Who Learns Better

Achieving Long-term Knowledge Retention by Programming-based Learning

Stefano Federici, Claudia Medas and Elisabetta Gola

Dept. of Education, Psychology and Philosophy, University of Cagliari, Italy

Keywords: Knowledge Retention, Active Learning, Programming-based Learning, Exponentiation, Block Languages,

Scratch, Computational Thinking.

Abstract: In this paper we describe the experience of a year-long experiment devoted to understanding if retention of

knowledge acquired by students while learning a specific subject can be improved by letting them build by

themselves interactive models of that knowledge by means of a visual programming language based on the

block metaphor. What we propose is along the lines of active learning and learning-by-teaching. Students

build an interactive model that tests the knowledge of a specific topic and it is assumed that the topic will be

better memorized and understood than using standard learning strategies. To test this hypothesis, we run an

experiment on the students of two 5th grade classes, split in three groups. One group learned the topic by

both following standard explanations and by creating by themselves multimedia interactive projects by

means of a block language. A second group learned by following standard explanations and by playing with

multimedia interactive projects created by their peers in the first group. A third group learned by only

following standard explanations. The experiment outcome shows that there is a significant improvement in

the retention rate after several months for those students that build their digital tools by themselves with

respect to both students that use digital tools built by others and students that do not use digital tools at all. It

is our opinion that this strategy can be applied to topics of all disciplines, providing the bases of what we

can define as programming-based learning, a general learning methodology based on computer

programming.

1 INTRODUCTION

Can the usage of a block programming language, for

example a tool such as Scratch (scratch.mit.edu,

figure 1), help students to better remember topics

that are usually felt as particularly difficult to recall

after a long time?

Figure 1: Interactive explanation with Scratch.

The study of long-term retention of knowledge and

how this retention can be improved, is something

that has been analysed many times (Bridge and

Porteus, 1965; Fogel and Drew, 2008; Palha et al,

2015). Specific studies concentrated on knowledge

acquired at school (Semb and Ellis, 1994; Bethune,

2011; Boulton, 2013; Kirby, 2013) and especially

scientific knowledge (Engelbrecht et al, 2007;

Custer, 2008; Upadhyay and DeFranco, 2008;

Darland and Carmichael, 2012; Chin et al, 2013;

Deng and Gluckstein, 2014).

We often forget what we have learnt when we

have to remember it after a long time so that just

looking at the problem does not turn on anymore in

out mind the path from problem to solution. Several

studies have suggested different ways of facilitating

the recall of distant memories, from highligthing the

importance of visual help (Brady et al, 2008) to

proposing multimodal learning (Seemüller et al,

2012; Udomon et al, 2013), active learning (Prince,

2004; Bachelor et al, 2012), personalized review

124

Federici, S., Medas, C. and Gola, E.

Who Learns Better.

DOI: 10.5220/0006705001240133

In Proceedings of the 10th International Conference on Computer Supported Education (CSEDU 2018), pages 124-133

ISBN: 978-989-758-291-2

(Lindsey et al, 2014), and inquiry learning (Schmid

and Bogner, 2015).

One of the methods proposed to improve

retention has been the learning-by-teaching strategy

(Leelawong and Biswas, 2008; Chase et al, 2009;

Murphy-Paul et al, 2011) that states that the best

way to understand something is trying to teach

someone else that topic. By teaching someone

indeed you must have fully understood the internal

mechanisms of the topic and how the individual

parts of the explanation fit together.

What we propose in this paper is along the lines

of active learning and learning-by-teaching

strategies. Indeed students, by using a programming

language, build an interactive model that tests a

specific topic. By using this strategy, they not only

have the possibility of further memorize the topic,

but must fully understand how all parts of the topic

at stake fit together in order to correctly describe

their behaviours by using a programming language.

With this strategy we are enhancing computer-

supported education by programming-based

learning.

In order to test this hypothesis, we have run an

experiment on the students of two 5th grade classes.

The topic selected for the experiment has been one

that the teachers felt as particularly difficult to

remember for students of this grade, namely the

execution of the exponentiation operation.

Our working hypothesis is that, by assembling an

interactive model by themselves, students will

remember for a longer time how it really works, by

putting at work different learning strategies at the

same time (Seemüller et al., 2012; Udomon et al.,

2013).

2 A DIFFICULT TOPIC TO

REMEMBER

Why do students forget so easily what is the

meaning of the mathematical operation of

exponentiation? This is something that always struck

us. Students do not forget how to do a summation or

the multiplication of two numbers, but they forget

very easily what n

means.

Does maybe 2

mean that we have to multiply 2

by 3 (wrong; Pershan, 2013; Pershan, 2017; Liu,

2017, p.54), or that we have to multiply 3 by itself 2

times (wrong), or maybe that we have to sum 2 to

itself 3 times (wrong) or that we have to multiply 2

by itself 3 times (wrong, Pershan, 2017), or, in the

end, that we have to multiply three 2s by each other

(correct)?

Here you are the correct definition of

exponentiation (MathsIsFun, 2017):

“The exponent of a number says how many

times to use that number in a multiplication.”

To give an example, 2

means 2x2x2=4x2=8. So,

what we really have to remember is that the “small

number” at the top (the 3 in our example, called the

“exponent”) says how many times to use the “big

number” at the bottom (the 2 in our example, called

the “base”) in a multiplication.

What is that makes remembering how to

correctly execute exponentiation so difficult with

respect to, let us say, executing a summation or a

multiplication? The operations involved are

relatively simple (you have just to multiply several

numbers) but the meaning slips very easily from the

student’s mind. One possible explanation is that,

whereas summing or multiplying numbers is

something that can happen quite often in the

everyday life of a student, calculating an exponent is

instead something that, until you are not in a high

grade, you do not see so often, except maybe for

calculating the squared of a number, that is the

practical operation of calculating the area of a square

whose sides are a given measure. Another possible

reason is that the definition of exponentiation that

you find in books or websites is often misleading, as

for example in (iCoatchMath, 2017):

“An Exponent is a mathematical notation that

implies the number of times a number is to be

multiplied by itself.”

or in (Liu, 2017, p.53):

“An exponent means the number of times a

quantity is to be multiplied.”

So, students can think that to calculate 2

you have

to multiply 2 by itself 3 times, that is you do 3

multiplications, that is 2x2x2x2=16. But this is

clearly wrong. If you think this should be the correct

operation by reading the definition of exponentiation

and you then realize this is not the case by looking at

the examples, you can be confused and this

confusion can impair your recall.

A further source of problem is the possible

confusion (Liu, 2017, p. 54) arising when the student

is exposed to a wrong very first example. If the

student is shown at start that 2

=4, they can wrongly

remember that 2

is the same than 2x2.

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3 THE EXPERIMENT:

PROGRAMMING AND

EVALUATING

EXPONENTIATION

The experiment involved 36 students from two 5

grade classes from a local elementary school. The

experiment started during the same period of the

year when the two classes were studying

exponentiation, that is about at the beginning of the

school year, and was run during school hours

already devoted to mathematics. In order not to

interfere too much with the completion of the

explanation of all mathematics topics usually

explained in 5

grade, the teachers required that the

time spent by students in creating interactive

projects should have been limited to at most 3

sessions of 2 hours each. One further session of 2

hours was used to be able to discriminate at the end

of the experiment between the contribution of

computer-based learning and programming-based

learning (see section 3.2).

3.1 Beginning of the Experiment

At the beginning of the experiment the students were

all taught exponentiation in a standard classroom

lesson. Then the students were split in 3 groups in

order to understand the influence, if any, of

computer programming, by using a block language

such as Scratch, on long-term retention of the ability

to correctly solve standard exponentiation problems,

that is exponentiation problems that did not involve

“special cases” were the exponent is 0

or when both

the base and the exponent are 0’s

3.2 Splitting the Students in Groups

As doing well in the experiment could potentially

involve a lot of distinct factors (previous math

knowledge, concentration, interest and enthusiasm

with respect to technology, etc) and not having

enough time to run a thorough examination at the

beginning of the year of all the students involved in

the experiment, we asked the teachers of the two

classes, that had been working with the kids for 5

years, to split the classes in three roughly similar

groups basing on their general skills.

So, in each class we had group A, that would

have been working with exponentiation both by

following standard explanation and by creating

multimedia interactive projects by means of a block

language; group B, that would have been working

with exponentiation both by following standard

explanation and by playing with multimedia

interactive projects created by their peers; and group

C, that would have been working with

exponentiation only by following standard

explanation (see Table 1). So, we had a total of 12

students in each group.

Table 1: Learning in the different groups.

Group Learning

A Standard lessons

Creation of interactive projects

B Standard lessons

Usage of interactive projects

C Standard lessons only

From group A we wanted to clearly understand if

long-term retention could improve by allowing

students to create by themselves interactive

explanations. Group C instead was the control group

that was learning exponentiation by simply

following the teacher lessons. Group B was a second

control group to understand if just the usage of an

interactive project could have been as good as the

personal creation of an interactive project, that is

allowing us to discriminate between the usage of

digital tools supported by the computer-based

learning approach and the usage of computer

programming in the proposed programming-based

learning approach.

To avoid that the time devoted to learning

exponentiation would have been longer in groups A

and B with respect to group C and longer in group A

with respect to group B -as group A would have

spent several days in creating exponentiation

projects and group B would have spent several hours

in using those projects- students in groups B and C

kept exercising on exponentiation while the students

in the other groups were involved in creating or

using interactive projects. It is worth noting that

students in group A, in the end, spent less time in

exercising on exponentiation than students in groups

B and C, as their peers kept exercising on

exponentiation while they were learning about block

programming.

3.3 Teaching 5

Grade Students How

to Build Multimedia Interactive

Projects

In order to allow the students to learn how to build

an interactive project about exponentiation they

were first exposed to projects created by using a

programming language and then they were taught

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the basics of computer programming. We choose a

programming language based on the block

metaphor, Scratch (Maloney et al. 2010),

specifically designed to easily teach computer

programming to children 8-11 and to easily allow to

create colourful interactive objects.

The structure of a visual programming

environment for a block language is very easy and

quick to grasp (figure 2). All “instructions” indeed

are represented by coloured blocks that are visible in

the block area at the left-hand side of the window.

By dragging blocks from the block area to the

central part of the window, users can build

sequences of blocks, called “scripts”, for their

characters to behave and interact as expected.

Figure 2: Creating block sequences by drag-and-drop from

the block area (to the left) to the script area (to the right).

3.3.1 First Session: Arousing Enthusiasm

In the first session we allowed students to play with

several projects created with Scratch. Having only 3

sessions available, we had to arouse students’

enthusiasm very quickly towards the possibility of

creating the projects that they had to develop so to

have them work quickly and effectively. The

projects were all based on the SuperMario

characters. The reaction of the class was what we

had supposed, that is delighted. The first project was

a minigame that allowed them to move Supermario

and make it jump by using arrow keys to collect

coins by hitting boxes and avoiding the Goombas,

the bad guys (figure 3). When answering correctly or

wrongly, the student were getting the classic

Supermario’s “correct” or “wrong” sounds. The

purpose of this project was to make them familiar

with the simple move-and-jump mechanism that we

had chosen to use in the exponentiation project to let

them select what they thought as the correct answer.

This was, of course, more complex than a simple

point-and-click mechanism, but it was something

that a big part of them already knew and loved and

that was eager to use and to program.

Figure 3: Move-and-jump in Supermario minigame.

3.3.2 First Session: Introducing the

Structure of the Final Project

The main project shown in the first session aimed at

showing to the students the structure of the projects

they will have to develop during the next sessions.

By using the same move-and-jump mechanism of

the previous introductory project, this project tested

their knowledge about multiplications (figure 4).

Figure 4: Minigame to test multiplication.

For example, in the exponentiation project, the users

are asked to select the correct operation (figure 5) or

the correct factor (figure 6) by hitting the correct

yellow cube with the Yoshi character.

We started with multiplication as this is an

already well-known topic since 3

grade, but the

structure of this project was the same as the final

project about exponentiation that they had to

develop in their third session.

At the end of the project the students could see a

short minivideo of Supermario defeating the monster

Bowser. The minivideo made the students jump for

happiness.

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Figure 5: Selecting correct operation in exponentiation.

Figure 6: Selecting correct factor in exponentiation.

3.3.3 First Session: Final Free Exploration

The final part of the first session was aimed at

leaving the students free to explore the Scratch

environment. They quickly discovered several

features of Scratch such as how to add new

characters to the projects, how to draw their own

characters or backgrounds by themselves, how to

play sounds, etc. At the end of the first session they

were eager to start developing projects with Scratch.

3.3.4 Second Session: Developing

Multimedia Interactive Projects About

Multiplications

In the second session the students built the testing

project to check multiplications, as shown in figure

4. Knowing the topic very well since 3

grade they

did not have to think about what the project should

illustrate. The project taught how to decompose a

multiplication of n x m as a summation in which the

number n was used m times (figure 7).

Figure 7: “unpacking” 5x4 as the summation of four 5’s.

They learnt how to use a block programming

language by importing pictures of their characters

and their sounds and by creating scripts to describe

the behaviour of the characters by building

sequences of blocks and by finding events to trigger

the behaviours described by those sequences.

At the beginning of this very first session, blocks

and events were identified only after explaining

step-by-step to the students in plain language what

we wanted to happen and showed them how to find

the correct block in the block area and how to build

the correct sequence in the script area.

After a few scripts were built, the students

started to propose themselves how to go on and we

were then mainly busy in following (and correcting,

when necessary) their work.

3.3.5 Third Session: Developing Multimedia

Interactive Projects About

Exponentiation

In the third session the students built the same

testing project but this time about exponentiation.

The structure of the project was the same of the

multiplication project, so they had to express the

exponentiation n

as a multiplication in which the

number n was used m times (figure 8).

Figure 8: “unpacking” 2

as a multiplication of three 2’s.

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As the structure of the two projects was the same

(same blocks, same events, etc) and they already

knew how to use a block programming language,

this time the construction of the project was very

quick. At the end of the session, the students had

time to play with their projects.

They worked mainly by themselves, so that we

had only to help them a few times and correct them

when necessary.

3.3.6 Fourth Session: Playing With

Multimedia Interactive Projects About

Exponentiation

In the fourth session the students from group A and

B played both with the projects built by their peers

in group A and with further projects prepared by us

that they could use in order to test their knowledge

about exponentiation by solving an infinite sequence

of randomly-generated powers.

3.4 Blind-testing Knowledge About

Exponentiation

After the fourth session had ended, the knowledge

acquired by the students of all three groups (A, B

and C) about exponentiation has been tested by

giving them sequences of mixed multiplications and

exponentiations. In order to test how effective

computer programming was on long-term recall of

how to do exponentiation operations, the students

were tested three times, starting immediately after

the end of the four sessions and finishing at the end

of the school year. So, they were tested

• the day immediately after the fourth

session;

• after two weeks from the forth session;

• after six months from the forth session,

without prior notice.

The tests were prepared and administered by the

teachers of the two classes. The results of the three

tests were anonymized (both for privacy reasons and

for blind-testing purposes) and then sent to us. What

it is important to note is that the final test was

administered without giving prior notice to the

students, so that they had no time to refresh their

knowledge about exponentiation.

All three tests showed the same kind of errors.

The errors were mainly due to transforming

exponentiations in:

• summation instead of multiplication, e.g.

=2+2+2=6 (summation error);

• multiplication of the base times the

exponent, e.g. 2

=2x3=6 (times exponent

error);

• multiplication with a wrong number of

factors, e.g. 2

=2x2x2x2=16 (number of

factors error).

3.4.1 Immediate Test: Results

The results of the first test administered right after

the end of the fourth session were not able to really

discriminate among the three groups (figure 9).

Group A had a correctness rate of 99.82%, group B

99.83% and group C 100%. The difference Δ

between the top and the bottom group was less than

0.2%, which is really non-meaningful.

Figure 9: Results of “immediate” test.

From the results of this first experiment we could

see that all students had learned pretty well how to

calculate the result of an exponentiation. Not

surprisingly, students from group C, which had time

to exercise on exponentiation for 6 more hours while

students from group A were learning about block

languages, did better than any other group. But

being the test very close to the explanation, they all

did very well.

3.4.2 Two-weeks Test: Results

During the two weeks after the first test, the teachers

had time to introduce further topics of Mathematics,

such as decimal numbers and relative numbers, but

this didn’t affect the knowledge of the students

about exponentiation. So, even in the results of the

second test administered after two weeks, the

difference among the three groups was really small

(figure 10). Nonetheless, if results from groups B

and C had only slightly decreased, results from

Group A had instead increased, even if by a

negligible amount. Group A had indeed a

correctness rate of 100%, group B 98.6% and group

C 99.3%. The difference Δ between the top and the

bottom group was anyway less than 2%.

∆<0.2%

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Figure 10: Results of test after two weeks.

All students are still remembering pretty well how to

calculate the result of an exponentiation. Students

from group A showed a slight improvement with

respect to both groups B and C, and students from

group C started showing a small decrease.

3.4.3 Six-month Test: Results

After six months, that is very close to the end of

school year, we prepared a final test without giving

prior notice to the students. The students, since the

end of the second test, had not made further exercise

on exponentiation at school.

What we expected this time was a general, and

substantial, decrease in the correctness rate of the

three groups. But what we were very interested in

was how the students from group A, which had 6

hours less of exercise than students from group C

and 4 hours less than students from group C, would

have done with respect to their peers. The absolute

performance was as expected: all three groups

showed a substantial decrease with respect to the

previous results, showing a clear decrease by more

than 20% for all three groups. The best group, group

A, had this time a correctness rate of about 78%.

The best group this time was group A by far. The

relative performance this time was much better than

we expected, almost surprising.

Figure 11: Results of test after six months.

The differences among the three groups are in

our opinion extremely meaningful (figure 11). If

group A had a correctness rate of 78%, group B had

73% and group C 67%. The difference Δ between

the top and the bottom group was this time more

than 10%.

4 PROGRAMMING-BASED

LEARNING: ANALYSIS OF

THE RESULTS

What follows from the results of the three tests is

that just adding something to the standard classroom

explanation, different from the usual battery of

exercises, improves the long-term retention of the

knowledge of a topic that teachers know as a

difficult one to correctly remember by students. The

positive contribution of computer-based learning is

very-well known.

However, adding self-made, programming-based

interactive explanations gives even better results

than by using computer-based tools created by

others. And this even if, to creates these

explanations, we devote less time to exercising. This

is the positive apport of programming-based

learning.

We explore the possible reasons in the following

sections. We want just to notice here that

programming-based learning does not require, for

every new topic, 3 or 4 more two-hour sessions than

the standard classroom learning. Indeed, we must

remember that the first two-hour session was

devoted to “arousing the enthusiasm” of the students

towards the creation of digital projects and that the

bigger part of the second and third sessions were

devoted to learning how to use Scratch. In our view,

when this computer-supported educational

methodology is acquired by the class, part of the

time spent in teaching and exercising can be

fruitfully replaced by creating interactive

explanations of each given topic.

4.1 Explanation of the Results

Clearly the results of this experiment show that even

less exercise is not a drawback if it is replaced by

other kinds of meaningful activities that gives the

students further insight in what is behind the specific

topic they are studying. A lot of exercise (more than

8 hours spent in doing just exponentiation) proves

certainly effective for a short- or medium-term

evaluation. But then, when time passes by, student

do not remember very well what they have learnt

about the exponentiation operation because they

∆<2%

∆>10%

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have just memorized how to calculate it, but they

have not deeply understood what an exponentiation

does really mean. The students instead, by building

by themselves the kind of interactive projects that

we design for them, are forced to see the elements

that corresponds to the abstract definition of

exponentiation.

So let us go now into some more details in the

kind of project we have designed for both

multiplication and exponentiation. In the following,

given that the structure of the two projects is exactly

the same, we will be discussing the exponentiation

project.

4.1.1 Creating Interactive Objects to

Understand and Remember a Given

Topic

To allow the student to test their knowledge about

exponentiation, we can use a programming language

to build several different kinds of projects. One of

the simplest projects could be just showing the value

of a base and of an exponent randomly selected and

then just compare the user answer with the result of

calculating the power by using the operators of the

programming language, for example the exponent

operator with base e (Euler’s number) and the

natural logarithm operator again with base e

iii

(figure

12).

Figure 12: Calculating 2

as e

3 ln 2

by using the e^ and ln

mathematical operators of the Scratch language.

However, using the mathematical operators that are

already available in a programming language, for

example the e^ and ln operators available in Scratch,

clearly does not give us a better understanding of the

exponential operation. It is like using the “x”

multiplication operator of a calculator to calculate

2x3. This does not allow us to learn or understand

more deeply about multiplication.

A good way of using a visual programming

language such as Scratch is instead to create an

interactive model of the problem by creating

interactive objects for each single component of the

problem. To create this model the student will have

then to know how many elements compose the

correct solution. For example, to build the

interactive solution of 2

the student will have to

create 3 interactive 2’s and 2 interactive x’s (figure

13).

Figure 13: Calculating 2

as the result of two

multiplications of three 2’s.

All these elements are clearly visible in the object

area of Scratch (figure 14) so that for the

programmer are tangible objects.

Figure 14: Interactive objects of the exponentiation project

clearly visible in the object area of Scratch.

So, the deeper learning of the student will come out

due to several concurrent reasons, all concurring to

getting rid of the more common mistakes (“times

exponent” error, “number of factor” error,

“summation” error; see section 3.4) done by the

students:

• the student will have to place on the design

area copies of the base, not the exponent.

This will allow the user to get rid of the

“times exponent” error;

• the student will have to place on the design

area as many copies of the base as

indicated by the exponent. This will allow

the user to get rid of the “number of

factors” error;

• the student will have to place on the design

area copies of the multiplication operator.

This will allow the user to get rid of the

“summation error”;

• the student will have to add to the project

several behaviours that reject the wrong

answers or accept the correct answers given

by the users of the project -when the user

select the correct/wrong factor or the

correct/wrong operation- by playing, for

example, the “correct” and “wrong” sounds

as in the first Supermario minigame. This

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131

will allow the user to get rid of both the

“summation error” and the “factors error”.

Several different learning strategies are working in

this case together (Udomon et al., 2013, Seemüller et

al., 2012) to build an interactive virtual model that

will help the student to improve the recall of the

topic. Indeed, each element of the correct answer

(each factor, each operation, etc) is “physically”

represented in the project by an interactive object

that can be seen. Furthermore, each element must be

“physically” manipulated by the student (for

example by selecting its picture and by dragging and

dropping it) in order to correctly place it on the

design area. Finally, elements are manipulated in

order to assign them the correct behaviour when the

user of the project will interact with it.

4.2 Applying Programming-based

Learning to Other Disciplines

The strategy discussed in this paper, that allows

students to acquire a deeper understanding of school

topics by programming-based learning and

illustrated via the exponentiation operation that has

been chosen as the topic of this experiment in 5

grade classrooms, is not limited to

mathematical/scientific topics.

Other experiments are currently under way by

actively testing how applicable and effective this

very same strategy can be when applied to other

“non-scientific” disciplines such as arts at the high

school level and foreign language learning at the

elementary school. The fundamental part of these

experiments is to find a suitable representation -as

interactive objects- of the elements and concepts

explained in the most complex parts of the standard

classroom lessons for these topics.

5 CONCLUSIONS

In this paper we illustrated the positive outcomes of

a recent experiment in two 5

grades classes proving

that computer programming can be introduced as an

effective strategy to improve retention of knowledge

of difficult school topics.

The devised strategy is not limited to scientific

topics and can be fruitfully applied to further topics

of all disciplines that are felt as particularly difficult

to remember by students.

The double outcome of the programming-based

learning strategy described in the paper is that not

only long-term retention is significantly improved,

but that students are given at the same time the

chance to learn computational thinking (Wing,

2006), a skill that will be really important in their

future lives.

ACKNOWLEDGEMENTS

Stefano Federici expresses his gratitude for the

support of Fondazione Banco di Sardegna within the

project ``Science and its Logics: The

Representation's Dilemma'', Cagliari, number:

F72F16003220002.

All authors would like to thank the school

principal Claudia Aroni of the Santu Nigola

elementary school in Selargius, for her support to

this experimentation, and the teachers Adele Sechi

and Simona Quartu for their help in designing and

administering the experiment.

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Indeed, when the exponent is 0, there is no series of

multiplications that can be used to calculate the result. So, in

order to be coherent in the successive grades of the school with

the operation of division of powers with the same base, n

is 1 for

all values of n

When the base and the exponent are both 0’s there are different

interpretations of what the result should be. Usually. the result is

considered undetermined.

iii

In Scratch the exponentiation looks more complex than

necessary, due to the lack of a general exponentiation operator

that is instead available in other common programming languages

such as C/C++

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