Fostering Scientiﬁc Reasoning Skills through Interactive

Learning Tasks

Immanuel Albrecht and Hermann K¨orndle

Institute of Educational and Developmental Psychology, Technische Universit¨at Dresden,

Dresden, Germany

Keywords:

Scientiﬁc Reasoning, Interactive Learning Task.

Abstract:

Scientiﬁc reasoning is a key skill in academic contexts and may be trained with interactive learning tasks, that

require learners to explicitly give reasons for their solution. We provide a general, mathematically motivated

algebraic model for reasoning tasks that enables computer-based analysis of answers and feedback generation,

especially in the case of tasks that have distinct permissible correct solutions; furthermore we present our

ready sample implementation guided by that model.

1 INTRODUCTION

Scientiﬁc reasoning has been known to be an impor-

tant skill for university students in order to obtain

higher academic degrees, such as master’s and PhD

degrees. In 1933 The American Physics Teacher fea-

tured an article that links better ability to solve tests

that involve reasoning to higher achieved academic

degrees (Worthing, 1933).

Zimmerman considers the study of the develop-

ment of conceptual knowledge in particular scien-

tiﬁc domains along with the study of the reasoning

and problem solving strategies involved in hypothesis

generation, experimental design, and evidence eval-

uation to be the two main approaches to the study of

scientiﬁc thinking and ﬁnds that these two approaches

distinguish different connotations of scientiﬁc rea-

soning (Zimmerman, 2000). Domain-speciﬁc scien-

tiﬁc reasoning typically requires the use of concep-

tual knowledge of a particular scientiﬁc phenomenon

(Zimmerman, 2000). It has been studied among oth-

ers in the domain of physics, where individuals had

to use their conceptual understanding to generate so-

lutions to tasks, but were not required to make ob-

servations, evaluate evidence, or conduct experiments

(Zimmerman, 2000).

Ziegler (1990) studied solution rates for the Wa-

son selection task (1968) for abstract implications and

found an improvement of correct solution rates after

training measures (Meiser and Klauer, 2001). Klauer

et al. (1997) researched interference effects regarding

propositional reasoning and found a signiﬁcant effect

of training on the number of correct solutions (Meiser

and Klauer, 2001). Klauer et al. (2000) compared

the effects of different training conditions on proposi-

tional reasoning: both abstract semantic training and

domain-speciﬁc semantic training were signiﬁcantly

more effective than both syntactic and no training,

whereas there were no signiﬁcant differences between

abstract and domain-speciﬁc training (Klauer et al.,

2000).

A study conducted by Cheng et al. (1986) sug-

gests that human reasoning relies rather on available

inference schemes than on content-independent syn-

tactic rules (Meiser and Klauer, 2001). Klaczynski

et al. (1989) showed that better solution skills in one

domain may be transferred to other domains if the

training measures led to the acquisition of new men-

tal representations of the logical connectives, which

may be achievedby either abstract training or content-

oriented training where participants are confronted

with contradictions between their previous represen-

tation and the formal correct meaning of the premises

(Meiser and Klauer, 2001). Content-oriented training

measures that do not challenge previous representa-

tions showed no transfer effects (Meiser and Klauer,

2001; Klaczynski et al., 1989). Therefore it is im-

portant to challenge errors and misconceptions in or-

der to train scientiﬁc reasoning skills. This may be

achieved by training measures that give interactive

feedback that points out possible contradictions be-

tween the mental representations of the logical con-

nectives and their formal correct meaning. Suitable

training measures may combine answer-until-correct

393

Albrecht I. and Körndle H..

Fostering Scientiﬁc Reasoning Skills through Interactive Learning Tasks.

DOI: 10.5220/0004352103930398

In Proceedings of the 5th International Conference on Computer Supported Education (CSEDU-2013), pages 393-398

ISBN: 978-989-8565-53-2

 2013 SCITEPRESS (Science and Technology Publications, Lda.)

or multiple-try feedback strategies with knowledge of

performance feedback, knowledge of result feedback

and elaborated feedback, such as knowledge of the

location and count of mistakes (Narciss, 2008).

1.1 Interactive Learning Tasks

An interactive learning task consists of two main

parts: the question or problem to be solved and its

solution (Proske et al., 2012). Such a task is designed

such that the series of cognitiveoperations and actions

conducing to its outcome lead learners to be actively

engaged in knowledge construction, and such that the

learner may interact with a system or a person dur-

ing the execution of the task in a way that supports

in performing the necessary cognitive operations and

actions (Proske et al., 2012). Working on interactive

learning tasks may help in overcoming obstacles or

in correcting incorrect solution steps, thus interactive

learning tasks provide mastery experiences and foster

learners’ motivation (Proske et al., 2012).

Design Requirements

In general, interactive learning tasks should give stu-

dents opportunities for repetition and correction, tu-

tor learning task processing, and reciprocally react

on learners’ actions by providing feedback or other

means (Proske et al., 2012). Furthermore “instruc-

tions should enable students to apply basic scientiﬁc

principles ﬂexibly, to explain or predict diverse phe-

nomena, and to become good problem solvers and in-

dependent learners.” (Reif and Scott, 1999)

In order to train scientiﬁc reasoning skills with an

interactive learning task, the task must involve scien-

tiﬁc reasoning and provide a possibility for the learner

to see at which points their own reasoning is not cor-

rect in the sense of proper scientiﬁc reasoning. Thus

interactive learning tasks should provide interactive

feedback that not only gives information whether the

solution is correct or incorrect, but also which parts

of the solution contain mistakes. This should be done

by providing multiple response steps with elaborated

feedback components that guide the learner toward

successful task completion without offering the cor-

rect response immediately (Narciss, 2008). This feed-

back may be given either by automated solutions or

by human tutors.

1.2 Example Learning Task

We want to give an example of a learning task that

involves scientiﬁc reasoning in the domain of physics.

Problem P:

Consider the schematic

to the left!

How do the luminosities

of the bulbs A, B, and

C relate to each other, if

all three bulbs are of the

same kind?

Solution. Bulb A has higher luminosity than the

other bulbs and the luminosities of bulb B and bulb C

are equal.

In order to give the correct solution, a student un-

familiar with such problems has to extract informa-

tion from the schematic, that the bulbs B and C are

connected in series and that the bulb A is connected

in parallel with the bulb chain BC. Afterwards the stu-

dent has to use conceptual knowledge regarding both

kinds of connections in order to infer the luminosity

qualities of the bulbs. On the other hand, a student

familiar with such problems may be able to give the

solution right away. Thus the problem has to be mod-

iﬁed in order to train scientiﬁc reasoning:

Problem Q:

Consider the schematic

to the left!

How do the luminosities

of the bulbs A, B, and

C relate to each other, if

all three bulbs are of the

same kind?

Give reasons for your an-

swer!

Although the modiﬁed problem is well deﬁned, it

is quite cumbersome to give the solution beforehand,

because there are lots of different rationales that infer

the solution from the problem all of which are correct.

Thus a supervisor has to undertake the tiresome and

arduous task of checking each student’s answer for

factual correctness and completeness by following the

given reasoning steps and checking their soundness.

1.3 Computer based Interactive

Learning Tasks

Reif and Scott (1999) give an example computer

based PAL

tutorial for Newton’s law and its appli-

cations regarding basic Newtonian mechanics. Their

computer based system offers three modes of oper-

ation: the student may be coached in implementing

Personal Assistant for Learning

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394

speciﬁed actions, the student may assess and correct

the work of the PAL, and the student is provided with

independent practice on similar problems (Reif and

Scott, 1999). All problems of the computer based

PAL tutorial example by Reif and Scott (1999) in-

volve the creation of a diagram of all forces relevant

to the mechanical system as the key step towards the

solution. Although there is some non-linearity in the

construction process, there is only a single valid dia-

gram of the relevant forces per problem, which makes

it easy to decide whether there are components miss-

ing and whether there are misplaced arrows or errors

in the calculations – it sufﬁces to compare the stu-

dent’s work against the correct solution of the prob-

lem, and to give feedback accordingly.

1.4 Reasoning in Learning Tasks

Learning tasks that require the student to explicitly

do scientiﬁc reasoning as part of the solution have

more than only one distinct correct answer in gen-

eral: Consider problem Q. We might argue that the

same voltage means the same luminosity. But we also

might argue that the same current means the same lu-

minosity. If we chose the ﬁrst argument, we could

say that the current through bulb B is the same as the

current through bulb C, thus bulb B and bulb C are

equal bright. If we chose the second argument, we

would argue that the voltage of bulb B is as big as

the voltage of bulb C, thus they have the same lu-

minosity. In order to systematically give interactive

feedback for learning tasks that require scientiﬁc rea-

soning, we need a model of reasoning. Although a

complete model of scientiﬁc reasoning could be used

as well, incomplete – and sometimes much easier –

models that only cover those aspects of scientiﬁc rea-

soning that are relevant to give interactivesupport and

to check the student’s answer will sufﬁce.

2 ALGEBRAIC MODEL OF

REASONING IN INTERACTIVE

LEARNING TASKS

In this section, we will provide an algebraic back-

ground model that is sufﬁcient to generate appropriate

interactive learner’s feedback for scientiﬁc reasoning

tasks.

The atomar entity of reasoning that we are dealing

with is an assertion, and the set of all assertions will

be denoted by A. Furthermore we will denote the two-

elementary complete lattice by

L = (L, ≤,

, 0, 1)

and interpret 0 as false or incorrect, and 1 as true or

correct.

Each implementation of an interactive learning

task has a set of assertions that a learner may use in or-

der to generate her answer. This set is called assertion

domain and will be denoted by D

′

⊆ A. For obvious

reasons any assertion a ∈ D

′

must be of a form such

that it is either is true or false within the context of the

learning task, thus there is a map v: D → L that maps

each decidable assertion a ∈ D ⊆ A to its truth value

va ∈ L, and D

′

⊆ D.

2.1 Stating Reasons as Inverse Inference

If we ask for reasons for a speciﬁc assertion we would

be satisﬁed if we got some assertions from which we

could somehow infer the former assertion. This cir-

cumstance may be captured by the following: We let

n be a natural number, then we will call any n+ 1-ary

relation on D an inference rule, i.e. I is an inference

rule if I ⊆ D

n+1

for some natural number n that de-

pends on I. We will interpret

, a

, . . . , a

, a

n+1

) ∈ I

such that the assertions a

through a

are considered

to be reasons for a

n+1

w.r.t. I.

Of special interest are valid inference rules: An

inference rule I ⊆ D

n+1

is called valid, if for all

, a

, . . . , a

, a

n+1

∈ D

i=1

≤ va

n+1

holds. If we have a given set of valid inference

rules, we can use it to generate new correct asser-

tions from known-to-be-correctassertions, and to ver-

ify that some given reasons are indeed sufﬁcient for

some assertions.

2.2 Using Inference Bases to Decide

Correctness in D

′

If we want to check whether an assertion a ∈ D

′

correct, we can use an initial set of correct assertions

⊆ D and a set of valid inference rules R. We will

successively extend our knowledge of correct asser-

tions: starting with A

we apply all the rules I ∈ R to

all combinations of correct assertions we know and

continue with combinations involving assertions we

just gained knowledge of until no more new correct

assertions arise. Thus we are closing A

under R:

{A ∈ 2

| A

⊆ A,

∀I ∈ R, a

, . . . , a

∈ A,

n+1

∈ D:

, . . . , a

, a

n+1

) ∈ I ⇒ a

n+1

∈ A}

FosteringScientificReasoningSkillsthroughInteractiveLearningTasks

395

Although we can use any such pair (A

, R) to verify

that an assertion a ∈ D

′

is indeed correct, we need an-

other property of (A

, R) in order to know that an in-

correct assertion a is indeed incorrect: We consider a

pair (A

, R) – where A

⊆ D and R is a set of inference

rules – to be a D

′

-base, if for all a ∈ D

′

va = 1 ⇔ a ∈ A

This means that if we have a given D

′

-base we may

close its set of correct assertions under its set of in-

ference rules and use the resulting set of correct as-

sertions to check whether an assertion a ∈ D

′

from

the assertion domain of the interactive learning task

implementation is correct within this context. If the

assertion is in the closure, i.e. a ∈ A

, it is correct,

otherwise it is incorrect. An author creating an imple-

mentation of such a task now only has to give a sufﬁ-

cient amount of both valid inference rules and correct

assertions

in contrast to having to enter all correct

assertions from D

′

2.3 Checking Reasons for Assertions

We also want to use valid inference rules to check

whether a given argumentation – which we consider

to be merely a set of assertions P ⊆ D

′

– contains rea-

sons for all of the non-trivial and non-obvious correct

assertions that it contains. Therefore we want to use

a set R of inference rules, where every inference rule

I ∈ R represents a satisfactory way of arguing.

Let (A

, R) be a D

′

-base where every I ∈ R also

represents a way of arguing, and let P ⊆ D

′

be a given

argumentation. We further assume that P ⊆ A

, i.e.

that all assertions from P are correct. In order to check

whether the argumentation P is not missing any rea-

sons from the assertion domain D

′

, we will start with

the trivial and obvious assertions from P, and then try

to use rules I ∈ R to successively justify new asser-

tions from P. Thus we compute the relative closure of

the empty set

0 with regard to P under R:

{A ∈ 2

| ∀I ∈ R,

, . . . , a

∈ P∪ (A

′

n+1

∈ P:

, . . . , a

, a

n+1

) ∈ I ⇒ a

n+1

∈ A}

Clearly, the set

consists of those assertions from

the argumentation P that are either trivial or obvious,

Those assertions do not necessarily have to be from the

assertion domain the student is composing her answer from.

Note that 1-ary inference rules I ⊆ D

represent ob-

vious or trivial assertions, since they are contained in the

closure of the empty set

Figure 1: Screenshot of a sample implementation of prob-

lem Q.

or that may be satisfactory justiﬁed by other given as-

sertions. In other words, the set P\

contains the

assertions from P for which the student should give

more reasons.

3 IMPLEMENTING AN

INTERACTIVE LEARNING

TASK ON SCIENTIFIC

REASONING

In order to demonstrate that our algebraic modeling

approach is fruitful we have developed and imple-

mented an interactive learning platform that works in

a standard Java and JavaScript enabled web-browser.

Below we will sketch how an interactivelearning plat-

form web page as seen in ﬁgure 1 can be created

for problem Q. The interactive learning web page

contains a description of the problem, along with a

template kit that can be used to construct sentences,

which subsequently can be dragged into separate ar-

eas, one for the answer of the question and one for

reasons that lead to the answer. After entering the

answers and reasons the student can request the web

site to check the answer, in which case the student is

provided with information whether each point is cor-

rect, whether the student should give more reasons for

each point, and whether there are points regarding the

schematic or the underlying physical laws missing.

3.1 Working with the Algebraic Model

of Reasoning

First, we need to choose a good assertion domain

′

for the learning task. Any number of sentences

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396

Table 1: Sentence template for the description of the schematic.

bulb A is serial connected with bulb A

bulb B is connected in parallel with bulb B

bulb C bulb C

bulb chain BC bulb chain BC

the battery the battery

Table 2: Sentence template for the comparison of circuit element parameters.

the current through bulb A is smaller than the current through bulb A

the voltage of bulb B is as big as the voltage of bulb B

the resistance of bulb C is bigger than the resistance of bulb C

the input power of bulb chain BC the input power of bulb chain BC

the luminosity of the battery the luminosity of the battery

Table 3: Sentence template for the relations between the parameters.

a smaller current means, for bulbs, a smaller current

bigger voltage bigger voltage

resistance resistance

input power input power

luminosity luminosity

Table 4: Examples for the inference rule set of our implementation of problem Q.

rule name example reasons example conclusion

schematic to

comparison

bulb B is serial connected with bulb C the current through bulb B is as big as the

current through bulb C

comparison transitivity

the voltage of bulb A is as big as the

voltage of bulb chain BC

the voltage of bulb A is bigger than the

voltage of bulb B

the voltage of bulb chain BC is bigger than

the voltage of bulb B

parameters &

comparison

the voltage of bulb A is bigger than the

voltage of bulb B

the luminosity of bulb A is bigger than the

luminosity of bulb B

a bigger voltage means, for bulbs, a bigger

luminosity

comparison inversion the voltage of bulb A is bigger than the

voltage of bulb B

the voltage of bulb B is smaller than the

voltage of bulb A

parameter transitivity

a bigger current means, for bulbs, a bigger

voltage

a bigger current means, for bulbs, a bigger

luminosity

a bigger voltage means, for bulbs, a bigger

luminosity

parameter inversion a bigger current means, for bulbs, a bigger

voltage

a bigger current means, for bulbs, a bigger

voltage

quantiﬁer negation a bigger voltage means, for bulbs, a bigger

luminosity

a smaller voltage means, for bulbs, a

smaller luminosity

schematic inversion bulb B is serial connected with bulb C bulb C is serial connected with bulb B

schematic transitivity

the battery is connected in parallel with

bulb A

the battery is connected in parallel with

bulb chain BC

bulb A is connected in parallel with bulb

chain BC

from this domain may be chosen by the student and

dragged into the points or conclusions areas of the

web page. We would like to point out that the choice

of a good assertion domain D

′

is the key step in our

endeavor of creating a good interactive learning task

implementation for a given problem. Serious effort

and consideration should be put into this step before

doing any of the technical steps, since changes regard-

ing the assertion domain usually effect all subsequent

work. Clearly, the student has to describe the compo-

nents of the schematic. In order to do this, the student

may compose sentences by choosing an option from

each of the columns given in table 1. The student

also has to compare some of the electrical and physi-

cal parameters of the circuit elements by constructing

sentences from options given in table 2. And last the

student has to give information on how the parameters

will inﬂuence each other regardingthe bulbs. This can

FosteringScientificReasoningSkillsthroughInteractiveLearningTasks

397

Table 5: Initial set of correct assertions for our implementation of problem Q.

bulb A is connected in parallel with bulb chain BC

the battery is connected in parallel with bulb A

bulb B is serial connected with bulb C

the resistance of bulb A is as big as the resistance of bulb B

the resistance of bulb A is as big as the resistance of bulb C

the resistance of bulb chain BC is bigger than the resistance of bulb C

the voltage of bulb chain BC is bigger than the voltage of bulb B

a bigger voltage means, for bulbs, a bigger current

a bigger voltage means, for bulbs, a bigger input power

a bigger input power means, for bulbs, a bigger luminosity

be done by composing sentences from table 3. These

three sentence templates constitute the assertion do-

main D

′

, which has 2025 elements – sentences

which

the student may use to complete the task.

After we have chosen the assertion domain for our

implementation we have to think about the relations

between the assertions and come up with an appropri-

ate set R of valid inference rules. Since giving all the

inference rules I ∈ R in detail is a technical and tire-

some task that does not provide deeper insights, we

will only sketch the inference rules of our implemen-

tation here by sparing the technicalities and giving an

example for each rule in table 4 instead.

Further we consider all correct assertions regard-

ing the schematic, the fact that the voltage of the bulb

chain BC is bigger than the voltage of each of the

bulbs B and C, and the relations between the param-

eters to be obvious for our problem and hence do not

demand reasons for them.

Having ﬁxed the assertion domain D

′

and the set

of inference rules R we need to give a set of assertions

⊆ D such that (A

, R) is a D

′

-base. In table 5 we list

a set of assertions sufﬁcient to determine whether any

assertion a ∈ D

′

from the assertion domain is correct.

4 CONCLUSIONS AND FURTHER

WORK

In this paper we showed that scientiﬁc reasoning is

an important skill that can be trained by appropriately

designed interactive learning tasks. We elaborated a

profound model that can be used to generate interac-

tive web-based learning platforms that may provide

feedback and tutor learners in order to improve their

reasoning skills across different tasks and domains.

We presented a sample implementation using a gen-

eral framework. As part of future work this imple-

Notice that there are different sentences that essentially

carry the same information, but since we allow for distinct

solutions anyway, there is no need to enforce a normalized

way of generating sentences from underlying information.

mentation framework may be used to create further

computer-based interactive learning tasks, on which

highly needed further empirical studies on training

scientiﬁc reasoning may be based.

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