The VideoM@T Project

Engaging Students on Learning Tricky Topics in Mathematics Through Creative

Skills

Sara Cruz, José Alberto Lencastre

and Clara Coutinho

Institute of Education, University of Minho, Campus de Gualtar, 4710-057, Braga, Portugal

Keywords: Threshold Concepts, Tricky Topics, Technology-enhanced Learning, Creative Video Editing.

Abstract: This article presents the VideoM@t project, designed to enhance students' understanding of mathematical

concepts through creative video editing. VideoM@t was founded on the JuxtaLearn process, an eight-stage

pedagogical framework that uses an online platform to assist the students in planning, editing, and sharing

knowledge about threshold concepts in a flipped classroom model. The project involved 52 students from

grade and three teachers of mathematics. Qualitative and quantitative data were collected to understand

students' level of comprehension on tricky topics in mathematics. The results show that students were able

to overcome their difficulties during the creative video editing process. The comparison between the first

and the final quiz radar charts suggest that students have developed understandable knowledge on tricky

topics in mathematics.

1 INTRODUCTION

VideoM@t was one of the winning projects of the

contest “Ideias com Mérito” [Ideas with Merit]

promoted by the Portuguese Ministry of Education

to encourage schools to develop innovative projects

that use information and knowledge to support the

school curriculum. The prize was used to buy tablets

that students used throughout the project

implementation. In the VideoM@t project, we seek

to stimulate students' understanding of mathematical

threshold concepts through the production of

creative videos. Threshold concepts are reported in

the literature as complex concepts that students have

difficulty in understanding, sometimes taking refuge

in the memorisation of the concept without really

understanding it (Meyer and Land, 2003). For

students, threshold concepts are troublesome

because they are conceptually difficult to

comprehend (Perkins, 2006). An abstract concept

describes something general, but concrete

representations and real-world examples always

describe something specific and are very important

when connecting concrete and abstract mathematical

contexts (Rystedt, Helenius and Kilhamn, 2016).

VideoM@t project was founded on the

JuxtaLearn learning process. The JuxtaLearn process

uses creative video editing by students to get them to

a deeper understanding of a threshold concept or a

tricky topic (Adams, Rogers, Coughlan, Van-der-

Linden, Clough, Martin, and Collins, 2013). In the

JuxtaLearn process, the terminology ‘tricky topic’ is

used to refer to issues identified by teachers as

difficult for their students (Adams and Clough,

2015), even though these difficulties are not the

same as those reported in the literature as core

threshold concepts. In the JuxtaLearn process, to

understand the tricky topic, students have to surpass

some stumbling blocks that are outstripped first

during storyboarding and then in video editing.

During the whole process, CLIPIT coordinates all

user interaction and data such as documents,

storyboards, quizzes and videos.

This article is structured in five sections: in

Section 2, we introduce VideoM@t and the

JuxtaLearn learning process, while Section 3

presents the methods for data collection, then

Section 4 presents our main results and reflections.

We conclude in Section 5 with a synthesis and

proposals for future work.

342

Cruz, S., Alberto Lencastre, J. and Coutinho, C.

The VideoM@T Project.

DOI: 10.5220/0006771703420349

In Proceedings of the 10th International Conference on Computer Supported Education (CSEDU 2018), pages 342-349

ISBN: 978-989-758-291-2

2 BACKGROUND

2.1 VideoM@t Project

The search for solutions that foster academic success

in mathematical subjects for a group of students and

our willingness to implement the JuxtaLearn

learning process led to the elaboration of the

VideoM@t project. VideoM@t is centred on a

taxonomy developed by the JuxtaLearn project that

helps teachers to promote students' interest in

threshold concepts through the creation of original

explanatory videos. With VideoM@t, our primary

goals were to implement methodological alternatives

in which students construct their knowledge through

actions where they develop mathematical literacy to

understand complex math concepts. The project was

funded and the money was used to buy tablets. The

use of tablets, due to their portability, allows higher

efficacy in accessing digital contents (Lencastre,

Bento, and Magalhães, 2016). With this project, we

promote the sharing and involvement of students in

the production of videos that explore the

mathematics curricula. We developed in students a

creative inspiration, as well as an improvement in

their conceptual understanding and their knowledge.

2.2 The JuxtaLearn Learning Process

The JuxtaLearn learning process is founded on a

specific pedagogic framework that aims to identify

and promote knowledge in threshold concepts in

STEM areas (Science, Technology, Engineering,

and Mathematics) through creative video editing.

The JuxtaLearn process involves the students in

eight steps, and is user-centred (Martín, Gértrudix,

Urquiza-Fuentes, Haya, Hernán-Losada and

Castellanos, 2014); i.e., the student is the protagonist

in the learning process, and the teacher is a

facilitator between the student and the knowledge

(Lencastre and Coutinho, 2015).

Figure 1: The JuxtaLearn Process.

Step 1 (Identify) – The teacher identifies the

tricky topics based on their previous experience.

Each tricky topic can be divided into smaller

stumbling blocks.

Step 2 (Demonstrate) – The teacher creates

one or more Standard Teaching Activities (STA)

around the stumbling blocks.

Step 3 (Interpret) – Students perform a

diagnostic quiz to determine their level of

understanding about the tricky topic.

Step 4 (Perform) – Students create a

storyboard to explain the tricky topic.

Step 5 (Compose) – In groups, the students

make a video explaining the tricky topic.

Step 6 (Share) – Videos are shared with the

class via CLIPIT.

Step 7 (Discuss) – Debate among students is

promoted, allowing the social construction of

knowledge while promoting the consolidation of the

concept.

Step 8 (Review) – Students return to the quiz

from Step 3 to re-assess their understanding of the

tricky topic.

The entire process is tracked online on the

CLIPIT platform (see Figure 1). CLIPIT is a web

space that allows collaboration, peer assessment, and

analysis of the learning progression in a flipped

classroom model. The productive failure-based

flipped classroom pedagogical design, allows

students to have more time for thinking and

discovering, and may help to improve students’

problem-solving skills (Song and Kapur, 2017).

CLIPIT was developed to support the JuxtaLearn

learning process by allowing comments and analysis

of the results (Adams and Clough, 2015). CLIPIT

has a database of tricky topics, and their related

stumbling blocks, examples of student’s problems,

quizzes and teaching material. To learn more about

CLIPIT, see the article from Cruz, Lencastre,

Coutinho, Clough, and Adams (2016) - Threshold

Concepts Vs. Tricky Topics - Exploring the Causes

of Student's Misunderstandings with the Problem

Distiller Tool, reported in the references.

3 METHOD

VideoM@t was strongly anchored on JuxtaLearn

learning steps. The study included the identification

of tricky topics in mathematics with three teachers

and the application of the entire process with 52

students. The teachers collaborated voluntarily,

involving three of her own classes.

The VideoM@T Project

343

Diverse methods were used to collect the data: (i)

interviews with the teachers; (ii) system logs on the

platform, (iii) a diary to gather direct observations,

(iv) a final focus group with the students to

understand their perceptions about the whole

process.

3.1 Identifying the Tricky Topics

The first step was to identify the threshold concepts

with the teachers. The three teachers assembled in a

group, reflected on the difficulties of their students

and identified threshold concepts that, from their

teaching experience, are tricky topics. Thus, based

on their knowledge, teachers identified the following

tricky topics: solving equations with denominators,

literal equations, solving 1st-order equations, and

solving equations with parentheses. Then, with the

guidance of the Problem Distiller tool, they divided

each tricky topic into stumbling blocks, and wrote a

brief description of the specific problems. The

Problem Distiller tool displays a set of tabbed panes

prompting teachers to reflect on and select possible

reasons why their students might be having a

particular problem, connecting all the information

entered to the appropriate tricky topic and stumbling

block or blocks (Adams and Clough, 2015). The

gathered tricky topics were then used by the students

to develop their videos.

3.2 Creative Video Editing

The creative video editing process involved six tasks

for each group of students: (1) diagnostic test (initial

quiz available on CLIPIT); (2) create a storyboard;

(3) edit the video, (4) watch the video and discuss it

with peers, (5) post-knowledge test (final quiz

available on CLIPIT) and (6) reflect on the results.

Initially (Identify) with the help of the Tricky

Topic Tool, we identified tricky topics and

mathematical topics that teachers considered

difficult for their students. The data collection was

done through system logs on the platform and a

diary to collect direct observations.

Next, (Demonstrate step) the teachers made

CLIPIT available through students’ activities

(videos, PDFs, links) with relevant information

about the identified tricky topics. The students

accessed the information, clarified doubts and then

completed a diagnostic quiz to determine their level

of understanding about the tricky topic. A diagnostic

quiz is the starting-point for students participating in

the JuxtaLearn Process (Adams and Clough, 2015).

Figure 2 shows a student verifying the result

obtained in the questionnaire.

Figure 2: Students checking the quiz radar charts.

Based on the results obtained in the diagnostic quiz,

the teachers established work groups comprising two

students. The group was set so that a student with

more difficulty in a certain topic would work with a

student who presented less difficulty. So, in pairs,

students drew storyboards to explain one of the

tricky topics or the initially identified stumbling

blocks (Perform step). The storyboards were

scientifically and pedagogically validated by the

teachers and the students created explanatory videos

based on these storyboards (Compose step).

The videos were shared in the class (Share

step) and a discussion was organised around the

work done (Discuss step). Then, the students

performed a final quiz (with the same questions as

the diagnostic quiz) to be able to compare results

and see their evolution.

In the end, with students, we performed a

focus-group to understand their perception of the

JuxtaLearn learning process. After transcribing the

material from the focus-group, a content analysis

was done following the guidelines of Bardin (2013).

A set of dimensions and categories emerged from

data, which are as follows: (i) Students' perception

of the storyboard design process, (ii) Students'

perception of the value of video editing, and (iii)

reflection about the process.

3.3 Participants

Three math teachers (T1, T2, and T3) working in a

public school, all being women aged between 42–50

years old. 52 students (Si, com i∈



1, …, 52



) from

the 9

grade, 31 girls and 21 boys, ages from 13–15

years old. Each teacher was responsible for

developing the JuxtaLearn process in her own class.

CSEDU 2018 - 10th International Conference on Computer Supported Education

344

4 RESULTS

The Problem Distiller Tool helps teachers reflect on

the causes of student problems they had identified

(Cruz, Lencastre, Coutinho, Clough, and Adams,

2016). So, based on their teaching practice, teachers

identified the tricky topics in mathematics that are

problematic for their students, and checked if the

tricky topics were already listed in the Tricky Topic

Tool and the database of CLIPIT.

Studies consider that concepts poorly

understood in arithmetic constitutes an obstacle to a

student's understanding of algebra (Guimarães,

Arcavi, Gómez, Ponte, and Silva, 2006). There is a

mathematical connection between algebra and

arithmetic as each is normally taught using

abstraction and generalisation processes. The

teachers identified arithmetical difficulties in

understanding and apprehending the algebraic

process for solving equations. So, teachers identified

the following tricky topics: (i) solving 1st-order

equations, (ii) solving equations with denominators,

(iii) solving equations with parentheses, and (iv)

literal equations.

Then teachers reflected on the difficulties

they usually encounter with their students and tried

to identify stumbling blocks and comprehension

gaps in tricky topics (Table 1). When teachers

expressed problems explaining why their students

had difficulty understanding the tricky topic, they

were guided by the Problem Distiller Tool.

Table 1: Tricky Topics and their stumbling blocks.

Tricky Topic

Stumbling Blocks

Solving 1st-

order

equations

Translation of statements of current

language for symbolic language

Simplification of algebraic

expressions

Principles of equivalence

Verification of solution

Notion of unknown and notion of

solution of an equation

Solving

equations

with

denominators

Distributive property of

multiplication

Priority of elementary operations,

Equivalence principles of equations,

notion of equation

Notion of solution

Simplification of algebraic

expressions and simplification of

fractions

Tricky Topic Stumbling Blocks

Solving

equations

with

parentheses

Distributive property of

multiplication

Distributive property of

multiplication

Property of elementary operations

Principles of equivalence of

equations

Use of rules to solve 1st degree

Equations with a non-denominator

unknown

Notion of unknown

Current language translation to

symbolic language

Simplification of algebraic

expressions and rational numbers

Literal

equations

Principles of equivalence of algebraic

equations

Simplification of algebraic

expressions

Solve a literal equation in order to an

unknown

Notion of solution and notion of

equation

The Problem Distiller tool lists a set of problems that

typically challenge students, helping the teacher to

think and reflect on their experience working with

students. Through this reflection, the teacher is able

to identify the gaps in an understanding of the tricky

topic and associate their own students’ difficulties to

the comprehension problems listed in the Problem

Distiller tool. As they made selections from the

Problem Distiller tool, teachers were identifying

problems that students typically encounter in

understanding tricky topics. At the same time,

teachers were also able to reflect on why these

problems occur and how they can be solved.

Figure 3: Problem Distiller to a 1st grade equation.

The VideoM@T Project

345

For example, on the tricky topic 1

-Grade equation

(Figure 3), the teachers reported that students do not

know the principles of equivalence and have

considerable difficulty in simplifying algebraic

expressions, which makes it difficult to work with

equations. Teachers also reported that their students

sometimes cannot verify whether a number is a

solution to a given equation because they cannot

recognise the meaning of unknown. On the Problem

Distiller Tool, teachers also associate possible

causes for difficulties on the tricky topic 1

-Grade

equation. They said that the causes for the

difficulties may arise from the students’ incomplete

knowledge of concepts that they should already

know, or a misunderstanding of the method for

solving equations.

The tricky topics identified in Step 1 of the

JuxtaLearn process have been revised. Then,

teachers shared material available in CLIPIT for

students to review the mathematical contents (Step 2

of the JuxtaLearn process). All students had an

initial quiz (Step 3 of the JuxtaLearn process),

previously prepared by the teachers on the Quiz

Tool in CLIPIT. We used the Radar Chart to help

students diagnose their own comprehension

problems in a tricky topic and to help teachers

reflect on ways of aiding the student to overcome

these stumbling blocks. The visualisation by

students of their own radar chart helps them to

identify and to diagnose the stumbling blocks they

encounter when trying to understand the tricky topic

(Hartnett and Adams, 2016); this can assist them to

focus on overcoming these difficulties. The

reflection on one's mistakes is relevant

(Cherepinsky, 2011) to overcoming gaps in

understanding and overcoming difficulties in

learning mathematics. Based on the results obtained

in the initial quiz, each group of two students created

a storyboard (Step 4 of the JuxtaLearn process) on a

mathematical subject in which they had difficulty.

Then, based on the storyboard created, the students

edited a video (Phase 5 of the JuxtaLearn process)

on the following topics: (i) solving a literal equation

in order to an unknown, (ii) the distributive property,

(iii) principles of equivalence between equations,

(iv) check if a value is a solution to an equation, (v)

notion of solving an equation, (vi) notion of

unknown of an equation, (vii) check if an ordered

pair is a solution, notion of unknown, (viii)

simplification of algebraic expressions, and (ix)

properties of the elementary operations. A

storyboard is a set of drawings as a representation of

a film in sequences, and these drawings can contain

elements such as dialogues, pictures, sketches

(Hartnett, Malzahn and Goldsmith, 2014). At the

end of this phase, 25 storyboards and their videos

were created. Storyboards and video scripts are

potential objects that allow the transfer of

knowledge between different students through the

creation of a movie. The creation of storyboards

constitutes a creative step on which students

collaborate, share knowledge and reflect in order to

identify and clarify differences (Hartnett et al.,

2014). The collaborative construction of videos

favours motivation for tasks (Cruz, Lencastre and

Coutinho, 2015). The videos created were shared

(Step 6 of the JuxtaLearn process) in class and a

discussion (Step 7 of the JuxtaLearn process) was

promoted around the results achieved. In the end,

students completed a final quiz (Step 8 of the

JuxtaLearn process) to compare performances. The

visualization of their quiz results as a radar chart

helps students to diagnose their own progress. In the

following image, we present an example of a radar

chart of the initial and final quizzes by one of the

students involved – S4

Figure 4: Radar chart with initial and final quizzes.

Comparing the chart radar observations for the

initial and final quizzes, we found that the student

improved in overcoming some stumbling blocks. We

observed that the student increased the number of

correct answers to questions that involve having the

notion of unknown, knowing the equivalence

principles of equations, knowing the distributive

property of multiplication and knowing how to

simplify algebraic expressions. The student kept the

same number of correct answers to questions that

involved knowing the priority of elementary

operations.

Comparing the results obtained on the radar

of the initial quiz with the ones obtained on the final

quiz (Table 2), in all three classes it was found that

most students improved their scores.

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Table 2: Comparison between the initial and final quiz.

Class

Teacher

Variation of the final to the initial quiz

Positive

variation

There was

no variation

Negative

variation

A T1

87% 13% 0%

B T2

50%

28% 22%

C T3

69% 12% 19%

Total

67% 18%  14%

Song and Kapur (2017) in their quasi-experimental

study comparing the “traditional flipped classroom”

pedagogical design to the “productive failure”

pedagogical design in the flipped classroom for a

curriculum in a Secondary school found something

similar. In this study, authors worked in two Grade 7

classes, one of them with “traditional flipped

classroom” and the other class with the “productive

failure-based flipped classroom”, with students who

had more difficulty.

The content analysis was developed

according to the phases suggested by Bardin (2013),

so Table 3 presents students’ voices according to the

three categories considered.

Table 3: Category of analysis.

Tricky

topic

N.º Stumbling Blocks

Students'

perception

of the

storyboard

design

process

5 "The most difficult thing is to have the

idea for the storyboard" (S2).

"Because we had to find a way to

explain an equation and it was

complicated" (S24).

"It is as if we were to teach" (S32).

"Was the one who gave more work, to

have ideas" (S41).

"Was the one that gave more work, to

have ideas" (S41).

Students'

perception

of the

value of

video

editin

3 "I enjoyed recording the video" (S13).

"The one I liked the most was making

the video" (S11).

"We did the same job, but on the

computer, so it's more appealing"

(

S32

)

Reflection

about the

process

"The first problem is that we had to

know the matter, then we had the

problem of perceiving how we are

going to explain that. The third

problem was getting it to the paper,

which was in our head. The fourth

problem was to convey to reality

"(S4).

"This work has clarified some

misunderstandings, almost all of

them" (S51).

Interpreting Table 3, we verified that during

reflection at the end of the cycle, the students

considered that "storyboard phase" (S4) was the

stage of the process they felt to be the most difficult

as they had to "get the idea for the storyboard" (S2).

Finding "a way to explain an equation and it was

complicated" (S24), worked "as if we were

teaching" (S32), so this step "was what worked the

most" (S41).

According to the opinion of the students, the

most enjoyable step in the process was to "record the

video" (C4A13), or "make the video" (C4A11).

They enjoyed doing creative video-editing work and

having the opportunity to work out more exercises

using this method, because "on the computer, then

it's more appealing" (S32). These results are similar

to those obtained by Kearney and Schuck (2006); in

a study with a group of students who had to choose

the content for a video, they wrote their own scripts

and storyboards and proceeded to the creative

edition of the video. During this work, creative

video production has motivated, enveloped, and

enthused students in learning and working with

mathematical concepts. All the students admit that

the process helped them to think differently,

"because it clarified some doubts, almost all of

them" (C4A51). Students need to feel that they can

create and choose their own path in learning through

clear guidelines in order to improve their

understanding and creative performance (Adams et

al., 2013).

In general, students consider that thinking

about and planning the videos helped them to

overcome the stumbling blocks that were obstacles

to learning. However, they admit that they had

difficulties in doing the work: "The first problem is

that they had to know the matter, then they had the

problem of realising how they were going to explain

it. The third problem was getting what was in the

head on to paper. The fourth problem was to convey

the reality" (S4). By awakening students' curiosity in

concepts, the JuxtaLearn learning process is

intended to support students in a deeper

understanding of a specific concept through a

creative process of video editing that is based on a

stimulating and flexible approach (Adams et al.,

2013).

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347

5 CONCLUSIONS

In this article, we described the VideoM@t project

based on the JuxtaLearn learning process. During

the study, we identified and discussed ways in which

the process helped the students to overcome

misunderstandings on mathematical concepts.

Teachers identified the tricky topics that their

students have, and we uploaded them into the Tricky

Topic Tool. Then, with the help of the Problem

Distiller Tool, teachers were led to reflect about

misunderstandings that they usually find among

their students. Teachers were able to put into

practice the whole JuxtaLearn process with their

students, by guiding them in the production of

storyboards and instructional videos in a

collaborative way. Students created 25 explanatory

videos about concepts they had difficulty in. They

considered that producing videos helped them –

“work has clarified some misunderstandings, almost

all of them" (S51). In this phase, they admit to

having experienced increased difficulty, because

they "had to find a way to explain an equation and it

was complicated" (S24). In general, all students

enjoyed doing the work, mainly "recording the

video" (S13), because the process involved students

by making them an active part in their own learning.

The results of Rystedt, Helenius and Kilhamn (2016)

in a case study investigates how a group of 12-year-

old pupils contextualise a task formulated as an

equation expressed in a word problem, showing the

importance of giving pupils opportunities to realise

the position of symbolic mathematical

representations when dealing with mathematical

concepts. In line with Rystedt et al. (2016), our

analysis indicates that engaging students in concrete

activities that involve them helps to improve their

skills.

Data analysis showed that the VideoM@t

involved the majority of the students. All of them

completed the JuxtaLearn learning process and most

improved the results in the post-knowledge test.

According to the results obtained by Rystedt et al.,

2016), the concrete representations (such as real-

world situations) are conceptually different from

abstract mathematical concepts. Pirhonen and Rasib

(2017), in a study about the learning method in

which students produce instructional videos about

the content matter of their learning process, realised

that producing a video combined with the content

approach can be an efficient and motivating way of

learning. A didactical implication of this case study

is that it is difficult to incorporate the rich meaning

of an abstract concept. However, the video creation

involve the students in recreational activities that

allowed them to develop skills around these

concepts. It also seems appropriate to analyse in

future research if the level of reflection achieved

with the use of the Problem Distiller Tool

contributes to changing the teachers' professional

practice.

The radar chart works as a digital tool for

evaluation and visualisation of the results by

students and teachers. The students’ view of the

radar chart, however, should be regarded as a

significant means to support reflection alone.

Although the role of the teacher is also important, it

is a teacher's task to manage the students’ reflection

in order to promote deeper thinking. In line with

Cruz, Lencastre, Coutinho, Clough and Adams

(2016), findings suggest that students are receptive

to making videos and can improve their

mathematical knowledge around complex concepts.

These results are important to foster curiosity around

mathematical topics, but further research is needed

to study the pedagogical relevance of this.

In today's innovation society, mathematical

knowledge becomes ever more relevant in the

development of the next generation of creative

thinkers and innovators. This VideoM@t project

was set out to solve problems in the understanding

of mathematical concepts, through creative video

editing. The ease with which students deal with

video, mobile technology, and digital resources

should be used in the learning process for

educational purposes (Lencastre et al., 2016). Do

teachers conceive the idea of being able to work

remotely, to create digital resources to help the

student and guide a student-centred work in a non-

presentational way? Global connectivity and new

forms of communication are some of the drivers that

reshape the way we think, which influences how we

learn and develop skills. Are schools taking

advantage of the potential of digital technologies,

including the possibility of having personalised

information and open content? Do teachers use the

interactivity that this type of material make possible?

To improve the teaching of mathematics, it is

necessary to establish a new vision for learning. It

would be beneficial if students could learn with

study tools that adapt to their capabilities. CLIPIT

helped students to assess their own knowledge about

a mathematical topic. Students are positively

reinforced during their individual learning processes.

In future research, it would be interesting to create

some courses in a similar way to create the

storyboard and video in the same application, aiming

for a more immediate support to students’ work by

CSEDU 2018 - 10th International Conference on Computer Supported Education

348

the teacher and at the same time broadening the

possibility of online co-production, breaking away

from the traditional way of teaching and learning.

ACKNOWLEDGEMENTS

The VideoM@t project received funding from the

Ministry of Education and the Ministry of Culture,

through a contest promoted by the School Libraries

Network (Portugal). We would like to sincerely

thank all the students and teachers from School of

Palmeira (Portugal), which agreed to participate in

the project.

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The VideoM@T Project

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