Motivating Upper Secondary Students to Learn Mathematics with

Working Life Exercises

Päivi Porras

and Johanna Naukkarinen

Technology, LAB UAS, Skinnarilankatu 36, Lappeenranta, Finland

School of Energy Systems, LUT University, Lappeenranta, Finland

Keywords: Mathematics, STACK, Moodle, GeoGebra, Virtual Reality.

Abstract: This paper describes a massive open online course (MOOC) that targets upper secondary school students.

During the years that we have been working in LUMA Centre Saimaa (an organization to inspire and motivate

children and youth in mathematics, science and technology), we have noticed that upper secondary school

students often fail to see the connection between mathematics studied at that level and their future career plans.

This work-in-progress paper describes a construction and first user experiences of project TyöMAA, which

aims at strengthening the high school students’ perceptions of the applicability of mathematics in the working

life. This is done by giving upper secondary school mathematics teachers real working life examples

connected to topics in their courses and developing a MOOC for students in which they can solve work-

related mathematical problems.

1 INTRODUCTION

A decreasing interest in mathematics is not only a

problem in technology and other STEM fields but

also in fields like physiotherapy, nursing, tourism,

and hospitality. Contextual framing of mathematics

problems has often been suggested as means to

motivate and engage students, but the related

empirical evidence is still somewhat scarce (Beswick

2011). Appropriate contextual framing naturally

depends on the topics and level of mathematics

taught, but also on the age and interests of the

learners. Kärkkäinen and Luojus (2019) discovered

that more than 75% of Finnish high school students

were indecisive of their occupational interests and

had related concerns and worries. Hence, it can be

deduced that the future working life is a meaningful

context for many high school students and could

provide a fruitful starting point also for

contextualizing mathematics problems.

Mathematics-oriented teachers are usually more

familiar with technology and STEM fields and, for

that reason, may unintentionally neglect the

application of mathematics in other fields. However,

mathematics is needed everywhere. Expecting

teachers to be able to provide a wide array of working

life related mathematics examples is unrealistic and

the teachers need to be supported in this by other

professionals (Nieminen 2015). In our project, we

create examples of mathematical problems related to

all fields covered at our campus: technology, nursing

and health care, business, tourism and hospitality and

the arts. This helps teachers to motivate students, as

they can illustrate where mathematics is needed in

those areas.

Prior experiment of using engineering problems in

high school mathematics teaching indicates that these

exemplars can increase the student perception of

practicality and usefulness of mathematics even if the

examples are not taken from students’ everyday life or

situations that they can directly and personally relate

to. In this case the practical value of mathematics was

enhanced through meaningful connection of

mathematics to the scientific problems and working

life. (Nieminen 2015). Earlier studies show also that

the perception of usefulness of mathematics for real

life and future career increase the student motivation

towards the subject (Summala 2020). Although the

utility value of mathematics can be argued to increase

specifically the extrinsic motivation of the students, it

has been noted not to decrease the intrinsic motivation

to learn (Porras, 2015).

Little and Jones (2010) point out possible

dilemmas in the use of real-world contextual framing.

First dilemma relates with the perceived utility of

mathematics, where “[o]n the one hand, by making a

connection between the abstract world of

mathematics and everyday, or scientific contexts, we

208

Porras, P. and Naukkarinen, J.

Motivating Upper Secondar y Students to Learn Mathematics with Working Life Exercises.

DOI: 10.5220/0010429102080215

In Proceedings of the 13th International Conference on Computer Supported Education (CSEDU 2021) - Volume 2, pages 208-215

ISBN: 978-989-758-502-9

are reinforcing the utility of mathematics as a

language for explaining the patterns and symmetries

of the ‘real’ world. On the other hand, if we

manipulate and ‘sanitise’ real-world experiences to

enable them to be modelled by a pre-ordained set of

mathematical techniques, then the result can appear

to be artificial and contrived.” ( Little & Jones, 2010,

p. 137) Another dilemma concerns the effect of

framing the questions in real-life contexts. On one hand

this has been argued to help to solve the mathematical

task by providing mental scaffolding, on the other hand

it can complicate the task by making assumptions of

certain context knowledge outside mathematics. (Ibid.)

We aim to address both these dilemmas by searching

and offering as genuine working-life problems as

possible without extensive “sanitation”, but with

prerequisite context knowledge.

We believe that the high school students’

motivation towards mathematics can be enhanced by

presenting them mathematical tasks contextually

framed in working-life problems from different

occupations. In addition to enhancing the interest in

mathematics, this is also hoped to provide students

support in the development of their professional

identities. The following sections provide an

overview of the work we have conducted so far, and

we finish with some ideas of how to investigate the

outcomes and effectiveness of our solutions.

2 THE FRAMEWORK OF THE

MOOC

One important aspect of planning the massive open

online course (MOOC) was that it should not be

confined to time or place. Upper secondary school

mathematics is mainly studied over three years, so it

is not reasonable to assume that students will use this

MOOC in a short period of time. Repetition is also an

important factor in deep learning (Roedinger & Pyc,

2012).

A second aspect was that the MOOC should

appeal to both female and male students, regardless

of whether they were planning futures in STEM fields

or other areas. All students seeing the importance of

mathematics would be a victory for us, especially if

they initially considered mathematics as difficult and

not needed after school.

Due to the first aspect, the use of the MOOC

should be as automated as possible. The teacher(s) of

this MOOC cannot be available whenever the

students want to access it. In addition, if help is not

available when needed, it may decrease motivation.

Thus, a third aspect was to create the course in a form

in which it provides hints and advises students during

their learning without the presence of teachers. This

kind of support is sometimes called instructional

scaffolding (Reid et al., 2015).

2.1 Technical Setup of the MOOC

This section describes the technical elements of the

course. Technical resources have a major effect on

what and how the material can be produced. They

may also influence a student’s motivation and self-

regulation levels. Unfortunately, online material does

not always take advantage of many of the possibilities

offered by the Internet (Kainulainen, 2006).

Moodle (www.moodle.org) is a free and open-

based learning management platform that is

commonly used in Finnish universities. As it enables

automatic grading and has good analytic tools for

analysing learning, it suited this course well. Moodle

is easy to use, even if learners like the upper

secondary school students have had no prior

experience using it.

STACK is a computer-aided assessment package

for mathematic questions on the Moodle platform

(https://moodle.org/plugins/qtype_stack). It enables

the randomizing of variables, as well as providing

feedback based on a student’s answer. Various

question types can be formed, for example, algebraic,

numerical, multiple choice (radio button or checkbox)

and equivalence reasoning. When combining

different kinds of question types, understanding can

be reviewed in addition to calculation skills. STACK

supports JSXGraph (http://jsxgraph.uni-bayreuth.de/

wiki/) and GeoGebra for graphing. JSXGraph is more

convenient if a graph is based on provided functions

(either by a teacher or by a student as an answer), but

GeoGebra enables curve-sketching problems and has

3D-graphing for better illustrations.

GeoGebra is an open-source dynamic

mathematics software application (www.geogebra.

org), in which geometry (2D and 3D), algebra,

spreadsheets, graphing, statistics and calculus are

presented in an illustrative way. For example, 3D

geometric objects can be easily rotated with the

software. It can have a major effect on understanding,

especially if a student’s spatial conceptualization is

not strong. GeoGebra also allows teachers to write

interactive lecture books with GeoGebra applets,

create videos, etc.

Although the examples and exercises follow the

curriculum of upper secondary level mathematics, in

the real working life examples, there may be concepts

that are not familiar to the students. As GeoGebra is

Motivating Upper Secondary Students to Learn Mathematics with Working Life Exercises

209

commonly used in Finnish upper secondary schools,

it was also selected by us as a main source for

additional material for students. As mentioned earlier,

GeoGebra can also be used in STACK questions.

Virtual reality (VR) makes it possible to study

things in a simulated environment (Poitras, 2020). In

some cases, studying in a simulated environment may

even be safer than studying in the real world, such as

with cliff blasting or handling dangerous chemicals

by a beginner. Virtual reality is becoming more

common, but it is still not an everyday activity for

most of us. Because we are not able to take students

to different kinds of workplaces during this project,

we will make the most of virtual reality to give them

simulated working life experiences as best as we can.

2.2 Learning Outline

This course was planned in close cooperation with

local upper secondary school teachers. The teachers

gave us insights and tips about difficult topics and

pointed out the ones in which students do not see the

connection to their future careers.

In upper secondary school in Finland, students can

select either a long or short syllabus in mathematics.

Even when selecting the long syllabus in

mathematics, they can still skip physics and

chemistry except for one compulsory course. Those

students who select the short syllabus usually select

only compulsory physics and chemistry. Hence,

mathematical applications in even physics and

chemistry remain out of reach for many students. For

instance, vectors are mainly connected with forces,

and forces are usually applied to technology in

mathematics. Forces are rarely connected with bodily

movements in examples, although they have a big

role in areas like physiotherapy. In addition, vectors

are studied only in the long syllabus, but students

interested in physiotherapy studies mainly select the

short syllabus and therefore make no connection

between mathematics and their career interests.

Figure 1 presents one interactive graph in

GeoGebra with a background photo selected. This

example is in the teaching material to demonstrate

how a kettlebell of 20 kg causes a force of 3.8 kN at

point D if the lifting is done with the back, not the

legs. Standing straight upright, this force on your

spine would be equivalent to the force of supporting

an object of 386 kg on the top of your head.

This is only one example in which a broader

understanding of mathematics (and physics) would

improve comprehension of a professional field,

although there may not be a need to perform the actual

calculations until later in one’s education.

Figure 1: Vectors in physiotherapy.

2.2.1 Course Structure

The starting point in planning this MOOC was

motivation. A person modifies his or her motivation

from external settings and, little by little, intrinsic

motivation may be aroused (Legault, 2016).

Although most upper secondary level students may

come to this MOOC for an external reward (to get a

course mark for their curriculum), success in the

exercises and real-life cases is hoped to also increase

their intrinsic motivation.

The course is divided into separate exercises for

the short and long syllabuses. The local teachers also

discussed that the first-year mathematics could be on

its own and the last two years presented together. The

main reason for this was that the third year is more

about preparing for the matriculation exam than

studying new topics. Students can work on the course

until they graduate from upper secondary school.

Although the course was divided into short and

long syllabus content, the students were permitted to

select any of the exercises. Some students in the short

syllabus may have good calculation skills and may

want to challenge themselves with exercises from the

long syllabus. Also, those struggling in the long

syllabus may want to try exercises from the short

syllabus to improve their self-esteem.

One part of using extrinsic motivation to cultivate

intrinsic motivation is to reward, not punish. Thus,

students do not need to solve all the exercises of the

package to get acceptable scores. The scores were

weighted by their difficulty level to motivate students

to select more challenging exercises. Applied

problems were weighted twice as much as mechanical

exercises, and exercises of the long syllabus were

worth more points than corresponding exercises in the

short syllabus.

This course was planned to be studied in close

connection with upper secondary mathematics

courses. Thus, extra lecture material was provided

only in some special cases. There was an interactive

GeoGebra book available in cases like that of the

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vectors mentioned earlier. Some topics were handled

in videos (MP4 and H5P). These videos also provided

guidance on correct answering techniques for the

STACK questions. H5P is an interactive video format

in which it is possible to add clarifying questions. In

a question type called “Crossroads”, a student can be

made to start a video again from a preselected time if

he or she answers incorrectly.

Students do not need to do all the exercises from

the selected package at once. The idea behind this is

that it is better to do one than not to do anything.

Secondly, the packages can contain question topics

that have not yet been handled by their teacher, so

they may not even have the knowledge to solve them.

Thirdly, a student may notice the need to review

earlier topics before continuing in exercises.

2.3 STACK Exercises

The Moodle activity called “Quiz” has different

behavioural modes. The mode “Interactive with

Multiple Tries” was used for all the exercises in this

MOOC. In STACK questions, the feedback on a

selected answer can be given both in a potential

feedback tree and in an option with hints. In Figure 2,

there is an example of solving a normal line equation.

In the potential response tree, sub-question a is first

checked, and it is indicated as incorrect. The second

comment in the yellow box tells the student that the

value of the slope is incorrect and that the equation

was not checked. The third comment was given by the

Figure 2: Feedback in STACK.

first hint. Hints make it possible for a student to

attempt the same exercise several times to correct his

or her mistakes. If the second attempted answer was

incorrect, then the second hint would be given. Hints

are general and cannot be customized based on a

student’s answer. A small deduction on a student’s

score is made whenever the answer is incorrect. With

two used hints, the maximum score for the exercises

would be 0.80 instead of one.

2.3.1 Equivalence Reasoning

In Figure 2, there is also an example of “Equivalence”

reasoning in STACK. The last two white boxes are

the validation boxes for the student’s answer: what

the student entered and how STACK interpreted the

given answer. In this case, all the given intermediate

steps were logical, so no errors were found. This

illustrates how entering answers or other mistakes are

noted before any reference as to whether the answer is

mathematically correct or not is made. As noted, the

slope was incorrect, so this answer cannot be correct.

In Figure 3, the student has corrected the slope and

uses it in the first row of question b. As a student has

not yet corrected it in the second line, the red question

mark can be seen at the beginning of the line. Thus,

the student will need to change his or her answer

before asking for it to be checked. This may help in

motivation, as answers are not judged to be incorrect

for keying or minor calculation mistakes. If a student

solves the exercises on paper first (as instructed), a

keyed solution is quite easy to review for further

unnoticed mistakes.

Figure 3: Error in an intermediate step.

2.3.2 Radio Buttons and Dropdown Menus

Mathematics is not only solving exercises with

methods provided by a teacher but also understanding

why they are used. Languaging (Joutsenlahti & Kulju,

Motivating Upper Secondary Students to Learn Mathematics with Working Life Exercises

211

2017) is an excellent way for a student to explain his

or her thinking when solving an exercise. However,

this kind of method is not suitable for a MOOC, in

which the feedback is obtained instantaneously. One

way for a student to express his or her thinking in a

system with automatic feedback is with radio buttons

and dropdown menus. Although the choices are pre-

scripted, the process does force students to think

through their solutions.

Figure 4: Example with radio buttons and a dropdown

menu.

Figure 4 shows an exercise for solving a quadratic

polynomial inequality. The main method of solving

for zeros from the standard form has been omitted

here. The main aspect is interpreting the solved zeros

with the original inequality to form the solution.

2.3.3 Graphs for Feedback

One way of providing feedback for a student without

showing the correct answer is with graphs. The

equation of a line shown in Figure 5 is incorrect.

Although the validation box on the right shows that

the equivalence reasoning is correct, the student has

given values of y in the wrong order. The line in the

student’s solution is shown together with the given

points (rather than just having the system judge the

solution to be incorrect). This hopefully helps

students to figure out their mistakes and/or

misunderstandings. This graph is not shown if there

are errors in the equivalence reasoning for defining an

equation (indicated by the red question mark at the

beginning of a line).

Figure 5: The equation of a line is defined incorrectly.

2.3.4 Applied Exercises

The applied exercises are verbal information, and

only a final answer is required. There are different

kinds of paths for solving applied exercises, and we

did not want to restrict the solution to only one correct

method. However, the final solution should be the

same despite the method selected.

An exercise shown in Figure 6, is part of exercises

in short syllabus. In this exercise, currency, amount,

and the transaction fee are all randomized. Although

the final answer is given, it will give hints for some

most typical mistakes.

Figure 6: Applied problem in economics.

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Students with their plans in social and health care

as, for example, nurses or paramedics do not always

see mathematics very important part of their work. In

Figure 7, is one example of math needed in

paramedics. If the amount oxygen is too low, it may

be life-threatening. If there too much over the

minimum requirement, there may not be enough

space in an ambulance.

Figure 7: Paramedics also need mathematics.

In Figure 8, there is an example of exercise in

geometry, which could be easily faced in civil or

mechanical engineering. At the first sight, the

exercise may look easy. The closer look reveals that

actual radius is not given (but chord is) and must be

solved. Solving this exercise requires knowledge in

circles, cylinders, and density.

Figure 8: Geometry is important in technology.

2.4 Applying Mathematics in Virtual

Reality

The upper secondary students who actively take part

in this course will be asked to visit campus as a final

activity (if COVID-19 restrictions allow it at the time).

Part of this project was to produce a virtual reality

experience in which students can solve applied

problems related to working life. All the activities in

the virtual reality will be connected to the exercises

solved in the MOOC, but they will be extended

versions of them.

We were able to liaise with Pulsan Asema

(https://www.pulsanasema.fi/en/), which is a very

popular resort in Lappeenranta, Finland. An

inventory model of the resort was digitalized some

years ago by Saimaa UAS, Finland, and our project

can use that digital information in the VR model. The

VR model is so accurate that even the location of the

plumbing can be checked. This allows us to add

actual working life exercises from civil engineering

through hospitality in the same VR model. Figure 9

shows an exercise concerning hospitality. An order

made by a customer is given on the screen to the right,

a recipe is to the left of the window, and a cake tin

needs to be found to see measurements. The volume

of this “old” cake tin is not known, so the student must

calculate it to know how much pastry is needed.

Figure 9: Exercise about an order made to Cafe.

3 NEXT STEPS

The project started in 2019. At that time, co-operation

with upper secondary teachers in science, mostly in

mathematics, occurred to find an appropriate level for

the exercises. The teachers also provided ideas and

identified topics that were neglected or were difficult

for the students (and therefore required attention). For

example, the concept of percentage is experienced as

quite difficult by students in the short syllabus,

although it is one of the most important topics in

many postgraduate studies, like economics, tourism

and hospitality.

The first students were enrolled in this course in

June 2020. A total of 25 students were accepted to the

course; 12 of them joined the Moodle platform, and

one student from the short syllabus passed Part A

(Part B will be available in spring 2021). This student

was very active and asked for help several times. She

Motivating Upper Secondary Students to Learn Mathematics with Working Life Exercises

213

did not lose her motivation, although there were

several coding mistakes. Thanks to her, we were also

able to code some different kinds of solution methods,

which had not been anticipated by the teachers in

engineering. As mentioned previously, there is

usually not just one correct method to solve a problem

in mathematics.

There are several possible reasons for a low

commitment to the course. In general, the completion

rate of MOOCs has been known to be weak (Alraimi

et al., 2015); self-paced MOOCs especially appear to

have low retention rates (Ihantola et al., 2020). In our

MOOC, over half of the enrolled students did not

even start the course. Of the 12 students that joined

the MOOC platform, only a few, in fact, solved

anything, and we suspect that most of them just joined

the course to get access to material. However, the

COVID-19 pandemic might have affected behaviour

in the course in many ways. Because of the pandemic,

the upper secondary school students thought that they

could not get any summer jobs in 2020 and enrolled

in this course to at least promote their studies. The

situation was surprisingly better than assumed, and

jobs became available, although later than normally.

Another pandemic-related explanation is that because

the students were studying online several months

during spring 2020, they had become restless with

online study and wanted a break from it. In any case,

we need to study this situation more.

To better understand the situation and student

experiences with the MOOC and to develop the

exercises and materials further, we are currently

collecting feedback with a form linked to the MOOC.

The feedback is provided anonymously, and it can be

targeted either to specific exercises or the course in

general. In the future, we are hoping to be able to

translate the course into English and Russian, as there

are two special upper secondary schools in our area.

The correct feedback is important part of a good

online exercise (Mäkelä et al, 2016), and especially if

feedback is automated. If a student feels positive and

encouraged after feedback, it may affect positively in

motivation and in engaging their studies (Kennette &

Chapman, 2021). Therefore, we collect students’

observations of cases where the feedback should be

improved to encourage instead of discouragement.

4 CONCLUSION

The worry of low interest in mathematics seems to be

worldwide (Yeh & al., 2019, Azmidar & al., 2017). If

the connection to one’s own life cannot be captured,

the interest is unlikely to arise. Like Legault (2016)

mentions, the inner interest arise motivation and will

to progress. The mathematics teacher of 2020 in

Finland Piia Haapsaari, who was selected by

mathematics teachers’ union MAOL, mentions that

she thought as a teenager not to be good enough in

mathematics. A good teacher and appropriate

teaching methods opened the lock: the success in

given tasks increased the inner interest

(https://esaimaa.fi/uutiset/kotimaa/33d7a047-b57a-

4bec-af99-f4495a0bb901).

Based on the feedback we have received at the

project steering group meetings and teacher webinars,

local upper secondary teachers are excited about this

course and material, want to learn more about it and

want to offer it to students. Of course, the demand for

upper secondary schools to cooperate with higher

education from fall 2021 forward helps us as well.

When this cooperation really starts, we will be able to

better see how much students are able to utilise the

course. One definite challenge is the already packed

upper secondary school curriculum and the resulting

heavy timetable of students, which may result in

reluctance to engage in any non-compulsory activities.

As both, contextual framing and use of modern

technology in the teaching of mathematics are

complex issues with positive and negative aspects,

the evaluation of the effect of MOOC on student

motivation must be carefully planned and executed.

We have started this work by establishing feedback

channels to the students and teachers, but more and

more versatile data is needed for proper data

triangulation and analysis. This is an essential part of

future work in the project.

ACKNOWLEDGEMENTS

We thank European Social Fund for funding this

project (S21637).

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