This case story illustrates the significance of using the arts in community development
work
which not only speaks to aesthetics but to how we can
heal communities and promote well-being.
The Big Picture
In the late ’60s, Chicago Black Theater companies began to grow during a time called the
Blacks Arts Movement
.
There were several Black women, all iconic by today’s standards that led the charge. First, there was the mother of Black Theater,
Val Gray Ward
. Val gave us Kuumba Theatre where I became a member in the early ’80s. Val was the mother of Black Theater and mentored many.
Abena Joan Brown
former social worker, dancer, founded Ebony Talent Agency later becoming eta Creative Arts Foundation Theater. Then came
Jackie Taylor
founder of the Black Ensemble Theater (BET) Company whose mission was and still is today, to eradicate racism. All of these women participated in the Black Arts Movement including Illinois Poet Laureate
Gwendolyn Brooks
, and
Margaret Taylor–Burroughs
founder of the South Side Community Art Center (home of Black visual arts) and founder of the Du Sable Museum of African American Art. These Black Women were trailblazers and pre-community psychologists in their own right. If you were a performing, visual, or musical artist in Chicago between the 60’s-2005, at some point you were touched by their grace and wisdom. The Black Arts Movement gave Black people a sense of community, pride, and voice by creating a space to tell our stories through the arts and cultural experiences. It was a holistic approach, led by several daring Black women with intentionality to use the arts as a tool for liberation.
This experience motivated my work as a performing artist, curator of multidisciplinary arts, in addition to being an art consultant. By 2004, I was working in three different communities: Albany Park (north side of the city), Humboldt Park (northwest side of the city), and South Chicago (the far south side of the city), all very culturally rich and diverse communities yet struggling in their own way to sustain their arts communities. This is where I learned that I had to know the history of each community. What I found was:
Albany Park
is a cultural mecca, a trip around the world in one visit. It is a place where the average school has students that speak at least 50 different languages. The community is so physically dense that finding space for cultural activities and artistic expression was difficult.
Humboldt Park
is the home of a large Puerto Rican community that was gentrified out of their original homes in Lincoln Park, an affluent neighborhood near the lakefront. Humboldt Park is art activism at its best; a community where grassroots artists use the arts for social justice practices. They are determined to never be moved again as the sculpture of the Puerto Rican flag hovers over the street and benchmarks the gateway into the community. Their challenge is sustainable funding and competition with larger arts organizations in the area.
South Chicago
is a proud industrial community, known for its economic heyday before the steel mills shut down. It is tucked under a toll bridge called the Skyway, a visual marker that indicates your geographic location in the city of Chicago. South Chicago is 75% Africian American and 36% Mexican. At the time it had plenty of artisists who lived there but they needed to be reclaimed to come home and work in their own community. They also lacked resources for art-making.
In 2007, I returned to South Chicago in a new role. I became the intermediary with an arts background and the responsibility to support the implementation of a Quality of Life Plan (QLP) written by the residents and stakeholders of South Chicago. The QLP consisted of projects and program strategies that responded to social conditions that were a concern of the community. South Chicago identified economic development, safety, education, environment, food access, health, housing, youth development, and the arts as their strategic focus.
The challenge was to integrate the arts into community development practices. This meant bringing city government, residents, and other stakeholders to the table with the arts community. This project was complex because arts and cultural exchanges had never been used strategically in this fashion in Chicago. While working and navigating with a small team, a funder, an artist, and a scribe, I knew that we were too small to meet the masses and we would have to rely on a snowball effect in order for this concept to work. In each community, we were met by some form of skepticism. I learned that we had to wait to be invited into the community. When we allowed the time for relationship building we were eventually invited into each community. We engaged in cultural exchanges, tours, educational and reflective conversations as we broke bread in order to find our commonalities and deepen our relationships. Blending arts/culture and bricks/mortar is not an easy task when both groups do not have experience in working together. They both see their worlds in very different ways. However, the QLP provided the template for action and my past experience gave me the core knowledge I needed to engage both groups. What I did not realize was that I had more to learn.
Cultural Development and Prompting Creative Responses
In the beginning of this work, my colleagues and I spent many hours in meetings discussing issues, reflecting on history, looking at data, mapping where issues occurred, and discussing root causes, but we were not getting anywhere. These discussions were important and useful in understanding the issues but they never seemed to change anything. It felt like we were stuck on information but didn’t know what to do with it and how to move forward. Of course, we worked on collective behavioral and policy changes but it seemed more complicated when it came to social conditions deeply rooted in the community’s culture, such as violence, mental health and the needs of Black women, who historically have been underrepresented. Of course, there were some wins in deescalating gang violence but domestic violence and its impact on women of color in the community was much more complex. Domestic violence seemed to be a silent ill of society and difficult to detect and prevent from happening without witness support.
Mental health is similar, especially in communities of color where it is rarely addressed because of stigma. However, when we looked at issues impacting the community through the lens of art and culture there always seemed to be a stronger level of engagement from the residents.
So we asked the question, how can we better engage the community to prompt quality responses that promote social change?
The answer we were looking for was discovered after attending a conference on the facilitation of community meetings. I was introduced to the Art of Hosting (AoH). AoH is the practice of using different methodologies of discourse with groups of any size based on the context of the gathering. It is supported by principles that help maximize collective intelligence while being inclusive of diversity in addition to minimizing and transforming conflict. When utilizing AoH, the result is collective clarity, wiser actions, and sustainable workable solutions to the most complex problems. The approach ensures that stakeholders buy into the process because their participation in the design of the process is by definition transparent. This led me to change how I hosted the community as a community psychologist
(
Art of Hosting
).
To foster solutions, we followed the same processes as before. Together we would educate ourselves about the issue.
I hosted café style conversations where we would break up into small groups and respond to questions related to the social condition. We took the time to reflect and this method helped to give voice to all that participated. We were becoming active listeners. In addition, it increased our collective efficacy. By being in a circle, it erased the hierarchy and reduced conflicts and high expectations. We invited everyone that wanted to have a seat at the table: residents, elected officials, business owners, youth, law enforcement, faith-based leaders, and artists. We were no longer limited by our titles. Using a cultural development lens gave the artists a context of how the social condition impacted the community; everyone became more transparent about their feelings and they let go of their personal agendas. These community conversations changed my trajectory and experience of community psychology. Using AoH allowed me to bring my humility and willingness to experience what communities have to offer. We learned and healed together. It was restorative and engaging and broke barriers and unleashed our truths. Now we were ready for change by using AoH to inform our use of the arts for Healing Centered engagement. The term Healing Centered expands how we think about responses to trauma and offers a more holistic approach to fostering well-being (Ginwright, 2018). By using this approach, participants can use the arts as a tool to collectively address their trauma and restore their well-being.
Arts and Healing Centered Engagement Promoting the Well-being Among Black Women
After one of our AoH café sessions, I recall several Black women expressing feelings of a lack of belonging in the community. They talked about feeling like outcasts because the housing complex where they lived was riddled with violence and trouble, and they felt that it reflected poorly on them and their families. I knew at that point I needed to connect them to something that would make them feel valued. The idea was to reduce and ease the impact of historical trauma by creating space through a healing-centered experience that encourages collective voice, the celebration of shared identity, and build a sense of community through belonging.
Historically, Black women have always taken on the weight of the family unit by taking on the challenges of caregivers. Without having any trusted support systems, Black women often forgo self-care. When self-care is ignored, so is your overall health. Lack of self-care increases stress and leads to chronic health diseases that impair Black women’s well-being. Therefore, participating in shared cultural engagement can play a significant role in defining good health and supporting ones’ well-being, resilience, and healing. Experiences such as family connections, expressions through spirituality or music, reliance on community networks, and the church can be great sources of strength and support (Nami, 2020). Integrating the arts is a way of achieving these goals to wellness. I thought about putting on a play, but as much as I love theater, I knew that it would take way too long with the planning, auditions, rehearsals, staging, and finding the right play and location. It would take a considerable amount of time and cost to pull it off, but I wanted them to be a part of something. We needed a quick win; something just as powerful but more spontaneous, celebratory, and memorable. I felt it would be better to do another aspect of theater. I was thinking of a
“spectacle”.
Something that would happen one time only and the process would unite us all through the effort of participating in it.
Responding to the Needs of Black Women
Assets
I believe the voices of Black women are powerful assets when used collectively. This assumption is supported by the
MeToo,
GirlTrek
, and
Black Lives Matter
movements. Even politicians recognize Black women’s power during the most recent election. The challenge is to center their voices universally. Black women today demonstrate that the road to their well-being is traveled by holding space and holistically sharing their hidden stories. These stories define the commonality and range of their lived experiences. When Black women gather in supportive settings, it creates a safe space away from the atrocities of abuse and assaults against their mental and physical health and stability. It occurs in meaningful ways. Some might revert back to ancient and traditional behaviors of their ancestors, such as hosting circles, Bible study, or something of a spiritual nature. They also use their creativity through cooking, art-making, writing, music, and performance. They form groups such as book clubs, sororities, or auxiliaries. They also retain their childhood girlfriends by extending their relationships through social settings such as dinners or travel. The impact of COVID-19 has also increased gatherings through social media, for example, virtual panel discussions or talks, in addition to live internet events. Whichever way that Black women come together it provides them with a moment to collectively cleanse themselves of their griefs and sorrows, in addition to celebrating their shared identity and experiences.
Needs
The core needs for Black women is suggested foster relief from Racial Battle Fatigue (RBF) to improve mental health. Racial Battle Fatigue or RBF comes from the impact of experiencing daily battles of attempts to deflect racism, stereotypes, and discrimination and the necessity to always be on guard or wary of the next attack they may face. Coupled with caregiving, work, and maintaining the household adds layers to this toxic stress. The result can be suppressed immunity and an increase of sickness that causes multiple illnesses from tension headaches to elevated blood pressure, among other factors (Goodwin, 2018). The challenge is that these gateway maladies left untreated over time can eventually lead to chronic illnesses. Although healthcare professionals have recognized how COVID-19 has added another layer to health disparities, particularly within communities of color, it is yet to be seen what actions will be taken to promote health equity. In the meantime, community-based healing-centered engagement can be an accentual component to inspiring collective self-care experiences. So now the stage was set. We hoped to improve the way the community communicates and implemented the QLP strategies. We needed to address the feeling of exclusion from the community for Black women that participated in our gatherings. Now our goal was to find the right event.
When Black Women Gather: Gele’ Day
When Black women struggle with acceptance of their body image it is also a result of RBF. Black women are judged by the color of their skin, the size of their lips and hips, and often by the way they wear their hair. The irony is that it is acceptable for others to artificially create these features through tanning lotions, Botox, and fashion statements such as the bustle of the 19th century or the modern-day buttocks injections. However, for Black women, even how they wear their hair can potentially interfere with them keeping their job. The beauty of the Black woman has always been in question. Over the last decade, there has been more of a concerted effort to acknowledge the beauty of Black women in commercials. Actress Pilar Audain was featured in a Dove/Walmart commercial where Pilar walks down the street singing a song adorned in this beautiful head-wrap. Thus, was born Pilar’s
“
Wrap Your beYOUty Movement”:
One day after I was hosting a community meeting about trauma-informed care, Pilar shared with me about the desire to host an event in the parks called
Gele’ Day
.
It was a day to celebrate the beauty of Black women. When Pilar explained the event I was immediately sold. I had the resources to produce the project and Pilar knew the perfect location, a lakeside park on the south side of Chicago. Pilar shared how Gele’ Day had been done before on a smaller scale. All that was needed was to identify a location for women of color to gather and we would meet in the park and symbolically celebrate womanhood through activities and providing beautiful fabrics to wrap around each other’s heads. The adornment was called a Gele’. According to Pilar, Gele’ Day is another way of saying that you are “atoning your spirit”. However, there’s another custom out of Africa which is called the mass dancers. The mass dancers come out to honor a secret society, the mother spirit of the universe. Taking on this idea, Pilar created Gele’ Day for Black women in Chicago.
Black women vendors are featured at these events and sell their wares while other Black women provide performances, meditations, testimonials, prayer, and African dance exercises. Men are also welcome but mostly serve in a supportive role. At the end of the day, the women gather and rhythmically walk to the beach led by the elders and continue walking into the lake to cleanse themselves of all of life’s challenges. Gele’ Day sounded so beautiful I immediately agreed to support the next event. The event was held in Jackson Park on the south side of Chicago, and Pilar used the support of the women of her church to help set everything up for that day. I arrived early as an organizer and participant, to claim my spot and I brought my 91-year-old mother with me. We arrived, found our spot on the grass, registered, and immediately got in line to get our heads wrapped.
The fabrics were beautiful and free of charge. There were women that were wrapping the heads of other women in the most nurturing way. Another special moment was the acknowledgment of our elders. My mom was 1 of 3 in their 90’s and it made it a very special day for her. Women would come to my mom and kneel beside her and ask to shake her hand or for a hug. They praised her longevity and asked for her youthful secrets. At one point I think I was getting a bit jealous because I wanted the attention from my mom. It was very humbling. Later a sea of Black and Brown women filled the park while Pilar opened the day in prayer. They explained the meaning of Gele’ Day and summoned a group of men to lead us in meditation as they played their Tibetan bowls during the most perfect summer day. There were performances by children, face painters, poets, musicians, and singers. We were also led in a group African dance exercise. We laughed, talked, shared our life experiences.
Near the end of the day, we rhythmically lined up by age as
Pilar is never short of giving back her time, guidance, and healing efforts to those that give and support her. There is an unspoken reciprocity noted between Pilar and her followers which I will call “the Village approach”. Some call it, “paying it forward”.
we began to walk to the water.  My mom looked at me and said, “Do I get in the water too?” I said, “Yes you do” with a smile wondering if they would actually do it. I didn’t think my mom would do it but they marched right in that water. People in the park would stop me and ask who we were and what were we doing as they watched us in awe. I felt like a queen. There was such beauty in the collective cleanse. When my mother and I walked backed to the car I could not help but kneel to clean the sand off her feet. I hope my mom felt as special as I did by being together on Gele’ Day.
Outcomes and Impact
“Gele’ Day” represented healing-centered experiences through spectacle by preserving culture in the way of sharing untold stories, promoting collective pride, acknowledging ones’ ancestors, and influencing citizen participation in an open and safe space. The spectacle being both visual and performance-based, also successfully demonstrates that by utilizing the arts as a healing-centered tool, women can feel collectively empowered, cherished, and valued. As much as there is singing and laughter there is also an emotional release that is symbolically enacted by the rhythmic walk to the beachfront and actually manifests based on the reactions that you see and hear. There was inquiry of amazement from onlookers, demonstrations of love, respect and affection among the participants, and the collective response through engagement of the mindfulness activities. The experience was an overall movement, a metaphoric dance, and a holistic healing experience. As intended, it is an experience that one will remember for a lifetime.
A most powerful aspect of the “Wrap Your beYOUty Movement” is Pilar’s skills and ability to use citizen participation to reach so many women without standard forms of marketing. Every year there is a noticeable increase in attendance to these events, resulting from a snowball effect–from word-of-mouth. There are no subscriptions, no brochures, no flyers, no posters, and no ads in periodicals. The communication style of the Wrap Your beYOUty Movement can easily be equated to a modern example of the traditional use of the beat of the African Drum to communicate to the Village. Gele’ day represents Empowerment and Citizen Participation in its purest form. This can also be compared to the Black Arts Movement where space was also intentionally created to support and sustain the aesthetic voices of the Black Arts Community.
Lessons Learned
Community Engagement and Citizen Participation
It is important to identify the best approach in facilitation that works for you. I prefer the Art of Hosting (AoH) because it not only gives the participant a voice, it also offers different options of facilitation based on the needs of the community. When there are sensitive matters that need addressing such as listening to the victims of violence, we used methods that encouraged storytelling and active listening. When there were community disagreements (and there will be disagreements) there are methods for having courageous conversations that will help get the group back on track. Always keep an open mind to new methods, that is how I discovered AoH. As much as I feel comfortable working with community groups, I feel my lesson learned through this event is that you have to decide what methods of engagement work best for you in order to achieve the outcomes you desire.
Collaborative Ways of Investing in Underrepresented Communities
There were two positions held in my life that influenced my work as a community psychologist,
It was always a joy exploring a character in a play but it was temporary. However, exploring, connecting, and engaging with diverse populations and cultures in a community setting was more fulfilling.
that of an arts consultant specializing in theater, and that of a community development intermediary for a neighborhood in Chicago. As much as I enjoyed performing, I enjoyed working with people in communities even more. The combination of the two careers built my foundation and prepared me for community psychology. As a community psychologist, the arts provide a platform for collaboration while promoting social change and working at different ecological levels to address social conditions through a creative lens. My work covers many domains but the focus of this work is using arts and culture as tools to support underrepresented voices, specifically Black women to improve social conditions. I have been fortunate to observe best practices through my travels and engaging with creative people that have impacted the world.
A Community Psychologist’s Role in Disinvested Communities
It cannot be assumed that as a community psychologist one must take the lead, teach, or have power over the community. Although the role of a community psychologist can be subtle, it is imperative to be foremost an active listener and observer as this will guide your actions. Other best practices proposed are:
Building your knowledge about the community that you are working with.
Allowing yourself to be invited in and knowing the community’s history before you enter.
Building your networking skills and leveraging resources but never offering anything that you cannot deliver.
Finding the commonalities to connect and build relationships with the people you plan to engage with.
Be willing to adapt to the unexpected and watching for any influence that creates barriers for others.
Reflecting on your work, reflecting with others, while making the effort to center and raise all voices.
Bringing humility and willingness to experience what the community has to offer you. This helps to form relationships where lessons are learned, trust is restored, and engagement is sustained; and
Acting with intentionality to promote social change.
Recommendations
Community Engagement and Citizen Participation
When working with the community, planning is important but I also believe in planning while having smaller events in order to build relationships in the community. Educate the community on the issue that you are addressing so that you are on the same page when you begin to address the issue. Research the multiple ways that you can host a meeting and determine what suits your leadership style. However, make sure your style of facilitation is open to everyone. If they live in the community they have every right to participate if they so choose, prepare to address conflicts, respect the time of others, and make sure meetings are engaging enough where people will want to come back for more.
Working with communities and diverse populations can be stressful, but an equitable representation of the community must be a part of the process. Identify the artists that live in and serve the community. Use their talents. Besides producing their work, I have hired artists to do graphic note-taking in meetings and have found it to be more detailed than writing notes (figures below). There is something about images that stimulates memory. Honor their talents by paying them. Their time is money. Make sure you are working with artists that enjoy working with the community. There are some great artists that prefer to create on their own. This type of artist might be more suitable for showcasing by creating themed pop-up galleries, performances in the park or public art. Artists that enjoy working with the community make great organizers. Engage them in every aspect of community planning and implementation. I have had stakeholders tell me that there are no artists in the area. I always laugh at that because artists are everywhere. If you can offer the use of free or shared space, believe me, they will appear out of nowhere. Just remember to do a contract or memo of understanding so that there are no surprises at the end of the day and everyone is on the same page.
Graphic notes from our community meeting
My Work Relative to Community Psychology Practice
Empowerment Theory
Through this case study, we have looked at underserved communities where Black women have felt undervalued and the communities discussed have been underrepresented. We looked at empowerment and citizen participation from a community psychology perspective to better understand how it was achieved in this case study. The
empowerment
theory comes to mind in this case story.
While there are many definitions out there for empowerment, I favor some of the tenets of empowerment that have been defined by the Cornell Empowerment Group (1989), such as
intentionality,
ongoing process
, and
mutual respect
. For instance, intentionality is extremely important because it is the foundation of empowerment that gives the community psychologist their purpose. Intentionality is the reason behind the passion that fuels the action. In the Black Arts Movement, the iconic Black Women that led the charge to make space for Black artists recognized their absence in society, and then determined to create space for them. Their mentorship and coalition building was the driving force for sustainability. Many Black actors have trailblazed alone, but having a vision and recognizing that your needs are in common with others becomes the catalyst to mobilizing others for the cause. So when you are working with a community and you recognize that the group is at a stalemate, you use your influence to expose the group to new ideas and challenge their thinking. In South Chicago, we recognized that the arts were a great tool but it was AoH that unleased their voice and their truths.
The Wrap Your beYOUty Movement recognizes the beauty and value of Black women, so Gele’ Day used its influence to help Black women see their beauty.  It also opens up space for others to see the Beauty of a Black Women. Remember how people inquired about the Black women walking to the lakefront. This means that the Black women’s presence was no longer invisible. They were shown respect through acknowledgment. The care and nurturing, the ongoing process of wrapping the beauty of each woman commands mutual respect by being invited into the community of Black Women. When you enter, you enter with humility and a willingness to experience what the community has to offer. This reminds the community psychologist of ones’ own vulnerability and we must treat everyone with care and compassion. This Empowerment Framework model is shown below:
Empowerment Framework Table
Empowerment
Black Women in the Black Arts Movement
The Role of Community Psychology Building Communities Through the Arts
Wrap Your beYouty Movement for Black Women
Intentionality
To crate opportunities and recognize the talent and contributors of Black Artists
To use the arts as a tool for healing, empowerment, and citizen participation
Holistic healing, atonement, and collective empowerment of Black Women
Ongoing Process
The development of Black institutions dedicated to the uplifting of Black Culture
Program support and the reclamation of art as a community development tool
Annual tradition and celebration of Gele Day and She Through Me to promote collective pride
Mutual Respect
Engagement and mentoring of Black Artists
Inviting into the community and entering with humility and willingness to experience what the community has to offer
The reciprocity of sharing and celebration of each other’s talents
Citizen Participation
Citizen participation is another aspect of Empowerment where knowing how to engage others over time requires skill. There is Critical Awareness that informs the purpose of the collective action. It is the social barriers that ignite the need for action. The Black Arts Movement recognizes the need to acknowledge the creative contributions of Black Artist. The Community Psychologist sees the inequities and disinvestment that challenges the quality of life of underrepresent communities. The Wrap Your beYOUty Movement recognizes the need to bring attention to the value of Black Women. Once the awareness is achieved then we must reflect on how we arrived to this this issue and what did we learn. This is where the skills of Community Psychology are needed. Organizing and the ability to mobilize others to bring awareness requires skills, relationship building, leveraging resources, and trust. Once this is achieved the commitment of others will follow. In South Chicago it was AoH that brought us to the level of commitment. This is where engagement becomes strong. In the Black Arts Movement, 3 Black Women are now the founders of theater companies. Gwendolyn Brooks breaks barriers and become the first Black Women Poet Laureate of the state of Illinois, and Margaret Burroughs opens a museum on city property that showcases Black excellence. South Chicago has a plan with a vision and mission to implement. Wrap Your beYOUty Movement starts with one day and becomes an annual event. Once all of this is steps are achieved then long lasting relational connections are made which leads to sustainability. The Citizen Participation Table is shown below.
Citizen Participation Table
Citizen Participation
Black Women in the Black Arts Movement
The Role of Community Psychology Building Communities Through the Arts
Wrap Your beYouty Movement for Black Women
Critical Awareness
Recognizing the significance of Black talent and cultural
Attention to resources: finding space and disinvestment
Recognizing the significance of Black women in society
Participatory Skills
Mobilizing and building relationships with Black artist and audiences
Mobilizing and building relationships with community artists, residents, and stakeholders
Mobilizing and building relationships with Black women
Participatory Values and Commitment
Respect and honoring Black pride
Collectively respecting the writing and implementation of strategic plans (Arts and Quality of Life Plans)
Respect and honoring pride of Black women
Relational Connections
Mentoring actors and support of the artistic community
Hosting of the community in circle to share wants and needs; Active listening
Sharing of talent and resources to support celebration
Conclusion
I am hoping that by reading through this case story you are inspired to begin to think about ways you can use arts and culture in community psychology work or other work seeking to foster resilience and build community—leaning into advancing social and racial justice. I continue to do this work using my lived experiences and education as a community psychologist and educator. Here is a website with more on Gwendolyn Brooks:
https://www.poetryfoundation.org/poets/gwendolyn-brooks
From Theory to Practice Reflection and Questions
Share with your classmates or others the ways in which the information in this chapter challenged or expanded your thinking about how the arts and culture can be used to build community.
Provide and discuss examples of how gaining an understanding of an underrepresented community will affect your ongoing work.
What questions does this chapter raise for you related to community psychology, community practice work, or other related fields of study?


2.37: Philosophy
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The love of wisdom, aka Philosophy,seeks to study the fundamental nature of knowledge, reality, and existence, especially when considered as an academic discipline. People can learn fundamental truths about themselves, the world in which they live, and their relationships to both the world and to each other. While Philosophy is a foundational building block for all other academic disciplines, it has been shaped by structural racism, and this shaping has had an effect on its growth, development and its demographic. From the early work of Immanuel Kant in 1781, who famously began his work describing the superiority of Whites over Blacks and Indigenous Peoples, philosophy rests in that foundation (Rutledge,2019). It is important to establish that racism has broad implications for how the entire field of philosophy is practiced.
At present, all members of the discipline should be on notice that racism has historically impacted, and continues to impact their field. Philosophy is highly utilized, built upon and central to the growth and development of other disciplines. An honest analysis of race and racism can make all schools of philosophy, including ethics, political philosophy, and abstract debates of metaphysics, philosophy of mind, and epistemology, all richer fields. For race theorists, philosophy is highly significant for their work, however it has been observed that contemporary philosophy continues to evade a discussion of racism in the field and, as a result,often helps to promote it. At the same time, anti-racist theorists in many disciplines regularly draw on crucial notions of objectivity, rationality, agency, individualism, and truth without adequate knowledge of philosophical analyses of these very concepts (Cook, 2003). Evidently there remains a disconnect.
There remains alack of diversity in the use and recognition of Black, Indigenous, people of color (BIPOC) Philosophers in most college level Philosophy classes. For new students studying the field, this leaves them with a misunderstanding of who has contributed to the field. From very early on, Philosophers came from all parts of the globe and had differing epistemologies, that if taken as a whole would create a wider philosophical lens for students to gaze through (Rutledge, 2019).


6.6: Childhood Mental Health
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Mental health problems can disrupt daily life at home, at school or in the community. Without help, mental health problems can lead to school failure, alcohol or other drug abuse, family discord, violence or even suicide. However, help is available. Talk to your health care provider if you have concerns about your child’s behavior.
Mental health disorders are diagnosed by a qualified professional using the Diagnostic and Statistical Manual of Mental Disorders (DSM). This is a manual that is used as a standard across the profession for diagnosing and treating mental disorders.42
When You Have a Concern About a Child. What’s in a Label? 43
Children are continually evaluated as they enter and progress through school. If a child is showing a need, they should be assessed by a qualified professional who would make a recommendation or diagnosis of the child and give the type of instruction, resources, accommodations, and support that they should receive.
Ideally, a proper diagnosis or label is extremely beneficial for children who have educational, social, emotional, or developmental needs. Once their difficulty, disorder, or disability is labeled then the child will receive the help they need from parents, educators and any other professionals who will work as a team to meet the student’s individual goals and needs.
However, it’s important to consider that children that are labeled without proper support and accommodations or worse they may be misdiagnosed will have negative consequences. A label can also influence the child’s self-concept, for example, if a child is misdiagnosed as having a learning disability; the child, teachers, and family member interpret their actions through the lens of that label. Labels are powerful and can be good for the child or they can go detrimental for their development all depending on the accuracy of the label and if they are accurately applied.
A team of people who include parents, teachers, and any other support staff will look at the child’s evaluation assessment in a process called an Individual Education Plan (IEP). The team will discuss the diagnosis, recommendations, and the accommodations or help and a decisions will be made regarding what is the best for the child. This is time when parents or caregivers decide if they would like to follow this plan or they can dispute any part of the process. During an IEP, the team is able to voice concerns and questions. Most parents feel empowered when they leave these meetings. They feel as if they are a part of the team and that they know what, when, why, and how their child will be helped.
Childhood Mental Health Disorders
Social and Emotional Disorders
- Phobias
- Anxiety
- Post-Traumatic Stress Syndrome - PTSD
- Obsessive Compulsive Disorder –OCD
- Depression
Developmental Disorders
- Autism Spectrum Disorder (ASD)
- Attention Deficit Disorder (ADHD)
- Pervasive Developmental Disorder (PDD)44
Phobias
When a child who has a phobia (an extreme or irrational fear of or aversion to something) is exposed to the phobic stimulus (the stimuli varies), it almost invariably provokes an immediate anxiety response, which may take the form of a situational bound or situational predisposed panic attack. Children can show effects and characteristics when it comes to specific phobias. The effects of anxiety show up by crying, throwing tantrums, experiencing freezing, or clinging to the parent that they have the most connection with. Related Conditions include anxiety.
Anxiety
Many children have fears and worries, and will feel sad and hopeless from time to time. Strong fears will appear at different times during development. For example, toddlers are often very distressed about being away from their parents, even if they are safe and cared for. Although fears and worries are typical in children, persistent or extreme forms of fear and sadness feelings could be due to anxiety or depression. Because the symptoms primarily involve thoughts and feelings, they are called internalizing disorders .
When children do not outgrow the fears and worries that are typical in young children, or when there are so many fears and worries that interfere with school, home, or play activities, the child may be diagnosed with an anxiety disorder. Examples of different types of anxiety disorders include:
- Being very afraid when away from parents (separation anxiety)
- Having extreme fear about a specific thing or situation, such as dogs, insects, or going to the doctor (phobias)
- Being very afraid of school and other places where there are people (social anxiety)
- Being very worried about the future and about bad things happening (general anxiety)
- Having repeated episodes of sudden, unexpected, intense fear that come with symptoms like heart pounding, having trouble breathing, or feeling dizzy, shaky, or sweaty (panic disorder)
Anxiety may present as fear or worry, but can also make children irritable and angry. Anxiety symptoms can also include trouble sleeping, as well as physical symptoms like fatigue, headaches, or stomachaches. Some anxious children keep their worries to themselves and, thus, the symptoms can be missed.
Related conditions include Obsessive-Compulsive Disorder and Post Traumatic Stress Disorder.
Post-Traumatic Stress Syndrome (PTSD)
Exposure to traumatic events can have major developmental influences on children. While the majority of children will not develop PTSD after a trauma, best estimates from the literature are that around a third of them will, higher than adult estimates. Some reasons for this could include more limited knowledge about the world, differential coping mechanisms employed, and the fact that children’s reactions to trauma are often highly influenced by how their parents and caregivers react.
The impact of PTSD on children weeks after a trauma, show that up to 90% of children may experience heightened physiological arousal, diffuse anxiety, survivor guilt, and emotional liability. These are all normal reactions and should be understood as such (similar things are seen in adults. Those children still having these symptoms three or four months after a disaster, however, may be in need of further assessment, particularly if they show the following symptoms as well. For older children, warning signs of problematic adjustment include: repetitious play reenacting a part of the disaster; preoccupation with danger or expressed concerns about safety; sleep disturbances and irritability; anger outbursts or aggressiveness; excessive worry about family or friends; school avoidance, particularly involving somatic complaints; behaviors characteristic of younger children; and changes in personality, withdrawal, and loss of interest in activities.46
Obsessive Compulsive Disorder (OCD)
Although a diagnosis of OCD requires only that a person either has obsessions or compulsions, not both, approximately 96% of people experience both. For almost all people with OCD, being exposed to a certain stimuli (internal or external) will then trigger an upsetting or anxiety-causing obsession, which can only be relieved by doing a compulsion. For example, a person touches a doorknob in a public building, which causes an obsessive thought that they will get sick from the germs, which can only be relieved by compulsively washing their hands to an excessive degree. Some of the most common obsessions include unwanted thoughts of harming loved ones, persistent doubts that one has not locked doors or switched off electrical appliances, intrusive thoughts of being contaminated, and morally or sexually repugnant. 47
Depression
Occasionally being sad or feeling hopeless is a part of every child’s life. However, some children feel sad or uninterested in things that they used to enjoy, or feel helpless or hopeless in situations where they could do something to address the situations. When children feel persistent sadness and hopelessness, they may be diagnosed with depression.
Symptoms
We now know that youth who have depression may show signs that are slightly different from the typical adult symptoms of depression. Children who are depressed may complain of feeling sick, refuse to go to school, cling to a parent or caregiver, feel unloved, hopelessness about the future, or worry excessively that a parent may die. Older children and teens may sulk, get into trouble at school, be negative or grouchy, are irritable, indecisive, have trouble concentrating, or feel misunderstood. Because normal behaviors vary from one childhood stage to another, it can be difficult to tell whether a child who shows changes in behavior is just going through a temporary “phase” or is suffering from depression.
Treatment
With medication, psychotherapy, or combined treatment, most youth with depression can be effectively treated. Youth are more likely to respond to treatment if they receive it early in the course of their illness.49
Developmental Disorders
Autism Spectrum Disorder
As introduced in chapter 8, autism spectrum disorder (ASD) is a developmental disorder that affects communication and behavior. Although autism can be diagnosed at any age, it is said to be a “developmental disorder” because symptoms generally appear in the first two years of life.
According to the Diagnostic and Statistical Manual of Mental Disorders (DSM-5), a guide created by the American Psychiatric Association used to diagnose mental disorders, people with ASD have:
- Difficulty with communication and interaction with other people
- Restricted interests and repetitive behaviors
- Symptoms that hurt the person’s ability to function properly in school, work, and other areas of life
Autism is known as a “spectrum” disorder because there is wide variation in the type and severity of symptoms people experience. ASD occurs in all ethnic, racial, and economic groups. Although ASD can be a lifelong disorder, treatments and services can improve a person’s symptoms and ability to function. The American Academy of Pediatrics recommends that all children be screened for autism.
Changes to the diagnosis of ASD
In 2013, a revised version of the Diagnostic and Statistical Manual of Mental Disorders (DSM) was released. This revision changed the way autism is classified and diagnosed. Using the previous version of the DSM, people could be diagnosed with one of several separate conditions:
- Autistic disorder
- Asperger’s’ syndrome
- Pervasive developmental disorder not otherwise specified (PDD-NOS)
In the current revised version of the DSM (the DSM-5), these separate conditions have been combined into one diagnosis called “autism spectrum disorder.” Using the DSM-5, for example, people who were previously diagnosed as having Asperger’s syndrome would now be diagnosed as having autism spectrum disorder. Although the “official” diagnosis of ASD has changed, there is nothing wrong with continuing to use terms such as Asperger’s syndrome to describe oneself or to identify with a peer group.
Signs and Symptoms of ASD
People with ASD have difficulty with social communication and interaction, restricted interests, and repetitive behaviors. The list below gives some examples of the types of behaviors that are seen in people diagnosed with ASD. Not all people with ASD will show all behaviors, but most will show several.
Social communication / interaction behaviors may include:
- Making little or inconsistent eye contact
- Tending not to look at or listen to people
- Rarely sharing enjoyment of objects or activities by pointing or showing things to others
- Failing to, or being slow to, respond to someone calling their name or to other verbal attempts to gain attention
- Having difficulties with the back and forth of conversation
- Often talking at length about a favorite subject without noticing that others are not interested or without giving others a chance to respond
- Having facial expressions, movements, and gestures that do not match what is being said
- Having an unusual tone of voice that may sound sing-song or flat and robot-like
- Having trouble understanding another person’s point of view or being unable to predict or understand other people’s actions
Restrictive / repetitive behaviors may include:
- Repeating certain behaviors or having unusual behaviors. For example, repeating words or phrases, a behavior called echolalia
- Having a lasting intense interest in certain topics, such as numbers, details, or facts
- Having overly focused interests, such as with moving objects or parts of objects
- Getting upset by slight changes in a routine
- Being more or less sensitive than other people to sensory input, such as light, noise, clothing, or temperature
People with ASD may also experience sleep problems and irritability. Although people with ASD experience many challenges, they may also have many strengths, including:
- Being able to learn things in detail and remember information for long periods of time
- Being strong visual and auditory learners
- Excelling in math, science, music, or art
Causes and Risk Factors
While scientists don’t know the exact causes of ASD, research suggests that genes can act together with influences from the environment to affect development in ways that lead to ASD. Although scientists are still trying to understand why some people develop ASD and others don’t, some risk factors include:
- Having a sibling with ASD
- Having older parents
- Having certain genetic conditions—people with conditions such as Down syndrome, fragile X syndrome, and Rett syndrome are more likely than others to have ASD
- Very low birth weight
Treatments and Therapies
Treatment for ASD should begin as soon as possible after diagnosis. Early treatment for ASD is important as proper care can reduce individuals’ difficulties while helping them learn new skills and make the most of their strengths.
The wide range of issues facing people with ASD means that there is no single best treatment for ASD. Working closely with a doctor or health care professional is an important part of finding the right treatment program.
A doctor may use medication to treat some symptoms that are common with ASD. With medication, a person with ASD may have fewer problems with:
- Irritability
- Aggression
- Repetitive behavior
- Hyperactivity
- Attention problems
- Anxiety and depression
People with ASD may be referred to doctors who specialize in providing behavioral, psychological, educational, or skill-building interventions. These programs are typically highly structured and intensive and may involve parents, siblings, and other family members. Programs may help people with ASD:
- Learn life-skills necessary to live independently
- Reduce challenging behaviors
- Increase or build upon strengths
- Learn social, communication, and language skills 50
Attention Deficit/Hyperactivity Disorder (AD/HD)
The exact causes of AD/HD are unknown; however, research has demonstrated that factors that many people associate with the development of AD/HD do not cause the disorder including, minor head injuries, damage to the brain from complications during birth, food allergies, excess sugar intake, too much television, poor schools, or poor parenting. Research has found a number of significant risk factors affecting neurodevelopment and behavior expression. Events such as maternal alcohol and tobacco use that affect the development of the fetal brain can increase the risk for AD/HD. Injuries to the brain from environmental toxins such as lack of iron have also been implicated.
Symptoms
People with AD/HD show a persistent pattern of inattention and/or hyperactivity–impulsivity that interferes with functioning or development:
1. Inattention: Six or more symptoms of inattention for children up to age 16, or five or more for adolescents 17 and older and adults; symptoms of inattention have been present for at least 6 months, and they are inappropriate for developmental level:
- Often fails to give close attention to details or makes careless mistakes in schoolwork, at work, or with other activities.
- Often has trouble holding attention on tasks or play activities.
- Often does not seem to listen when spoken to directly.
- Often does not follow through on instructions and fails to finish schoolwork, chores, or duties in the workplace (e.g., loses focus, side-tracked).
- Often has trouble organizing tasks and activities.
- Often avoids, dislikes, or is reluctant to do tasks that require mental effort over a long period of time (such as schoolwork or homework).
- Often loses things necessary for tasks and activities (e.g. school materials, pencils, books, tools, wallets, keys, paperwork, eyeglasses, mobile telephones).
- Is often easily distracted
- Is often forgetful in daily activities.
2. Hyperactivity and Impulsivity: Six or more symptoms of hyperactivity-impulsivity for children up to age 16, or five or more for adolescents 17 and older and adults; symptoms of hyperactivity-impulsivity have been present for at least 6 months to an extent that is disruptive and inappropriate for the person’s developmental level:
- Often fidgets with or taps hands or feet, or squirms in seat.
- Often leaves seat in situations when remaining seated is expected.
- Often runs about or climbs in situations where it is not appropriate (adolescents or adults may be limited to feeling restless).
- Often unable to play or take part in leisure activities quietly.
- Is often “on the go” acting as if “driven by a motor”.
- Often talks excessively.
- Often blurts out an answer before a question has been completed.
- Often has trouble waiting his/her turn.
- Often interrupts or intrudes on others (e.g., butts into conversations or games)
In addition, the following conditions must be met:
- Several inattentive or hyperactive-impulsive symptoms were present before age 12 years.
- Several symptoms are present in two or more settings, (such as at home, school or work; with friends or relatives; in other activities).
- There is clear evidence that the symptoms interfere with, or reduce the quality of, social, school, or work functioning.
- The symptoms are not better explained by another mental disorder (such as a mood disorder, anxiety disorder, dissociative disorder, or a personality disorder). The symptoms do not happen only during the course of schizophrenia or another psychotic disorder.
Based on the types of symptoms, three kinds (presentations) of AD/HD can occur:
- Combined Presentation: if enough symptoms of both criteria inattention and hyperactivity-impulsivity were present for the past 6 months
- Predominantly Inattentive Presentation: if enough symptoms of inattention, but not hyperactivity-impulsivity, were present for the past six months
- Predominantly Hyperactive-Impulsive Presentation: if enough symptoms of hyperactivity-impulsivity, but not inattention, were present for the past six months.
Because symptoms can change over time, the presentation may change over time as well.54 The diagnosis of AD/HD can be made reliably using well-tested diagnostic interview methods. However, as of yet, there is no independent valid test for ADHD.
Among children, AD/HD frequently occurs along with other learning, behavior, or mood problems such as learning disabilities, oppositional defiant disorder, anxiety disorders, and depression.
Treatment
A variety of medications and behavioral interventions are used to treat AD/HD. The most widely used medications are methylphenidate (Ritalin), D-amphetamine, and other amphetamines. These drugs are stimulants that affect the level of the neurotransmitter dopamine at the synapse. Nine out of 10 children improve while taking one of these drugs.
In addition to the well-established treatments described above, some parents and therapists have tried a variety of nutritional interventions to treat AD/HD. A few studies have found that some children benefit from such treatments. Nevertheless, no well-established nutritional interventions have consistently been shown to be effective for treating AD/HD.56
Pervasive Developmental Disorder (PDD) or PPD (NOS) Not Otherwise Specified PDD –NOS
Pervasive developmental disorder (PDD) is a term used to refer to difficulties in socialization and delays in developing communicative skills. This is usually recognized before 3 years of age. A child with PDD may interact in unusual ways with toys, people, or situations, and may engage in repetitive movement. PDD is diagnosed and treatment is similar to ADHA and ASD. In 2013 the DSM- 5 discontinued using this as a diagnosis, however it is still used informally.57
Contributors and Attributions
42. Disease Prevention and Healthy Lifestyles by Judy Baker, Ph.D. is licensed under CC BY-SA (modified by Dawn Rymond)
43. Disease Prevention and Healthy Lifestyles by Judy Baker, Ph.D. is licensed under CC BY-SA (modified by Dawn Rymond)
44. Content by Dawn Rymond is licensed under CC BY 4.0
46. Abnormal Psychology by Lumen Learning references Abnormal Psychology: An e-text! by Dr. Caleb Lack, licensed under CC BY-NC-SA
47. Disease Prevention and Healthy Lifestyles by Judy Baker, Ph.D. is licensed under CC BY-SA
49. Educational Psychology by Kelvin Seifert is licensed under CC BY 3.0
Disease Prevention and Healthy Lifestyles by Judy Baker, Ph.D. is licensed under CC BY-SA
50. Autism Spectrum Disorder by the NIH is in the public domain
54. Symptoms and Diagnosis of ADHD by the CDC is in the public domain
56. Disease Prevention and Healthy Lifestyles by Judy Baker, Ph.D. is licensed under CC BY-SA
57. Lifespan Development: A Psychological Perspective by Martha Lally and Suzanne Valentine-French is licensed under CC BY-NC-SA 3.0


15.8: Sight
The eyes are the organs of sight. They consist of spherical eyeballs situated in deep depressions in the skull called the orbits . They are attached to the wall of the orbit by six muscles, which move the eyeball. Upper and lower eyelids cover the eyes during sleep and protect them from foreign objects or too much light, and spread the tears over their surface.
The nictitating membrane or haw is a transparent sheet that moves sideways across the eye from the inner corner, cleansing and moistening the cornea without shutting out the light. It is found in birds, crocodiles, frogs and fish as well as marsupials like the kangaroo. It is rare in mammals but can be seen in cats and dogs by gently opening the eye when it is asleep. Eyelashes also protect the eyes from the sun and foreign objects.
Structure of the Eye
Lining the eyelids and covering the front of the eyeball is a thin epithelium called the conjunctiva . Conjunctivitis is inflammation of this membrane. Tear glands that open just under the top eyelid secrete a salty solution that keeps the exposed part of the eye moist, washes away dust and contains an enzyme that destroys bacteria.
The wall of the eyeball is composed of three layers (see diagram 15.4). From the outside these are the sclera , the choroid and the retina .
Diagram 15.4 - The structure of the eye
The sclera is a tough fibrous layer that protects the eyeball and gives it rigidity. At the front of the eye the sclera is visible as the “ white ” of the eye, which is modified as the transparent cornea through which the light rays have to pass to enter the eye. The cornea helps focus light that enters the eye.
The choroid lies beneath the sclera. It contains a network of blood vessels that supply the eye with oxygen and nutrients. Its inner surface is highly pigmented and absorbs stray light rays. In nocturnal animals like the cat and possum this highly pigmented layer reflects light as a means of conserving light. This is what makes them shine when caught in car headlights.
 This is the coloured part of the eye that controls the amount of light entering the pupil of the eye. In dim light the pupil is wide open so as much light as possible enters while in bright light the pupils contract to protect the retina from damage by excess light.
The pupil in most animals is circular but in many nocturnal animals it is a slit that can close completely. This helps protect the extra-sensitive light sensing tissues of animals like the cat and possum from bright sunlight.
The inner layer lining the inside of the eye is the retina . This contains the light sensing cells called rods and cones (see diagram 15.5).
The rod cells are long and fat and are sensitive to dim light but cannot detect colour. They contain large amounts of a pigment that changes when exposed to light. This pigment comes from vitamin A found in carrots etc. A deficiency of this vitamin causes night blindness.
The cone cells provide colour vision and allow animals to see details. Most are found in the centre of the retina and they are most densely concentrated in a small area called the fovea . This is the area of sharpest vision, where the words you are reading at this moment are focussed on your retina.
Diagram 15.5 - A rod and cone from the retina
The nerve fibres from the cells of the retina join and leave the eye via the optic nerve . There are no rods or cones here and it is a blind spot . The optic nerve passes through the back of the orbit and enters the brain.
The lens is situated just behind the pupil and the iris. It is a crystalline structure with no blood vessels and is held in position by a ligament. This is attached to a muscle, which changes the shape of the lens so both near and distant objects can be focussed by the eye. This ability to change the focus of the lens is called accommodation . In many mammals the muscles that bring about accommodation are poorly developed, Rats, cows and dogs, for example, are thought to be unable to focus clearly on near objects.
In old age and certain diseases the lens may become cloudy resulting in blurred vision. This is called a cataract . Within the eyeball are two cavities, the anterior and posterior chambers , separated by the lens. They contain fluids the aqueous and vitreous humours respectively, that maintain the shape of the eyeball and help press the retina firmly against the choroid so clear images are seen.
How The Eye Sees
Eyes work quite like a camera. Light rays from an object enter the eye and are focused on the retina (the “film”) at the back of the eye. The cornea, the lens and the fluid within the eye all help to focus the light. They do this by bending the light rays so that light from the object falls on the retina. This bending of light is called refraction . The light stimulates the light sensitive cells of the retina and nerve impulses are produced that pass down the optic nerve to the brain (see diagram 15.6).
Diagram 15.6 - How the light travels from the object to the retina of the eye
Colour Vision In Animals
As mentioned before, the retina has two different kinds of cells that are stimulated by light - ' rods' and ' cones' . In humans and higher primates like baboons and gorillas the rods function in dim light and do not perceive colour, while the cones are stimulated by bright light and perceive details and colour.
Other mammals have very few cones in their retinas and it is believed that they see no or only a limited range of colour. It is, of course, difficult to find out exactly what animals do see. It is thought that deer, rats, and rabbits and nocturnal animals like the cat are colour-blind, and dogs probably see green and blue. Some fish and most birds seem to have better colour vision than humans and they use colour, often very vivid ones, for recognizing each other as well as for courtship and protection.
Binocular Vision
Animals like cats that hunt have eyes placed on the front of the head in such a way that both eyes see the same wide area but from slightly different angles (see diagram 15.7). This is called binocular vision . Its main advantage is that it enables the animals to estimate the distance to the prey so they can chase it and pounce accurately.
Diagram 15.7 - Well developed binocular vision in predator animals like the cat
In contrast plant-eating prey animals like the rabbit and deer need to have a wide panoramic view so they can see predators approaching. They therefore have eyes placed on the side of the head, each with its own field of vision (see diagram 15.8).
Diagram 15.8 - Panoramic monocular vision in prey animals like the rabbit


20.2: Addition and subtraction rules
As usual in mathematics, breaking a big problem into smaller parts is a useful strategy.
Assume \(U\) is a finite set.
- If \(U = A_1 \sqcup A_2\text{,}\) then \(\vert U \vert = \vert A_1 \vert + \vert A_2 \vert\text{.}\)
- If \(U = A_1 \cup A_2\text{,}\) then \(\vert U \vert = \vert A_1 \vert + \vert A_2 \vert - \vert A_1 \cap A_2 \vert\text{.}\)
- Proof Idea.
-
After recalling the definition of disjoint union , Statement 1 should be obvious. To prove Statement 2, apply Statement 1 to the following disjoint unions:
\begin{align*} U & = A_1 \sqcup (A_2 \setminus A_1), & A_2 & = (A_2 \setminus A_1) \sqcup (A_1 \cap A_2). \end{align*}
Then combine the resulting equalities of cardinalities.
Statement 1 of Theorem \(\PageIndex{1}\) can be extended to a disjoint union of any number of subsets.
How many words of length \(3\) or less are there using alphabet \(\Sigma = \{ \alpha, \omega \}\text{?}\)
Solution
Write \(\Sigma ^{\ast}_{\le 3}\) to mean the set of words in alphabet \(\Sigma\) of length \(3\) or less. Then
\begin{equation*} \Sigma ^{\ast}_{\le 3} = \Sigma ^{\ast}_0 \sqcup \Sigma ^{\ast}_1 \sqcup \Sigma ^{\ast}_2 \sqcup \Sigma ^{\ast}_3 \text{,} \end{equation*}
so we can break into cases based on length and then apply the
Addition Rule
.
Count \(\Sigma ^{\ast}_0\).
There is only one word of length \(0\text{:}\) the empty word. So \(\vert \Sigma ^{\ast}_0 \vert = 1\text{.}\)
Count \(\Sigma ^{\ast}_1\).
There are only two words of length \(1\text{:}\) the single-letter words \(w_\alpha = \alpha\) and \(w_\omega = \omega\text{.}\) So \(\vert \Sigma ^{\ast}_1 \vert = 2\text{.}\)
Count \(\Sigma ^{\ast}_2\).
We can count be simply listing the elements:
\begin{equation*} \Sigma ^{\ast}_2 = \{ \alpha \alpha, \alpha \omega, \omega \alpha, \omega \omega \} \text{.} \end{equation*}
So \(\vert \Sigma ^{\ast}_2 \vert = 4\text{.}\)
Count \(\Sigma ^{\ast}_3\).
This time we will just use inductive reasoning. Each word in \(\Sigma ^{\ast}_2\) may be extended to a word in \(\Sigma ^{\ast}_3\) by appending either an \(\alpha\) or an \(\omega\) onto the end. So there must be twice as many words in \(\Sigma ^{\ast}_3\) as in \(\Sigma ^{\ast}_2\text{,}\) i.e. \(\vert \Sigma ^{\ast}_3 \vert = 8\text{.}\)
Total count.
Using the
Addition Rule
, we obtain the total by adding up our preliminary results:
\begin{equation*} \vert \Sigma ^{\ast}_{\le 3} \vert = 1 + 2 + 4 + 8 = 15 \text{.} \end{equation*}
Another common strategy in mathematics is to consider the opposite.
Assume \(U\) is a finite set. For every subset \(A \subseteq U\text{,}\) we have \(\vert A \vert = \vert U \vert - \vert A^C \vert \text{.}\)
- Proof Idea.
-
Since \(U = A \sqcup A^C \) is always true, simply apply Statement 1 of Theorem 20.2.1 to this disjoint union and rearrange to isolate \(\vert A \vert\text{.}\)
For alphabet \(\Sigma = \{a, b, c, \ldots, y, z\} \text{,}\) how many words in \(\Sigma ^{\ast}_2\) do not begin with the letter \(\mathrm{a}\text{?}\) It's much easier to count the number of words in \(\Sigma ^{\ast}_2\) that do begin with \(\mathrm{a}\text{,}\) as there are only \(26\) possibilities for the second letter.
Later in this chapter we will learn a rule that will allow us to easily calculate the total number of words in \(\Sigma ^{\ast}_2\) to be \(26^2\) (see Worked Example 20.3.6 ). Accepting this fact for the moment, we can then use the Subtraction Rule to compute
\begin{align*} \# \{ 2\text{-letter words not beginning with } \mathrm{a} \} & = \vert \Sigma ^{\ast}_2 \vert - \# \{ 2\text{-letter words beginning with } \mathrm{a} \}\\ & = 26^2 - 26 \\ & = 26 (26 - 1) \\ & = 26 \cdot 25 \text{.} \end{align*}


12.6: Low-Mass Stars
Low-Mass Stars fuse hydrogen into helium, the proton-proton cycle. The classic low-mass star is the Sun. Low-mass stars have large convection zones when compared to intermediate- and high-mass stars. In very low-mass stars , the Convection Zone goes all the way to the star’s core!Over time, a low-mass star consumes all of the hydrogen in its core – what happens now? Think about a car that runs out of gas. Unless you put more gas in the tank, the car will not run. The same is true with stars; no more fuel in the stellar core will end the stellar fusion process.
When the core hydrogen is used up and no more nuclear fusion occurs, the star’s outer stellar layers expand and the core shrinks. At this point, the star becomes a Subgiant Star . The star’s outer layers continue to expand and the star brightens. The star then becomes a Red Giant Star . In about one billion years, the Sun will begin its Red Giant phase.
So how does the star expand and get brighter if it has ceased to fuse hydrogen in its collapsing core? Helium is left in the star’s core and gravity continues to shrink the core and the surrounding layers. These surrounding layers contain hydrogen; the surrounding shell of hydrogen begins to fuse, called Hydrogen Shell Burning . The now red giant star is now larger than out to the orbit of Mars.
Next, helium fusion begins, for which very high temperatures are required.
3 He→ 12 C
This occurs when three helium nuclei are fused into one carbon.
The star begins to dim and shrink in size. Now the cycle reverses ; hydrogen and helium are fused at a tremendous rate. This process takes a few million years. Now the star’s outer layers flow outward from the star, with the star’s core is mostly composed of carbon (from the fusion of the remaining helium into carbon).


14: The Somatic Nervous System
The somatic nervous system is the part of the peripheral nervous system and is associated with skeletal muscle voluntary control of body movements. The somatic nervous system is traditionally considered a division within the peripheral nervous system. However, this misses an important point: somatic refers to a functional division, whereas peripheral refers to an anatomic division. The somatic nervous system is responsible for our conscious perception of the environment and for our voluntary responses to that perception by means of skeletal muscles. Peripheral sensory neurons receive input from environmental stimuli, but the neurons that produce motor responses originate in the central nervous system.
-
- 14.0: Prelude to The Somatic Nervous System
- The distinction between the structures (i.e., anatomy) of the peripheral and central nervous systems and functions (i.e., physiology) of the somatic and autonomic systems can most easily be demonstrated through a simple reflex action.  Sensory receptors in the skin sense extreme temperature and the early signs of tissue damage. This triggers an action potential, which travels along the sensory fiber from the skin.
-
- 14.1: Sensory Perception
- A major role of sensory receptors is to help us learn about the environment around us, or about the state of our internal environment. Stimuli from varying sources, and of different types, are received and changed into the electrochemical signals of the nervous system. This occurs when a stimulus changes the cell membrane potential of a sensory neuron. The stimulus causes the sensory cell to produce an action potential that is relayed into the central nervous system (CNS).
-
- 14.2: Central Processing
- Specific regions of the CNS coordinate different somatic processes using sensory inputs and motor outputs of peripheral nerves. A simple case is a reflex caused by a synapse between a dorsal sensory neuron axon and a motor neuron in the ventral horn. More complex arrangements are possible to integrate peripheral sensory information with higher processes.
-
- 14.3: Motor Processing
- The defining characteristic of the somatic nervous system is that it controls skeletal muscles. Somatic senses inform the nervous system about the external environment, but the response to that is through voluntary muscle movement. The term “voluntary” suggests that there is a conscious decision to make a movement. However, some aspects of the somatic system use voluntary muscles without conscious control.


12.7: Benefits and Challenges of Workplace Diversity
- How can managers reap benefits from diversity and mitigate its challenges?
Much theoretical work has espoused the benefits of workplace diversity, but empirical studies have often had conflicting results, which have shown researchers that certain conditions can affect how successful initiatives to increase and enhance workplace diversity are. Managers can work to make sure that the efforts and initiatives they enact to increase diversity in the workplace come from a perspective that ensures and strives for equity and fairness, and not simply from the perspective of only benefitting the company’s bottom line. By approaching diversity and diversity issues in a thoughtful, purposeful way, managers can mitigate the challenges posed by a diverse workforce and enhance the benefits a diverse workforce can offer.
Three Perspectives on Workplace Diversity
Ely and Thomas’s work on cultural diversity was designed to theoretically and empirically support some of the hypothesized relationships between diversity and workplace outcomes. Their research yielded a paradigm that identifies three perspectives regarding workplace diversity: 143 integration and learning, access and legitimacy, and discrimination and fairness.
The Integration-and-Learning Perspective
The integration-and-learning perspective posits that the different life experiences, skills, and perspectives that members of diverse cultural identity groups possess can be a valuable resource in the context of work groups. Under this perspective, the members of a culturally diverse workgroup can use their collective differences to think critically about work issues, strategies, products, and practices in a way that will allow the group to be successful in its business operations. The assumption under this perspective is that members of different cultural identity groups can learn from each other and work together to best achieve shared goals. This perspective values cultural identity and strongly links diversity of the group to the success of the firm.
Downfalls of the integration-and-learning perspective can be that White members of the work group can feel marginalized when they are not asked to join in on diversity-related projects or discussions. Similarly, workforce members of color might experience burnout if they are always expected to work on those projects and discussions that specifically deal with diversity issues.
The Access-and-Legitimacy Perspective
The access-and-legitimacy perspective focuses on the benefit that a diverse workforce can bring to a business that wishes to operate within a diverse set of markets or with culturally diverse clients. Work groups that operate under this perspective are doing so in order to gain access to diverse markets and because their diversity affords them some level of legitimacy when attempting to gain access to diverse markets. This type of workplace diversity is more of a functional type of diversity that does not attempt to integrate or value diversity at the business’s core. The danger of this diversity perspective is that it can limit the roles of certain minority groups by valuing members of these groups only because they can increase the access to diverse markets and clients and not because they can make other potentially valuable contributions. 144
The Discrimination-and-Fairness Perspective
The discrimination-and-fairness perspective stems from a belief that a culturally diverse workforce is a moral duty that must be maintained in order to create a just and fair society. This perspective is characterized by a commitment to equal opportunities in hiring and promotions, and does not directly link a work group’s productivity or success with diversity. Many times firms operating under this perspective will have a spoken or unspoken assumption that assimilation into the dominant (White) culture should take place by the members of other cultural identity groups. One drawback of this perspective is that because it measures progress by the recruitment and retention of diverse people, employees of traditionally underrepresented groups can feel devalued. Often, assimilation is pushed on diverse employees under the guise of reducing conflict or in an effort to demonstrate that differences between cultural identity groups are unimportant. 145
Exhibit 12.8 shows the degrees of effectiveness and benefits for each perspective.
Exhibit 12.8 Cultural Diversity Perspectives at Work Source: Adapted from Ely, Robin J., and David A. Thomas. “Cultural diversity at work: The effects of diversity perspectives on work group processes and outcomes.” Administrative science quarterly. 46.2 (2001): 229-273.
- How can managers reap the benefits of diversity?
- How can managers mitigate the challenges of diversity?
- What is the access-and-legitimacy perspective? Differentiate it from the discrimination-and-fairness perspective
References
143. Ely, Robin J., and David A. Thomas. "Cultural diversity at work: The effects of diversity perspectives on work group processes and outcomes." Administrative science quarterly. 46.2 (2001): 229-273.
144. Ely, Robin J., and David A. Thomas. "Cultural diversity at work: The effects of diversity perspectives on work group processes and outcomes."Administrative science quarterly.46.2 (2001): 229-273.
145. Ely, Robin J., and David A. Thomas. "Cultural diversity at work: The effects of diversity perspectives on work group processes and outcomes."Administrative science quarterly.46.2 (2001): 229-273.


5.3: Lipids
Lipids include oils, fats, and waxes. Lipids provide stored energy, are essential components of cell membranes and are the building blocks of certain hormones. Dietary lipids are insoluble in water and cannot be utilized by the body unless broken down into smaller molecules. The body digests lipids by breaking them down into tiny components by emulsification with bile salts and by enzymes called lipases. The emulsification of lipids occurs in the small intestine.
Emulsification of lipids
Materials
- test tubes and rack
- vegetable oil
- water
Procedure
- Draw a line at the 1 cm mark and the 2 cm mark on 2 test tubes.
- Add vegetable oil to the 1 cm mark in both test tubes.
- Add an additional cm of water to each test tube.
- Add 10 drops of detergent to one of the tubes
- Cover the tubes with parafilm and shake vigorously about 30 times (instructor will demonstrate).
Analysis
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Describe the results (do not include the presence of foam) with respect to lipid emulsification.


8: Analysis and Synthesis Last updated Save as PDF Page ID 58178 Lumen Learning Lumen Learning 8.1: Why It Matters- Analysis and Synthesis 8.2: Introduction to Analysis As Critical Thinking 8.3: What Is Analysis? 8.4: Overcoming Barriers to Analysis 8.5: Suspending Judgment 8.6: Introduction to the Keys to Successful Analysis 8.7: Analytical Thesis Statements 8.8: Making Inferences 8.9: Introduction to Types of Analysis 8.10: Rhetorical Analysis 8.11: Process Analysis 8.12: Critical Analysis 8.13: Introduction to Synthesis 8.14: Synthesis 8.15: Synthesis in Practice 8.16: Putting It Together- Analysis and Synthesis 8.17: Discussion- Ad Rhetorical Analysis 8.18: Assignment- The Role of Inference in Reading and Understanding Satire


2.E: How We See the Invisible World (Exercises)
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- Last updated
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- Ying Liu
- City College of San Francisco
2.1: The Properties of Light
Visible light consists of electromagnetic waves that behave like other waves. Hence, many of the properties of light that are relevant to microscopy can be understood in terms of light’s behavior as a wave. An important property of light waves is the wavelength, or the distance between one peak of a wave and the next peak. The height of each peak (or depth of each trough) is called the amplitude.
Multiple Choice
Which of the following has the highest energy?
- light with a long wavelength
- light with an intermediate wavelength
- light with a short wavelength
- It is impossible to tell from the information given.
- Answer
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C
You place a specimen under the microscope and notice that parts of the specimen begin to emit light immediately. These materials can be described as _____________.
- fluorescent
- phosphorescent
- transparent
- opaque
- Answer
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A
Fill in the Blank
When you see light bend as it moves from air into water, you are observing _________.
- Answer
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refraction
Short Answer
Explain how a prism separates white light into different colors.
Critical Thinking
In Figure 2.1.6 , which of the following has the lowest energy?
- visible light
- X-rays
- ultraviolet rays
- infrared rays
2.2: Peering into the Invisible World
Italian scholar Girolamo Fracastoro is regarded as the first person to formally postulate that disease was spread by tiny invisible seminaria. He proposed that these seeds could attach themselves to certain objects that supported their transfer from person to person. However, since the technology for seeing such tiny objects did not yet exist, the existence of the seminaria remained hypothetical for a little over a century—an invisible world waiting to be revealed.
Short Answer
Why is Antonie van Leeuwenhoek’s work much better known than that of Zaccharias Janssen?
Why did the cork cells observed by Robert Hooke appear to be empty, as opposed to being full of other structures?
Multiple Choice
Who was the first to describe “cells” in dead cork tissue?
- Hans Janssen
- Zaccharias Janssen
- Antonie van Leeuwenhoek
- Robert Hooke
- Answer
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D
Who is the probable inventor of the compound microscope?
- Girolamo Fracastoro
- Zaccharias Janssen
- Antonie van Leeuwenhoek
- Robert Hooke
- Answer
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B
Fill in the Blank
A microscope that uses multiple lenses is called a _________ microscope.
- Answer
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compound
2.3: Instruments of Microscopy
The 20th century saw the development of microscopes that leveraged nonvisible light, such as fluorescence microscopy, which uses an ultraviolet light source, and electron microscopy, which uses short-wavelength electron beams. These advances led to major improvements in magnification, resolution, and contrast. In this section, we survey the broad range of modern microscopic technology and common applications for each type of microscope.
Multiple Choice
Which would be the best choice for viewing internal structures of a living protist such as a Paramecium ?
- a brightfield microscope with a stain
- a brightfield microscope without a stain
- a darkfield microscope
- a transmission electron microscope
- Answer
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C
Which type of microscope is especially useful for viewing thick structures such as biofilms?
- a transmission electron microscope
- a scanning electron microscopes
- a phase-contrast microscope
- a confocal scanning laser microscope
- an atomic force microscope
- Answer
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D
Which type of microscope would be the best choice for viewing very small surface structures of a cell?
- a transmission electron microscope
- a scanning electron microscope
- a brightfield microscope
- a darkfield microscope
- a phase-contrast microscope
- Answer
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B
What type of microscope uses an annular stop?
- a transmission electron microscope
- a scanning electron microscope
- a brightfield microscope
- a darkfield microscope
- a phase-contrast microscope
- Answer
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E
What type of microscope uses a cone of light so that light only hits the specimen indirectly, producing a darker image on a brighter background?
- a transmission electron microscope
- a scanning electron microscope
- a brightfield microscope
- a darkfield microscope
- a phase-contrast microscope
- Answer
-
D
Fill in the Blank
Chromophores that absorb and then emit light are called __________.
- Answer
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fluorochromes
In a(n) _______ microscope, a probe located just above the specimen moves up and down in response to forces between the atoms and the tip of the probe.
- Answer
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atomic force microscope
What is the total magnification of a specimen that is being viewed with a standard ocular lens and a 40⨯ objective lens?
- Answer
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400⨯
Short Answer
What is the function of the condenser in a brightfield microscope?
Label each component of the brightfield microscope.
Critical Thinking
When focusing a light microscope, why is it best to adjust the focus using the coarse focusing knob before using the fine focusing knob?
You need to identify structures within a cell using a microscope. However, the image appears very blurry even though you have a high magnification. What are some things that you could try to improve the resolution of the image? Describe the most basic factors that affect resolution when you first put the slide onto the stage; then consider more specific factors that could affect resolution for 40⨯ and 100⨯ lenses.
2.4: Staining Microscopic Specimens
In their natural state, most of the cells and microorganisms that we observe under the microscope lack color and contrast. This makes it difficult, if not impossible, to detect important cellular structures and their distinguishing characteristics without artificially treating specimens. We focus on the most clinically relevant techniques developed to identify specific microbes, cellular structures, DNA sequences, or indicators of infection in tissue samples, under the microscope.
Multiple Choice
What mordant is used in Gram staining?
- crystal violet
- safranin
- acid-alcohol
- iodine
- Answer
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D
What is one difference between specimen preparation for a transmission electron microscope (TEM) and preparation for a scanning electron microscope (SEM)?
- Only the TEM specimen requires sputter coating.
- Only the SEM specimen requires sputter-coating.
- Only the TEM specimen must be dehydrated.
- Only the SEM specimen must be dehydrated.
- Answer
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B
Fill in the Blank
Ziehl-Neelsen staining, a type of _______ staining, is diagnostic for Mycobacterium tuberculosis.
- Answer
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acid-fast
The _______ is used to differentiate bacterial cells based on the components of their cell walls.
- Answer
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Gram stain
Short Answer
How could you identify whether a particular bacterial sample contained specimens with mycolic acid-rich cell walls?
Critical Thinking
You use the Gram staining procedure to stain an L-form bacterium (a bacterium that lacks a cell wall). What color will the bacterium be after the staining procedure is finished?


6.3.10: Managerial Decision Exercises
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1. You have recently been promoted to the position of president of the division from your current role as VP of accounting and finance. Many people thought that the VP of sales and marketing would get the position, but you and he had always been friendly, and you thought that things would go smoothly. After about six months in the new position, you notice that he has been fighting you in small and subtle ways. You recognize his value, so you decide to let things play out and even mention other possibilities for promotion within the organization that he could apply for and that you would be supportive. After 11 months, things have not improved, and you are considering letting your colleague go. You are hesitant, however, because your organization needs a strong sales and marketing department. What should you do? If this power struggle continues, how do you think it will affect the larger organization?


11.9: Quiz 8-Confined Space Entry
1. Which of the following are considered to be confined spaces?
________ Tanks.
________ Vessels.
________ Hoppers.
________ Vaults.
________ Trenches.
________ Silos.
________ All of the above.
2. True or False... "engulfment" is a type of hazard that may be found in a confined space?
3. True or False... According to OSHA there can be too much, as well as too little, oxygen in a confined space?
4. When testing a confined space for atmospheric hazards, what should be tested for first?
________ Flammable gases.
________ Vapors and dust.
________ Oxygen content.
________ Toxic contaminants.
5. True or False... Forced-air ventilation alone can always protect entrants from toxic gases?
6. True or False... Normally an attendant is not allowed to enter a confined space?
7. True or False... An entry supervisor must sign an entry permit before work can begin in a confined space?


7.6: Dealing with Test Anxiety- Managing Your Stress for Success
The Dos and Don’ts of Managing Anxiety Related to Exams
The stress brought on by a major exam in a course can be extreme enough that it impairs the clear thinking needed for optimal performance. Most of us have experienced this. It is normal to feel stress before an exam, and in fact, that may be a good thing. Stress motivates you to study and review, generates adrenaline to help sharpen your reflexes and focus while taking the exam, and may even help you remember some of the material you need. But suffering too many stress symptoms or suffering any of them severely will impede your ability to show what you have learned. Test anxiety is a psychological condition in which a person feels distress before, during, or after a test or exam to the point where stress causes poor performance. Anxiety during a test interferes with your ability to recall knowledge from memory as well as your ability to use higher-level thinking skills effectively. Consider the Do's and Don'ts listed below for managing anxiety related to exams.
DO…
- Do prepare for an exam using the “Five-Day Study Plan”. Students who feel prepared will have less anxiety overall.

- Do plan to reward yourself with something relaxing or fun after the exam. Think about that when stressful thoughts may occur.
- Do relax the last hour before the exam to reduce tension and stressful thoughts.
- Do eat a moderate breakfast that includes both protein and healthy carbohydrates.
- Do periodically conduct checks on the tension in certain areas of your body and try to relax those areas. Breathing deeply and engaging in some positive imagery can also reduce tension quickly during an exam.
- Do survey the entire exam and plan carefully.
- Do ask questions of your professor if you are unsure about what to do on a particular question.
DON’T…
- Don’t cram for an exam. Underprepared students naturally have something to worry about.
- Don’t let negative thoughts or worrying get in the way of clear thinking. If you catch yourself worrying about what you do not know, stop yourself and replace it with positive affirmations and what you do know.
- Don’t spend time with classmates who might confuse you or generate stress about the exam on the day of the exam.
- Don’t stay up late the night before the exam. A good night’s sleep will improve your mental state and promote clearer thinking.
- Don’t drink a lot of caffeine before the exam. Arousal from caffeine can add to stress and make you jumpy.
- Don’t show up late for an exam. Feeling rushed to finish adds to the stress.
- Don’t panic if you “go blank” on a question. Go answer other questions and come back to it later. If all else fails, guess or write down what you do know.
- Don’t resort to looking at anyone else’s paper if you are unsure of your performance. Maintaining your integrity is far more important than the results of this exam.
If you feel that you are unable to manage your stress, please utilize the resources through the health center at your school or university. You don’t have to do this alone!
| My boogie statement | How rational is this thought? Do you have any evidence that it is true? | Reasonable reinforcing or affirmation statements you can use to replace it. |
|---|---|---|
| Example: I’m drawing a blank.…I’ll never get the answer…I must really be stupid. | I’ve missed questions on things that I studied and knew before. | I studied this and know it. I’ll visualize where it’s written in my notes to help me trigger my memory. |
Key Takeaways
Checkpoint Exercises
- List three things you should do before a test or exam to combat test anxiety.
- List three things you can do during an exam to reduce stress.
Activity – Test anxiety Assessment
Test Anxiety Assessment
Do you experience test anxiety?
Rate yourself on these items.
| Usually | Sometimes | Not usually | |
|---|---|---|---|
| I am so nervous on tests that I don’t do my best, even when I have studied well and am prepared. | |||
| My stomach gets tight and upset before or during a test | |||
| My hands get cold and sweaty during a test. | |||
| I get headaches before or during a test. | |||
| I have trouble sleeping the night before a test. | |||
| I find my mind racing or becoming dull and “muddy” so that I can’t think clearly while taking a test. | |||
| During a test, I forget material I have studied and learned, only to remember it again after the test is over. | |||
| I “over-analyze” questions, see too many possibilities, choose complex answers, and overlook the simpler, correct answers. | |||
| I make careless errors on a test. |
The more checks you put in the “usually” or “sometimes” columns, the greater the likelihood that you may be experiencing test anxiety. This is a common issue, and there is help available.


11.4: Reading- IMF and the World Bank- How Do They Differ?
If you have difficulty distinguishing the World Bank from the International Monetary Fund, you are not alone. Most people have only the vaguest idea of what these institutions do, and very few people indeed could, if pressed on the point, say why and how they differ. Even John Maynard Keynes, a founding father of the two institutions and considered by many the most brilliant economist of the twentieth century, admitted at the inaugural meeting of the International Monetary Fund that he was confused by the names: he thought the Fund should be called a bank, and the Bank should be called a fund. Confusion has reigned ever since.
The attached document explains, in detail the difference.
Source: http://www.imf.org/external/pubs/ft/exrp/differ/differ.htm
- The IMF and the World Bank How Do They Differ?. Authored by : David D. Driscoll. Provided by : International Monetary Fund. Located at : http://www.imf.org/external/pubs/ft/exrp/differ/differ.htm . License : Public Domain: No Known Copyright . License Terms : Fair Use