Literature Reviews

In preparation for formal research, a new found awareness of a dissertation literature review brings about a whole new view of its value and importance. Consistent through readings are the necessity of literature reviews. Boote and Beile (2005) stress comprehensive and up-to-date literature review as the best ways for aquiring knowledge for a dissertation but these reviews are more in-depth than Crewell’s (1994) five-step process of identifying terms, finding literature, reading and checking for relevance, organizing selected literature and writing reviews. Boote and Beile (2005) suggest the use of Strike and Posner (1983) three categories to identify a good synthetic review, which includes the clarification and a possible resolution to an problem within one’s field of study, the development of a new perspective, and satisfying the criteria of good theory. A dissertation literature review summarizes similar studies, links to ongoing research, provides a basis for research as a result of previous studies. Boote and Beile (2005) make note of Hart’s extensions to these basic requirements which include a clear articulation of research which needs to be done and why it is important, a clear articulation of it’s practical significance, a synthesis of prior research so as to develop a new perspective and a critical analysis of the methodologies using in prior research. This is above and beyond the basic level of the literature review Creswell discusses.

Boote and Beile (2005) provide a higher level perspective on a literature review which are necessary for a doctoral dissertation. Taking the time to compare each annotation in a literature review against the categories (i.e. coverage, synthesis, methodology, significant and rhetoric) are essential to writing a review where the researcher demonstrates an ability to do research which advances important educational issues (Boote and Beile, 2005). A doctoral literature review requires more than simple summaries and should meet Hart’s criterion as suggested by Boote and Beile (2005) to include:

•    a justification criteria for inclusions and exclusions

•    distinguishing what has been done in the field from what needs to be done

•    placing the research in broader literature

•    placing the research in a historic context

•    acquiring and enhancing related vocabulary

•    articulating important variables and phenomena

•    synthesizing and gaining new perspectives

•    identifying the main methodologies and research techniques that have been used and analyze their advantages and disadvantages

•    relating ideas and theories to research methodologies

•    rationalizing the scholarly and practical significance of the research 

•    a clear and coherent structure.

Specific to me is the developed understanding that the literature review should be a central focus my research. I can expect to review and reread literature throughout this process expecting to change my focus to develop workable and important problems to show a thorough and sophisticated understanding of the field (Boote and Beile 2005). For now, I will review my current annotations to determine if they meet the criterion and will add value to a doctoral literature review.

Boote, D. & Beile, P. (2005). Scholars before researchers: On the Centrality of the Dissertation Literature Review in Research Preparation, Educational Researcher, 34(6), 3-15.

A Comparison of Two Approaches in Qualitative Research

Merriam (2009) describes qualitative research as the process of uncovering the meaning of a phenomenon (p. 5). Merriam (2009) expresses it’s design as desire to understand how people interpret their experiences, how they construct their worlds and what meaning they attribute to their experiences. As this type of research has spread across multiple disciplines, various approaches have been identified to further describe this interest in understanding phenomenon. Creswell (2013) discusses five approaches to describe and organize the different strategies and approaches to qualitative research – ethnography, narrative, grounded theory, case study and phenomenology. Merriam (2009) adds to this list by including basic qualitative research and critical qualitative research. Additional authors have added numerous approaches to this few, however, for the purposes of this paper only two traditional approaches will be discussed; phenomenology and case study.

Phenomenology

Drawing from a philosophical background, phenomenology is described by Lichtman (2012) as “a way to research the gaps in a discipline, those areas that previously were not considered important to research” (p. 86). The focus of phenomenology is on a phenomenon and the essence of the lived experience; not on an individual. Creswell (2013) quotes Melau-Pony as “the researcher transcending past knowledge and experience to understand a phenomenon at a deeper level” (p. 331). Phenomenology is not interested in modern science’s efforts to categorize, simplify and reduce phenomena to abstract laws (Merriam, 2009, p. 24). The intent suggested by Creswell (2013) is to describe the common meaning for several individuals of their lived experiences with phenomenon elicit rich and descriptive data.
Researchers choose phenomenology when it is important to understand several individuals’ common or shared experiences of a phenomenon to develop practices or polices or to develop a deeper understanding about the features of the phenomenon. (Creswell, 2013). The phenomenological approach allows the researcher to examine a phenomenon and the meaning it holds for individuals by seeking out individual subjective views (Seidman, 2012). This is primarily done through interviewing where researchers “strive to understand a person’s experience from their point of view by studying affective, emotional and intense human experiences” (Merriam, 2009, p. 26).
Essentially this approach is a philosophical discussion. It relies on more than selecting a coding scheme and constant-comparative methods. The researcher must understand the some of the underlying philosophical assumptions (Lichtman, 2012). Creswell (2013) extends this to the researcher bracketing out of the study by discussing personal experiences with the phenomenon, setting aside personal beliefs feelings and perceptions. Phenomenology’s approach is to “suspend all judgements about what is real until they are founded on a more certain basis” (Creswell, 2013, p. 77).
Phenomenology primarily uses interviewing to collect data on the individuals who have lived the experience. And although a several interviews may be asked on each participant, Creswell (2013) suggest two broad interviewing questions: “What have you experienced in terms of this phenomenon? What contexts or situation have typically influenced or affected your experiences of the phenomenon?” (p. 81). For some individuals this question may be answered with alternative methods such as documents, observations, journals, art work or other documentation, however, the process of collecting information is primarily in-depth interviews (Creswell, 2013). The intention is to gather information from several individuals, that unit of analysis, to develop descriptions of essences and not to provide explanations. These descriptions consist of what Moustakas (1994) simplifies as “what” individuals experienced and “how” they experienced it (Creswell, 2013).
The collection of data from individuals who have experienced the phenomenon culminates in a description of the essence of the phenomenon through the analysis of the data. An approach which Creswell (2013) details as “a systematic procedure that moves from the narrow units of analysis (the significant statements) to broader units (meaning units) and then the detailed descriptions that summarize what individuals have experienced and how they have experienced it” (p. 79). The result of phenomenological research is feeling like “I understand better what it is like for someone to experience that” (Merriam, 2009, p. 26).
In summary, the phenomenological approach requires the researcher to interview the individuals, ground the study in philosophical tenets of phenomenology, follow set procedures and end with the essence of the meaning. (Creswell, 2013, p. 124)

Case Study

Drawing from a psychology, Creswell (2013) uses a case study to develop and in-depth description and analysis of a case or multiple cases with the intent to understand a specific issue, problem or concern. Specifically, an instrumental case or cases is selected to best illustrate the complexity of the issue and understand the problem (Creswell, 2013). Intrinsic case studies may also be used where they illustrate a unique case that has unusual interest in and of itself and needs to be described and detailed (Creswell, 2013). Case studies are identified by Creswell (2013) as being “a good approach when a clearly identifiable case with boundaries has been identified and the researcher seeks to provide an in-depth understanding of the cases or a comparison of several cases” (p. 100).

Creswell (2013) recognizes that a case study begins with the identification of a specific case, which can be an individual, several individuals, a program, an event or an activity. A case can even be “limited to a characteristic, trait or behavior” (Lichtman, 2012, p. 91). “If the researcher has a specific entity, program, or project and the questions being asked are involved with asking what happened when the program was developed, or how did an individual behave then the researcher can probably do a case study" (Lichtman, 2012, p. 93). The challenge is to study a case with clear boundaries (Creswell, 2013)

“A good case study presents an in-depth understanding of the case, which is accomplished through various forms of data; relying on one source of data is not enough to develop an in-depth understanding” (Creswell, 2013, p. 98). These multiple sources may include documents, interviews, observations and artifacts but are not limited to one source. The data collection process involves a wide array of procedures to build an in-depth picture of the study, which includes contextual material to describe the setting of each case (Creswell, 2013).

Case studies can be identified according to Merriam (2009) as particularistic (focused on a particular even, program or phenomenon), descriptive (the end product is a rich, thick description of the phenomenon under study) or heuristic (brings about the discovery of new meaning, extends the reader’s experience or confirms what is know). Creswell (2013) further types case studies by intent: intrinsic with the focus is on the case itself because the case presents an unusual or unique situation, instrumental which focuses on an issue or concern and then selects one bounded case to illustrate this issue or as multiple case where one issue or concern is selected but the researcher selects multiple case studies to illustrate the issue. As a result, the unit of analysis in a case study may be multiple cases (a multi-site study) or a single case (a within-site study).

The analysis of data requires the description of the case and themes of the case as well as cross-case themes. Creswell (2013) recognizes the four specific formats of data analysis. Categorical aggregation seeks a collection of instances from the data hoping that the issue-relevant meanings will emerge, direct interpretation looks at a single instance and draws meaning from it without looking for multiple instances, the establishment of patterns which looks for a correspondence between two or more categories and naturalistic generalizations which is the development of generalizations that people can learn from the case either for themselves or to apply to a population of cases (Creswell, 2013).

The culmination of the analysis is the development of a detailed analysis of one or more cases where the researcher details the history of the case, the chronology of events or a day-by-day rendering of the activities of the case (Creswell, 2013). The researcher then focuses on a few key issues (the analysis of themes) not for generalizing but for understanding the complexity of the case (Creswell, 2013). When multiple cases are chosen a typical format is to provide a detailed description of each case and themes within the case, followed by a thematic analysis across the cases as well as assertions of the meaning of the case. However, the final phase is the conclusion which Creswell (2013) reports as “the meaning of the case, whether the meaning comes from learning about the issue of the case (an instrumental case) or learning about an unusual situation (an intrinsic case)” (p. 101). It is here where the researcher includes a description of the case and themes/issues that were uncovered in the study as well as general lessons learned; assertions, patterns or explanations (Creswell, 2013).

“Case studies are particularly appealing for applied fields of study such as education” (Merriam, 2009, p. 51). Researchers may choose a case study for what it can reveal about a phenomenon (Merriam, 2009). When a researcher needs information about the characteristics of a given population or an area of interest, a descriptive case study is a good choice. The results should not be used to predict behavior however insights from the research can be construed as tentative hypotheses that help structure future research; case studies plan an important role in advancing a field’s knowledge base (Merriam, 2009, p. 51). Merriam (2009) states that “what researchers learn in a particular case can be transferred to similar situations and bring about understanding that in turn can affect and may even improve practice” (p. 51).

Case studies are intensive descriptions and explanations, which require the analysis of a single entity, phenomenon or social unit called a case. Researchers choose the case study approach to examine a case, bounded in time or place and look for contextual material about the setting of the case. They gather extensive material from multiple sources of information to provide and in-depth picture of the case (Creswell, 201). Researchers explore a case or cases over time though detailed, in-depth data collection involving multiple sources of information and report a case description and case themes (Creswell, 2013). Creswell (2013) describes the focus of a case study as the development of an in-depth understanding of a singe case or exploration of an issue or problem using the case as a specific illustration. It is ultimately up to the researcher to describe the case in detail and mentions several issues or focus on a single issue that emerged when examining the case (Creswell, 2013).

In the end, case studies explore an issue or problem and a detailed understanding emerges from examining a case or several cases (Creswell, 2013). It is necessary, to use multiple data collection strategies to collect a wide array of information about the case to provide an in-depth picture so generalizations that can be learned from studying the case or cases end the case study report (Creswell, 2013).

Although Creswell (2013) defines each of these approaches as flexible there are considerable differences between the two. One difference between the two approaches is the strategies, which are used to collect data. Phenomenology primarily uses interviews, and several interviews per participant, with the option of using alternate documents. A case study approach requires the use of multiple data collection strategies and looks down upon the use of one primary format. A second difference between the two approaches is in the area of describing the data. Within phenomenology personal experiences are shared through epoche, which is not seen in a case study. The case study describes the case and its context, however, lacks in the directive to include an epoche as described by Creswell (2013). An additional difference is the way in which the data is interpreted for these traditional approaches. Within phenomenology a reader will find a textural description, which describes what happened, a structural description, which describes how the phenomenon was experienced and a conclusion which develops the essence of the phenomena. Within a case study there great reliance on description in direct interpretation and the development generalizations of what was learned from the research (Creswell, 2013). A third defining difference can be found within the basic defining factors of each approach. Phenomenology is defined by the focus of the study while a case study is defined by the unit of analysis. Merriam (2009) points out the fact that case studies are focused on the unit of analysis or the bounded case while phenomenology is focused on the understanding of the essence of the phenomena. This difference allows for some overlapping of approaches and provides a backing for research methodologies, which combine these approaches.

Proposed Study

My proposed study is to describe middle school students’ attitudes and self-concept towards mathematics. At stated in previously, the mathematical attitudes are generally defined as a student’s emotions, beliefs and behaviors towards mathematics (Hart, 1989). Mathematical self-concept is described as a student’s perception or belief to do well in mathematics and confidence in learning mathematics (Reyes, 1984).

Literature has identified interventions, which include teacher support, cooperative learning, classroom tools and technology, modeling, and self-efficacy as having direct effects on the intrinsic motivation of students. What are factors students identify with as influencing their attitudes? What factors influence the middle school students’ self-concept? Is there a direct correlation between their performance and these concepts? What are other countries doing to positively affect their students’ attitudes and self-concept? And are these factors lacking in lower performing countries?

Using the phenomenological approach would require data collection primarily through interviews. However, with the intent of interviewing students I recognize that other forms of data are acceptable and may in actuality be preferable to a student. This will provide for a richer and more in-depth study. Multiple data collection strategies will help to understand “what” students experienced and “how” they experienced it in relation their mathematical attitudes; a phenomenological approach where I listen to students describe their experiences, and the events which led to their attitudes. Bromley states the importance of “getting as close to the subject of interest as possible, partly by means of direct observation in natural settings, partly by access to the subjective factors (thoughts, feelings, and desires)” (Merriam, 2009, p. 46).

This focus on one phenomena, the case, helps to define an instrumental case study where important themes can by analyzed. However, the boundries of such a case will need to be clearly defined to gain the appropriate sampling for a case study. Creswell (2013) suggests maximal sampling or purposefully selecting multiple cases to show different perspectives; limiting to a maximum of fives cases. Such sampling will allow me to look at students who have positive as well as negative attitudes towards mathematics rather than one specific attitude with a multi-case study.  

Choosing a phenomenological approach would allow me to understand the mathematical experience of middle school students through their eyes. Such understanding and sharing of experience would hopefully shed new light on educational practices and develop a deeper understanding of the attitudes of middle school students towards mathematics (Creswell, 2013).

As a mathematics teacher of several years, I have developed biases and assumptions related to students’ attitudes towards mathematics. As a result, it will be important to bracket myself from the study, which is a necessity in a phenomenological study. Remaining absolute and objective is never 100% guaranteed. A case study does not require the examination of biases and assumptions in the format of a epoche however Merriam (2009) states that this process has become common practice for all researchers.

Despite the fact that these two approaches have several recognizable differences, they both have been used for educational research. Phenomena can be described using either research approach. However, Creswell (2013) suggests that consideration must be taken into what is needed most as contributing to the scholarly literature in the field of education. The possibility of overlapping a case study and a phenomenological approach has crossed my mind as a result of this paper. I can see the usage of a textural description to describe the students self-concept and the structural description to describe how they experienced it to further share the overall experience of what it is like to hate math and the lack of self-concept being able to do it. Creswell (2013) suggests “designing a study within one of the approaches to enhance the sophistication of the project and to convey a methodological expertise for readers of qualitative research” (p. 279). A case study is the chosen approach.

References

Creswell, J. (2013). Qualitative Inquiry and Research Design: Choosing Among Five Approaches, Newbury Park: Sage Publications.

Hart, L. E. (1989). Describing the affective domain: Saying what we mean. In Affect and mathematical problem solving (pp. 37-45). Springer New York.

Lichtman, M. (2012). Qualitative research in education: A user's guide. Sage.

Merriam, S. (2009). Qualitative Research: A Guide to Design and Implementation. San Francisco: Jossey-Bass Publications.

Reyes, I., H. (1984). Affective variables and mathematics education. Elementary School Journal, 84, 558-581.

Seidman, I. (2012). Interviewing as qualitative research: A guide for researchers in education and the social sciences. Teachers college press.

Keeping a Journal

Keeping a journal has never been a consistent habit for me. Thinking back to years when all of my friends wrote in the journals, I attempted to join in the common girl activity but never kept up with regular writing. This has behavior has followed me into adulthood.

Currently, I have a three-year memory book where I write one sentence to represent a thought or memory for each given day. Just this past month, I realized I had forgotten about this book. When I opened up the book to write inside, I quickly realized that my writings were all very emotional entries. I tend to journal and record when I have very emotional to express; otherwise the entries are blank. Knowing I do not have a history of consistency with keeping a journal, I am looking for strategies to help me keep consistent with writing. How can I make journal writing a habit and not one more thing to do?

I started a research journal. Actually, I started two research journals; one in electronic form and one in paper form. When journaling it is much easier to express thoughts and reflect using a computer; typing is so much cleaner and faster than writing by hand. The challenge I have run into is that I do not have a computer with me every time I have the need to write. This has led to the use of a paper journal. As a traditional Type A personality, having two journals is not something I am comfortable with; I feel disorganized and disjointed. What suggestions do others have to better organize my journal keeping?

As for journal content, it is reflective informative and valuable to me as I look back. Stevens and Cooper (2009) mention one of the values of writing is to help a researcher understand their personal values and beliefs to ensure a clear perception when collecting data. Truly this is not something I had considered. Journal writing has been a place where for keeping notes, questions and ideas for 

Stevens and Cooper (2009) offer a list of journal possibilities, which are down to earth and possible. The suggestions to keep areas for lists, logs, notes, and research focus are all valuable and possible. However, my brain is questioning again. What is the best method; paper or electronic? What strategies do others use to ensure consistent writing?

           

Stevens, D. & Cooper, J. (2009). Journal Keeping: How to Use Reflective Writing for Learning, Teaching, Professional Insight and Positive Change. Sterling, VA: Stylus Publishing, LLC.

Potent Leadership #leadership

I have lost touch with what is happening. I am definitely the individual who tries to do what is right. Although this is less potent it is still a calculated behavior based on the concept of right. And sadly, this is considered manipulative; based on the idea of what should happen. I have a lot of work ahead of me as a leader. I am rethinking my skills.

Do I have the right qualities?

The wise leader is conscious yet spontaneous; can I be spontaneous? This means responding to what is here-and-now; no calculation and no manipulating. For me, this means losing the sense of immediacy.

It is okay to sit back for a while and absorb what is happening. I don't need to respond right away or make an immediate decision. Deep breaths!

Who am I?

PMAI Score

 Sage – 28

Warrior - 24

Seeker - 21

Caregiver - 21

Innocent - 20

Creator - 20

Jester - 19

Ruler - 19

Orphan - 18

Magician - 17

Lover - 17

Destroyer - 11

At first glance of the PMAI results, I saw Sage, Warrior, Seeker, Destroyer and Caregiver all in bold and immediately thought of these areas as strengths.  This left Innocent, Creator, Jester, Ruler, Orphan, Magician and Lover as my weaknesses.  The common quote “Sage on the stage” and the negativity associations with the terms warrior and destroyer could not be good qualities of a leader.  And all the terms associated as with being a good, fun and loving person appeared to be stuck in the middle; Innocent, Creator, Jester, Magician and Lover.  Without having knowledge of the various archetypes, I developed an immediate concern as to who I was as a person.  For this reason, I couldn’t wait to learn about the Peason-Marr Archetype Indicator (2002).

            To begin my reading, I decided to focus on the bolded areas which I quickly learned were the archetypes most and least active in my currently life’s journey. If the Sage is active in your life, you assume that "the truth will set you free." (Pearson & Marr, 2002)  An initial sense of relief came over me as this is a quote which is true to my beliefs and life today.

            With the Sage in my life I tend to show wisdom, nonattachment, knowledge and skepticism and I can be overly critical, or lack empathy at times. In Carol Burbank’s Archetypes, Story and Leadership Webinar (2013), certain there were notes which certainly hit home for me. Sages like details, questions, mysteries, and research.  We like to have all of order and like to persuade others with logic, reason and proof.  Sages do not enjoy small talk and get can get restless in situations where it is apparent.  Sages tend to get comfortable in areas which we are protected and when those protections are removed we are pushed outside of our realm.  The message to balance my life with the archetypes of the Jester and Orphan has been made. This includes being able to go with the flow and realize that sometimes decisions need to be made immediately and cannot wait for research or data; sometimes I will need to go with the feelings or insights of the group.

“If the Warrior is active in your life, you assume that the tough prevail.” (Pearson & Marr, 2002) The appearance of the archetype story provides me with discipline, courage, determination and skill but I can appear as ruthless.  As an individual and leader, I have the outward appearance of being tough, competent, and in control; certainly not weak. In teaming situations, I am often the goal setter and motivator. If the group can’t make a decision, I consistently ask if what we doing is best for students. This is my mantra for students and leading in the building.  However, there are times when this Warrior archetype is a front for the true person that I am inside. To those who I truly do not let into the true life of Katrina Hall, there the appearance of being a strong, decisive and ready to compete at all times. And it is those individuals who only see me in roles where I can seem as ruthless, and without regard to feelings.  However, for those who I trust to let into the personal life of which I live they will see the other side of Katrina Hall; the Caregiver.

As a mother of three, the archetype of Caregiver is one which cannot be avoided; nurturance, compassion and generosity.  As a Caregiver leader, I am able to observe the stress or anxieties in group situations and like to help individuals work through such challenges.  My family is number one to me and the story line of the Warrior can certainly be seen if my family is being challenged.  This is also true of individuals who are friends, students and team members; they are considered my family.  When individuals are essential or key aspects to my life and work then I ensure they are cared for.  This makes me think wonder if the archetypes of Warrior and Caregiver will forever be a part of my life’s cycle.

Within my current life’s journey one can certainly see the archetype of the Seeker; “the grass is always greener somewhere else” (Pearson & Marr, 2002).  Ever sense I can remember this archetype has been present in my life.  I tend to be an individual who does not follow the crowd and is certainly is not willing to wait for the crowd.  The Seeker in me tends to set my eye on something and go for it. I am often quoted as saying, “Let’s try it” as I am always willing to try out new ideas. The worse that can happen is failure and a chance to try again.  I see life as a way to strive for perfection; if that is possible.

The Destroyer in archetype appears to be least active in my life.  However, during times of turmoil and change I must say that I have seen these characteristics rise.  During times of personal challenges, very rarely do I let others see the hurt or pain I am feeling.  And there have been times when there has been an injustice in the community, world, or workplace where I have thought that the individuals will get what they deserve; karma.  However, I would hope never to see the extremes of the Destroyer in my life’s cycle as they tend to be characteristics of individuals who are harmful to themselves and to others.

Underlying the high activity and lack of activity of the archetypes mentioned, lay the archetypes of the Innocent, Creator, Jester, Ruler, and Orphan.  Happily I have the archetypes to inspire and have empathy for others, to use my skills to be creative and take control when chaos reigns, and to be happy, and laugh. Knowing that these archetypes may not be at their highest levels right now in my life but they are there when I need them is comforting in itself as I see these as qualities which any team player or leader should have.

Currently, I tend to put aside my own needs; physically and emotionally. Putting others first tends to be a priority; and I often fail to accept the help of others.  I am definitely one who can spread myself thin but working beyond what is necessary; ensuring all cared for. Taking the time to enjoy the moment and not worry about what is next is an area I can certainly work on.  Ensuring that I take time for myself and saying “no” to the extra tasks are some of the archetypes I would like to cycle more frequently into my life.

            The PMAI results have provided me with insight into developing in my leadership style and life’s journey.  Within my workplace, staff members often see me as an advisor and look for me to lead the way in tough situations.  However, I do understand that there are times when I need to stop, listen and learn. Winning is not everything and I should focus on choosing my battles.  Can I decrease my focus on winning, striving for perfection, and motivating the team? I am not sure but I can see ways in which I can balance these archetypes when leading. 

            The results of the PMAI, proved to be thought provoking and insightful.  Burbank’s webinar made it clear to me that my world as leader is not stagnant but instead an ever changing story of what has happened, what is happening and what will happen in life.  The Caregiver and Warrior archetypes are my survival skills.  The Seeker is my expression of self.  The Sage is what supports me in “living authentically, making a positive contribution to the world while also experiencing personal fulfillment” (Pearson & Marr, 2002).  It would be intriguing to learn about the individuals with whom I work with to so see how we may or may not balance one another and where they are in their journeys of life.  Who are the archetypes I am working with?

References

Pearson, C., & Marr, H. K. (2002). Introduction to Archetypes: A Companion for Understanding and Using the Pearson-Marr Archetype Indicator Instrument. Center for Applications of Pyschological Type.

Burbanks, Carol. (2013). Archetypes, Story and Leadership Webinar [Webinar]. Retrieved from http://elearn.une.edu/bbcswebdav/pid-748888-dt-content-rid-5086188_1/courses/21581-201402-EDU-801-A2/EDU%20801%20Burbank%20Webinar%20Thurs%209-26-13%207.55%20PM.mov

Inspiring Students with a Tin Man #mathed #mathchat

The time of year came when students were ready to study surface area. How was I going to make this interesting and real? The students in my classes were itching for geometry. The common chant heard, “I love geometry!” I had to make sure I kept this level of excitement within the students.

As I began searching through my vast amount of resources, I couldn’t quite find the “best fit.” This led me to Twitter. Reaching out to my PLN, a fellow math teacher had shared a lesson she did with robots. This sparked the idea of creating a “Tin Man”.

The task for students was to create their own version of the Wizard of Oz’s Tin Man. As they created groups of 4 and 5 students, they were given further direction. All groups had to use at least one sphere, one cone, one cylinder and one rectangular prism in the creation of their Tin Man. The final product had to fit on a school desk and had to stand on its own when complete. The planning began, as did the excitement for the task.

Groups brought in objects from home such as cereal boxes, wrapping paper tubes, and Styrofoam spheres. Birthday hats and unused Snowcone wrappers were used for cones, although some groups used nets to create their own cones. When the final designs were ready to be implemented, students then began to question how they were going to make it “silver.” Great question!

Each Tin Man was to be covered with aluminum foil, “tin.” Students had to work together to determine the amount of “tin” needed for their Tin Man by determining its surface area. This meant measuring, calculating and using formulas correctly. This also meant students had to recognize which areas needed to be covered and which did not. For instance, when a cylinder was connected to a prism the circular area would not need foil. It was great to see students then determine that this area then had to be account- ed for twice. Do you know why?

Precise measurements and calculations would lead to a relatively precise amount of foil needed to cover the Tin Man. Once the total surface area was determined, students were given a roll of foil to cut the needed amount. Important to know here is that students were only allowed to cut once. Whatever they cut for foil was what they needed to use. They could not come back for more. They also could not throw away extra.

The cutting of the foil turned out to be another task. Students were allowed to use any unit of measure for their work. As they approached the roll of foil some realized that their measurements in centimeters or feet needed to be converted. The second challenge came when they realized the number which they had was in square units and they needed to determine the correct linear measurement, or length, before cutting the foil.
A great deal of discussions happened around the rolls of foil.

As groups realized they needed to divide their calculated surface area by the width of the foil, the rolling of the foil began. This step proved to be telling for some groups. They knew that as soon as the foil was cut, that was what they had to use. Using estimation skills, some were quick to realize that they were going to have too much or too little foil. For some groups, this meant going back to check measurements and calculations.

When groups made the official cut of foil they were on their way to covering their Tin Men, another challenge. The piece of foil, which was cut, was rectangular in shape. Students had to determine how to cover the surface area of the Tin Man. Some areas were going to be covered with scraps of foil and not full sheets. Appearance of the Tin Man was important, as it was a part of their grade.

The grading of the Tin Men was easy. Students were graded on calculations, precision, quality, and collaboration. Each student had to submit a calculation sheet showing the formulas and mathematics used to determine the surface area of the Tin Man. Precision was determined based on the precision of the foil. These two grades were math grades where quality and collaboration were responsibility grades. Students earned their individual grade.

The final products varied in quality and precision but they were all displayed. Students were proud of their efforts and even named their Tin Men.

As a teacher, I felt I had achieved my goals of making the lesson interesting and real. I was looking for students to work with surface area and hadn’t thought of the other aspects of mathematical learning which students encountered. The best aspect was reading student reflections at the end of the year. Students loved this project despite the challenges and hard work they encountered. Students even spoke about the Tin Man Project during the school’s Day of Learning, expressing how proud they were in persevering, and collaborating to complete a very challenging task.

Getting the “right answer” isn’t the way to inspire students.