SEARCH

SEARCH BY CITATION

Keywords:

  • Teaching;
  • Experimental design;
  • Hands-on activity;
  • Introductory statistics;
  • Cockroach

Summary

  1. Top of page
  2. Summary
  3. INTRODUCTION
  4. THE ACTIVITY
  5. THE EXPERIMENT
  6. WHAT DID STUDENTS LEARN?
  7. CONCLUSION
  8. Appendix: Randomizing roaches activity hand-out
  9. Appendix: Randomizing Roaches instructor guide
  10. REFERENCES
  11. RESOURCES

Understanding the roles of random selection and random assignment in experimental design is a central learning objective in most introductory statistics courses. This article describes an activity, appropriate for a high school or introductory statistics course, designed to teach the concepts, values and pitfalls of random selection and assignment using the not-easily-forgotten Madagascar hissing cockroach. Evidence is summarized demonstrating conceptual gains for students performing the Randomizing Roaches activity, and follow-up activities are suggested.


INTRODUCTION

  1. Top of page
  2. Summary
  3. INTRODUCTION
  4. THE ACTIVITY
  5. THE EXPERIMENT
  6. WHAT DID STUDENTS LEARN?
  7. CONCLUSION
  8. Appendix: Randomizing roaches activity hand-out
  9. Appendix: Randomizing Roaches instructor guide
  10. REFERENCES
  11. RESOURCES

Understanding the roles of random selection and random assignment in experimental design is a central learning objective in most introductory statistics courses (Zieffler et al. 2008; Sawilowsky 2004; Schield 2004). However, due to conceptual and vocabulary difficulties, it is often challenging for students to understand the distinct roles of random selection and random assignment in research studies (Rubin et al. 1990; Enders et al. 2006; Kaplan et al. 2009).

This article describes an activity designed to teach the concepts, values and pitfalls of random selection and random assignment. This activity, appropriate for a high school or freshman/sophomore university level introductory statistics course, requires active participation of the students using living subjects for devising plans for random selection and random assignment. Additionally, this activity increases the likelihood that students will stay engaged and remember the lesson throughout the course as its focus is on the memorable, Madagascar hissing cockroach (MHC) (figure 1). The use of this subject (i.e. the MHC) has many practical advantages for teaching these concepts because of the following: (1) MHCs are communal animals and socialize or group in a manner similar to human populations; (2) MHCs may be easily studied in a very short period; (3) MHCs are harmless to humans; (4) MHCs are readily available at universities, zoos and nature centres and can often be borrowed and returned; and (5) students of any age tend to have a keen interest in MHCs and thereby may retain a more accurate memory of the activity. Moreover, any activity that employs ‘fun’ can change the classroom environment by fostering a classroom community, reducing anxiety and encouraging a more open learning atmosphere (Lesser and Pearl 2008).

image

Figure 1. Adult male Madagascar hissing cockroach

Download figure to PowerPoint

Madagascar hissing cockroach

The Madagascar hissing cockroach (Gromphadorhina portentosa) is a large insect indigenous to the island of Madagascar. MHCs are slow moving, cannot bite or fly and are easy to handle. They do not transmit disease to humans and do not infest human habitations. Both male and female MHCs can produce a load ‘hissing’ sound when disturbed. This vocalization is produced by the roach forcing air through a modified breathing hole on the side of its body. The weight of a MHC varies from approximately half a gramme at birth to approximately 24 g when an adult. The length can also vary with a fully developed adult roach being from 5 to 8 cm in length.

The MHCs are insects with a complex social hierarchy. Male MHCs fight other male MHCs to establish and defend territories within their colony to attract female MHCs for mating. These territories, once established, consist of one dominate male MHC, a few female MHCs and many nymphs. These territories or clusters produce different groups anywhere throughout the enclosure that have very different proportions of adult, juvenile, female and male MHCs from the overall population. Clusters within the enclosure also occur around the food source, water source and in the vertical egg cartons that are present in the MHC's enclosure (figure 2). If you decide to set up your own colony of MHCs instead of borrowing them from a university, zoo or nature centre, there are helpful articles that can assist you in the Resources section (Wagler, R. 2005; Wagler, R. 2009; Wagler, R. 2010; Wagler, R. 2011). If you would prefer to not use MHCs for the activity, terrestrial isopods (i.e. sow bugs or pill bugs) may be substituted.

image

Figure 2. Madagascar hissing cockroach enclosure

Download figure to PowerPoint

Teaching the role of randomization

Derry et al. (2000) documented that students in beginning statistics courses demonstrate confusion about the roles of random selection and random assignment. Sawilowsky (2004) contends that students not only have difficulty comprehending the concept of random assignment but ‘harbour considerable distrust’ of the procedure (p. 221). There are examples of activity-based instruction for teaching the role of randomization in experimental designs (Labov and Firmage 1994; Schaeffer et al. 1996; Smart 1999; Enders et al. 2006). However, most of these activities employ computer simulation and lack a hands-on component. Hands-on activities can be a useful first step that builds the conceptual groundwork that may be deepened via computer simulation activities. For example, in a study concerned with developing conceptual knowledge of variability, Shaughnessy (2007, p. 982) found that students' conceptual knowledge increased with the use of hands-on activities.

Some examples of existing hands-on activities include the following. Enders et al. (2006) proposed a hands-on activity utilizing playing cards for teaching randomization in an effective and engaging method. ‘Random Rectangles’ and ‘The Gettysburg Address’ are both frequently used hands-on activities which focus on teaching the effect of random selection and the meaning of a representative sample. These are highly engaging and effectively teach the core concepts, but also utilize inanimate objects (i.e. rectangles and words) rather than living subjects. In contrast, the proposed activity, Randomizing Roaches, not only uses actual research subjects but also produces ‘real data’ that can be used throughout the rest of the semester.

THE ACTIVITY

  1. Top of page
  2. Summary
  3. INTRODUCTION
  4. THE ACTIVITY
  5. THE EXPERIMENT
  6. WHAT DID STUDENTS LEARN?
  7. CONCLUSION
  8. Appendix: Randomizing roaches activity hand-out
  9. Appendix: Randomizing Roaches instructor guide
  10. REFERENCES
  11. RESOURCES

Begin the activity by giving a very brief introduction about the MHCs where students are shown how to differentiate between adult and juvenile MHCs (adults are at least 5 cm in length), and adult female and male MHCs (male MHCs have protruding large bumps on the plate behind their head when sexually mature but male juvenile MHCs do not have these bumps) (figure 1). The task for this activity is to devise an experiment to assess whether age influences MHCs' preference for a high-protein or a high-carbohydrate snack. Each group will receive two clear containers with secure lids, a ¼ cup of dry dog food and a ¼ cup of high-carbohydrate cereal in cups. Each student should also have a timer (Table 1). Once the supplies are distributed to the students, the research question is displayed.

Table 1. Materials list for the Randomizing Roaches activity
Materials
One Madagascar hissing cockroach enclosure containing a colony of Madagascar hissing cockroaches
One container per student group
Two clear containers with secure lids per student group
One measuring cup
Two small cups that can hold a ¼ cup of solid material per student group
One box of high-carbohydrate cereal
One bag of dry dog food
One box of latex or plastic gloves
One timer per student
One Randomizing Roaches activity hand-out per student group (Appendix I)
Research question: is age a factor in food preference?

Remind students that MHCs are classified as juvenile if less than 5 cm in length and that the diets to be compared are high-protein (dog food) versus high-carbohydrate (cereal). Show the students the MHCs in the enclosure (figure 2). Encourage observations about how the MHCs are clustered or grouped within the container. Following these observations, ask the following question.

Method question 1: how should each group select MHCs for the research study?

Time is allowed for individual reflection, followed by small group discussion and then class discussion. If students are having difficulty devising a selection strategy, point out that female MHCs tend to prefer high-protein foods and male MHCs tend to prefer high-carbohydrate foods (Carrel and Tanner 2002). The instructor guide (Appendix II) contains questions to anticipate and suggested questions that may be useful for assisting students in devising a selection strategy.

Open the enclosure and remind the students that MHCs cluster in groups, much like human populations. This reminder usually leads students to observe that they could easily end up with all juveniles or male MHCs and so on if we are not careful to sample across the entire container. Ask students to reflect individually on how to select MHCs so that each MHC has an equal chance of being selected. Allow for group discussion time following the individual reflection. After students have obtained their MHCs, ask the following question.

Method question 2: how do we assign the roaches to the two food groups?

Allow time for individual reflection, group and class discussion. Many groups will likely focus on concepts such as equal numbers of male MHCs versus female MHCs or having an equal number of MHCs with opposite characteristics. The instructor guide (Appendix II) provides questions to anticipate and examples of prompting questions to assist students that have difficulty devising a strategy.

THE EXPERIMENT

  1. Top of page
  2. Summary
  3. INTRODUCTION
  4. THE ACTIVITY
  5. THE EXPERIMENT
  6. WHAT DID STUDENTS LEARN?
  7. CONCLUSION
  8. Appendix: Randomizing roaches activity hand-out
  9. Appendix: Randomizing Roaches instructor guide
  10. REFERENCES
  11. RESOURCES

After the assignment to treatment groups, each group member should choose an MHC to ‘watch’ and ready their timer. There are two feeding periods for the MHCs. Allow each group to randomly select which of the two food types will be given in the first feeding period. Instruct the groups to be prepared to gently scatter the food in the appropriate container so that every MHC has equal opportunity to consume the food (figure 3). When given the signal, each group should distribute the food in the appropriate containers and record the time spent eating for each MHC over a period of 5 min. At the end of the feeding period, each group should record the MHC age (juvenile or adult), food type and time spent feeding (in seconds). Record these data for future use in class. The hand-out (Appendix I) includes an example table for recording the data. It is convenient if all students record time in seconds and age as a categorical variable, juvenile or adult. Now, select a new group of MHCs and repeat the procedure for the other food type. It is easiest if one student watches one MHC for each feeding period. If more observations are desired, then just repeat a particular feeding period until the desired number of observations is obtained.

image

Figure 3. Madagascar hissing cockroachs feeding on high-carbohydrate cereal

Download figure to PowerPoint

The summary statistics on feeding times, type of food and age obtained during the activity was utilized throughout the semester for in-class activities and homework. First, the data may be utilized to see and reflect on the consequences of the varying sampling plans utilized by the student groups. This reflection exercise, performed during a subsequent class, can provide a real-life rationale for why random sampling and random assignment are important practices in the design of an experiment. The topics of random assignment and random selection were explored in more detail in the following weeks of class (and using computer simulations to further develop the concepts) with frequent reference to the MHC activity. In class, more explicit ties were made about how this MHC population is similar to and dissimilar to human populations. The data may also be used for illustrating confidence intervals, hypothesis testing, ANOVA or generalized linear models.

WHAT DID STUDENTS LEARN?

  1. Top of page
  2. Summary
  3. INTRODUCTION
  4. THE ACTIVITY
  5. THE EXPERIMENT
  6. WHAT DID STUDENTS LEARN?
  7. CONCLUSION
  8. Appendix: Randomizing roaches activity hand-out
  9. Appendix: Randomizing Roaches instructor guide
  10. REFERENCES
  11. RESOURCES

Study participants were students in a large urban border region university in the southwest United States and enrolled in an introductory probability and statistics course designed for biology and pre-medicine majors. The ‘Randomizing Roaches’ activity took place during the first week of class and served as a model for the semester-long research projects used in the course. The pre-test was taken as students entered the classroom, and the post-test was taken before leaving the classroom.

Although ‘Randomizing Roaches’ is a learning activity designed to lay the groundwork for introducing the procedures of random selection and random assignment, the authors utilize neither method for assessing the impact of this activity! Namely, a pre-test/post-test design is utilized with no random selection of study participants and no random assignment. Despite the weakness of this design, some insights may be made about the effectiveness of the proposed learning activity. Table 2 contains the proportion responding from n = 62 respondents for each item of the three questions in the survey consisting of selected Assessment Resource Tools for Improving Statistical Thinking items (ARTIST (https://app.gen.umn.edu/artist/index.html)). The correct response is B for all items. With no direct discussion of the ARTIST items, we observed that the percentage responding with the correct answer increases for the first two items (p-values were <0.0001 and 0.0013, respectively). For the third item, the difference was not statistically significant (p = 0.1011). This provides some evidence of a relationship between performing this activity and gaining a better understanding of the role of randomization in experiments.

Table 2. Percentage responding to each option of Assessment Resource Tools for Improving Statistical Thinking items (correct answer in bold)
ItemsABCDEMissing
Pretest
53.240.36.546.81.61.6
816.145.222.611.30.04.8
98.137.150.00.00.04.8
Post-test
51.680.63.211.31.61.6
88.171.06.511.30.03.2
91.648.445.21.60.03.2

Student comments

There were three open-ended questions in the pretest survey consisting of the three ARTIST items assessing knowledge of random assignment and random selection. These open-ended questions were not included with the post-test. The responses were coded independently by the two authors to categorize the reasons given for each answer choice with 97% initial agreement and, after discussion, 100% agreement. Table 3 outlines the major reasons cited for choosing answers to the ARTIST items expressing misconceptions. When statistical terms are used incorrectly by the student, they are placed in quotation marks by the authors.

Table 3. ARTIST Items and Open Ended Responses Associated with Each Answer
MisconceptionReasons cited for choosing misconception
Misconceptions about random assignment
• Preferring systematic assignment over random assignment• Balances out the groups
• Preferring nonrandom assignment over random assignment• Is a ‘random’ way to assign groups
• All methods of random assignment are equal• All are ‘random’ methods; no difference between any method; all methods appropriate as long as there are equal groups
• No methods of random assignment are appropriate• 10 samples per group are not enough
Misconceptions about random selection
• Preferring a volunteer sample over random sample• Obtains a wide variety of subjects or opinions; obtains interested subjects; 200 subjects is better than 50
• Preferring a systematic sample over random sample• Gets all possible subjects
• All methods of selecting subjects are equally effective• Any work with a wide variety of subjects

CONCLUSION

  1. Top of page
  2. Summary
  3. INTRODUCTION
  4. THE ACTIVITY
  5. THE EXPERIMENT
  6. WHAT DID STUDENTS LEARN?
  7. CONCLUSION
  8. Appendix: Randomizing roaches activity hand-out
  9. Appendix: Randomizing Roaches instructor guide
  10. REFERENCES
  11. RESOURCES

This article presents a hands-on activity appropriate for a high school or introductory university level probability and statistics course. It may be utilized early or mid-semester and produces useful ‘real data’ for later use in class. The strengths of this activity are that it is highly engaging, hands-on, builds on student's correct intuitions, can be accomplished within a class period (50–80 min. and creates a memorable experience useful for further elaboration and clarification in later class periods. In fact, as randomization is typically difficult for many students to conceptually grasp (Enders et al. 2006), it is suggested that this activity (carried out early in the semester) be a starting point for future reflection, discussion and real-life data analysis.

Appendix: Randomizing roaches activity hand-out

  1. Top of page
  2. Summary
  3. INTRODUCTION
  4. THE ACTIVITY
  5. THE EXPERIMENT
  6. WHAT DID STUDENTS LEARN?
  7. CONCLUSION
  8. Appendix: Randomizing roaches activity hand-out
  9. Appendix: Randomizing Roaches instructor guide
  10. REFERENCES
  11. RESOURCES

Group members:

Randomizing Roaches: instructions and questions

  1. Select the roaches for the study

Discuss with your group how you think the roaches should be selected for the study. Assume we will not use all the roaches, but a subset of them. Compose a statement about how you plan to select the roaches and a justification of why this is the best plan.

After our class discussion, describe any changes you may or may not make to your original plan.

Describe any foreseeable consequences of your selection plan.

Now, select your roaches.

  • 2.
    We plan to study the effect of a low-protein versus high-protein diet on the time spent feeding for adult and juvenile Madagascar hissing cockroaches (MHCs). Discuss as a group how you should select your roaches for your low-protein or high-protein groups. Justify why you think (as a group) that this is the best plan.

After our class discussion, describe any changes you may or may not make to your original plan.

Describe any foreseeable consequences of your plan.Now, place your roaches in the low and high-protein groups.

The rest of the steps are outlined below for completing this experiment.

  • 3.
    Allow the roaches to acclimate to their containers for 3 min. During this acclimation period, decide who watches each of the roaches in your container. Prepare your stopwatches for timing the eating activity.
  • 4.
    Have each group member identify whether the roach is a juvenile or a mature adult.
  • 5.
    Sprinkle the low or high-protein foods into the container at the same time. Allow the food to be uniformly distributed throughout the container. Make sure everyone is watching their respective roaches with a timer ready.
  • 6.
    Start timing whenever your roach begins to eat. Pause the timer when the roach quits eating. It is possible that the roach may eat on and off during the feeding period. Do this for 5 min. and record the time in seconds that your roach feeds.
  • 7.
    Record your times and age for each roach.
image

REFERENCES

  1. Top of page
  2. Summary
  3. INTRODUCTION
  4. THE ACTIVITY
  5. THE EXPERIMENT
  6. WHAT DID STUDENTS LEARN?
  7. CONCLUSION
  8. Appendix: Randomizing roaches activity hand-out
  9. Appendix: Randomizing Roaches instructor guide
  10. REFERENCES
  11. RESOURCES
  • Carrel, J.E. and Tanner, E.M. (2002). Sex-specific food preferences in the Madagascar hissing cockroach Gromphadorhina portentosa (Dictyoptera: Blaberidae). Journal of Insect Behavior, 15(5), 707714.
  • Derry, S., Levin, J.R., Osana, H.P., Jones, M.S. and Peterson, M. (2000). Fostering students' statistical and scientific thinking: lessons learned from an innovative college course. American Educational Research Journal, 37, 747773.
  • Enders, C.K., Laurenceau, J. and Stuetzle, R. (2006). Teaching random assignment: a classroom demonstration using a deck of playing cards. Teaching of Psychology, 34(4), 239242.
  • Kaplan, J.J., Fisher, D.G. and Rogness, N.T. (2009) Lexical ambiguity in statistics: what do students know about the words association, average, confidence, random and spread? Journal of Statistics Education, 17(3), from www.amstat.org/publications/jse/v17n3/kaplan.html
  • Labov, J.B. and Firmage, D.H. (1994). Introducing concepts of random ordering and random assignment of subjects: computer assisted classroom and laboratory exercises. The American Biology Teacher, 56, 169173.
  • Lesser, L.M. and Pearl, D.K. (2008). Functional fun in statistics teaching: resources, research and recommendations. Journal of Statistics Education, 16(3), from www.amstat.org/publications/jse/v16n3/lesser.html
  • Rubin, A., Bruce, B., Tenney Y. (1990). Learning about sampling: trouble at the core of statistics. ICOTS 3, 314319.
  • Sawilowsky, S.S. (2004). Teaching random assignment: do you believe it works? Journal of Modern Applied Statistical Methods, 3(1), 221226.
  • Schaeffer, R.L., Gnanadesikan, M., Watkins, A. and Wimer, J.A. (1996). Activity-based Statistics. New York, NY: Springer-Verlag.
  • Schield, M. (2004). Statistical literacy curriculum design. Curricular development in statistics education, Sweden.
  • Shaughnessy, J.M. (2007). Research on statistics learning and reasoning. In F.K. Lester, Jr. (ed.). Second Handbook of Research on Mathematics Teaching and Learning, pp. 9571009. Greenwich, CT: Information Age.
  • Smart, T. (1999). The BioSS challenge – a demonstration of sampling bias. Teaching Statistics, 21(2), 3638.
    Direct Link:
  • Zieffler, A., Garfield, J. delMas, R. & Reading, C. (2008). A Framework to Support Research on Informal Inferential Reasoining. Statistics Education Research Journal, 7(2), 4058, http://www.stat.auckland.ac.nz/serj

RESOURCES

  1. Top of page
  2. Summary
  3. INTRODUCTION
  4. THE ACTIVITY
  5. THE EXPERIMENT
  6. WHAT DID STUDENTS LEARN?
  7. CONCLUSION
  8. Appendix: Randomizing roaches activity hand-out
  9. Appendix: Randomizing Roaches instructor guide
  10. REFERENCES
  11. RESOURCES
  • Wagler, R. (2005). Cockroaches in the classroom: incorporating the Madagascar hissing cockroach into your science curriculum. Science Scope, 28(6), 3437.
  • Wagler, R. (2009). Chow down! Using Madagascar hissing cockroaches to explore basic nutrition concepts. Science Scope, 32(7), 1218.
  • Wagler, R. (2010). Home sweet home: how to build a Madagascar hissing cockroach habitat out of recycled materials. Science Scope, 33(8), 3439.
  • Wagler, R. (2011). Look at that! Using Madagascar hissing cockroaches to develop and enhance the scientific inquiry skill of observation in middle school students. Science Scope, 35(4), 3647.