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Case 7
Where are the Examinations? Using Learning Journals in Mathematics Assessment

Contributor

Michael Lanigan

Email

mlanigan@WIT.ie

Telephone

+353-51-302-885

Affiliation

Department of Adult and Continuing Education, School of Education and Professional Development, Waterford Institute of Technology, Room CL6, St. Dominic’s, College Street Campus, Waterford, Ireland.

7.1 Context

The Waterford Institute of Technology (WIT) Certificate in Foundation Studies, accredited by the Further Education and Training Awards Council (FETAC) and WIT, targets adult learners intending to progress onto 3rd level education. The assessment methodology, outlined here, relates to the Business Mathematics and Technology Mathematics modules. The objective of these modules is to enable the learner to undertake any full-time Business or Science/Engineering course at WIT. Although achieving these objectives requires varying levels of mathematics, the overall level approximates the FETAC level 5/Leaving Certificate (National Qualification Authority of Ireland [NQAI] level 5). Some areas are necessarily covered in greater depth than others so that the levels approach that of 1st year mathematics.

Assessment is by means of formative and summative examinations and a 50/50 weighting of continuous assessment/final examination exists providing an overall final mark.

7.2 Learning Outcomes being Assessed

The overall aims and learning outcomes for the programme are stated in the course document as follows:

At the end of the course, the participants will have:

The learning journal assessed the so-called ‘softer’ or transferable skills more than the ‘harder’ skills; in other words, learning was assessed by the learner in the form of a dialogue between learner and tutor as opposed to, say, simply assessing mathematical ability or competency in a written examination. A major aim of the programme is to enable learners to transform their typically didactic expectation of learning to a more self-directed type; the journal facilitated learners and the tutor in this regard. In addition, a primary goal was to assist the learners in engaging with members of their study groups and with myself, as tutor, so that they would become interdependent learners. This goal was expressed as an overall programme aim, however, the course document was not specific in terms of how this goal was to be achieved, and the use of learning journals for mathematics was never expressed or implied.

Against this backdrop, using learning journals placed me in somewhat uncharted territory in terms of my own pedagogy and assessment methodology. To begin with, I framed the journal learning outcomes, conscious of the primary goal noted above, by stating that at the end of the module, the learner should be able to:

7.3 Assessment Procedures/Details

The module assessments, including the journal, break down as shown in Table 7.1.

Table 7.1: Breakdown of Assessments

Assessment

Format

Weight

Mid-term Assessment

1-hour written exam

5%

Written Assignment #1

Hand-up worksheet

5%

Written Assignment #2

Hand-up worksheet

5%

Christmas Assessment

1-hour written exam

10%

PowerPoint Assignment

15-minute peer-evaluated presentation

10%

Learning journal

On-going; Tutor assessed

15%

Summer Examination

2-hour written terminal exam

50%

The learners used the journal both inside and outside the classroom. Typically, the learners made entries after each of the three 1-hour sessions in the week; some made entries more often, some less, but each student was encouraged to write in the journal on a weekly basis at least.

I attempted to assist the learners who were not familiar and/or comfortable in reflecting by simplifying the process as much as possible, for example, encouraging them to answer questions as presented in Driscoll’s (19942000) model of reflective practice, summarised in Table 7.2.

Table 7.2: The ‘What?’ Model of Reflective Practice (Driscoll19942000)

What?

A description of event

So What?

An analysis of event

Now What?

Proposed actions following event

The learners were also provided with guidance on how to reflect, and on the assessment itself, i.e.:

What will be assessed?

  1. How your learning and engagement with the subject matter is progressing.
  2. Your identification of your strengths and weaknesses as an adult learner and as a student of mathematics.
  3. Your identification of any remedial actions that need to be considered.
  4. Noting improvements where you have taken action(s).
  5. Your engagement with the dialogue afforded by the learning journal

As a percentage of the learners’ continuous assessment, the journal was worth 30% (15% of the total module assessment). I provided each learner with formative submission milestones, throughout the year, and a final summative deadline towards the end of the academic year. The journal was assessed across four categories, each comprising 25% of the overall marks. The categories, based on the points above, were:

7.3.1 The benefits of journals

From the many journals read over the last two years, I have noted just some of the benefits of such an enterprise and have quoted portions for explanation/illustration.

Confidence building

A major goal of the project from the outset was confidence building. Examples of quotes from various students include the following:

I’m helping out in my local homework club and I’m breaking the maths down so a kid can get it—I’m loving it! Before this course I’d never have bothered because I didn’t think I could do it but now I know I can and if I don’t do it I’ll always regret not trying.

We did formulae today again. I had a very good ‘maths day’. I got the sums right and more importantly I understand what I was doing. I asked the right questions and understood the answers. It feels very good when you actually know what you’re doing …

A student, who was later to get an overall result of 89% in maths, wrote:

Since the day I left school I never envisaged myself being confident about maths. I did Leaving Certificate maths twice and got an F-grade both times. That “F” has represented “FEAR” to me and maths for the past 20 years. In the last 8 months “We” [student and tutor] managed to change it to “FEARLESS”.

In a unique class that I remember vividly, this same somewhat timid woman, who had struggled hard with mathematics for years, derived a new and improved method of working out a solution. Here is her entry from that occasion:

Michael said today I got the ‘x-factor’; didn’t quite know what he meant by that but later at the tutorial I accidentally! made known a simpler way to do the sum. Quite honestly it was the first day the statistics made sense to me and I just saw what Michael had explained moments before in the sum. Sometimes its so easy to miss that which is most obvious—happens [to] me all the time! It’s really given me a boost so it seems having the ‘x-factor’ means using logic in a unique way …

Another student who wrote, looking back over the year, wrote:

I’m really glad I kept the journal now because reading through it not only helped me relive the highs and lows, but has also helped me to see the growth that’s taken place in me.

Health and attitude ‘check-up’

Students noted their feelings and attitudes, for example, one student wrote:

I’ve been thinking over the stuff I discussed yesterday and I am realising that its ok for me to feel the way I do, it’s the realities of my life that are staring me in the face and the amount of time I can give to the course is limited. I’m going to take stock of my time management again! It’s all gone out the window with me over the past few weeks. Looking forward to the break next week, take a bit of time out to make some realistic decisions.

Another student stated:

Not really making head or tail of the maths today, but have felt like this before and I know that “this feeling too shall pass”, if I hang in there. Michael’s going to give me extra help on Monday so … hopefully.

Earlier in the year the same student wrote:

… sometimes how I’m looking at a situation has a huge effect on the outcome. If I sit in class thinking ‘I can’t get this—I can’t understand’, chances are I won’t. Whereas if I think I’m here to learn—I’m listening up in class, I am attempting to understand, then eventually I will.

Dealing with examinations and anxiety

In terms of examinations and anxiety, the students made statements, such as:

Feel pretty good about the test even though I missed all the classes in the week before.

Another wrote after her midterm result:

Words cannot describe—I got 74% in my test. I nearly knocked Michael over with the hug I gave him. I really didn’t think I’d do that well, I’m so thrilled—the kids and my mother were at home when I walked in with my results—think everyone in [my] Street knows!

The open nature of the learner-tutor dialogue that is afforded by the learning journal is indicated in the words of a veteran of a previous examination:

I did worry that my mind would go blank and I wouldn’t know how to do any of the sums as I’d been out last week, but I remained calm and I didn’t have a headache this time.

Assessment of one’s own needs including learning blocks and hang-ups

A student who had negative experiences of institutional education wrote:

… I can’t believe how upset I’ve been over maths. I’ve been taking a deeper look at why it is I’m so upset about the maths—it definitely relates back to my time in school and the beliefs I developed in myself about me and maths.

Earlier the same student had written:

I feel more inadequate than ever towards maths after today’s test. I know these feelings of incapability are deep-rooted. I used to think the fact that I was inattentive in class whilst in school was the reason I didn’t do well at maths but I’ve been at every maths class and tutorial bar one and I feel more inadequate and confused than ever … and that’s leaking into other areas of the course for me. I said in a few entries ago that it “couldn’t hurt” to do the test but by golly it did.

Collaboration and interdependent learning

Having the learners cooperate and work together in groups is something that is almost entirely dependent on the learners themselves. One student, who was pleasantly surprised by this type of experience, wrote:

… what surprised me was that I had to explain Permutations & Combinations to S [male student, quite competent at maths]! I couldn’t believe it! What surprised me even more was that when I explained it—he got it!’

This female student had been intimidated somewhat by her male colleague, but through collaboration with him, on this occasion, and on others, she developed confidence and used his experience and knowledge to help her with a presentation on maths later on in the year.

Another group of students who collaborated in the same study group wrote the following entries—individuals’ names are represented by initials:

Didn’t have a clue today. Totally lost the plot. Couldn’t understand a thing. Personally having a bad day, so it was probably more that than the lesson. I pulled myself together though and a few of us stayed behind after class and things started to make sense.

Today was a bit of an ‘Eureka day’ for me. I understood the maths and managed to keep up. Stayed behind with a few people (no tutorial). After B explained one part to me, I got it all and I was then able to explain it to P. I found that by explaining it to him I understood even more myself. A very good day.

Had it, lost it and found it again after class with some of the others! Stayed for tutorial and found that great. B and H are very good. They take time to help and explain. What I did know I tried to explain to S and M.

We went back over formulae today. I was very positive and concentrated well. The hour is just not long enough. A few of us stayed back. H and I did a sum. B already had it done and Michael said it was right. So we asked B to check ours. We both had it wrong. So B (God bless her) did it on the board for us. We’d be lost without that girl. She is so helpful and ready to share her knowledge. She went through it all step-by-step and I think I really understand it now.

7.4 Strengths and Limitations

Strengths

Limitations

Assessment of the students’ own needs

Feedback is time consuming

Confidence building

Student opposition to journaling

Gradual awareness

Superficiality

Monitoring and evaluation of own progress

Tutor’s own prejudices

Change in attitude (+ve)

Not for everyone

Self-directed learning

Making mistakes is ‘okay’

These strengths and limitations are discussed further below with students’ quotations in italics.

7.4.1 Strengths

7.4.2 Limitations

7.5 Contributor’s Reflections on the Assessment

I attempted to assess maths levels and ability early in the programme as historically, [mathematically] weaker students disengaged and I believed early intervention would mean a better prognosis. A traditional means of assessment, i.e., examination is not effective in preventing learners from disengaging. Therefore, a means of self-assessment, in the form of the learning journal was devised. Although the term ‘self-assessment’ is used throughout this case study, the term applies to the learners’ assessment of their own learning needs with respect to mathematics. Ultimately, the execution of the journal constituted 15% of overall module results.

One of my goals, in this experiment, was to help adult learners become more self-directed and assertive, especially in seeking and requesting assistance from the most appropriate source(s), once needs were assessed. I desired an outcome, whereby the learner would emerge from the reflexivity process having gained insights into his/her own learning preference(s) and needs. The student gained an insight into his/her own learning style(s), and how s/he internalised learning—s/he developed discernment. By participation in this experiment, the learner gradually learned to learn in a manner that was unique to him/her.

From an administrative perspective, the amount of commitment on my behalf was considerable as the weekly readings of journals took much time and effort. I managed this task because I kept the following in mind:

The learning journal has become an integral part of my pedagogy repertoire. The weaker students are identified and assisted earlier, thereby, increasing the chances of retention and completion; thus, their dream becomes achievable.

The continuity of the learning journal is encouraging for the future. Prior to the collation of the data for this case study, I observed attitudinal and behavioural changes in the group that, anecdotally, I attributed to the learning journal (this was subsequently validated). These changes were manifested as increased questioning of material, greater diligence in problem solving, improvement in interpersonal collaboration, and prioritising and addressing one’s own needs. This latter phenomenon caused much soul-searching, exposed in journaling as false humility, in some, guilty that they could take time for their own needs, exclusively however, a female trait, remarkable amongst those with a partner/ex-partner and family and/or other commitments.

Assertiveness to ask questions is paramount for 3rd level students, therefore, there existed within the journal, an open learner-tutor dialogue. Noticeably, increased personal development paralleled growing assertiveness. Moreover, tutor reliance diminished with self-directedness.

The learner-tutor dialogue explored learning issues; some reflected deeper than others, providing personal learning insights; others accepted the ‘necessary evil’ status of mathematics in humorously philosophical accounts. Under- or over-estimations of maths ability was recognised and dealt with.

In conclusion, most of the learners adjusted their attitudes; over time, some developed personal learning strategies illustrating one benefit of the mathematics journal. Moreover, the journal was the student’s space; s/he was relatively secure in controlling the environment. The students perceived learner-tutor equality, perhaps, something that is not perceived within the classroom context. The learner-tutor dialogue occurred semi-informally; the student ‘safely’ questioned his/her perceptions, attitudes, pre-suppositions, even, prejudices. The students’ vulnerability and exposure were minimised through this indirect relationship. My findings were presented to and validated by the learner groups.

7.6 Bibliography

7.7 Useful Resources