clbrdrt\brdrs\brdrw15 \clbrdrl\brdrs\brdrw15 \clbrdrb\brdrs\brdrw15 \clbrdrr\brdrs\brdrw15 \cltxlrtb\clftsWidth3\clwWidth1701 
\cellx1701\clvertalt\clbrdrt\brdrs\brdrw15 \clbrdrl\brdrs\brdrw15 \clbrdrb\brdrs\brdrw15 \clbrdrr\brdrs\brdrw15 \cltxlrtb\clftsWidth3\clwWidth7371 \cellx9072\clvertalt\clbrdrt\brdrs\brdrw15 \clbrdrl\brdrs\brdrw15 \clbrdrb\brdrs\brdrw15 \clbrdrr
\brdrs\brdrw15 \cltxlrtb\clftsWidth3\clwWidth567 \cellx9639\pard \ql \li0\ri0\sa120\sl-320\slmult1\widctlpar\intbl\faauto\adjustright\rin0\lin0 {\fs24 Ownership\cell \'93I really wanted to know what the answer was because we were fighting about it\'94
\cell }\pard \qc \li0\ri0\sa120\sl-320\slmult1\widctlpar\intbl\faauto\adjustright\rin0\lin0 {\fs24 2\cell }\pard \ql \li0\ri0\widctlpar\intbl\aspalpha\aspnum\faauto\adjustright\rin0\lin0 {\fs24 \trowd \trgaph108\trbrdrt\brdrs\brdrw15 \trbrdrl
\brdrs\brdrw15 \trbrdrb\brdrs\brdrw15 \trbrdrr\brdrs\brdrw15 \trbrdrh\brdrs\brdrw15 \trbrdrv\brdrs\brdrw15 \trftsWidth1\trpaddl108\trpaddr108\trpaddfl3\trpaddfr3 \clvertalt\clbrdrt\brdrs\brdrw15 \clbrdrl\brdrs\brdrw15 \clbrdrb\brdrs\brdrw15 \clbrdrr
\brdrs\brdrw15 \cltxlrtb\clftsWidth3\clwWidth1701 \cellx1701\clvertalt\clbrdrt\brdrs\brdrw15 \clbrdrl\brdrs\brdrw15 \clbrdrb\brdrs\brdrw15 \clbrdrr\brdrs\brdrw15 \cltxlrtb\clftsWidth3\clwWidth7371 \cellx9072\clvertalt\clbrdrt\brdrs\brdrw15 \clbrdrl
\brdrs\brdrw15 \clbrdrb\brdrs\brdrw15 \clbrdrr\brdrs\brdrw15 \cltxlrtb\clftsWidth3\clwWidth567 \cellx9639\row }\pard \ql \li0\ri0\sa120\sl-320\slmult1\widctlpar\intbl\faauto\adjustright\rin0\lin0 {\fs24 (Resolved) Desire to know\cell \'93I wasn\rquote 
t satisfied at the end...I thought \lquote Damn I wished I could have done something more.\rquote  \'94\cell }\pard \qc \li0\ri0\sa120\sl-320\slmult1\widctlpar\intbl\faauto\adjustright\rin0\lin0 {\fs24 1\cell }\pard 
\ql \li0\ri0\widctlpar\intbl\aspalpha\aspnum\faauto\adjustright\rin0\lin0 {\fs24 \trowd \trgaph108\trbrdrt\brdrs\brdrw15 \trbrdrl\brdrs\brdrw15 \trbrdrb\brdrs\brdrw15 \trbrdrr\brdrs\brdrw15 \trbrdrh\brdrs\brdrw15 \trbrdrv\brdrs\brdrw15 
\trftsWidth1\trpaddl108\trpaddr108\trpaddfl3\trpaddfr3 \clvertalt\clbrdrt\brdrs\brdrw15 \clbrdrl\brdrs\brdrw15 \clbrdrb\brdrs\brdrw15 \clbrdrr\brdrs\brdrw15 \cltxlrtb\clftsWidth3\clwWidth1701 \cellx1701\clvertalt\clbrdrt\brdrs\brdrw15 \clbrdrl
\brdrs\brdrw15 \clbrdrb\brdrs\brdrw15 \clbrdrr\brdrs\brdrw15 \cltxlrtb\clftsWidth3\clwWidth7371 \cellx9072\clvertalt\clbrdrt\brdrs\brdrw15 \clbrdrl\brdrs\brdrw15 \clbrdrb\brdrs\brdrw15 \clbrdrr\brdrs\brdrw15 \cltxlrtb\clftsWidth3\clwWidth567 \cellx9639
\row }\trowd \trgaph108\trbrdrt\brdrs\brdrw15 \trbrdrl\brdrs\brdrw15 \trbrdrb\brdrs\brdrw15 \trbrdrr\brdrs\brdrw15 \trbrdrh\brdrs\brdrw15 \trbrdrv\brdrs\brdrw15 \trftsWidth1\trpaddl108\trpaddr108\trpaddfl3\trpaddfr3 \clvertalt\clbrdrt\brdrs\brdrw15 
\clbrdrl\brdrs\brdrw15 \clbrdrb\brdrs\brdrw15 \clbrdrr\brdrs\brdrw15 \cltxlrtb\clftsWidth3\clwWidth1701 \cellx1701\clvertalt\clbrdrt\brdrs\brdrw15 \clbrdrl\brdrs\brdrw15 \clbrdrb\brdrs\brdrw15 \clbrdrr\brdrs\brdrw15 \cltxlrtb\clftsWidth3\clwWidth7371 
\cellx9072\clvertalt\clbrdrt\brdrs\brdrw15 \clbrdrl\brdrs\brdrw15 \clbrdrb\brdrs\brdrw15 \clbrdrr\brdrs\brdrw15 \cltxlrtb\clftsWidth3\clwWidth567 \cellx9639\pard \ql \li0\ri0\sa120\sl-320\slmult1\widctlpar\intbl\faauto\adjustright\rin0\lin0 {\fs24 
Appreciation\cell \'93You learn maths, you learn probability, but now I\rquote m finding it because I have to do an activity to find the chances of this child having a disease.\'94\cell }\pard \qc \li0\ri0\sa120\sl-320\slmult1
\widctlpar\intbl\faauto\adjustright\rin0\lin0 {\fs24 1\cell }\pard \ql \li0\ri0\widctlpar\intbl\aspalpha\aspnum\faauto\adjustright\rin0\lin0 {\fs24 \trowd \trgaph108\trbrdrt\brdrs\brdrw15 \trbrdrl\brdrs\brdrw15 \trbrdrb\brdrs\brdrw15 \trbrdrr
\brdrs\brdrw15 \trbrdrh\brdrs\brdrw15 \trbrdrv\brdrs\brdrw15 \trftsWidth1\trpaddl108\trpaddr108\trpaddfl3\trpaddfr3 \clvertalt\clbrdrt\brdrs\brdrw15 \clbrdrl\brdrs\brdrw15 \clbrdrb\brdrs\brdrw15 \clbrdrr\brdrs\brdrw15 \cltxlrtb\clftsWidth3\clwWidth1701 
\cellx1701\clvertalt\clbrdrt\brdrs\brdrw15 \clbrdrl\brdrs\brdrw15 \clbrdrb\brdrs\brdrw15 \clbrdrr\brdrs\brdrw15 \cltxlrtb\clftsWidth3\clwWidth7371 \cellx9072\clvertalt\clbrdrt\brdrs\brdrw15 \clbrdrl\brdrs\brdrw15 \clbrdrb\brdrs\brdrw15 \clbrdrr
\brdrs\brdrw15 \cltxlrtb\clftsWidth3\clwWidth567 \cellx9639\row }\pard \ql \li0\ri0\sa120\sl-320\slmult1\widctlpar\faauto\adjustright\rin0\lin0\itap0 {\fs24 Analysis of the interview transcripts revealed the following evidence of Mason\rquote 
s implications:}{\fs28 
\par }\trowd \trgaph108\trbrdrt\brdrs\brdrw15 \trbrdrl\brdrs\brdrw15 \trbrdrb\brdrs\brdrw15 \trbrdrr\brdrs\brdrw15 \trbrdrh\brdrs\brdrw15 \trbrdrv\brdrs\brdrw15 \trftsWidth1\trpaddl108\trpaddr108\trpaddfl3\trpaddfr3 \clvertalt\clbrdrt\brdrs\brdrw15 \clbrdrl
\brdrs\brdrw15 \clbrdrb\brdrs\brdrw15 \clbrdrr\brdrs\brdrw15 \cltxlrtb\clftsWidth3\clwWidth1418 \cellx1418\clvertalt\clbrdrt\brdrs\brdrw15 \clbrdrl\brdrs\brdrw15 \clbrdrb\brdrs\brdrw15 \clbrdrr\brdrs\brdrw15 \cltxlrtb\clftsWidth3\clwWidth7654 \cellx9072
\clvertalt\clbrdrt\brdrs\brdrw15 \clbrdrl\brdrs\brdrw15 \clbrdrb\brdrs\brdrw15 \clbrdrr\brdrs\brdrw15 \cltxlrtb\clftsWidth3\clwWidth568 \cellx9640\pard \ql \li0\ri0\sa120\sl-320\slmult1\widctlpar\intbl\faauto\adjustright\rin0\lin0 {\b\fs24 Type}{\fs24 
\cell An }{\b\fs24 observed example}{\fs24  of which is;\cell }\pard \qc \li0\ri0\sa120\sl-320\slmult1\widctlpar\intbl\faauto\adjustright\rin0\lin0 {\fs24 Fq.\cell }\pard \ql \li0\ri0\widctlpar\intbl\aspalpha\aspnum\faauto\adjustright\rin0\lin0 {\fs24 
\trowd \trgaph108\trbrdrt\brdrs\brdrw15 \trbrdrl\brdrs\brdrw15 \trbrdrb\brdrs\brdrw15 \trbrdrr\brdrs\brdrw15 \trbrdrh\brdrs\brdrw15 \trbrdrv\brdrs\brdrw15 \trftsWidth1\trpaddl108\trpaddr108\trpaddfl3\trpaddfr3 \clvertalt\clbrdrt\brdrs\brdrw15 \clbrdrl
\brdrs\brdrw15 \clbrdrb\brdrs\brdrw15 \clbrdrr\brdrs\brdrw15 \cltxlrtb\clftsWidth3\clwWidth1418 \cellx1418\clvertalt\clbrdrt\brdrs\brdrw15 \clbrdrl\brdrs\brdrw15 \clbrdrb\brdrs\brdrw15 \clbrdrr\brdrs\brdrw15 \cltxlrtb\clftsWidth3\clwWidth7654 \cellx9072
\clvertalt\clbrdrt\brdrs\brdrw15 \clbrdrl\brdrs\brdrw15 \clbrdrb\brdrs\brdrw15 \clbrdrr\brdrs\brdrw15 \cltxlrtb\clftsWidth3\clwWidth568 \cellx9640\row }\trowd \trgaph108\trbrdrt\brdrs\brdrw15 \trbrdrl\brdrs\brdrw15 \trbrdrb\brdrs\brdrw15 \trbrdrr
\brdrs\brdrw15 \trbrdrh\brdrs\brdrw15 \trbrdrv\brdrs\brdrw15 \trftsWidth1\trpaddl108\trpaddr108\trpaddfl3\trpaddfr3 \clvertalt\clbrdrt\brdrs\brdrw15 \clbrdrl\brdrs\brdrw15 \clbrdrb\brdrs\brdrw15 \clbrdrr\brdrs\brdrw15 \cltxlrtb\clftsWidth3\clwWidth1418 
\cellx1418\clvertalt\clbrdrt\brdrs\brdrw15 \clbrdrl\brdrs\brdrw15 \clbrdrb\brdrs\brdrw15 \clbrdrr\brdrs\brdrw15 \cltxlrtb\clftsWidth3\clwWidth7654 \cellx9072\clvertalt\clbrdrt\brdrs\brdrw15 \clbrdrl\brdrs\brdrw15 \clbrdrb\brdrs\brdrw15 \clbrdrr
\brdrs\brdrw15 \cltxlrtb\clftsWidth3\clwWidth568 \cellx9640\pard \qc \li0\ri0\sl-320\slmult1\widctlpar\intbl\faauto\adjustright\rin0\lin0 {\fs24 (Implication 
\par One)
\par Rel > Inv
\par \cell }\pard \ql \li0\ri0\sa120\sl-320\slmult1\widctlpar\intbl\faauto\adjustright\rin0\lin0 {\fs24 \'93I was fascinated at first \lquote cos I always liked biology.... I felt very interested. I hadn\rquote 
t used these types of graphs before. I tried to understand it and get involved with it.\'94\cell }\pard \qc \li0\ri0\sa120\sl-320\slmult1\widctlpar\intbl\faauto\adjustright\rin0\lin0 {\fs24 3\cell }\pard 
\ql \li0\ri0\widctlpar\intbl\aspalpha\aspnum\faauto\adjustright\rin0\lin0 {\fs24 \trowd \trgaph108\trbrdrt\brdrs\brdrw15 \trbrdrl\brdrs\brdrw15 \trbrdrb\brdrs\brdrw15 \trbrdrr\brdrs\brdrw15 \trbrdrh\brdrs\brdrw15 \trbrdrv\brdrs\brdrw15 
\trftsWidth1\trpaddl108\trpaddr108\trpaddfl3\trpaddfr3 \clvertalt\clbrdrt\brdrs\brdrw15 \clbrdrl\brdrs\brdrw15 \clbrdrb\brdrs\brdrw15 \clbrdrr\brdrs\brdrw15 \cltxlrtb\clftsWidth3\clwWidth1418 \cellx1418\clvertalt\clbrdrt\brdrs\brdrw15 \clbrdrl
\brdrs\brdrw15 \clbrdrb\brdrs\brdrw15 \clbrdrr\brdrs\brdrw15 \cltxlrtb\clftsWidth3\clwWidth7654 \cellx9072\clvertalt\clbrdrt\brdrs\brdrw15 \clbrdrl\brdrs\brdrw15 \clbrdrb\brdrs\brdrw15 \clbrdrr\brdrs\brdrw15 \cltxlrtb\clftsWidth3\clwWidth568 \cellx9640
\row }\trowd \trgaph108\trbrdrt\brdrs\brdrw15 \trbrdrl\brdrs\brdrw15 \trbrdrb\brdrs\brdrw15 \trbrdrr\brdrs\brdrw15 \trbrdrh\brdrs\brdrw15 \trbrdrv\brdrs\brdrw15 \trftsWidth1\trpaddl108\trpaddr108\trpaddfl3\trpaddfr3 \clvertalt\clbrdrt\brdrs\brdrw15 
\clbrdrl\brdrs\brdrw15 \clbrdrb\brdrs\brdrw15 \clbrdrr\brdrs\brdrw15 \cltxlrtb\clftsWidth3\clwWidth1418 \cellx1418\clvertalt\clbrdrt\brdrs\brdrw15 \clbrdrl\brdrs\brdrw15 \clbrdrb\brdrs\brdrw15 \clbrdrr\brdrs\brdrw15 \cltxlrtb\clftsWidth3\clwWidth7654 
\cellx9072\clvertalt\clbrdrt\brdrs\brdrw15 \clbrdrl\brdrs\brdrw15 \clbrdrb\brdrs\brdrw15 \clbrdrr\brdrs\brdrw15 \cltxlrtb\clftsWidth3\clwWidth568 \cellx9640\pard \qc \li0\ri0\sl-320\slmult1\widctlpar\intbl\faauto\adjustright\rin0\lin0 {\fs24 (Implication 

\par Two)
\par }\pard \qc \li0\ri0\sa120\sl-320\slmult1\widctlpar\intbl\faauto\adjustright\rin0\lin0 {\fs24 Inv > Rel\cell }\pard \ql \li0\ri0\sa120\sl-320\slmult1\widctlpar\intbl\faauto\adjustright\rin0\lin0 {\fs24 At the beginning I though there\rquote 
s no absolutely no point in doing this but I\rquote ll do this anyway \lquote cos you asked us to do it. At the middle I thought \lquote oh this is kind of interesting\rquote  - I wanted to see if I can actually do this. I wasn\rquote 
t satisfied at the end. Whoah! That changed \lquote cos I went from thinking \lquote This sucks I don\rquote t wanna do this\rquote  to \lquote damn I wished I could have done something more\rquote  \'94\cell }\pard \qc \li0\ri0\sa120\sl-320\slmult1
\widctlpar\intbl\faauto\adjustright\rin0\lin0 {\fs24 3\cell }\pard \ql \li0\ri0\widctlpar\intbl\aspalpha\aspnum\faauto\adjustright\rin0\lin0 {\fs24 \trowd \trgaph108\trbrdrt\brdrs\brdrw15 \trbrdrl\brdrs\brdrw15 \trbrdrb\brdrs\brdrw15 \trbrdrr
\brdrs\brdrw15 \trbrdrh\brdrs\brdrw15 \trbrdrv\brdrs\brdrw15 \trftsWidth1\trpaddl108\trpaddr108\trpaddfl3\trpaddfr3 \clvertalt\clbrdrt\brdrs\brdrw15 \clbrdrl\brdrs\brdrw15 \clbrdrb\brdrs\brdrw15 \clbrdrr\brdrs\brdrw15 \cltxlrtb\clftsWidth3\clwWidth1418 
\cellx1418\clvertalt\clbrdrt\brdrs\brdrw15 \clbrdrl\brdrs\brdrw15 \clbrdrb\brdrs\brdrw15 \clbrdrr\brdrs\brdrw15 \cltxlrtb\clftsWidth3\clwWidth7654 \cellx9072\clvertalt\clbrdrt\brdrs\brdrw15 \clbrdrl\brdrs\brdrw15 \clbrdrb\brdrs\brdrw15 \clbrdrr
\brdrs\brdrw15 \cltxlrtb\clftsWidth3\clwWidth568 \cellx9640\row }\pard \ql \li0\ri0\sa120\sl-320\slmult1\widctlpar\faauto\adjustright\rin0\lin0\itap0 {\fs28 There are clearly many factors driving th
e involvement witnessed in this activity. Accounting for involvement also included analysis of each group\rquote 
s discussions. It was found in many of these discussions that a tension existed between opposing cognitive ideas present in a group. For example, the following extract [Students 1, 2 and 3 have correctly found in Question 2 that P(One child has Smith
\rquote s disease)=1/4]
\par }\pard \ql \fi-510\li510\ri0\sl-320\slmult1\widctlpar\faauto\adjustright\rin0\lin510\itap0 {\fs24 S 1:\tab Ok, if Shalini and Niraj have two children, what is the probability that at least one will have Smith\rquote s disease?\tab \tab \tab 
[Reads Question 3]
\par S 2:\tab Again, it adds up - it\rquote s 1/4 plus 1/4 - a half again - there\rquote s a half chance that one of them would have it, yep
\par }\pard \ql \li0\ri0\sl-320\slmult1\widctlpar\faauto\adjustright\rin0\lin0\itap0 {\fs24 S 1:\tab \lquote Cos the father has a 50% chance so...
\par }\pard \ql \fi-510\li510\ri0\sl-320\slmult1\widctlpar\faauto\adjustright\rin0\lin510\itap0 {\fs24 S 2:\tab \lquote ...exactly, and the child will have a 25% chance, but they are having two childs now, so
 they are taking twice the risk, so there is a 50% chance that at least one of the kids will have Smith\rquote s disease\'94\tab \tab \tab [Accepted by group as correct answer to Question 3]
\par S 2:\tab \'93If Shalini and Niraj have three children, what is the probability that at least one will have Smith\rquote s disease?\tab \tab \tab [Reads Question 4]
\par }\pard \ql \li0\ri0\sl-320\slmult1\widctlpar\faauto\adjustright\rin0\lin0\itap0 {\fs24 S 3:\tab \'9375%\'94
\par S 2:\tab \'93No, it can\rquote t be 75, because...\'94\tab \tab 
\par S 1:\tab \'93It\rquote s 25 plus 25 plus.... yeah it is\'94\tab \tab 
\par S 2:\tab \'93You add up for ever and ever, so like if it is 5 children it is 125%\'94
\par }\pard \ql \li0\ri0\sa120\sl-320\slmult1\widctlpar\faauto\adjustright\rin0\lin0\itap0 {\fs24 S 3 and S 1 laugh.}{\fs28 
\par Here S2 seems to equate the words \lquote two children\rquote  with doubling the probability of the simple event. He may have ignored the important \lquote at least one\rquote  in the question, or he may have simply used a na\'ef
ve logic. In any case, the error is only established when it leads to contradiction of a formal axiom of probability. The range of skills and facts used here is of interest because it illuminates Tversky and Kahneman\rquote s (1982) findings that \'93.}{
\i\fs28 ..peo
ple rely on a limited number of heuristic principles which reduce the complex tasks of assessing probabilities ...to simple judgmental operations. In general, these heuristics are quite useful, but sometimes lead to severe and systematic errors.\'94 }{
\fs28 (p. 3) Cl
early, follow-up sessions and guidance from the teacher could benefit the students greatly and lead to another attempt at the activity motivating the use of precise techniques. Question 6, involving conditional probability, challenged students greatly and
 ultimately evaded their best efforts.
\par RELATING BACK TO MASON\rquote S IMPLICATIONS:
\par This study serves to illuminate Mason\rquote s quote. The students in this class have well-formed concerns about the relevance of their maths education that run deeper than Mason\rquote s suggestion that they only become concerned when \lquote 
they are no longer coping\rquote  would imply. The diametrically opposing perspectives \lquote Future\rquote  and \lquote Formalist\rquote  must influence the background against which relevance is constructed, since the former value motivates the 
question \'93Why are we doing this?\'94 whilst the latter considers it a non-issue.
\par This study suggests that Mason\rquote s two models embody different types of relevance constructs. The evidence of primary and secondary relevance gathered here is indicative of relevan
ce as a process - a collection of variables that vary over time, not just an outcome. Interestingly, the \lquote real-world\rquote 
 context of the task (and maturity of the students) may have led to the committed involvement in attempting to understand the \lquote noise\rquote  associated with the context, hence increasing involvement, showing that the \'93correspondence\'94
 Mason mentions }{\i\fs28 can}{\fs28  be established by a \lquote real-world\rquote  context.
\par The claim cannot be made that simply because this activity was embedded in a \lquote real-world\rquote  context it immediately became relevant. However, it was neither \lquote misconceived\rquote  nor \lquote doomed to failure\rquote 
, as the prevalence of the value \lquote Relate\rquote  and the primary relevance \lquote Interest\rquote  demonstrate. Further study would need to be undertaken to investigate to what extent students\rquote  \lquote choice\rquote 
 of Implication relates to their values regarding relevance, and to investigate further sets of primary and secondary relevance, perhaps in other types of activities.
\par INFLUENCING FACTORS AND LIMITATIONS:
\par }\pard\plain \s15\ql \li0\ri0\sa120\sl-320\slmult1\widctlpar\faauto\adjustright\rin0\lin0\itap0 \fs28\lang2057\langfe1033\cgrid\langnp2057\langfenp1033 {This study takes place against a backgrou
nd of influencing factors. The Hawthorne effect, whereby a change is received positively simply because it is new, will have had a certain impact, since this task was so unusual for the students. The tension generated in student discussion between differi
n
g cognitive standpoints will obviously generate involvement, leading to relevance, however this may give another justification for activities of this type, for to stimulate authentic discussion of such an applicable yet misconceived topic as probability b
y stepping outside the formalist \lquote quarantine\rquote 
 surely gives potential to improve the understanding of this topic. It must also be said that the compulsory status of mathematics in the IB program brings issues of relevance to the fore for the students, who ar
e challenged by issues of time management given the rule of thumb that the IB diploma is considered as demanding as four and a half A-levels. This can lead to students being somewhat mercenary regarding their use of time. Interestingly, the IBO (1998) aim
 for mathematical methods to cater \'93for those students planning further studies in such fields as chemistry, economics, geography and business administration.\'94 (p. 4)
\par The varied backgrounds of the students involved in this study bring issues of generalisability to the fore. Responses of other students, be they from international, bi-lingual or national schools, to the \lquote Be a Genetic Counsellor}{\fs22  }{\rquote 
 activity might resonate with those described in this study. The readers are left to judge how likely the findings are to generalise to their own situations, or to try it out for themselves.
\par }\pard\plain \ql \li0\ri0\sa120\sl-320\slmult1\widctlpar\faauto\adjustright\rin0\lin0\itap0 \fs20\lang2057\langfe1033\cgrid\langnp2057\langfenp1033 {\fs28 7958 students sat for the Mathematical Methods course worldwide in 1998.
\par HEIGHTENING RELEVANCE AND INVOLVEMENT:
\par Mathematics teaching cannot be \lquote all things to all people\rquote : a scheme of work which includes only career-embedded activities such as \lquote Be a Genetic Counsellor}{\fs22  }{\fs28 \rquote 
 would run the risk of reducing the curriculum to a contrived and tokenist contextualisation which would not necessarily lead to \lquote relevance\rquote  and \lquote involvement\rquote , missing the point that, as Ainley (1997) wrote, the real world }{
\i\fs28 is}{\fs28  the classroom to an extent. For these students with their varied nationalities, languages and career plans it is certainly true that one thing that they hold in common is the classroom and the activ
ities that they participate in: there is potential to achieve relevance without use of \lquote real-world\rquote  examples in Koirala\rquote s (1998)}{ }{\fs28 call for students to discuss different concepts of probability and in Shaughnessey and Bergman
\rquote s (1993) call for classroom probability explorations. But we should not ignore the potential of activities like \lquote Be a Genetic Counsellor\rquote : despite Mason\rquote 
s warnings, the example in this study has addressed both his implications.
\par Teachers can improve their teaching of probability by increasing their understanding of the values of relevance and constructs held by their students. This class, which seems to be divided by \lquote Formal\rquote  and \lquote Future\rquote 
 values could benefit from judicious use of both Mason\rquote s implications in a balanced approach to heighte
ning relevance and involvement in the teaching of probability. The new IB Portfolio assessment for Mathematical Methods, requiring written work under the categories Mathematical Investigation, Extended Closed Problem Solving and Mathematical Modelling for
 20% examination credit, gives potential to achieve these goals.
\par REFERENCES:
\par }\pard \ql \li0\ri0\sa120\widctlpar\faauto\adjustright\rin0\lin0\itap0 {\fs22 Ainley J (1997) }{\i\fs22 Constructing Purpose in Mathematical Activity}{\fs22 
 in Pehkonen E (Ed.) Proceedings of the 21st International Conference for the Psychology of Mathematics Education Vol. 2 pp17-24 Lahti:Finland
\par Cockcroft W H (1982) }{\i\fs22 Mathematics Counts: A Report of the Committee of Inquiry into the teaching of Mathematics in Schools}{\fs22  London:HMSO
\par Cooper B (1994) }{\i\fs22 Authentic Testing in mathematics? The boundary between everyday and mathematical knowledge in national curriculum testing in English Schools}{\fs22  in Assessment in Education Vo1 1, No 2 (pp143-166)
\par Freudenthal H (1973) }{\i\fs22 Mathematics as an Educational Task}{\fs22  Holland:D Reidel
\par International Baccalaureate Organisation (1998) }{\i\fs22 Group 5 Subject Guide}{\fs22  in IB Vade Mecum
\par Jacobs H (1998) }{\i\fs22 The teacher as designer: integrating the curriculum}{\fs22  in International Schools Journal Gellar C (Ed.) ECIS (pp22-33)
\par Tversky A and Kahneman D (1982) }{\i\fs22 Judgement under Uncertainty: Heuristics and Biases}{\fs22  in Tversky et al (Eds) Judgement under Uncertainty: Heuristics and Biases (pp3-20) CUP
\par Kiorala H (1998) }{\i\fs22 Preservice teachers Conceptions of Probability in relation to its History}{\fs22  in Olivier A&Newstead F (Eds.) Proceedings of the 22nd Conference of the Inte
rnational Group for the Psychology of Mathematics Education VIII (pp135-142)
\par Kotelawala U (1997) }{\i\fs22 A sample genetics project: Consider Yourself a Genetic Counsellor}{\fs22  at http://www.columbia.edu/~umk1/genetics.html accessed 01/22/99 18:34:06
\par Maslow A H (1954) }{\i\fs22 Motivation and Personality}{\fs22  New York:Harper Row
\par Mason J (1988) }{\i\fs22 Modelling: What do we really want pupils to learn?}{\fs22  in Mathematics, Teachers and Children Pimm D (Ed.) Hodder&Stoughton (pp201-215)
\par Middleton J and Spanias P (1999) }{\i\fs22 Motivation for Achievement in Mathematics: Findings, Generalizations, and Criticisms of the Research}{\fs22  Journal for Research in Mathematics Education., Vol. 30, No. 1 pp 65-88
\par NCTM (1998) }{\i\fs22 Beliefs Statement}{\fs22  NCTM Virginia
\par Shaughnessey J M & Bergman B (1993) }{\i\fs22 Thinking about Uncertainty: Probability and Statistics}{\fs22  in Wilson P (Ed.) Research Ideas for the Classroom: High School Mathematics. (pp177-197) New York:Macmillan
\par Verscaffe L, De Corte E and Borghart I (1996) }{\i\fs22 Pre-Service Teachers\rquote  Conceptions and Beliefs about the Role of Real-World Knowledge in Arithmetic Word Problem Solving}{\fs22 
 in Puig L and Gutierrez A (Eds.) Proceedings of the 20th International Conference for the Psychology of Mathematics Education, Vol 4 387-394 Valencia, Spain
\par 
\par \'a9 David Kay Harris 1999-2001}{\fs28 
\par }}