transforming students’ approaches to learning and applying mathematics

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HD:Users:hazelowen:Documents:Research:Publications:Published:LTMMEC07_moran_owen_Math_Oman_2007_SultanQaboosPaper:LTMMEC

paper_Moran_Owenv2.doc of 17

Transforming students’ approaches to learning and applying

mathematics

D. Moran and H. Owen,

Higher Diploma Foundations, Dubai Men’s College, Higher Colleges of Education, Dubai, United

Arab Emirates

Please cite as: Moran, D., & Owen, H. (2007). Transforming students' approaches to learning and

applying mathematics [Electronic Version]. Proceedings: Learning Technologies and Mathematics

Middle East Conference from http://math.arizona.edu/~atp-

mena/conference/proceedings/Moran_Owen_paper.doc.

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Abstract

The increasing scope of curriculum content, time restraints and gateway assessment require

mathematics teachers to actively explore alternative learning strategies in order to effectively address

students’ learning needs. In addition to meeting curriculum-specific objectives, teachers are often

expected to directly address graduate outcomes at each stage of the learning experience. A cooperative

learning approach is one effective strategy to meet required objectives, while also addressing the

requisite holistic outcomes to help students be competitive in today’s work environment.

This paper discusses an approach utilised to integrate mathematics within the interdisciplinary

Foundations program: Computing, Research Skills and Projects (CRSP), at Dubai Men’s College

(DMC). The CRSP course, originally developed to address English language and research skills

objectives, has been designed with the intent of transforming students’ attitudes and approaches to

learning. CRSP is a blended learning course delivered through fifty percent face-to-face sessions, and

fifty percent through the learning management system, WebCT. The latter effectively incorporates the

meaningful application of learning technologies such as audio, video, animations, applets and online

quizzes. Mathematical tasks have been integrated in such a way as to exploit the course’s instructional

design strategies, as well as its inherent adherence to adult learning principles and learning

technologies. Mathematic objectives are dynamically related to other disciplines by providing relevant

tasks within authentic contexts. Students develop new mathematical understandings, critical thinking

and decision making skills that build on and enrich their knowledge, application and appreciation of

mathematics. These active learning experiences then provide the opportunity for students to effectively

transfer skills, knowledge and attitudes to Math-specific Foundations courses, as well as in subsequent

years of study.

This paper will refer to research findings which indicate that students who complete the CRSP course

have positive attitudes to the learning of mathematics and are better able to solve problems requiring

mathematical skills outside the classroom.

Introduction

Mathematics is a discipline that might be defined as the “deductive study of numbers, geometry, and

various abstract constructs, or structures” (Britannica Concise Encyclopaedia, 2006). However, this

definition omits the applied nature of mathematics necessary to solve and explain the problems of

everyday existence and fails to recognise the dynamic nature of mathematics (Hamming, 1980). The

learning and teaching of mathematics has been affected by the discipline’s increasing complexity along

with the requirement for “complex reasoning and performance on problem-solving tasks” especially

when applied to situations outside the learning environment (Bransford, Brown, & Cocking, 2000, p.

2). Additionally, Corr (2007) indicates that frequently graduates do not have the ability to take abstract

mathematical concepts and apply them, which “reflects the rigidity of education systems”. In response

to the identification of issues such as these, the Foundations’ faculty at Dubai Men’s College (DMC)

adopted an approach that integrated content areas (including mathematics) with the Computer,

Research Skills and Projects (CRSP) course.

This paper describes the theory behind designing and implementing such an approach, and reports the

results to date. Findings suggest that students who complete the CRSP course have positive attitudes to

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the learning of mathematics and are better able to solve problems requiring mathematical skills outside

the classroom.

Alternative learning strategies in the UAE and Gulf Region

Education is currently experiencing a paradigm shift that acknowledges learners as cultural and social

entities who are part of a wider community (Jaworski, 1996), and who need to be actively engaged in

order to enable them to acquire knowledge and skills. Learning in a more traditional sense is

underpinned by the notion that the world is ultimately ‘knowable’, and that students can learn proven

facts. In contrast, student-centered learning involves working collectively to solve problems (to which

there may not be a ‘correct’ answer), hone and apply skills, and produce artifacts that are relevant

outside of the classroom environment (Scardamalia & Bereiter, 2002), thereby preparing students for a

‘knowledge society’.

For the Arab world in general, and the UAE and Gulf region in particular, The Arab Human

Development Report (United Nations Development Programme, 2003) found that “students can do

little but memorise, recite and perfect rote learning” (p. 54). They also indicated that the pedagogical

methodology is largely didactic, teacher-centered and passive, with assessments that require

memorisation of formulae and superficial identification of set problems. Conversely, an active

“learning style is characterized by field-independent and analytical thinking” (Al-Harthi, 2005, p. 3),

in a student-centered environment with an active teaching approach (Seels & Glasgow, 1998). These

findings bleakly expose the gap between the preconceptions, skills and expectations with which many

students enter tertiary education and the magnitude of the required transformation of their approaches

to learning. As such, education in the Arab world needs to shift its focus from “providing instruction

to producing learning” (Barr & Tagg, 1995) equipping learners with the “wherewithal to think,

understand, create,…and adapt within many different material and cultural contexts” (Hall, 1996, p.

27).

When considering such a dramatic shift in pedagogical methodology, affective factors need to be

considered if effective learning is going to be achieved (Henderleiter and Pringle, 1999). For example,

student anxiety and resistance to a shift in the approach to learning and teaching must not be

underestimated. Hofstede’s (1991) uncertainty avoidance index reveals that Arab countries have

stronger uncertainty avoidance (score = 68) than, for example, the United States (score = 46) (Al-

Harthi, 2005). However, these reactions can, in part, be addressed by initially providing strongly-

scaffolded cooperative learning (CL) tasks, with clear instruction and expectations, and then gradually

removing the scaffolding in subsequent tasks.

Alternate learning strategies in Mathematics

“The failure of research and curriculum reform during the past fifty years to significantly affect the

mathematics classroom calls for alternative research paradigms that may bridge the gap between

research concerns and problems from the reality of the classroom” (Atweh, 2002, p. 1).

The Higher Colleges of Technology’s graduate outcomes include demonstrable requirements of

mathematical literacy as follows:

1. Applying relevant numerical analytical tools to solve problems in authentic contexts.

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2. Analysing and communicating mathematical concepts with confidence in authentic contexts

(Higher Colleges of Technology, 2006).

To support these outcomes, HCT has developed a Numeracy Learning Process Model, the core of

which is the effective application of Numeracy, as shown in figure 1. Whilst not prescribing one

specific methodology, the model does recommend activities applied to realistic situations.

Figure 1: HCT Numeracy Process Model, (UAE Ministry of Education 2005)

The HCT system requirement, along with the need to equip students with the range cognitive and

metacognitive skills which enable students to take control of their own learning and to monitor their

own progress (Bransford, Brown, & Cocking, 2000), alerted Foundations faculty at DMC to the

necessity of moving from a text-book focussed math course, to an actively applied skills focus.

Implementation Issues

It can be difficult for Mathematics teachers to include applied tasks in real world contexts when faced

with curriculum content volume and inflexible gateway assessments. Teachers of Limited English

Proficiency (LEP) students are doubly challenged in a content course. In addition to the intellectual

obstacles their students must overcome to understand the content, they are faced with the difficulty of

doing so through the filter of their limited English (Orthman, 2005). Orthmann (2005) suggests that, in

general, adult LEP learners have the cognitive ability to comprehend even complex content once the

language barriers have been breached. Whilst this ability in students supports teaching the effective

application of Numeracy in relevant contexts, the obstacles to overcoming the language barrier should

not be underestimated. When determining a strategy to teach a specific content objective, a

mathematics teacher must consider whether s/he has the time not only to teach the content vocabulary,

but also the ‘context’ vocabulary required by the student to understand the problem/situation presented.

Integrated Approach

Historically, the Foundations programme at DMC comprised four discrete courses: mathematics,

computing, Arabic and English. Study, research and academic skills were taught as part of each course

and supported by Learning Centre input sessions. The main issues included sparse communication

between the courses and ‘projects’ being completed in isolation and viewed as an ‘add-on’ to the

English course. Consequently, students were not graduating from Foundations with the required level

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of study, research and higher-order thinking skills. In response to this recognized learning deficit,

Foundations faculty designed and implemented an integrated programme that was informed by adult

learning theory, and which exploited the benefits of CL (see Figure 1).

Figure 2: The CRSP course and its integration with the Foundations’ content courses (Martin, 2005).

The resulting interdisciplinary CRSP Foundations program is a blended learning course, fifty percent

of which is delivered through face-to-face sessions, and fifty percent by means of the learning

management system, WebCT. The latter effectively incorporates meaningful application of learning

technologies such as audio, video, animations, applets and online quizzes. The course is designed to

foster students’ research and study skills, while simultaneously supporting English language learning

strategies and providing authentic opportunities to apply mathematical and computing skills.

Furthermore, it has been designed with the intent of transforming students’ attitudes and approaches to

learning.

Mathematical tasks have been integrated in such a way as to exploit the course’s instructional design

features, as well as its inherent adherence to adult learning principles and learning technologies.

Mathematic objectives are dynamically related to other disciplines by providing relevant tasks within

‘real world’ contexts. As a result of this approach, students develop new mathematical understandings,

critical thinking skills and decision making skills that build on and enrich their knowledge, application

and appreciation of mathematics. These active learning experiences equip students with transferable

skills, knowledge and attitudes to the Math-specific Foundations course that they then apply during

subsequent years of study.

The Foundations’ integrated approach aimed to assist students in their acquisition of the cognitive and

metacognitive skills required to overcome their sense of disorientation when progressing from a

passive to an active learning environment, as well as enabling them to study effectively after

graduating from Foundations. An iterative, experiential process has been developed around four main

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projects which were evenly distributed over the forty-week academic year. This approach within

CRSP course enables students to encounter concrete experiences, conceptualise, reflect and actively

experiment (Kolb, 1985) with the skills and concepts from the respective integrated content courses.

Students, through a cumulative process produce one main artifact per project which consists of a

variety of elements, including associated mathematics tasks.

Role of Information and Communication Technology: Learning strategies transformation

The versatility of information and communication technology (ICT), when used as a tool to enhance

the learning process, has the potential to support learners by, for instance, enabling educators to

provide multi-media learning objects that suit a wide range of learning styles. Furthermore, it provides

the opportunity to make available pedagogically sound active learning experiences that “allow for

multi-disciplinary projects, CL groups, flexible-scheduling, and authentic assessments” (Cheaney &

Ingebritsen, 2005, p. 3), especially in a blended-learning setting.

The design of the CRSP course includes a suite of ICT support tools to scaffold and enhance students’

learning including MSN chat, WebCT, Calendar, Camtasia, podcasts, online quizzes, and audio and

video learning objects. The adaptability of the tools enables teachers to gradually reduce student

reliance on a teacher-centered approach, although care is taken to provide enough support so that

students remain motivated, but not so much that they do not have a reason to collaborate with peers

and complete tasks in a self-directed manner (Erlendsson, 2001).

STRATEGY / TOOL SCAFFOLDING / ENHANCEMENTS PROVIDED /

OUTCOME SKILLS ACQUIRED

WebCT (online learning

management system)

• Provides a searchable, central location for

communication tools, calendar, quizzes etc, and a place

to upload homework and completed artifacts

• Gives access to all the models, examples, videos,

podcasts, materials, resources, instructions and rubrics

used during the 40 week course

• Enables students to consult and retrieve resources 24/7

• Empowers students as they do not have to wait for the

teacher to “reveal” what they are going to do next

• More advanced / motivated students can access /

complete work ahead of time

• Enables students who have to travel or be unavoidably

absent to keep up with course requirements

• Project management

• Empowerment

• Self-directed learning

Calendar (in WebCT) • Gives students an overview of the 40-week semester

• Has reminders of homework required each week

• Gives final project deadlines

• Provides live links from the calendar directly to the task,

rubric, instructions, tool, or explanation referred to in a

calendar posting

• Time management

• Project management

• Self-directed learning

Laptops • Allow students to collect and collate original research

data outside classrooms

• Encourages students to be organised (e.g. file naming

conventions and file management)

• Raises global awareness (e.g. security issues such as

viruses)

• Assists students to take responsibility for their own

• Data gathering

• Organisation

• Production and presentation of

artifacts

• Communication skills

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learning (e.g. regular backups)

Table 1: Scaffolded tools provided for learners participating in the CRSP blended learning course

(Owen, 2007, adapted from Krajcik, Blumenfeld, Marx, & Soloway, 1998)

Relevant Tasks and Authentic Contexts – Integration of Mathematics

For those who learn to think meaningfully, mathematics gets essentially simpler, while for those who

learn isolated techniques, it becomes increasingly complicated. (Hall, 1997). Teachers need to

incorporate a variety of appropriate teaching strategies in the intended learning experiences which can

be enhanced by available technologies and other resources (AAMT 2006).

The following section of the paper describes two fully-integrated math projects that have been run as

part of the CRSP course in the 2004-2005, and 2005-2006 academic years. Each year has seen

enhancements and additions to the math tasks in response to research data and feedback from

stakeholders. The description below is the most recent version of these tasks.

Project 1 Careers: decision analysis activities

In Semester 2 of their Foundations year at DMC students must select the specialisation they are going

to study after they have graduated from Foundations. The following specialisations are offered:

Business, Aviation, IT, Communications Technology and Engineering. Many students are unsure

which course will best prepare them for the workforce and what employment opportunities are

available to them following graduation from a course. Though everybody makes decisions on a daily

basis, Saaty (1996) suggests that making a decision is not purely a question of selecting the best

alternative. Instead, he advises that one should apply mathematics to decision making, whereby

dissecting a problem into its constituent parts, while establishing importance or priority by ranking the

alternatives, is a comprehensive and general way to look at the problem mathematically.

Foundations students are not ready to undertake a quantitative process of multi-criteria decision

making, yet the CRSP team’s task to teach students an effective process of decision analysis remained.

The scope of this objective included developing students’ ability to make informed decisions using key

considerations whilst ensuring they recognise the role mathematics plays in sound decision making.

Task 1 - Podcast and Analysis Task: To assist students in identifying and prioritising components

which would assist them in course decision making, the CRSP team developed a podcast episode and

linked it to an analysis task embedded in WebCT. Episode one of Research Skills Voice Podcast was

entitled ‘Career Considerations’ and included a recording of six Foundations students who appeared on

a local Talkback radio station, Dubai Eye. Students were recorded discussing which job they would

like to undertake after completing their studies at DMC. After listening to the Podcast, students were

required to:

a. identify the key reasons given by the students for wanting go into particular industries;

b. list the things that they themselves will consider before choosing a specialisation to study; and

c. prioritise this list of considerations.

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These integrated tasks were used to ensure that students reflected on and internalised the importance of

considering a number of relevant factors when making decisions. It also further developed their

understanding of the importance of prioritising these factors within a decision analysis process.

Task 2 - Using Excel to organise and display data: Opportunities should be taken to involve

students in mathematical activities beyond the scope of the classroom in contexts of interest and

relevance to the students (AAMT 2006). Students undertook an ‘off-campus’ task which required

them to interview people in the workplace and gather data on employees’ occupations, skills, training

and education. Data gathered by students also included the respondents’ nationalities and whether

their job was part of the public or private sector. This data was sorted in tables and represented in

graphs using MS Excel software; graphs displayed, for example, the representation of nationalities

working within the public and private sectors. In addition, students were asked to answer questions

about the hypothetical consequences of the collected responses in connection to themselves, their

respective careers decisions and where their courses may lead them. As such, the task was specifically

designed to encourage the use of critical thinking skills and to exploit the use of technology in

displaying and formulating data.

Task 3 - Interactive Web-based simulation activity: Using information provided by faculty

departments at DMC, the CRSP team scripted scenarios which required students to simultaneously

read and listen to information about different students and the course options available to them, analyse

the various options, and, using a list of key considerations, decide which course is best suited to the

individual. Also included was specific information about the job opportunities available following

graduation from DMC.

An example of one of these scenarios is shown in Figure 3. It was believed that the considerations list,

developed with students following the Podcast task, would enable students to make better decisions.

However, because individual students did not possess a sufficiently detailed understanding of the UAE

government’s policy of Emiratisation and the impact this should have on their career decision making

process, the CRSP course included several tasks which required students to learn about the policy.

Students completed English-related activities requiring them to investigate the following points:

a) What is the aim of Emiratisation?

b) What actions and events will be put in place?

c) What are people’s opinions of the policy?

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Figure 3: The Career project decision analysis scenario.

The scope of these tasks was information gathering and, in isolation, students were not required to

critically investigate the Emiratisation policy to see if it was meeting its aims. Consequently, there

existed a clear need for the development of tasks requiring students to use their mathematics skills to

investigate the policy in practice and formulate not only an holistic and informed opinion on its merits,

but also to enable them to prioritise Emiratisation as a consideration when choosing a career course.

Mathematics was ideal because it is a branch of science which develops the behaviour of drawing

logical conclusions and making justifiable generalisations (Tanisli & Saglam, 2006).

Task 4 - Quiz. A WebCT quiz was developed which linked to three key articles discussing

government Emiratisation employment objectives and industry’s adherence to these quotas, as shown

in figure 4. Students were required to gather, analyse and perform calculations on data, to determine

which industries were subject to national quotas, the specific percentage quotas set, and how these

matched industry practice. In addition, students researched which courses at DMC led students to jobs

in these industries. The research articles and questions were presented as part of the WebCT quiz,

which automatically graded completed quizzes and provided students with specific feedback on their

responses. Students’ conclusions were noted in their career project ‘fact sheet’ which serves to guide

their research. The fact sheet serves as a focus and guide for researching information fundamental to

the topic, which is in turn applied in a timed essay assessment, final PowerPoint presentation and an

assessed Website item.

By building the quiz within WebCT, the CRSP team was able to exploit a number of its inherent

features. WebCT supports links to a variety of formats ranging from Microsoft Word to audio files. It

automatically calculates quiz scores and gives feedback on both correct and incorrect responses. As

well as providing automatic feedback, this element allows the quiz to be conducted by non-Math

teaching faculty. Students can confidently navigate quizzes and feedback through WebCT and are

familiar with accessing results and reading the concluding comments generated.

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Figure 4: Emiratisation Analysis Quiz

After completing the quiz, students reflected on the effectiveness and shortfalls of the policy and

internalised their perspective on to what degree Emiratisation is important for them when undertaking

the career decision process. This was facilitated through group discussion. As a result of this

integrated task, students were able to add Emiratisation to their considerations list and expand their

decision making approach. The activity provided students with the opportunity to actively employ

their mathematics skills to effectively enhance their ability to solve problems in a real world context of

personal relevance. This type of activity would have been difficult to utilise in ‘stand-alone’ math

classes, as students would not have had the career context background and language, provided by

CRSP, to allow them to competently complete the task.

Innovation and Change

Using technology to develop mathematical ideas

Following the Career Project, the CRSP course requires completion of a final project entitled

‘Inventions, Developments and Change’ which provides excellent opportunities to exploit learning

technologies. The context requires students to reflect on historical events and current developments.

Using a model exemplified by Man-Keung in 1996, who presented the ABCD for the use of

mathematical history in the undergraduate classroom, the CRSP team provided opportunities for

students to investigate mathematical events from their own history to enable them to develop new

mathematical understandings that built on and enriched their knowledge and appreciation of

mathematics. (AAMT 2006)

A key idea to be fostered was empowering students to investigate historical material and to “learn from

the masters” (Man-Keung, 1996, p. 44). In this instance, the instructional objective was to facilitate

student research, through the work of historical Islamic mathematicians, to discover how the masters

accomplished their jobs. A variety of learning technologies were utilised to scaffold and influence

student learning in order to achieve these objectives, including a podcast, Internet Web quests, macro-

enabled Excel documents, Javascript programs and WebCT quizzes.

The Arabs’ contribution to innovation and change

In the ninth-century, the scientist, Abu Yusuf Ismail al-Kindi,, invented cryptanalysis, the science of

unscrambling a message without knowledge of the key. His technique of analysing the frequency of

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the characters in a cipher text showed that it is possible to discover the contents of a scrambled

message. The Arabs utilised this process as a method for breaking the monoalphabetic substitution

cipher - a cipher that had remained unbreakable for several centuries (Singh, 1999).

The invention of cryptanalysis depended on the growth of religious scholarship. Theologians

scrutinised the revelations of the prophet Muhammad (PBUH) as contained in the Koran, in order to

establish the chronology of the revelations. They followed the process of counting the frequencies of

words contained in each revelation. It was understood that certain words had evolved relatively

recently, and hence, if a revelation contained a high number of new words, this would suggest that it

was placed later in the chronology (ibid). The religious scholars also analysed individual letters, which

led them to discover that some letters are more common than others. This observation resulted in the

first great breakthrough in cryptanalysis.

Task 1 - Podcast: Students were introduced to Arab contributions to mathematical innovation and

related historical changes in Episode 2 of the Research Skills Voice Podcast. The episode explained

Al Hindi’s breakthrough in cryptanalysis as well as other innovations undertaken by early Islamic

mathematicians and scientists. Information was also provided on current developments and

innovations in the field of encryption and decryption, including Internet credit card security, military

communication and the use of the anti-plagiarism software such as ‘Turn-It-In’ - a program currently

used by the HCT. As with Episode 1 (on career considerations), students were again asked to answer

questions about the podcast episode. They were required to reflect on and internalise the achievements

of the mathematicians discussed. This task provided students with the cognitive understanding and

background knowledge necessary for them to undertake a similar investigative process in subsequent

tasks. The podcast also served as the precursor to the introduction of the main project topic, inventions,

developments and change.

Task 2 - Establishing the chronology of documents: The first task undertaken by students was to

determine the chronology of four separate written pieces of work. These comprised Microsoft-related

interviews and documents from the past three decades sourced from Bishop (2007). Students were

expected to analyse the text for key technological vocabulary and assess which terms evolved most

recently – for example ‘PDAs’, ‘email’, ‘www’, or a specific time, such as ‘Windows 95’.

Additionally, students identified and compared statistical data inherent in the articles, such as the

number of PC users in the United States. By applying their knowledge of known trends students could

better identify the chronology of the articles. Teachers reiterated the concept that language evolves the

same way as new innovations and technologies. Students were encouraged to undertake their

investigative work in pairs and discuss the process undertaken. Links were made to the historical

process employed by Arab Mathematicians and how the use of this process continues to evolve in

society. Discussion was encouraged regarding the use of the aforementioned anti-plagiarism software

‘Turn-It-In’, which itself undertakes a word search and matching process to identify the authenticity of

documents submitted. This approach is also supported by AAMT (2006) who endorse that the

enjoyment of learning and positive attitudes to mathematics should be promoted using information and

communication technologies.

Learning Objectives

The tasks undertaken by the student were designed to address the following math objectives:

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• identify and analyse mathematical statements within articles;

• search for and identify chronological word patterns; and

• recognise the evolutionary development of mathematical concepts.

Web CT Quiz: Students again completed a WebCT quiz requiring them to analyse a graph providing

data on the frequency of letters in the English alphabet, as shown in Figure 5. This task provided a link

to the overarching theme of innovations and was implemented in direct response to research carried

out by the UAE University’s College of Education, who concluded that a majority of science and

mathematics students at secondary school level lacked the ability to interpret the information contained

in graphs (UAE Ministry of Information and Culture, 2004).

Figure 5: Letter frequency of the English alphabet

An opportunity was provided for students to engage with and internalise the concept of frequency

analysis through the completion of an extension task. This task was offered at DMC’s Mathematics

Learning Zone in the Learning Centre, which provides assistance to students in order to extend their

mathematical skills and realise their potential. This particular task required students to use a ‘formula-

enabled’ Microsoft Excel sheet and Al-Kindi’s method of frequency analysis to ‘break’ codes in order

to successfully find the original message. Messages are coded using a JavaScript monalphaphabetic

coding programme , shown in Figure 6, and are then pasted into a ‘formula enabled’ cell of the Excel

sheet which generates a frequency list of the letters in the coded message. Students graph the data and

compare this graph to a graph of the expected frequency of letters in an uncoded message. By

identifying the expected patterns inherent in alphabet letter frequencies, students are able to find the

encryption key – in this case, the letter which has been substituted for the letter A. Once the key is

located, students use the Java programme to decrypt/decode the message.

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Figure 6: JavaScript monalphaphabetic coding programme (Hannon, 2006)

Transfer of skills, knowledge and attitudes

Following the completion of the Foundations year, students who enrol in a Higher Diploma

programme undertake studies in this specialisation (for example, Engineering or Business). In addition

to core units, in many programs students continue to complete formal studies in Mathematics as

outlined below:

• Math 101 (Aviation)

• ETEC 105 (Engineering)

• Math 100 (Business)

The integration of Mathematics within an interdisciplinary, blended learning Foundations programme

provides students with a greater ability to apply mathematics in a variety of authentic contexts. The

mathematical skills, experiences and knowledge, applied in context, have been identified as effective

building blocks which subsequent course mathematics teachers can exploit. As a result of the work

students completed in the Careers and Innovation and the Developments and Change projects, further

liaison is currently underway between the CRSP team, Foundation faculty and the programme math

teachers to develop activities building on these topic areas. Two examples under development are

outlined below:

1. Measurement: Using the decision analysis task model, students decide which premises would

best meet the needs of specific businesses.

2. Logarithmic Equations: Investigating ‘Zipf’ law concerning term frequencies (Robertson,

2007), students plot graphs of the log of word frequency against the log of word rank to

identify a straight line.

These types of activities can only be pursued with students possessing good levels of technical skills,

higher order thinking and analytical skills, higher order L2 skills, effective study and independent

learning skills, and experience with blended learning instructional strategies.

Research Findings

The findings from the informal study carried out to research the effectiveness of the integrated CRSP

programme approach adopted at DMC, support the general findings of similar research studies

whereby “student achievement is at least as high, and often higher, [than] …in traditional classrooms”

(Bossert, 1988-1989, p. 225). Certainly, positive interdependence was fostered, and observed to be

effective (for instance when students had to locate and analyse data which they later needed to

disseminate). In addition, individual accountability was enhanced when students worked alone on

separate aspects of the analytical tasks.

Faculty feedback has been collected through interviews, email, and the completion of online

questionnaires during the 2004 to 2007 academic years. The feedback can be divided into five main

categorical statements:

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1) Students perceive integrated projects as having a real purpose (i.e. adding to skills that they will

use in further study and in their careers), while also enhancing their mathematics learning

experience and proficiency.

2) The use of content material, resources, and skills in authentic tasks, coupled with integrated

assessment tasks, is motivational and constructive.

3) The integrated programme approach is effective at fostering research, study, and critical

thinking skills acquisition, and the application of content course concepts.

4) The skills acquired in HD Foundations are being applied when students graduate to HD.

5) When task completion expectations are high students are ‘challenged’ by these expectations

and a higher quality of work is produced and submitted.

Recommendations from stakeholder feedback have been implemented on an ongoing basis and have

resulted in further incorporation of skills, recycling of key concepts and vocabulary, as well as

increased focus on integrated assessment.

Limitations of the informal data referred to above include issues of reliability, validity and

generalisability. A formal study, using both quantitative and qualitative methodology, would be

required before dependable recommendations could be made about the effectiveness of integrated

programmes and cooperative tasks. By using a combination of research approaches it is felt that the

development of mathematical skills could be studied, while also taking into account improvement in

metacognitive strategies. The informal data collected as part of this study, nevertheless, appear

promising.

Conclusion

The CRSP course design is tailored to Emirati students and their specific needs as learners, with the

emphasis being placed on achieving key curriculum objectives through an experiential learning

process. The blended learning approach is valuable as it provides a supported shift toward self-

directed learning that recognises the importance of the training and empowerment of students, enabling

them to become lifelong learners. As such, learners are encouraged to adapt to a new learning culture

where research, original production, and creativity are particularly valued. The CRSP course employs

a functional, ‘authentic’ approach which focuses on process with ‘real-world’ significance. Thus, the

relevance of both content and skills to current and future learning, in addition to future workplace

competencies is consistently re-enforced through realistic examples and tasks. The successful

implementation within CRSP of active teaching strategies to teach mathematic skills and achieve a

transformation of students’ mathematical thinking, demonstrates the inherent strengths of an integrated

ICT program approach.

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References

Al-Harthi, A. S. (2005). Distance higher education experiences of Arub Gulf students in the United

States: A cultural perspective. The International Review of Research in Open and Distance Learning,

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Atweh, B. (2002). Random Reflections from Un/Biased Action Researcher. In P. Valero & O.

Skovsmose (Eds.), Proceedings of the 3rd International MES Conference (pp. 1-3). Copenhagen:

Centre for Research in Learning Mathematics.

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