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Paper ID #13115

How Misconceptions Might be Repaired through Inquiry Based Activities

Ms. Gina Cristina Adam, University of California, Santa Barbara

Gina C. Adam is pursuing her Ph.D. in Electrical Engineering and a M.A. in Teaching and Learning atUniversity of California, Santa Barbara. Her main research interest is conceptual understanding in engi-neering education. Additionally, she helped as a graduate student researcher in two large scale engineeringeducation projects, one related to developing a taxonomy for the field supervised by Dr. Cynthia Finelliat University of Michigan and one on pioneers in engineering education supervised by Dr.Cynthia Atmanat University of Washington, Seattle.

Dr. Brian P. Self, California Polytechnic State University

Brian Self obtained his B.S. and M.S. degrees in Engineering Mechanics from Virginia Tech, and hisPh.D. in Bioengineering from the University of Utah. He worked in the Air Force Research Laboratoriesbefore teaching at the U.S. Air Force Academy for seven years. Brian has taught in the MechanicalEngineering Department at Cal Poly, San Luis Obispo since 2006. During the 2011-2012 academic yearhe participated in a professor exchange, teaching at the Munich University of Applied Sciences. Hisengineering education interests include collaborating on the Dynamics Concept Inventory, developingmodel-eliciting activities in mechanical engineering courses, inquiry-based learning in mechanics, anddesign projects to help promote adapted physical activities. Other professional interests include aviationphysiology and biomechanics.

Dr. James M Widmann, California Polytechnic State University

Jim Widmann is a professor of mechanical engineering at California Polytechnic State University, SanLuis Obispo. He received his Ph.D. in 1994 from Stanford University and has served as a FulbrightScholar at Kathmandu University it Nepal. At Cal Poly, he coordinates the departments industry spon-sored senior project class and teaches mechanics and design courses. He also conducts research in theareas of creative design, machine design, fluid power control, and engineering education.

Alexa Coburn, California Polytechnic State University, San Luis Obispo

Alexa is a third year Mechanical Engineering student from Huntington Beach, California. She attendsCal Poly, San Luis Obispo and plans on graduating in June 2016. Alexa recently had a Space Operationsinternship at Raytheon Space and Airborne Systems and plans to go back for a second internship thissummer. While attending school, Alexa is a part of an educational research team where she developshands-on learning activities that facilitate student understanding of dynamics concepts. Alexa is passion-ate about working with children and young adults, specifically young women to broaden their technicalunderstanding and encourage them to pursue education and careers in STEM fields.

Mr. Baheej Nabeel Saoud, California Polytechnic State University, San Luis Obispo

Baheej Saoud is an Aeronautical Engineering senior at Cal Poly San Luis Obispo and is set to graduate inJune 2015. He will be continuing on to graduate school in Manufacturing Engineering. Baheej has beencontributing to the Cal Poly Dynamics Research team since 2013.

c©American Society for Engineering Education, 2015

Page 26.858.1

How Misconceptions Might be Repaired

through Inquiry Based Activities

Gina C. Adam, Brian P. Self, James M. Widmann, Alexa Cobrun, Baheej N. Saoud

Introduction

Undergraduate dynamics is often cited as one of the most difficult courses that engineering

students must take because many of the topics are in direct conflict with their perception of the

world around them. Newton‟s laws of motion are fundamental to the study of dynamics and

students are particularly prone to having misconceptions drawn from their daily life interaction

with moving objects. An apple may fall from a tree to the ground faster than a leaf (although

they have the same acceleration in the absence of air resistance); two football players may

collide and the smaller player may get hurt more than the larger player (although an equal force

is exerted on both players)1.

These misconceptions can survive even after extensive direct instruction. Concept inventories are

specifically designed tests that target common misconceptions, so they serve as useful tools to

assess student learning and effectiveness of teaching practices. Performance on the Dynamics

Concept Inventory (DCI) at the end of a large size dynamics class taught by traditional methods

shows a student average of only 32.1%2. Such a low score shows that simply learning the correct

equations needed to solve a problem does not mean a student has mastered the conceptual

content of a topic 3, 4

.

Considerable effort has been spent trying to find instructional approaches that can repair these

deeply rooted misconceptions. In a study involving 6,000 students taking introductory physics,

Hake5 showed that instruction involving active learning and stressing conceptual understanding

resulted in an average conceptual gain equal to 0.48, almost double the average gain in

traditional lecture-based courses. There is a growing body of literature supporting active learning

in engineering education (see Prince6 for a review). A pilot study

7 found that active-learning

based courses resulted in an 8.5% larger normalized gain on the DCI than traditional instruction.

All the evidence confirming increased conceptual gains in classes utilizing active learning

methods have created excitement among educational researchers and teachers, but more

questions need to be answered regarding their practical implementation in classrooms. A long

on-going academic debate exists on how much the students should be involved and how much

instructional guidance is most effective. Matlen and Klahr8 explore the efficacy of low vs. mixed

instructional guidance in the context of teaching 3rd

grade children about the Control of Variables

Strategy for scientific experimentation. Four experimental conditions were used, namely high

followed by high instruction (H-H), high followed by low (H-L), low followed by high (L-H)

and low followed by low instruction (L-L). High instructional guidance included a mix of

inquiry questions and direct instruction (explanations and summary provided by the

experimenter), while low instructional guidance included only inquiry questions. Their results

showed that, in domains where learners have difficulty assessing the correctness of their

6.858.2

solutions, inquiry activities are not sufficient to clarify concepts; therefore direct instruction is

needed for learning.

One type of active learning technique designed to increase conceptual understanding in

engineering is Inquiry-Based Learning Activities (IBLAs) 9-11

. IBLAs are based on a series of

Predict-Observe-Explain cycles that can incorporate direct instruction or teamwork as needed. In

an IBLA, individual students or teams of students are presented with a physical situation and

asked to predict what will happen. The students then investigate the situation by experimenting

with physical hardware that becomes the “authority”, thus forcing students to confront any

misconceptions (Figure 1).

Figure 1.The building blocks of an Inquiry Based Learning Activity (IBLA) are Predict-Observe-

Explain (P.O.E) series based on given scenarios. These P.O.E. series can be interspersed with

direct instruction and teamwork as desired by the instructor.

In previous studies, we have reported student performance on concept tests and their predictions

during the IBLAs 9-11

. This research, however, did not reveal how students approached solving

the problems, or what conceptual knowledge they used to attack the different scenarios. We

decided to use the qualitative technique of “think-aloud” to investigate how students‟ knowledge

is affected by the IBLA. For this study, students participated individually in either a purely

P.O.E-based IBLA or a P.O.E and direct instruction IBLA. We investigated how students‟

knowledge evolved during the IBLA and how P.O.E and direct instruction help students gain

conceptual understanding.

The goal of this study is to understand the process of repairing naïve misconceptions and of

acquiring desired scientifically approved models within the framework of an IBLA. The results

of this study help us understand how to design better IBLAs, particularly how to choose the

given scenarios for the P.O.E cycles and when to incorporate direct instruction.

Theoretical framework

The purpose of instruction is to help students acquire domain-specific knowledge and skills.

According to Shavelson, knowledge can be categorized as “knowing that” (declarative/factual

and conceptual knowledge), “knowing how” (procedural knowledge), schematic knowledge

(“knowing why”) and strategic knowledge (“knowing when, where and how”) 12

. Each type of

knowledge can be described in terms of its extent and its structure.

Students do not enter instruction with an empty mind. The naïve misconceptions (pre-instruction

“mental models”) that students bring to the classroom are typically based on everyday

experience and interfere with student‟s learning of the scientifically approved models.

Conceptual change refers to the shift in student‟s schematic knowledge from naïve models to

PredictionExperimental observation

Explanation and

re-evaluation

Page 26.858.3

desired scientifically approved models13, 14.

The knowledge shift due to instruction might not be

as dramatic and straight-forward as desired. Vosniadou & Brewer (1992)15

point out that students

can use both scientifically-sound propositions and their less-scientific prior propositions in the

same explanation of a phenomena. Helldén and Solomon (2004)16

found in their longitudinal

study that students tended to evoke the same, less-scientific explanations over time, despite being

exposed to contrary teaching. However, the students did use more scientifically-sound models

when prompted appropriately by the interviewer. Such accumulation of propositions might be

considered conceptual development rather than conceptual change13

. While conceptual change

focuses on developing a more scientifically approved schematic knowledge, the more gradual

conceptual development seen in practice can be considered more related to changes in the

declarative and procedural knowledge.

Studies have shown that experts have an extensive and highly interconnected declarative

knowledge organized according to broad scientific principles17

. Some questions require further

investigation. How are experts able to organize their declarative knowledge according to broad

scientifically accepted schematic knowledge? And how should the instruction be designed in

order to facilitate this process of knowledge organization in students‟ minds?

This study attempts to provide some insight into these questions by investigating how the extent

and the structure of the declarative knowledge changes as the students are exposed to an IBLA.

Literature review

A problem that is often used to demonstrate the application of Newton‟s 2nd

law to the motion of

a compound system is the Atwood machine. The system consists of two objects connected by a

string that passes over a pulley (Figure 2).

The Atwood machine can be a versatile problem to test students‟ conceptual understanding of

Newton‟s 2nd

law. Question 13 of the DCI is used to test for understanding of the relationship

between force, inertia and acceleration by comparing two versions of the Atwood machine. After

taking a course in dynamics, 44% - 64% of the students at different institutions responded

incorrectly to this question on a DCI post-test2. The primary incorrect proposition is that the

tension in a rope is always equal the weight suspended from it. McDermott, Shaffer and

Somers18

research on the Atwood machine also showed that many students had serious

difficulties with the acceleration, the internal and external forces, and the role of the string in the

Atwood machine. The students often failed to determine which force, which mass and which

acceleration should be associated with which system.

The conceptual knowledge (part of the declarative knowledge in Shavelson‟s framework)

necessary to understand Newton‟s 2nd

law relies on the concepts of acceleration, mass and force

(Figure 3). Also important is an understanding that the net force is the sum of all the different

forces (gravitational, tension, applied force, etc) acting on the object. There are links that

integrate all these concepts in a coherent framework. Newton‟s 2nd

law can be applied to an

individual object and extended to a system of interconnected objects (Figure 2, table).

A form of the procedural method explained in Figure 2 is traditionally presented to students as a

way of analyzing the Atwood machine and shows the connection to our conceptual propositions

used for coding. The procedural knowledge for completing this analysis often obscures the

Page 26.858.4

underlying concepts. The goal of the IBLA is to promote conceptual understanding rather than a

systematic mathematical solution to different problems. During our study, the students were

encouraged to discuss the problems conceptually and do as little math as possible.

Proposition

For one

object

(mass 2)

For the whole

system

D1. Mass is inversely proportional to acceleration

a ~ 1/m2 a ~1/ Mtotal

Mtotal = m1 + m2

D2. Net force is directly

proportional to acceleration

a ~ F2 a ~Fnet

D3. Net force is the sum of all forces acting on the object

F2 = T - G2

G2 = m2*g

Fnet= G1-G2

G1 = m1*g

G2 = m2*g

D4. Force and mass have a combined effect on acceleration

a = F2/m2 a = Fnet/Mtotal

Figure 2. Traditional Free Body Diagram (FBD) and mathematical explanation of Newton‟s 2nd

law in the Atwood machine

Figure 3. Concept map exemplifying the conceptual (declarative knowledge) involved in the

scientifically accepted framework of Newton‟s2nd

law.

Gravity

Tension

Applied force

gravitational field strength

(g)

Force

Mass

∑

Desired proposition D1(mass is inversely proportional to the acceleration)

Desired proposition D2(force is directly proportional to the acceleration)

Desired proposition D4(force and mass have a combined effect on acceleration)

Desired proposition D3(Net force is the sum of all forces acting on the object)

Acceleration

a

m2*ga

a2F2

m1*g

T

a1 F1

T

m2*g

m1*g

Page 26.858.5

Methods

Research goals

We investigated student‟s existing declarative knowledge of Newton‟s 2nd

law and how it

evolves as the student is exposed to different scenarios. Our study also tries to understand if the

inquiry-based modules can promote conceptual development and conceptual change. In this

exploratory study we used qualitative semi-structured interviewing with “think aloud” in order to

get a rich description of the student‟s understanding of pulley systems, and how this

understanding progressed during the inquiry-based learning activity.

The research goals of the study are to:

1) reveal the students „declarative knowledge of Newton‟s second law after they have been

exposed to traditional instruction during a course in dynamics.

2) determine how the declarative knowledge evolves as the student is exposed to different

scenarios in the IBLA.

3) examine the role of predict-observe-explain activities and the role of short direct

instruction in promoting conceptual development and conceptual change

Participants

The participants were either second or third year engineering students enrolled in an introductory

dynamics course. Students were in a variety of majors, predominantly mechanical engineering,

aerospace engineering, and civil engineering, and there were eight males and one female in the

study. At the time of the interview, the students have already been exposed to Newton‟s 2nd

law

in class. Participation was voluntary and unpaid, and informed consent was obtained before

conducting the think-aloud.

The Mass-Pulley IBLA

The students were assigned to individually participate in an IBLA that examined the relationship

between force, mass and acceleration in a classic Atwood machine. The IBLA used for this study

has been designed according to the principles of the variation theory30

. The theory can be applied

in lesson plans that take into consideration students‟ existing knowledge and guide the students

gradually to discern critical features of the object of learning. Several studies have demonstrated

the use of patterns of variation to improve student learning outcomes32, 33

.

The Mass-Pulley IBLA using the Atwood machine contains a sequence of four scenarios,

varying the total mass of the system, the mass difference between the weights and the structure

of the system (Figure 4 and Table 1). By using these different variations, we were able to gain a

better idea of student understanding of each desired proposition. For the first three scenarios in

the IBLA, the student was asked to (a) predict the correct answer and explain his/her reasoning,

(b) perform the hands-on experiment depicted in the Scenario, and (c) explain how the results of

the experiments compared with their original prediction. In order to emphasize conceptual

understanding, students were instructed to “think aloud” during the activities in order to make

their learning explicit and use as little mathematical tools as possible. Page 26.858.6

Figure 4. The four scenarios utilized for the IBLA (see Appendix A for the interview protocol)

Table 1. Pattern of variation used in designing the scenarios. The similarities and differences

refer to the system A and B in each Scenario

Similarities Difference Critical feature to be discerned

Scenario 1 Scenario 2

- Same type of system (2masses)

- Same mass difference between heavier and lighter block

Different total masses

Total mass of the system is inversely

proportional to acceleration when mass difference is the same

Scenario 3 - Same type of system (2masses) - Same total mass

Different mass

difference

Mass difference of the system is proportional to acceleration when total

mass is the same

Scenario 4 Same mass difference between heavier and lighter block

- Different type of system - Different

total masses

The relationship between mass difference, total mass and acceleration can be applied in the same way in different types of pulley systems.

Page 26.858.7

Data collection

The interviewing was done one-on-one, each student participating individually in a sequence of

instruction centered on the same IBLA. Three instructional sequences were investigated: (a)

IBLA only with predict-observe-explain (P.O.E) cycles, (b) IBLA with direct instruction after

Scenario 2 and (c) IBLA with direct instruction after Scenario 3 (Table 2, Figure 5). Three

students (A, B, C) were assigned per each instructional sequence (NoINT, INT2, INT3). Each of

the nine students was assigned a code for the sequence and the order in which they participated

(A, B, C). For example, INT2_B refers to student B (second one in the INT2 group) who had an

intervention after Scenario 2.

Table 2. Sequences of instruction. * P.O.E. stands for Predict-Observe-Explain

Sequence 1 Scenario 1

P.O.E

Scenario 2

P.O.E

Scenario 3

P.O.E

Scenario 4

P.


P.O.E

Scenario 2

P.O.E Direct instruction

Scenario 3

P.O.E

Scenario 4

P.


P.O.E

Scenario 2

P.O.E

Scenario 3

P.O.E Direct instruction

Scenario 4

P.

The interviewer who conducted all the nine interviews was a female research assistant. At the

beginning of the interview, the interviewer instructed the student to verbalize his/her thoughts as

he/she analyzed the different IBLA scenarios involving Atwood machines. The interviewer

provided the prompts during the IBLA, reminded the participant to continue verbalizing his/her

thought processes and conducted the direct instruction as required by the research design. The

direct instruction consisted of a succinct explanation of Newton‟s 2nd

law, ∑F = m*a. The

explanation included drawing on the whiteboard to help the student visualize the forces involved.

During the explanation, the interviewer checked for student understanding by asking questions

such as “What is the net force for each system?”, “What is the total mass of each system?”, “How

does the relationship between net force and total mass affect the acceleration?”.

Figure 5.Example of student involvement in the one-on-one IBLA

a) Student (left) experimenting with real pulley

systems (held by the interviewer – right)

during the one-on-one IBLA

b) The direct instruction part

of the one-on-one IBLA (student on the left,

interviewer on the right)

Page 26.858.8

Data coding

Video recordings of students‟ engagement were collected and the discourse was coded twice.

Four desired codes linked to the object of learning were predetermined before coding (see details

below). The first coding was exploratory and was used to extract trends and define other specific

codes of interest. The second used this coding scheme for the cognitive mapping12, 19

of the

interviews. These principles have been shown to provide a way to assess the structure of

declarative knowledge. A concept map is a graph in which the nodes represent concepts, the

lines represent relations, and the labels on the lines represent the nature of the relation between

concepts. The organization of the declarative knowledge can also give indications of the

schematic knowledge used by the students in their explanation.

In this study we use the following terms:

proposition (or concept link) = a pair of concepts and the labeled line connecting them;

mental model (or conception) = a set of interconnected propositions.

We extracted the concepts and propositions used by students indirectly from the IBLA

explanations. We limited our analysis to propositions because they already provide information

that includes the concepts and the link/relationship between them.

The selection of desired propositions was done keeping in mind the scientifically accepted

framework of Newton‟s 2nd

law. Four desired propositions linked to the object of learning were

predetermined before coding (see Figure 3).

D1. Total mass is inversely proportional to acceleration

D2. Net force is directly proportional to acceleration

D3. Net force is calculated from difference in existing forces (gravitational, external, etc)

D4. The acceleration is equal to the net force divided by total mass (F=m*a)

During the first round of coding, it became apparent that students sometimes utilize in their

explanations propositions that are naïve and based on daily life experiences, but true in limited

scenarios. We identified two such propositions that students used consistently and grouped them

under the label “weak propositions”. The students utilized either one or the other weak

proposition, but never both:

1. W1 - Single mass is proportional to the acceleration. Some students use the lighter block

in the system as the single mass (“counterweight”), while other students use the heavy

block (in their mind, the block responsible for the movement). The values selected for the

IBLA allow the students utilizing this weak proposition to make a correct prediction for

the scenarios 1, 2 and 3, but a wrong prediction for Scenario 4 (Table 1).

2. W2 - The ratio of the masses of the system (heavy mass/light mass) is directly

proportional to the acceleration. For the limited Scenario of a system of one pulley and

two masses, the ratio of masses in a pulley system does positively correlate with the

acceleration (see explanation and supporting equations in Widmann et al.20

). Because our

IBLA showed such systems in scenarios 1, 2 and 3, the students utilizing this method

Page 26.858.9

were likely to make a correct prediction. The ratio method cannot be used in Scenario 4,

since system A has only one mass pulled by an external force (Table 1).

Another type of proposition identified during coding was the incorrect proposition (naïve

propositions that were in contradiction with the scientific theory). All incorrect propositions

used were related to the inability to calculate the net force correctly. The difficulty was in

isolating the forces that contribute to the net force and then summing them vectorially. Some

students believed that different types of forces (gravitational, external, etc) of same magnitude

have different effects on the system.

We coded each student‟s IBLA as a coding map (Figure 6). The coding map provides an easy

visual way to investigate the evolution of student‟s declarative knowledge during a certain

sequence of instruction. The coding map graphically represents the matrix of propositions and

their respective confidence level for the entire sequence of instruction. The columns represent the

steps in the sequence of instruction, while the rows represent the propositions that students use to

solve that step. The specific codes were classified and color coded as desired propositions (blue),

weak propositions (purple) and incorrect propositions (orange) – see Figure 6.The area of the

bubble reflects the student‟s confidence in that particular code for that particular Scenario. This

confidence is based on the student self-declared confidence in their prediction and choice of

words during explanations. For example, words such as “I don’t know”, “I am trying to

remember from class”, “I have no idea why …” were used as an indication of low confidence.

Findings

In the Findings section, the coded data is grouped and analyzed using tables (see Tables 3-8).

This method was used as a means to analyze the data across students and to uncover potential

hidden patterns in students‟ handling of conceptual knowledge. The results are not meant to be

generalizable, but can be used as starting hypotheses for future larger scale research studies that

investigate conceptual understanding.

Research question 1 – What is the student’s declarative knowledge of Newton’s second law at

the beginning of the IBLA?

Table 3, column 1 shows that some students utilized only desired propositions, while some

utilized weak propositions, alone or together with desired propositions. The use of desired

propositions together with desired propositions is an indication that the students have

experienced conceptual development and no conceptual change.

Less than half of the students used only desired propositions. The majority, five out of nine

students, use done of the two weak propositions either together with desired propositions or by

itself. Three used the single mass weak proposition (W1) to explain their prediction for

Scenario 1.Two students used it in conjunction with desired propositions and one student used

just the single mass weak proposition. Two students used the ratio weak proposition (W2) to

explain heir prediction for Scenario 1. One student used just the ratio weak proposition. The

other student incorporated it together with desired propositions and an incorrect proposition.

Page 26.858.10

Figure 6.Coding map showing the evolution of a student‟s declarative knowledge during the sequence of instruction. The coding map is

a matrix of propositions. The rows are propositions utilized for a Scenario and the columns are the steps in the sequence of instruction.

Exemplified here is a coding map for student INT2_B participating in sequence 2 (direct instruction after Scenario 2). For Scenario 1

and Scenario 2, both Predict and Explain step, the student utilizes only one proposition to solve the problem, namely the ratio weak

proposition (numbered W2). His predictions are correct. After the direct instruction, in the Scenario 3 - Predict step, the student

utilizes the D2 net force proposition but also has an incorrect proposition (I1). After observing through experiment that his prediction

was wrong, the student uses D2 and D3 propositions with low confidence and reverts back to the W2 proposition in the

Scenario 3 - Explain step. In the last step (in the Scenario 3 – Explain), the student uses D3 and I3 propositions.

See the Appendix B for all the coding maps.

Sequence of instruction

Desired propositions

Incorrect

propositions

Weak proposition

Correct predictions Wrong predictions

Page 26.858.11

Table 3.Comparison between the number of students using different types of propositions at the

beginning of the IBLA (Scenario1 – Predict), the whole IBLA (all scenarios) and the end of the

IBLA (Scenario 4 – Predict).

Number of students

Explanation utilizing… Scenario 1.

Predict

Throughout

IBLA

(all scenarios)

Scenario 4.

Predict

1. Only desired propositions 4 2 7

2. Only weak propositions 2 0 0

W1 – Single mass 1 0 0

W2 - Ratio 1 0 0

3. Desired and weak propositions 2 5 1


W2 - Ratio 0 3 0

4. Desired and weak and incorrect propositions 1 2 0


W2 - Ratio 1 1 0

5. Desired and incorrect propositions 0 0 1

Research question 2 – How is the student’s declarative and schematic knowledge evolving as

the student is exposed to different scenarios in the IBLA?

As the IBLA progresses, the students‟ use of weak conceptions became more apparent. Two

students who used desired propositions in the prediction for Scenario 1 starting utilizing weak

propositions later in the IBLA (Table 3, row 1). Seven students utilized weak conceptions

throughout the IBLA, five in combination with desired conceptions and two in combination with

desired conceptions and with misconceptions. Students also seem to acquire incorrect

propositions along the way, probably due to misunderstandings of the data presented in the

intervention and as a way to explain their cognitive conflict. However, these incorrect

propositions were not persistent and didn‟t dominate the student‟s discourse.

Nevertheless, at the end of the IBLA, the students seem to have repaired their weak propositions

and started to utilize only desired propositions (Table 3, column 3). Seven students utilized only

desired propositions and one student utilized desired propositions and an incorrect proposition

(that gravitational forces determine a constant acceleration, while constant applied forces

determine an increasing acceleration). Only one student utilized the single mass proposition and

no students used the ratio proposition.

An analysis by scenarios shines some light on how student‟s declarative knowledge evolves over

the course of the IBLA. The high number of students exhibiting weak propositions during the

IBLA shows that these two weak propositions are widespread among students. It is important to

Page 26.858.12

notice that students either use the single mass proposition or the ratio proposition for the entire

IBLA, but never both simultaneously.

The two weak propositions were used by the students consistently as the IBLA progressed,

which seems to indicate that the students had naïve mental models based on these ideas (Tables

A and B). These propositions proved to be hard to change, especially because they were useful to

the students in certain limited scenarios. Table 4 shows that using these naïve mental models can

lead to correct intuitions in certain scenarios.

Table 4. Predictions (green = correct, red = wrong) using desired mental model (Newton‟s 2nd

law), ratio mental model and single mass mental model.

Scenario 1 Scenario 2 Scenario 3 Scenario 4

Scientific model

Correct Correct Correct Correct

Single mass model

Correct Correct Correct Wrong

Ratio model

Correct Correct Correct Not possible

The weak proposition regarding single mass appears to be repaired by the intervention in either

Scenario 2 or 3. Students INT2_Aand INT3_B had the weak proposition that the acceleration is

inversely proportional to the lighter mass and used it to explain Scenario 1 and Scenario 2.

INT2_A receives the standard intervention after Scenario 2 and understands that the total mass of

the system plays a role, not just the lighter mass. The student does not use the weak proposition

afterwards. INT3_B receives the standard intervention after Scenario 3. However, at the

beginning of Scenario 3 the interviewer asks the student to explain in more detail the role of the

mass. This question acts as a trigger for the student, who realizes that the total mass of the

system is inversely proportional to acceleration, not the lighter mass independently. The

intervention after Scenario 3 serves to strengthen this realization.

“Student: I feel like there is such a big discrepancy between these two masses that this

one will accelerate faster. At the same time F=ma, so mass here is bigger, therefore

acceleration will be smaller.

Interviewer: So mass of that block is bigger or mass of that system?

Student: Mass of the [pause] You’re right, mass of the [pause] Interesting [pause]. I

didn’t think about that.

Interviewer: I was just asking which mass you were talking about.

Student: I was talking about the 10oz one. But I didn’t even consider the fact that the

masses of the systems are the same.” (INT3_B, prediction for Scenario 3)

A closer examination across all students (Tables 5) shows that students who used the single mass

weak proposition (Table 5.1.) seem to not have the total mass proposition (Table 5.2). However,

they utilized the net force proposition (Table 5.3). The student with no instruction (NoINT_A)

did not repair the weak proposition and did not acquire the total mass propositions D1. Helped

by instruction, the other two students seem to replace the single mass weak proposition with the

total mass proposition (Table 5.1 and Table 5.2.).

Page 26.858.13

Tables 5.Students using W1 - Single mass proposition

* Low, Medium, High - student‟s confidence in the proposition at the time of explanation

** | marks the time of the direct instruction (after Scenario 2 or after Scenario 3) *** NoINTA – student A with no intervention; INT2_A – student A with intervention after Scenario 2

Student

5.1 - W1- Single mass proposition

Scenario 1. Scenario 2. Scenario 3. Scenario 4.

Predict Explain Predict Explain Predict Explain Predict

1 NoINT_A Low Medium High High High High High

3 INT2_A Low Medium Medium Medium

4 INT3_B Low Medium Medium Medium Low

Student

5.2 - D1 - Total mass influences acceleration



1 NoINT_A

3 INT2_A High

4 INT3_B Medium High

Student

5.3 - D2- Net force influences acceleration



1 NoINT_A High High High High High High High

3 INT2_A High High High High High High High

4 INT3_B Medium Medium High

Student

5.4 - D3 - Calculating Net force



1 NoINT_A High High High High High High High

3 INT2_A High High High High

High High

4 INT3_B Low Medium Low Medium High

The student without intervention uses it in scenarios

3 and 4, while the students with intervention don’t.

Three students use the W1 proposition

to explain scenarios 1 or 2.

The students with intervention acquire D1 while

the student without intervention does not.

The students do not use D1, but….

…they seem to use D2 and D3

Page 26.858.14

Tables 6.Students using W2 - Ratio proposition


** | marks the time of the direct instruction (after Scenario 2 or after Scenario 3) *** NoINT_B – student B with no intervention; INT2_B – student B with intervention after Scenario 2

Student

W2 - Ratio proposition

Scenario 1. Scenario 2. Scenario 3. Scenario 4. Predict Explain Predict Explain Predict Explain Predict

1 NoINT_B Medium Medium

2 NoINT_C Low Medium High

3 INT2_B High High High High Low

4 INT3_A Low

Student

D1 – Total mass influences acceleration


1 NoINT_B Medium High High High High High

2 NoINT_C High High High High High High

3 INT2_B

4 INT3_A Low High High High High High

Student

D2 – Net force influences acceleration


1 NoINT_B High High

2 NoINT_C Low Medium

3 INT2_B High Low

4 INT3_A Medium High

Student

D3 – Calculating Net force


1 NoINT_B Low Low Low High High

2 NoINT_C Low Low Low Low Low

3 INT2_B Low High

4 INT3_A Medium

Four students use the ratio conception to explain

cases 1, 2, or 3.

No student utilizes the ratio

proposition to explain case 4.

Three students seem to master D1 total mass

conception, but not utilize the D2 net force.

conceptoon

In scenarios 3 and 4, students

start to acquire D2

Page 26.858.15

The ratio proposition is harder to repair, but Scenario 4 creates cognitive conflict. For example,

INT2_B uses the ratio proposition exclusively and with high confidence to explain Scenario 1

and Scenario 2. The student receives the standard intervention after Scenario 2, and attempts to

use the scientific model for making a prediction in Scenario 3. After making a wrong prediction,

the student realizes that his understanding of the new framework is poor and reverses back to his

ratio framework. The student questions the necessity of understanding a new framework since he

would have made the correct prediction using his ratio framework.

“Is it because these forces are different? I guess that would be easier for me to see it

right now in an equation than to see it conceptually by looking at it [pause] but if I would

have solved this the same way I did it previously, Scenario A would have been the fastest

one, just because of the ratios. To me that is easier to understand conceptually, than to

do the math.”(INT2_B, explanation after experiment for Scenario 3)

The ratio proposition can be used to correctly solve the scenarios 1, 2 and 3. Scenario 4 cannot

be solved using the ratio of heavy to light masses since there is only one mass. At that moment,

the students realize that their framework is limited and tries to explain the system behavior using

the desired propositions.

I am still kind of stuck in my old way [weight ratio approach], but I can’t really apply that

to a Scenario such as this [Scenario 4] which is where I would have gotten stuck.”

(INT2_B, at the end of the IBLA)

Students who used the ratio proposition (Table 6.1) seem to show the opposite behavior as the

students with single mass proposition. These students utilized total mass proposition (Table 6.2)

and not the net force proposition (Table 6.3.).Case 4 serves to create conceptual conflict so that

students realize the limitations of their ratio based approach and experience conceptual change.

Research question #3– What is the role of predict-observe-explain activities and the role of

short direct instruction in promoting conceptual development and conceptual change?

Impact of the Predict-Observe-Explain activities on conceptual development and change

The coded data show that students go through a process of conceptual development as they

acquire or strengthen desired propositions during the IBLA thanks to P.O.E cycles. INT3_A

strengthens his understanding of total mass after Scenario 1 (see Table 7.1 with dark green).

INT2_A, INT3_B and INT3_C strengthen their understanding of net force and how to calculate

the net force after Scenario 3 (see Table 7.2 with dark green).

Unfortunately, the road to conceptual understanding does not seem to be straightforward.

Undesirable strengthening of weak propositions can also happen during experimentation. This is

the Scenario for NoINT_A strengthening the single mass proposition after Scenario 1 (see Table

7.1 with light red) and for NoINT_B, INT2_A and INT3_A after Scenario 3 (see Table 7.2 with

light red). Moreover, undesirable weakening of desired propositions is also common (see Table

7.2 with light green). For example in Scenario 3, the students seem make the prediction mostly

based on the total mass being equal. When the experimental results contradict their prediction,

they realize that the net force plays a role in the system. They conclude that the acceleration must

be different because the net forces are different.

Page 26.858.16


Table 7.1 – Scenario 1

Confidence in the proposition

Observations

Predict Explain

Student

NoINT_A

Prediction Same Student uses D2 to predict with high

confidence that both accelerations will

be the same, since the net force

(determined as the mass difference) is

the same. The contradictory

experimental results make the student

gain confidence in the single mass

proposition. The student still mentions

net force in his Explain step

D1 - Total mass - -

D2 - Net force High High

D3 - Calculating Net

Force High High

D4 - Newton‟s 2nd

law - -

W1 - Single mass Low Med

Student

INT3_A

Prediction Same Student uses Net force proposition to

predict with medium confidence that

both accelerations will be the same,

since the net force (determined as the

mass difference) is the same. The

contradictory experimental results make

the student gain confidence in the total

mass proposition. The student doesn‟t

mention net force in his Explain step.

D1 - Total mass Low High

D2 - Net force Med -


Force Med -

D4 - Newton‟s 2nd

law - -

W2 - Ratio - -

Desired acquisition/strengthening

Undesired acquisition/strengthening


Table 7.2 – Scenario 3 Predict Explain Observations

Student

NoINT_B

Prediction Same Student uses Total Mass proposition to

predict with high confidence that both

accelerations will be the same, since

their total mass is the same. In the

Explain step, he utilizes the ratio

proposition together with the net force

proposition to explain why the masses

are different.

D1 - Total mass High -

D2 - Net force Low High


Force - High

D4 - Newton‟s 2nd

law - -

W2 - Ratio - Med

Student

INT2_A

Prediction Same Student uses Total Mass proposition to




Explain step, he utilizes the Net force

proposition to explain why the

accelerations are different.




Force - High

D4 - Newton‟s 2nd

law - -

W2 - Ratio - -

Page 26.858.17

Student

INT2_B

Prediction Same The student has the incorrect

proposition that the net force is

determined by the total weight of the

system. Student predicts with high

confidence that both accelerations will

be the same. In the Explain step, he

reverts to the ratio proposition.

D1 - Total mass

D2 - Net force High Low


Force M1 Low

D4 - Newton‟s 2nd

law - -

W2 - Ratio - High

Student

INT3_A

Prediction Same

Student uses Total mass concept to




Explain step, he uses the ratio concept

to explain why the masses are different.


D2 - Net force - -


Force - -

D4 - Newton‟s 2nd

law - -

W2 - Ratio - Low

Student

INT3_B

Prediction Same After the instructor asks for

clarification on what mass he is

referring to, the student realizes that

total mass in determining the

acceleration. So he makes the

prediction with high confidence that the

accelerations are the same. In the

Explain step, he utilizes the Net force

concept to explain why the

accelerations are different.


D2 - Net force - Med


Force Low Med

D4 - Newton‟s 2nd

law Low -

W1 – Single Mass Low -

Student

INT3_C

Prediction Same Student uses Total Mass concept to




Explain step, he utilizes the net force

concept to explain why the masses are

different.

D1 - Total mass High High

D2 - Net force - High


Force Low High

D4 - Newton‟s 2nd

law Low High


Undesired weakening Undesired acquisition/strengthening

All students predicted Scenario 2 correctly since it is essentially the same as Scenario 1. For

Scenario 4, the students only did the Predict step, because no hardware was available for

experimentation. Nevertheless, Scenario 4 served as a promoter for conceptual change since it

challenged the students who utilized the ratio weak proposition.

Page 26.858.18

Impact of the direct instruction on conceptual development and change

The students acquire or strengthen desired propositions during the IBLA activity thanks to direct

instruction. For the direct instruction after Scenario 2, INT2_A strengthens the total mass

proposition while repairing the single mass proposition and INT2_B acquires the net force

proposition while challenging the ratio weak proposition (see Table 8.1). Unfortunately, these

students also acquire an incorrect proposition during the instruction. This proposition is short-

lived since the hands-on experiment presents contradictory evidence that the net force is

determined by the weight difference, not the weight sum. The problem is that the acquired

desired propositions are also short-lived since after making a wrong prediction, the student can

revert back to their previous strategies (for example INT2_A uses net force only and INT2_B

uses ratio).

For the direct instruction after Scenario 3 (see Table 8.2), INT3_A acquires two desired

propositions and weakens the ratio conception, while INT3_B acquires two desired propositions

and strengthens the other two desired propositions. Further scenarios would have been needed to

understand in-depth how students‟ knowledge changes.

This interplay between acquisition of desirable propositions, weakening of other desirable

propositions, while simultaneously strengthening some weak propositions poses problems when

designing IBLAs based on variation theory where multiple variables play a role in the system.


** | marks the direct instruction after Scenario 2 and before Scenario 3

Table 8.1.

Direct instruction

after Scenario 2

Scenario

2

Scenario

3

Scenario

3 Observations

Explain Predict Explain

Student

INT2_A

D1 - Total mass - High - Direct instruction helps

student understand that

total mass plays a role in

determining the

acceleration, not the single

mass. However, the student

gets confused and starts

utilizing total weight to

calculate net force instead

of the weight difference.

D2 - Net force High High High


Force High - High

D4 - Newton‟s 2nd

law - - -

W1 - Single mass Medium - -

I1 - Total weight=>Net

force - High -

Student

INT2_B

D1 - Total mass - - - Direct instruction helps

student understand that net

force plays a role in

determining the

acceleration. However, the

student gets confused and

utilizes total weight to

calculate net force instead

of the weight difference.

D2 - Net force - High Low


Force - - Low

D4 - Newton‟s 2nd

law - - -

W2 - Ratio High - High


force - Medium -

Page 26.858.19

Student

INT2_C

D1 - Total mass High High High No conceptual acquisition,

since the student already

has a strong knowledge. D2 - Net force High High High


Force High High High

D4 - Newton‟s 2nd

law High High High

W2 - Ratio - - -


force - - -


Desired weakening



** | marks the direct instruction after Scenario 3 and before Scenario4

Table 8.2.

Direct instruction

after Scenario 3

Scenario 3

Scenario 4

Observations

Explain Predict

Student

INT3_A

D1 - Total mass - High Student understands the limitation

of his approach based on ratio due

to Scenario 4. The Direct

instruction helps him acquire two

desired propositions.

D2 - Net force - High

D3 - Calculating Net Force - -

D4 - Newton‟s 2nd

law - -

W2 - Ratio Low -

Student

INT3_B

D1 - Total mass - High The Direct instruction helps the

student acquire the total mass

proposition and strengthen the net

force proposition. This allows the

student to get a big picture idea of

Newton‟s second law.

D2 - Net force Medium High

D3 - Calculating Net Force Medium High

D4 - Newton‟s 2nd

law - High

W1 - Single mass - -

Student

INT3_C

D1 - Total mass High High No conceptual acquisition, since

the student already gained the

concepts from previous wrong

prediction.


D3 - Calculating Net Force High High

D4 - Newton‟s 2nd

law High High


Desired weakening


Page 26.858.20

Summary of findings:

RQ #1: A large number of students use desired propositions together with weak propositions.

This is an indication that the students have experienced conceptual development and minimal

conceptual change. Two weak propositions are widespread among students and are used

consistently throughout the IBLA, which seems to indicate that the students had naive mental

models based on these ideas.

RQ #2: Weak propositions and desired propositions seem to be connected. There are weak

propositions that seem more likely to show up when particular desired propositions are

lacking. As those weak propositions are weakened, desired propositions are acquired.

RQ #3:

o Hands-on experiments can promote acquisition of desired propositions. However,

weakening of other desired propositions and strengthening of weak propositions

can also happen simultaneously.

o Direct instruction can promote acquisition of desirable propositions. However,

students can also misunderstand the explanation and acquire incorrect

propositions. Moreover, the acquired desired propositions can be short-lived since

after making a wrong prediction, the student can revert back to their previous

strategies and ignore the knowledge just learned.

Implications

For instruction:

In order to facilitate the acquisition of a desired framework, the instruction should target the

naïve model that limits the student‟s understanding. The hands-on experiments should be

carefully designed using variation theory to challenge the weak propositions that underline the

student‟s naïve mental model, otherwise weakening of desired knowledge can happen when the

students make the wrong prediction. Direct instruction can be important to highlight the fact that

the system has multiple variables that are all interconnected and important, while hands-on

experiments allow students to test their understanding.

For research:

Different sequences of instruction with more in-depth explanations should be investigated in

order to understand the process of conceptual acquisition and strengthening of desired

propositions. Scenarios that change both net force and total mass should be added, and additional

scenarios that challenge the single mass and ratio weak conceptions should be explored.

Scenarios that include multiple pulleys can also be added as challenge towards the end of the

IBLA.

Limitations

A limitation of the current study is the small male-dominated sample. The results from this

exploratory qualitative study will be tested in future work on larger size and more diverse

samples. Another limitation was that assignment of students to one of the three sequences of

instruction was made at the time of the interview, which has the potential for bias. Potentially

problematic is also the fact that the intervention was not fully scripted, which introduced slight

changes from student to student.

Page 26.858.21

Conclusions

Students had three distinct mental models that they use regarding Newton‟s second law (one

scientific and two naïve models). Both conceptual development and conceptual change happened

during the IBLA. Conceptual development was typical, as the students acquired and strengthened

desired propositions, but they did not necessarily give up on their prior naïve propositions. Not

surprisingly, if students had a naïve understanding that was not contradicted by the results of the

experiment, they maintained it.

Conceptual change was evident when students were exposed to a Scenario that revealed the

limitation of their naïve mental model. Both conceptual development and conceptual change are

needed for students in order to have an extensive declarative knowledge organized according to

scientific model.

References

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Dynamics, in Mechanical Engineering. 2013, California Polytechnic State University: San Luis Obispo, CA.

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experimentation skills: Is it all in the timing? Instructional Science, 2013. 41(3): p. 621-634.

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Engineering. InProceedings of the Annual Conference of the American Society for Engineering Education.

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Concepts, in ASEE Annual Conference & Exposition. 2006.

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InProceedings of the American Society for Engineering Education Annual Conference and Exposition. 2013.

12. Shavelson, R. J., Ruiz-Primo, M. A., & Wiley, E. W. (2005). Windows into the mind. Higher education, 49(4),

413-430.

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Education, 4(3), 231-240.

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childhood. Cognitive psychology, 24(4), 535-585.

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short‐term studies of students' scientific ideas.Science Education, 88(6), 885-900.

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Page 26.858.23

Appendix A: Interview protocol for the pulley IBLA

**Notes to Interviewer:

Students must sign release form

Make sure the student is speaking loud enough.

Ask the student to talk aloud if they are quietly studying the drawings.

The student may run the experiment more than once.

If after trying to explain the student says “I don‟t know,” move to the next question.

If the student wants to do a sketch or even a quick free body diagram (FBD), that is

okay. What we don‟t want is for them to crank through a bunch of equations without

really thinking about it conceptually

The student should repeat the tests once or twice.

Bring a scale in Scenario the student wishes to weigh the sacks.

The student can write on the board right over the projection, so we can video this.

Introduction

I am going to present you with a number of conceptual scenarios in Dynamics and we want to

know what you are thinking as you solve them. Although it may not seem natural to you, we are

asking you to talk aloud while you are thinking. The more you say is the better. We are really

interested in the process of how students reason through different dynamics problems. If you

like, you can write on the blackboard as you think through the problems, but please keep

talking. We will start with a practice question so you can get the hang of things. At the end, we

will fully explain all the concepts after the videotaped session.

Practice This first problem is a practice problem. Please read the question out loud and then talk me

through what you are thinking as you solve the problem. (Prompts: Can you tell me more about

that? Could you speak louder? I can tell that you are thinking, could you explain what thoughts

you have?)

* After the practice, give feedback. I like how you… (2), I wish you would…(1)

Scenario 1

1. Looking at the picture of Scenario 1, which block will accelerate faster, block A or block

B? Or do they accelerate at the same rate, or not at all?

2. Why do you think that is the Scenario? (Prompt: Can you tell me more about that?)

**If they end up talking about ratios, make sure you pin them down on exactly what ratio

they are talking about.

3. Please report your confidence level for your prediction as a total guess, low, low-to-

moderate, moderate, moderate to high, or high.

4. Would you please perform the Scenario 1 experiment?

5. What did you observe when performing the experiment?

6. Please explain what is happening. (Prompt: Can you tell me more about that?)

Page 26.858.24

Scenario 2









Scenario 3









**Explanation after Scenario 3, before they go to Scenario 4. We will do two sets like

this, then decide what we want to do next.

Scenario 4






Page 26.858.25

Note: 1 oz = 1/16 lbs

Confidence Scale

Total Guess Low Low-Moderate Moderate Moderate-High High

.858.26

Appendix B: Coding maps for the nine students assigned to three sequences of instruction

a. NoINT = IBLA only with predict-observe-explain (P.O.E) cycles;

b. INT2 = IBLA with direct instruction after Scenario 2;

c. INT3 = IBLA with direct instruction after Scenario 3.

Three students (A, B, C) were assigned per each instructional sequence (NoINT, INT2, INT3). Each of the nine students was assigned

a code for the sequence and the order in which they participated (A, B, C). For example, INT2_B refers to student B (second one in

the INT2 group) who had an intervention after Scenario 2.

Student NoINT_A

The student NoINT_A uses predominantly W1 single mass proposition to predict and explain all the scenarios. There is no direct

instruction and no Scenario to challenge this weak proposition, so the student does not experience any visible conceptual change.

Page 26.858.27

Student NoINT_B

In Scenario 1 – Predict, the student NoINT_B utilizes three out of four desired propositions (D1, D2 and D4), but with low

confidence. W2 ratio proposition and incorrect proposition I1 is also used. The experimental results confirm the student‟s prediction,

so more confidence is gained in the desired proposition D1 (area of the bubble increases). Scenario 2 is similar to Scenario 1 and the

student has no difficulty making the correct prediction. For Scenario 3, the student attempts to make a prediction using the same

propositions. The prediction is wrong; therefore the student is forced to seek additional explanations. The student realizes that the net

force plays a role in determining the acceleration, however has the tendency to introduce the ratio (W2) in the explanation as well.

Scenario 4 serves as a clarifying case, the student realizing that the ratio proposition (W2) has limited applicability.

Page 26.858.28

Student NoINT_C

In Scenario 1 – Predict, the student NoINT_C understands the role of total mass and uses confidently desired proposition D1. He also

has a vague idea of how to calculate the net force (D3), but does not know how to link net force to acceleration. The student makes

only correct predictions, but that is not indicator of robust scientific knowledge. In his explanations the student uses a mix of desired

propositions and the ratio weak proposition. Scenario 4 serves as a clarifying case, the student realizing that the ratio proposition (W2)

has limited applicability.

Page 26.858.29

Student INT2_A

In Scenario 1 – Predict, the student NoINT_C understands the role of net force and uses confidently desired propositions D2 and D3.

However, the weak proposition W1 single mass is the proposition that drives his predictions in Scenario 1 and Scenario 2. The direct

instruction after Scenario 2 helps the student understand that total mass and not single mass play a role in the whole system. However,

the student gets confused and starts utilizing total weight to calculate net force instead of the weight difference (I1). In Scenario 4, the

student utilizes the same desired propositions as used at the beginning of the IBLA, so no durable conceptual acquisition is visible.

Page 26.858.30

Student INT2_B

The student INT2_B participated in sequence #2 (direct instruction after Scenario 2). For Scenario 1 and Scenario 2, both Predict and

Explain step, the student utilizes only one propositionto solve the problem, namely the ratio weak proposition (numbered W2). His

predictions are correct. After the direct instruction, in the Scenario #3 - Predict step, the student utilizes the D2 net force proposition

but also has an incorrect proposition (I1). After observing through experiment that his prediction was wrong, the student uses D2 and

D3 propositions with low confidence and reverts back to the W2 proposition in the Scenario #3 - Explain step. In the last step (in the

Scenario #3 – Explain), the student uses D3 and I3 propositions.

Page 26.858.31

Student INT2_C

Student INT2_C utilizes proficiently the scientific framework in all the four scenarios. All the desired propositions are used with high

confidence.

Page 26.858.32

Student INT3_A

In Scenario 1 – Predict, the student INT3_A utilizes with medium confidence D2 and D3 related to net force and with low confidence

D1 related to total mass. By focusing on the Net force proposition, the student predicts that both accelerations will be the same, since

the net force (determined as the mass difference) is the same. The contradictory experimental results make the student gain confidence

in the total mass proposition (D1). The student doesn‟t mention net force in his Explain step. Scenario 2 is the similar to Scenario 1, so

the student has no difficulty in making the correct prediction. For Scenario 3, the student utilizes the same approach based on D1 and

makes a wrong prediction. In the Explain step, the student introduces the W2 ratio proposition with low confidence. The direct

instruction after Scenario 3 helps the student understand that the net force is important for determining the acceleration (D2).

Page 26.858.33

STUDENT INT3_B

The student INT3_B uses predominantly the W1 single mass weak proposition, alone (Scenario 1) or in a mix with desired

propositions (Scenario 2). In Scenario 3 – Predict,after the instructor asks for clarification on what mass he is referring to, the student

realizes that total mass in determining the acceleration. So he makes the prediction with high confidence that the accelerations are the

same. The experimental results prove his prediction wrong. In the Explain step, he utilizes the Net force concept to explain why the

accelerations are different. The Direct instruction helps the student acquire the total mass proposition and strengthen the net force

proposition. This allows the student to get a big picture idea of Newton‟s second law.

Page 26.858.34

Student INT3_C

For scenarios 1 and 2, the student INT3_C uses Total Mass concept to predict with high confidence that both accelerations will be the

same, since their total mass is the same. The student utilizes the same logic for the Scenario 3 and makes the wrong prediction that the

accelerations will be the same. In the Explain step, he utilizes the net force concept and Newton‟s 2nd

law framework to explain why

the masses are different. The direct instruction after Scenario 3 does not play a visible role in the conceptual acquisition, since the

student already gained the concepts from previous wrong prediction.

Page 26.858.35

how misconceptions might be repaired through inquiry-based ... · paper id #13115 how...

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