Over the past three decades, a dozen or more learning style taxonomies have been created by various educational researchers. For example, Howard Gardner of Harvard University (Multiple Intelligences Profile) based his taxonomy on mind psychology, and David Kolb (1984) of Yale University and the Bates Institute (LSI—Learning Styles Inventory) based his on experiential learning.
The latter two and other learning style inventories based on them, such as the Honey and Mumford Learning Styles model (1992). based on Kolb’s work; and Neil Fleming’s VARK (Visual, Auditory, Reading/Writing and Kinesthetic) (2001) of Lincoln University in New Zealand, and the Memletics Accelerated Learning Styles (Advantogy, 2003) models, both similar to Gardner’s Multiple Intelligences taxonomy, are particularly suited to online course delivery. All of these learning style models highlight student preferences and natural tendencies for processing information and understanding content. E-learning offers a rich medium for appealing to the diversity of learning styles if used in inventive, adaptive, and creative ways. The time to consider this is at the course planning stage, as the design team chooses the components and activities during the development process.
Multiple Intelligences
“We are all able to know the world through language, logical mathematical analysis, spatial representation, musical thinking, the use of the body to solve problems or to make things, and an understanding of ourselves and of others. Where individuals differ is in the strength of these intelligences: the so-called profile of intelligences—and in the way such intelligences are invoked and combined to carry out different tasks, solve diverse problems, and progress in various domains”. (Howard Gardner, 1991)
Howard Gardner, a professor at Harvard University, hypothesized that people are capable of eight unique ways of information processing, which he called multiple intelligence theory. Information processing is the person’s preferred intellectual approach to assimilating facts, information, and knowledge. Gardner suggested that individuals should be encouraged to apply their preferred intelligences in learning. Learners who have an understanding of their own particular learning styles can reflect on how to use their learning strengths and cultivate their less dominant ones. A key point in multiple intelligence theory is that most people can develop all eight of the intelligences to a relatively competent level of mastery.
Gardner’s eight unique intelligences are:
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linguistic—verbal
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visual—spatial
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logical-mathematical
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bodily—kinesthetic
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musical
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interpersonal
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intrapersonal
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naturalistic
As online courses become more prevalent, new research is being done on how the multiple intelligences can be cultivated, and appealed to through the use of technology and multimedia in education (Veenema & Gardner, 1996). Since it is unrealistic to expect that the design team will know the learners’ preferred learning styles beforehand, it makes sense to design activities and resources that can tap the strengths and meet the needs of all eight intelligences (Sims, 2006). Table \(\PageIndex{1}\) below provides some suggestions to guide this process.
Table \(\PageIndex{1}\): Multiple intelligences in online course planning
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INTELLIGENCE
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PREFERENCES
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APPEALING ONLINE ACTIVITIES
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Linguistic—Verbal
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Written and spoken word, language, Literary activities, reading
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Text, journals, forums, chats, wiki, blogs, written assignments, audio, dialogue, stories, debates
|
|
Visual—Spatial
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Visual and spatial thinkers, sensitive to colour, line, shape, form, space and the relationships between these
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graphics, movies, Flash, photos, multimedia, 3D modelling, design, charts, concept maps, diagrams
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|
Logical—Mathematical
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Detects patterns, scientific reasoning, deduction, mathematical calculations, cause and effect relationships
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Socratic questioning, problem based, pattern pames, puzzles, experiments, statistics, matrices
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|
Bodily—Kinesthetic
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Fine and gross motor movements, sense of timing, and direction. Also physical coordination, balance, dexterity, strength, speed, flexibility, and proprioceptive, tactile, and haptic capacities
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Role playing, psychomotor skills, demonstration, simulations, virtual reality, cooperative games, video games, ergonomic awareness
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Musical
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Musical ability and appreciation, Recognizes rhythmic patterns, pitch, melody, timbre, and tone colour
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Audio, sound and music recording, rhymes, background music, chants, raps, create music
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Interpersonal
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The capacity to interact with others, to understand them, and to interpret their behaviour accurately. The ability to notice distinctions among other people, and to recognize their moods, temperaments, motivations, and intentions. A sensitivity to other’s facial expressions, voices, and gestures, and the ability to respond effectively to these cues
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Group projects, forums, Chats, email, cooperative work, teams, interviews, coaching, counseling, listening, clubs, drills, community involvement
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Intrapersonal
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The ability to sense one’s inner being—to discover who we are, what feelings we have, and why we are the way the way we are. It represents our self –knowledge and our ability to act adaptively on the basis of this knowledge. It is our reflective self. Enables an accurate picture of the inner self, strengths and weaknesses, inner moods, goals, intentions, motivations, temperament, beliefs, and desires
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Journals, reflective activities, independent study, autobiography, portfolio, concentration work, metacognition techniques, personal growth activities, narratives
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Naturalistic
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Awareness of the forces, principles, and laws of nature. Recognize relationships among species, enjoy nature-related classification systems. Promotes ecological awareness and stewardship
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Ecological study, biology, natural sciences, charts, diagrams, taxonomies, genetic models, virtual field trips, systems, pattern recognition, nature analogies
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Kolb's Learning Styles Model
David Kolb’s learning style model is also quite amenable to course design planning. As well, this model provides a sort of developmental map for the cultivation of experiential learning throughout the human life span. Kolb described experiential learning as consisting of four stages: experiencing, reflecting, thinking, and acting. Kolb’s experiential learning taxonomy comprises four distinct activities:
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concrete experience—(CE)
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reflective observation—(RO)
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abstract conceptualization—(AC)
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active experimentation—(AE)
and a four-type definition of learning styles (each representing the combination of two preferred styles, rather like a two-by-two matrix of the four-stage cycle styles, as illustrated in Table \(\PageIndex{2}\) below), for which Kolb used the terms:
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diverging (CE/RO)
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assimilating (AC/RO)
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converging (AC/AE)
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accommodating (CE/AE)
Diverging (concrete, reflective). A characteristic question of this learning type is “Why?” These learners respond well to explanations of how course material relates to their experience, their interests, and their future careers. These learners prefer an instructor who functions as a Motivator.
Assimilating (abstract, reflective). A characteristic question of this learning type is “What?” These learners respond to information presented in an organized, logical fashion and benefit if they have time for reflection. To be effective, the instructor should function as an Expert.
Converging (abstract, active). A characteristic question of this learning type is “How?” These learners respond to opportunities to work actively on well-defined tasks and to learn by trial-and-error in an environment that allows them to fail safely. To be effective, the instructor should function as a Coach, providing guided practice and feedback.
Accommodating (concrete, active). A characteristic question of this learning type is “What if?” These learners like applying course material in new situations to solve real problems. To be effective, the instructor should adopt a supportive Constructivist role, giving opportunities for the students to discover things for themselves.
Table \(\PageIndex{2}\): Kolb’s learning styles model
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Active Experimentation
—AE—DOING
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Reflective Observation
—RO—WATCHING
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Concrete Experience
—CE—FEELING
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Accommodating
(CE/AE)
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Diverging
(CE/RO)
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|
Abstract Conceptualization
—AC—THINKING
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Converging
(AC/AE)
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Assimilating
(AC/RO)
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Learner Interactivity Preferences
“Interactivity is not simply a function of computer-based transactions, but a fundamental success factor for teaching and learning, especially when implemented in an online context. In most cases, regardless of any virtual community that exists, the learner will be working independently and therefore the effectiveness of those communications (interactions) will ultimately determine the effectiveness and efficiency of the learning environment” (Sims, Dobbs & Hand, 2001, p. 514).
The theory of learner interactivity preferences (developed by Rhodes and Azball in 1985) also has meaning to the course design team. Again, it is difficult to predict the actual preferences of future learners, but measures can be taken to promote all three levels within the course design. These three levels are reactive, co-active and proactive interactivity preferences in structure and presentation, which correspond to each learner’s cognitive activity. This theory described interactivity according to three different levels of quality. Later, other researchers added a fourth level, reciprocal interactivity (Sims, 1997; Sims, 2006). The four preferences are described on five functional levels through the following transactions: confirmation, pacing, navigation, inquiry, and elaboration.
Reactive interaction
A reactive interaction is a behaviourist response to presented stimuli, for instance, providing an answer to a question. This level of interaction within an online course structure shows very little learner control over content structure with program-directed options and feedback, the course components and activities are completely predetermined by the design team and instructor.
Co-active interaction
A co-active interaction preference means the learner prefers more opportunities for choice and setting the pace for their own learning. A co-active online course design allows more control, providing learner control for sequence, pace and style of interaction within the online environment.
Proactive interaction
“Proactive interaction is constructivist: the learner prefers to both construct and generate activities to support their learning. A proactive course design enables the learner’s actions to go beyond selecting available information and reacting to existing structures, and generate individual constructions and elaborations beyond the rules set up by the design team and instructor” (Sims, 1997, p. 160).
Reciprocal interaction
Reciprocal interaction preferences means the learner wants a dialogue-like, reciprocity- based interaction with the online course interface and participants. This sort of interaction is usually found only in designs where artificial intelligence or virtual reality are situated. In these learning environments, both learner and system reciprocally adapt to one other. This level of interaction is rare in online courses, but is anticipated to be much more feasible in the not so distant future.
Readiness for E-Learning
Design teams can help their prospective learners prepare for, or at the least assess their own readiness to learn within an online environment. Research supports this as a critical consideration, since an individual learner’s success in an online course often hinges on this foundation of readiness. Readiness entails three dimensions to assess: the learners’ computer or technical skill, learning skills, as well as their time management behaviours.
Design teams can help their prospective learners prepare for, or at the least assess their own readiness to learn within an online environment. Research supports this as a critical consideration, since an individual learner’s success in an online course often hinges on this foundation of readiness. Readiness entails three dimensions to assess: the learners’ computer or technical skill, learning skills, as well as their time management behaviours.
Computer/technical skills: The more experience a student has in using basic computer skills (use of networks, word processing and other software applications, ability to upload and download files, use of the World Wide Web and email, accessing online libraries and other resource databases, and experience with online forums and other discussion applications, the more ready they are to take an online course. Other foundational requirements include access to a stable Internet connection and dependable computer and printer.
Learning skills: Readiness is fortified by the ability to work independently, be self-motivated, possess mature reading and writing skills, and a proactive approach to learning, and a positive attitude.
Time management skills: Readiness is evident when a learner can safely plan blocks of time for participation and study within their existing lifestyle and commitments. Managing one’s time in order to complete an online course requires a respectable level of commitment and discipline.
Recommended online tools for gauging e-learning readiness
There are some excellent free online tools available for students to use (and design teams to examine) in gauging readiness for e-learning. Three highly recommended ones include:
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Novosel, S. (2000). Readiness Index for Learning Online (RILO). Indiana University School of Nursing. nursing.iupui.edu/About/default.asp?/About/C TLL/Online/RILO.htm
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Schrum, L. (2001). SORT: Student Online Readiness Tool. University of Georgia. www.alt.usg.edu /sort/
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DeSantis, C. (2002). eLearners Advisor. University of Guelph. www.elearnersadvisor.com


27.2.4: JavaScript Examples
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Overview
JavaScript , often abbreviated as JS, is a high-level, interpreted programming language. Alongside HTML and CSS, JavaScript is one of the three core technologies of the World Wide Web. JavaScript enables interactive web pages and therefore is an essential part of web applications. The vast majority of websites use it, and all major web browsers have a dedicated JavaScript engine to execute it. [1]
JavaScript is one of the most popular current programming languages [2] , and is the primary programming language for front-end web development. JavaScript has been implemented in multiple platforms with different I/O commands. Several examples follow.
Example
Hello World – Console Log
// This script displays "Hello world!". // // References: // https://www.digitalocean.com/community/tutorials/how-to-write-your-first-javascript-program console.log("Hello world!")
Output
Hello world!
Discussion
Each code element represents:
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//
begins a comment -
console.log()
writes to the JavaScript console output log -
"Hello world!"
is the literal string to be displayed
Hello World – Window Alert
// This script displays "Hello world!". // // References: // https://www.digitalocean.com/community/tutorials/how-to-write-your-first-javascript-program alert("Hello world!")
Output
Hello world!
Discussion
Each code element represents:
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//
begins a comment -
alert()
calls the window alert function to display a message -
"Hello world!"
is the literal string to be displayed
Hello World – Document Write
// This script displays "Hello world!". // // References: // https://www.w3schools.com/jsref/met_doc_write.asp document.write("Hello world!")
Output
Hello world!
Discussion
Each code element represents:
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//
begins a comment -
document.write()
writes output to the current document -
"Hello world!"
is the literal string to be displayed
JavaScript IDEs
There are many free cloud-based and local IDEs available to begin coding in JavaScript. Check with your instructor or do your own research for recommendations.


1.40: Let your pharmacist be your guide- navigating barriers to pharmaceutical access
Introduction
The high cost of healthcare in the United States, spanning from the ability to afford health insurance to paying for medications and medical bills, is a public health issue that hinders access to care and contributes to poorer health outcomes. Over the past ten years, the cost of healthcare services has grown more quickly than the cost of other goods and services. 1 In a 2019 poll, half of US adults reported that they or a family member put off or skipped healthcare or dental care services due to cost. 2 Moreover, 29% of all adults reported that they did not fill a prescription, cut pills in half, skipped doses, or otherwise did not take their medications as prescribed due to cost. 2 Patients reported resorting to other alternatives for care, such as relying on home remedies or over-the-counter drugs. 2 The consequences are detrimental, with three in ten (29%) individuals reporting their medical condition worsened because they did not take their prescription medications as recommended. 2 These barriers are particularly pronounced among those who face added challenges to care, such as patients who do not have insurance, are underinsured, or have serious medical conditions.
Specifically, lack of insurance coverage and underinsurance hinders healthcare access by impacting whether someone receives care, as well as when and where they can receive care. Access to healthcare is further influenced by multi-level factors that impact pharmaceutical care. At the policy level, this includes lack of timely availability of generic alternatives, lack of policies designed to improve medication adherence, and lack of transparency in drug costs. 3 These policies lead to patients paying for higher cost brand name drugs. At the community level, factors include the geographic location of pharmacies and existing transportation infrastructure. Pharmacy deserts, or neighborhoods and communities without a pharmacy or pharmacy services such as home delivery, hinder patients’ ability to get medications. 4 Organizationally, this includes disproportionate distribution of qualified and skilled healthcare workers and under-resourced health systems. These factors influence whether patients have access to a clinic nearby, which adds a notable barrier for rural communities. At the individual level, socioeconomic status in addition to the presence of complex medical conditions pose further challenges, as discussed above.
Several private and publicly funded mechanisms exist to help address barriers to medication access. For example, free clinics are safety-net organizations that often utilize volunteer health professionals to provide a range of medical, vision, behavioral health, dental, and/or pharmacy services to uninsured and underinsured patients. 5 Websites like the National Association of Free & Charitable Clinics (NAFC) and NeedyMeds provide ways to locate the closest free clinic. Federal programs such as the 340B drug pricing program enable health clinics that care for underserved populations to reallocate and stretch limited federal resources. 6 However, these programs are only available to qualified entities and to select patients. For individuals who need assistance with the cost of prescription drugs, prescription drug coupons and discount cards can be found through websites like GoodRx and NeedyMeds. Prescription drugs can also be obtained at little or no cost from pharmaceutical companies through patient medication assistance programs (PMAP). 7 However, the enrollment and refill processes are not standardized, and each manufacturer’s PMAP application may have different enrollment requirements. Many applications require patients to disclose their financial status, provide financial documentation such as federal income tax forms or social security benefit letters, or provide their social security number. 8 Although programs exist to fill in the gaps in pharmaceutical access, unfortunately they are insufficient and difficult to navigate. In addition, not all medications are available, requiring therapeutic substitution. This offers pharmacists the opportunity to play an important role in helping patients navigate the resources available so that patients can obtain affordable medications.
Case
You are a clinical pharmacist at a federally qualified health center (FQHC).
CC: “I want to start treatment for my Hepatitis C before I move.”
Patient: LM is a 56-year-old female (55 in, 82.6 kg) with newly diagnosed hepatitis C virus (HCV) infection who is an undocumented migrant farmworker. Over the past few months, it has been difficult for her to find work in the area, which has made it hard for her to pay for her medications and supplies. She is concerned about this because she knows she needs to take her medications to stay healthy and out of the hospital. Right now, she is holding on to hope that she might be able to find work over the next month or so but shares that she will likely need to move on to another area soon, since the seasons are changing.
HPI: After being diagnosed with HCV, the patient is feeling overwhelmed, especially due to the cost of the new medications. She states “I have heard treatment for hepatitis C is very expensive. Those medicines might cost more than everything I own!”. She is very worried but would still like to begin treatment as soon as possible, as she is unsure of when she will be able to re-establish care after she moves.
PMH: T2DM; HTN; HLD; HCV
FH:
- Mother: alive; T2DM
- Father: (deceased; MI); HTN
SH: History of substance use (alcohol)
Medications:
- Insulin aspart (Novolog) 10 units subcutaneously TID ac
- Insulin glargine (Lantus) 45 units subcutaneously daily
- Metformin 1000 mg BID
- Atorvastatin (Lipitor) 40 mg daily
- Lisinopril 20 mg daily
- Hydrochlorothiazide 25 mg daily
Allergies: NKDA
Vitals:
- BP 133/75 mmHg
- HR 78 bpm
- SpO 2 98%
- Temp 97.8°F
Labs:
- HgbA1c: 6.8%
- Hep C screen: reactive
- Hep C quant: 872,974 unit/mL
- Hep C genotype: 3a
- HBsAg: negative
- HBsAb: 95.1 IU/L
- HBcAb: negative
- HIV status: negative
- All other labs WNL
- Imaging/Staging:
- FibroScan: 5 kPa
- Fibrosis Score: F1
ROS:
- General: negative
- Eye: negative
- Ear/Nose/Throat: negative
- Respiratory: negative
- Cardiovascular: negative
- Gastrointestinal: negative
- Genitourinary: negative
- Gynecological: no abnormal bleeding, pelvic pain/discharge, breast pain or new/enlarging lumps on self-exam
- Skin: negative
- Heme/Lymph: negative
- Musculoskeletal: negative
- Neuro: negative
- Psychiatric: anxiety
- Endocrine: negative for symptoms of hypoglycemia/hyperglycemia
Surgical history: None
SDH: LM resides in a trailer home with six other relatives, including her parents, her husband, brother, and two children. She was born, raised, and lived most of her life in Mexico, where she completed only a few years of formal education. Her primary and only fluent language is Spanish. She has worked for the past few years as a migrant farmworker. Some members of her family are documented citizens in the US; however, she is not documented, and she does not have healthcare coverage. Currently, she has no personal income, but a few members of her family have found some temporary work in the area, so there is some money for food and other expenses in their household. Access to fresh foods is challenging and sometimes she struggles to afford her diabetes testing supplies. However, LM can access many of her medications and remain adherent to her insulin because this medication is currently available through the 340B program at her clinic.
Additional context: This patient falls into the category of ‘migrant farmworker’ based on her work moving from state to state to harvest different crops based on the season.
Case Questions
- What would be the best treatment and monitoring plan for LM, taking into consideration all the barriers the patient may face in completing HCV treatment?
- What challenges does accessing HCV medications present generally in the United States?
- How does the fact that LM is a migrant farmworker affect her access to HCV treatment?
- What resources are available to improve medication access for patients who are underinsured or uninsured and how do patients access these programs?
- What programs are available to patients who are not US citizens and/or are undocumented immigrants?
- Given LM’s undocumented status and lack of insurance, what specific programs or resources would you recommend to improve her access to care and help complete HCV treatment?
- In general, what factors influence access to affordable medications at policy, organizational, and individual levels?
- What are the consequences of lack of prescription insurance coverage medication access on patient health outcomes?
Author Commentary
Patients who lack insurance or are underinsured have complicated barriers to healthcare that can be difficult to navigate. Migrant farmworkers have added challenges to accessing adequate and consistent care. These barriers and gaps in care result from the fragmented nature of our current healthcare landscape and contribute to the pervasive health disparities and inequities that exist. Pharmacists will encounter patients who have barriers to care regardless of the pharmacy setting. Consequently, pharmacists play an important role in helping patients access affordable medications by informing themabout the resources available and helping patients utilize these resources.
In addition to resources like the 340B program and PMAPs, pharmacists can help make medication regimens more affordable for patients regardless of insurance status. For example, by recognizing clinically appropriate and cost-effective alternatives for higher cost drugs, pharmacists can recommend therapeutic exchanges. In addition, pharmacists can troubleshoot and find formulary alternatives for medications that are not covered by a patient’s health insurance or require prior authorization. Pharmacists can also provide education on the differences between brand and generic drugs and encourage patients to use generic drugs when appropriate. Modest adjustments, like switching certain drug formulations from capsule to tablet or cutting higher dosages in half, are other cost-cutting strategies pharmacists can recommend. Many patients have trouble affording the medications they are initially prescribed even when they do have insurance. It is important for pharmacists to recognize the responsibility they have in making medications more accessible to patients.
Patient Approaches and Opportunities
Navigating our complex healthcare systemcan be a challenging and confusing process for many patients, particularly for those who have added barriers such as uninsurance or underinsurance, lack of citizenship, unemployment, lack of transportation, or low health literacy. Programs like the 340B program enable qualified health clinics to provide care to patients who are uninsured on a sliding fee scale based on income, and PMAPs can help patients gain access to otherwise unaffordable medications such as long and rapid-acting insulin, GLP1 inhibitors, inhalers, direct acting antivirals, and direct oral anticoagulants. Although resources and programs are available to help improve access to care or lower prescription drug costs, there are wide variations in ways to enroll in programs and application processes, respectively. Furthermore, there is no standardized way to access all available resources. Consequently, many patients are not aware of the resources available or do not access them.
As the medication experts, pharmacists can help patients navigate these complex barriers and obtain affordable medications. Beyond that, pharmacists can help refer patients to other available programs. Because many patients may not know that these options exist, it is important to proactively broach this conversation in a sensitive and respectful way when red flags are present (i.e., inconsistently filling/refilling prescriptions, extended absences in care, or frequent emergency department visits for preventable conditions). By establishing rapport and building trusting relationships with patients, pharmacists may become increasingly aware of patients’ unique needs and identify opportunities for intervention that would otherwise have gone unnoticed.
Related chapters of interest:
- Plant now, harvest later: services for rural underserved patients
- Saying what you mean doesn’t always mean what you say: cross-cultural communication
- An ounce of prevention: pharmacy applications of the USPSTF guidelines
- Sweetening the deal: improving health outcomes for patients with diabetes mellitus
- Prescription for change: advocacy and legislation in pharmacy
- Uncrossed wires: working with non-English speaking patient populations
External resources:
-
Websites:
- Partnership for Prescription Assistance. http://www.pparx.org
- Rx Assist. www.rxassist.org
- Needymeds. www.Needymeds.org
- Bureau of Primary Health Care. https://bphc.hrsa.gov/
- Office of Pharmacy Affairs. https://www.hrsa.gov/opa/340b-opais/index.html
- 340B Program. https://www.hrsa.gov/opa/index.html
- 340B Prime Vendor Program. www.340bpvp.com
- National Association of Free and Charitable Clinics. https://www.nafcclinics.org/find-clinic
- RxHope: www.RxHope.com
- Medicare Part D. https://www.medicare.gov/drug-coverage-part-d
- Health Insurance Marketplace. https://www.healthcare.gov/marketplace/individual/
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Journal articles:
- Kesselheim AS, Huybrechts KF, Choudhry NK, et al. Prescription drug insurance coverage and patient health outcomes: a systematic review. Am J Public Health 2015;105(2):e17-e30.
References
- Consumer Price Index – December 2020. www.bls.gov/news.release/cpi.nr0.htm . Accessed February 3, 2021.
- Kirzinger A, Munana C, Wu B, et al. Data note: Americans’ challenges with health care costs. June 2019. https://www.kff.org/health-costs/issue-brief/data-note-americans-challenges-health-care-costs/ . Accessed February 3, 2021
- Kesselheim AS, Huybrechts KF, Choudhry NK, et al. Prescription drug insurance coverage and patient health outcomes: a systematic review. Am J Public Health 2015;105(2):e17-e30.
- Pednekar P, Peterson A. Mapping pharmacy deserts and determining accessibility to community pharmacy services for elderly enrolled in a State Pharmaceutical Assistance Program. PLoS One . 2018;13(6):e0198173.
- Darnell JS. Free clinics in the United States: a nationwide survey. Arch Intern Med 2010;170(11):946–53.
- 340B Drug Pricing Program. https://www.hrsa.gov/opa/index.html . Accessed December 21, 2020.
- Drug company programs help some people who lack coverage. Washington, DC: U.S. General Accounting Office, 2000 Nov; report GAO-01-137. https://www.gao.gov/products/GAO-01-137 . Accessed December 21, 2020.
- Chauncey D, Mullins CD, Tran BV, McNally D, McEwan RN. Medication access through patient assistance programs. Am J Health Sys Pharm 2006;63(13):1254-9.


1.5: The Role of Documentation
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- Gina Peterson and Emily Elam
- College of the Canyons
One of the cornerstones of a high-quality early care and education program is the practice of observing, documenting and assessing children’s development. According to NAEYC (2009), in order to make formative decisions that will guide what goes on in the classroom, there needs to be an organized system in place to collect information. When we record our observations and collect data, we “hold in memory the actions, nonverbal communication, or comments that seem to be significant to children’s thinking” (California Preschool Program Guidelines, 2015 p. 46). When we document children’s learning and collect key artifacts, we create tangible evidence that we can share with the children and their families, along with administrators and stakeholders. There are many ways you can record and document children’s learning. In fact, you should attempt to utilize several methods as part of your regular observation routines.
To collect and record data you can use the following methods :
- running records
- anecdotal notes
- checklists
- frequency counts
- learning stories
- time or event samples
- work samples
- taking photos, videotaping, or audio recordings
To store your documentation
To safely store your collected data, you will need to have an organized system in place. Portfolios are a popular strategy used by intentional teachers. To create a portfolio, you can use a binder or notebook, a file or accordion-style folder, or a cardboard box. As you collect observation evidence for each child, it is vital that you date everything so you can organize it chronologically. This will help you track each child’s progress throughout the school year more efficiently. Portfolios help you construct a well-rounded and authentic picture of each child in your class. Knowing the “whole child” you are better equipped to build on each child’s individual interests, and you are more apt to plan developmentally appropriate activities.
Each child should have their own portfolio. A well-organized portfolio will contain observations and artifacts of children's work that are collected at different time periods throughout the school year. It is recommended that you include some type of documentation that highlights each developmental domain. For example:
- Gross Motor : Take photographs of your child while they are engaged in outside activities like running, jumping, climbing, riding a bike or playing in the sandbox.
- Fine Motor : Keep a checklist of when your child learns to button, zip, and tie his shoes. Include work samples of their cutting, coloring, painting, and samples of emergent writing
- Social-Emotional : Write anecdotal notes when your child engages in open-ended, child-directed play. Take note of how they share and cooperate with others.
- Cognitive : Chart a science experiment and take photos. Photograph a completed puzzle.  And, as she explains her process and she had to figure out all the steps to take so that the bridge wouldn’t fall down – be sure to record that too.
- Literacy and Oral language : Save writing examples to track how the child writes her name. Include illustrations of stories they love and the stories they write themselves. Write down quotes in your running record or make audiotapes of conversations during circle time.
- Creative expression : Videotape your child while playing in the dramatic play area or while performing a dance during music and movement. Photograph a clay creation, painting or block tower.
To be clear, it isn’t the amount of documentation you collect for each portfolio that matters, it’s the quality of information you gather. Portfolios tell a story of the whole child. There should be a beginning, middle, and an end. Each work sample, anecdotal note, checklist, frequency count and learning story should be used to showcase how a child processes information, develops relationships, and learns while playing.
To document children’s learning
Whether you collect evidence through spontaneous or planned observations, you will use your documentation to ultimately assess a child’s learning, growth, and development. With well-organized documentation, intentional teachers can effectively communicate with a child’s family, using the evidence and artifacts they have collected over time. Families appreciate being able to see their child’s progression and how they interact with others. Families also enjoy seeing the types of activities their child engages in during a typical day at school. Here are a few ways documentation can be used to showcase a child’s learning, growth and development:
- rating scales and formal developmental assessments
- daily progress reports
- documentation boards
Pin It! Ten Teacher Tips When Gathering your Documentation
- Date – this is key in tracking development over time
- Time – start time and end time
- Setting – note the location (indoor or outdoor; center or play area)
- Purpose – what is the intended goal
- Note the child (or children) who are involved in the activity
- Record only the facts – Write down exactly what you see and hear
- Be as concise (to the point) as you can
- Record the facts in the order as they occur
- Be descriptive and provide vivid details -create a visual picture so others can “see” what is happening
- Be specific and avoid vague or general terms – this is helpful when you go back to review your dat


10.6: Stability of Alkenes
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Objectives
After completing this section, you should be able to
- explain why cis alkenes are generally less stable than their trans isomers.
- explain that catalytic reduction of a cis alkene produces the same alkane as the catalytic reduction of the trans isomer.
- explain how heats of hydrogenation ( ΔH ° hydrog ) can be used to show that cis alkenes are less stable than their trans isomers, and discuss, briefly, the limitations of this approach.
- arrange a series of alkenes in order of increasing or decreasing stability.
- describe, briefly, two of the hypotheses proposed to explain why alkene stability increases with increased substitution. [ Note: This problem is a typical example of those instances in science where there is probably no single “correct” explanation for an observed phenomenon.]
Key Terms
Make certain that you can define, and use in context, the key terms below.
- catalytic hydrogenation
- heat of hydrogenation ( ΔH ° hydrog )
- hyperconjugation
Study Notes
The two alkenes, cis -CH 3 CH=CHCH 3 and (CH 3 ) 2 C=CH 2 have similar heats of hydrogenation (−120 kJ/mol and −119 kJ/mol, respectively), and are therefore of similar stability. However, they are both less stable than trans -CH 3 CH=CHCH 3 (−116 kJ/mol).
You may wonder why an sp 2 - sp 3 bond is stronger than an sp 3 - sp 3 bond. Bond strength depends on the efficiency with which orbitals can overlap. In general, s orbitals overlap more efficiently than do p orbitals; therefore, the s - s bond in the hydrogen molecule is stronger than the p - p bond in fluorine. In hybrid orbitals, the greater the s character of the orbital, the more efficiently it can overlap: an sp 2 orbital, which has a 33% s character, can overlap more effectively than an sp 3 orbital, with only 25% s character.
Hydrogenation
Alkene hydrogenation is the addition of hydrogen gas (H 2 ) to an alkene which saturates the bond and forms an alkane. Alkene hydrogenation reactions require a transition metal catalyst, such as Pt or Pd, to speed up the reaction. The hydrogenation reaction is used in this section to investigate the stability of alkenes, however, it will be discussed in greater detail in Section 8.7 . Hydrogenation reactions are exothermic and the enthalpy change in this reaction is called the heat of hydrogenation ( ΔH ° hydrog ) . Since the double bond is breaking in this reaction, the energy released during hydrogenation is proportional to the energy in the double bond of the molecule. By comparing the heat of hydrogenations from a series of alkenes that produce the same alkane, a quantitative measure of relative alkene stabilities can be produced. These experiments will lead to an general understanding of structural features which tend to stabilize or destabilize alkenes.
The Catalyst
A catalyst increases the reaction rate by lowering the activation energy of the reaction. Although the catalyst is not consumed in the reaction, it is required to accelerate the reaction sufficiently to be observed in a reasonable amount of time. Catalysts commonly used in alkene hydrogenation are: platinum, palladium, and nickel. The metal catalyst acts as a surface on which the reaction takes place. This increases the rate by putting the reactants in close proximity to each other, facilitating interactions between them. With this catalyst present, the sigma bond of H 2 breaks, and the two hydrogen atoms instead bind to the metal (see #2 in the figure below). The \(\pi\) bond of the alkene weakens as it also interacts with the metal (see #3 below).
Since both the reactants are bound to the metal catalyst, the hydrogen atoms can easily add, one at a time, to the previously double-bonded carbons (see #4 and #5 below). The position of both of the reactants bound to the catalyst makes it so the hydrogen atoms are only exposed to one side of the alkene. This explains why the hydrogen atoms add to same side of the molecule, called syn-addition.
Note
The catalyst remains intact and unchanged throughout the reaction.
Heats of Hydrogenation
The stability of alkene can be determined by measuring the amount of energy associated with the hydrogenation of the molecule. Since the double bond is breaking in this reaction, the energy released in hydrogenation is proportional to the energy in the double bond of the molecule. This is a useful tool because heats of hydrogenation can be measured very accurately. The \(\Delta H^o\) is usually around -30 kcal/mol for alkenes. Stability is simply a measure of energy. Lower energy molecules are more stable than higher energy molecules. More substituted alkenes are more stable than less substituted ones due to hyperconjugation . They have a lower heat of hydrogenation. The following illustrates stability of alkenes with various substituents:
Cis/Trans Isomers
Between cis and trans isomers of an alkene, the cis isomer tends to be less stable due to the molecular crowding created nonbonding interaction between two alky groups on the same side of the double bond. The crowding creates steric strain which distorts bond angles creating less effective bond orbital overlap and desabilizing the molecule. Steric strain has previously been seen in gauche interactions in Newman projections ( Section 3.7 ) and 1,3-diaxial interactions in substituted cyclohexanes ( Section 4.7 ). Steric strain is directly related to the size of the species being crowded. The difference in energy between cis and trans 2-butene is 5 kJ/mol, however, this difference would be greater if larger group were being held in the cis position. Two cis - tert -butyl group can create over 40 kJ/mol of steric strain.
See the following isomers of butene:
Alkene Stabilization by Alkyl Substituents
In general, the stability of an alkene increases with the number of alkyl substituents. This effect is due by the combination of two factors:
Hyperconjugation
In classical valence-bond theory, electron delocalization can only occur by the parallel overlap of adjacent p orbitals. According to hyperconjugation theory, electron delocalization could also occur by the parallel overlap of p orbitals with adjacent hybridized orbitals participating in sigma bonds. This electron delocalization serves to stabilize the alkene. As the number of alkyl substituents increases, the number of sigma bonds available for hyperconjugation increases, and the alkene tends to become more stabilized. In the example of propene shown below, a p orbital from a sp 2 hybridized carbon involved in the double bond interacts with a sp 3 hybridized orbital participating in an adjacent C-H sigma bond.
In a molecular orbital description of hyperconjugation, the electrons in sigma molecular orbitals (C-H or C-C) of alkyl substituens, interact with adjacent unpopulated non-bonding or antibonding molecular orbitals from the double bond. The interaction creates a bonding molecular orbital which extends over the four atom chain (C=C-C-H) involved in hyperconjugation. The expanded molecular orbital helps to stabilize the double bond.
Bond Stability
Bond strengths play an important part in determining the overall stability of a molecule. A C-C bond between a sp 3 carbon and a sp 2 carbon is slightly stronger than a C-C bond between two sp 3 carbons. Increasing the number alkyl substituents of a double bond also increases the number of sp 3 -sp 2 C-C bonds making the alkene more stable. This is idea can be clearly seen when comparing the isomers 1-butene and 2-butene. The molecule 1-butene is monosubstituted and contains a sp 3 -sp 3 C-C and a sp 3 -sp 2 C-C bond. The disubstituted, 2-butene, contains 2 sp 3 -sp 2 C-C bonds which contributes to its greater stability.
Note
In cycloalkenes smaller than cyclooctene, the cis isomers are more stable than the trans as a result of ring strain.
Exercise \(\PageIndex{1}\)
Of the three following isomers which would be expected to be the most stable?
a)
b)
c)
- Answer
-
1)
a)
b)
c)
Exercise \(\PageIndex{2}\)
3-Bromobut-1-ene reacts with hydrogen gas in the presence of a platinum catalyst. What is the name of the product?
- Answer
-
2-Bromobutane ( numbering changes when alkene is no longer present )
Exercise \(\PageIndex{3}\)
Cyclohexene reacts with hydrogen gas in the presence of a palladium catalyst. What is the name of the product?
- Answer
-
Cyclohexane
Exercise \(\PageIndex{4}\)
What is the stereochemistry (syn or anti addition) of an alkene hydrogenation reaction?
- Answer
-
Syn-addition
Exercise \(\PageIndex{5}\)
When looking at their heats of hydrogenation, is the cis or the trans isomer generally more stable?
- Answer
-
Trans
Exercise \(\PageIndex{6}\)
Show the product for the following
- Answer
-
References
- Fox, Marye Anne, and James K. Whitesell. Organic Chemistry . 3rd ed. Sudbury, MA: Janes and Bartlett Publishers, 2004.
- Hanson, James R. Functional Group Chemistry . Bristol, UK: The Royal Society of Chemistry, 2001.
- Streitwieser, Andrew Jr., and Clayton H. Heathcock. Introduction to Organic Chemistry . 2nd ed. New York, NY: Macmillan Publishing Co., Inc., 1981.
- Vollhardt, Peter C., and Neil E. Schore. Organic Chemistry: Structure and Function . 5th ed. New York, NY: W.H. Freeman and Company, 2007.
- Zlatkis, Albert, Eberhard Breitmaier, and Gunther Jung. A Concise Introduction to Organic Chemistry . New York: McGraw-Hill Book Company, 1973.


3.3: What Network is on Now?
Digital marketing strategy plays a critical role in business growth. With the right strategy, you can raise brand awareness, attract the target audience, and build lasting relationships for a win-win situation. However, your marketing efforts can prove fruitful only if you understand how to use social platforms to your advantage.
Social media has become a part of our lives. Successful marketers put themselves in customers’ shoes and choose a strategy that focuses on their pain points. If you want to increase the efficacy of your digital marketing campaigns, you need to learn about popular social media websites.
While a myriad of social media websites is available these days, you can’t promote your brand on each and every website. By focusing your efforts on websites that are popular among your audience, you can drive results.
Why Do You Want One to Win Or Lose?
Myspace got the first-mover advantage and remained the leading social website for quite some time. However, when Facebook was introduced, it captured a huge market share in no time and left other social media websites struggling with their loss.
When an innovative company is launched with the right strategy, it has a good chance of eliminating the predecessor and becoming the market leader. In the past, we have seen many such examples. Netflix beat Blockbuster, digital camera companies killed Polaroid, and Circuit City lost to Best Buy.
This is a common trend that old and established businesses lose to new market entrants. It is because many traditional stores prefer to stick with the strategies and actions they have been using for years and fear change or innovation.
This practice isn’t good for anyone; neither marketers nor consumers. If there is no market competition, consumers would suffer the most.
Higher competition eliminates the monopoly. The more firms in the market, the more efforts would be needed for a business to make its place in the crowded market. They are motivated to innovate and offer value to consumers to stand out. It keeps them on toes and they constantly put in their best efforts to stay ahead and stay relevant. Similarly, they are also inclined to offer better quality goods and services at reasonable prices.
Now, let’s consider the example of social media in this scenario. It’s best for everyone that the competition is increasing amongst social media companies. The more the competition, the higher will be the service quality at lower rates. So, whether you use the internet for personal networking or you are a business marketer, this competition will benefit you in the long run.
How Do We Benefit From Each Network?
Investing time and money in social media is no longer optional for business marketers. With your competition gaining customers and building a good reputation via social websites, you can’t afford to miss out on this invaluable opportunity.
As marketers, your first step should be to get a website where you can display products, testimonials, and other relevant information. After that, you can gain several benefits from social accounts.
Regardless of which platform you choose, you can raise awareness via social posts as well as paid social media advertising. Your social posts should include a CTA that guides users about the next action. For instance, if you post a special discount for your social media followers, you ought to add the link to the online store where they can redeem it.
Customers tend to trust businesses that have a transparent system. Not only should you share detailed information about your business, but also share accurate pricing and terms and conditions. With this approach, you can earn their trust.
Many customers post reviews about their experiences with a brand. When a satisfied customer posts a positive comment, you should respond to them. However, it’s equally important to respond to negative comments. When you take action quickly to solve their problems, your popularity and sales are likely to elevate.
What’s Hot Right Now?
Being a marketer, you should be well-aware of current market trends. It will help you stay relevant and update your marketing strategy accordingly to reach your audience. On the other hand, if you don’t know which social media marketing channels are the most popular, you may lose customer attention before you know it.
With people confined to home due to COVID, the use of the internet, especially social media has significantly increased. A majority of people interact with their friends and families via social media. The use of digital media and social platforms for business purposes has also become the norm. So, you need to know which platforms are hot these days and which ones are losing popularity.
The trends for 2020 are out now and marketers can develop a strategy for 2021 based on these statistics. Here is a list of top social websites along with the number of active users on these sites.
- Facebook – 2,701 million
- YouTube – 2,000 million
- WhatsApp – Facebook – 2,000 million
- Facebook Messenger – 1,300 million
- WeChat – 1,206 million
- Instagram – 1,158 million
- TikTok – 689 million
If you don’t currently use the aforementioned sites for marketing purposes, it’s time to go through your social marketing strategy again and revise the strategy to adjust to these trends.
Let’s Explore
Whether you are promoting a new business or working with a business that has been in the industry for a long time, you need an effective marketing strategy for social channels.
In social marketing, there are no rules and standards. You can’t follow specific rules that guarantee to meet objectives. The best way to succeed in the social media world is to adopt the trial and error technique. You should come up with a plan to promote the brand and execute it on social channels of your choice. If it brings you the desired results, then it’s great! But there is a good chance that social marketing efforts won’t always prove effective.
Despite your efforts to boost awareness, gain customers, or generate leads, your social strategy won’t always work. This is why it’s important to have a contingency plan. If the first plan doesn’t get results, you should adjust it based on the performance metrics.
The good thing is that there are several options available for marketers. If Facebook doesn’t work, you may turn to LinkedIn for the next campaign. You should set clear objectives, choose the right platform that meets your criteria, and measure performance after the execution of the social marketing plan for making your social marketing campaigns fruitful.
https://sproutsocial.com/insights/social-media-marketing-strategy/
https://www.socialmediaexaminer.com/social-media-marketing-trends-2021-predictions-from-pros/


9.12: Claude Debussy
One of the towering figures of impressionism in music, though he did not approve of that term being applied to his music, is Claude Debussy. A child prodigy and difficult personality, his innovations are seen as the beginnings of modernism in music.
Introduction
Claude-Achille Debussy (22 August 1862–25 March 1918) was a French composer. Along with Maurice Ravel, he was one of the most prominent figures associated withImpressionist music, though he himself disliked the term when applied to his compositions. He was madeChevalier of the Legion of Honour in his native France in 1903. Debussy was among the most influential composers of the late 19th and early 20th centuries, and his use of non-traditional scales and chromaticism influenced many composers who followed.
Debussy’s music is noted for its sensory content and frequent usage of atonality. The prominent French literary style of his period was known as Symbolism, and this movement directly inspired Debussy both as a composer and as an active cultural participant.
Early Life
Debussy was born Achille-Claude Debussy (he later reversed his forenames) on 22 August 1862 in Saint-Germain-en-Laye, France, the oldest of five children. His father, Manuel-Achille Debussy, owned a china shop there; his mother, Victorine Manoury Debussy, was a seamstress. The family moved to Paris in 1867, but in 1870 Debussy’s pregnant mother fled with Claude to his paternal aunt’s home in Cannes to escape the Franco-Prussian War. Debussy began piano lessons there at the age of seven with an Italian violinist in his early 40s named Cerutti; his aunt paid for his lessons. In 1871 he drew the attention of Marie Mauté de Fleurville, who claimed to have been a pupil of Frédéric Chopin. Debussy always believed her, although there is no independent evidence to support her claim. His talents soon became evident, and in 1872, at age ten, Debussy entered the Paris Conservatoire, where he spent the next 11 years. During his time there he studied composition with Ernest Guiraud, music history/theory with Louis-Albert Bourgault-Ducoudray, harmony with Émile Durand, piano with Antoine François Marmontel, organ with César Franck, and solfège with Albert Lavignac, as well as other significant figures of the era. He also became a lifelong friend of fellow student and distinguished pianist Isidor Philipp. After Debussy’s death, many pianists sought Philipp’s advice on playing Debussy’s works.
Musical Development
Debussy was argumentative and experimental from the outset, although clearly talented. He challenged the rigid teaching of the Academy, favoring instead dissonances and intervals that were frowned upon. Like Georges Bizet, he was a brilliant pianist and an outstanding sight reader, who could have had a professional career had he so wished. The pieces he played in public at this time included sonata movements by Beethoven, Schumann andWeber, and Chopin’s Ballade No. 2, a movement from the Piano Concerto No. 1, and the Allegro de concert .
During the summers of 1880, 1881, and 1882, Debussy accompanied Nadezhda von Meck, the wealthy patroness of Pyotr Ilyich Tchaikovsky, as she travelled with her family in Europe. The young composer’s many musical activities during these vacations included playing four-hand pieces with von Meck at the piano, giving music lessons to her children, and performing in private concerts with some of her musician friends. Despite von Meck’s closeness to Tchaikovsky, the Russian master appears to have had minimal effect on Debussy. In September 1880 she sent Debussy’s Danse bohémienne for Tchaikovsky’s perusal. A month later Tchaikovsky wrote back to her: “It is a very pretty piece, but it is much too short. Not a single idea is expressed fully, the form is terribly shriveled, and it lacks unity.” Debussy did not publish the piece, and the manuscript remained in the von Meck family; it was eventually sold to B. Schott’s Sohne in Mainz, and published by them in 1932.
A greater influence was Debussy’s close friendship with Marie-Blanche Vasnier, a singer he met when he began working as an accompanist to earn some money, embarking on an eight-year affair together. She and her husband, Parisian civil servant Henri, gave Debussy emotional and professional support. Henri Vasnier introduced him to the writings of influential French writers of the time, which gave rise to his first songs, settings of poems by Paul Verlaine (the son-in-law of his former teacher Mme. Mauté de Fleurville).
As the winner of the 1884 Prix de Rome with his composition L’enfant prodigue , Debussy received a scholarship to the Académie des Beaux-Arts, which included a four-year residence at the Villa Medici, the French Academy in Rome, to further his studies (1885–1887). According to letters to Marie-Blanche Vasnier, perhaps in part designed to gain her sympathy, he found the artistic atmosphere stifling, the company boorish, the food bad, and the monastic quarters “abominable.” Neither did he delight in Italian opera, as he found the operas of Donizetti andVerdi not to his taste. Debussy was often depressed and unable to compose, but he was inspired by Franz Liszt, whose command of the keyboard he found admirable. In June 1885, Debussy wrote of his desire to follow his own way, saying, “I am sure the Institute would not approve, for, naturally it regards the path which it ordains as the only right one. But there is no help for it! I am too enamoured of my freedom, too fond of my own ideas!”
Debussy finally composed four pieces that were sent to the Academy: the symphonic ode Zuleima (based on a text by Heinrich Heine); the orchestral piece Printemps ; the cantata La damoiselle élue (1887–1888) (which was criticized by the Academy as “bizarre,” although it was the first piece in which the stylistic features of Debussy’s later style began to emerge); and the Fantaisie for piano and orchestra, which was heavily based on César Franck’s music and therefore eventually withdrawn by Debussy. The Academy chided him for “courting the unusual” and hoped for something better from the gifted student. Although Debussy’s works showed the influence of Jules Massenet, Massenet concluded, “He is an enigma.”
During his visits to Bayreuth in 1888–9, Debussy was exposed to Wagnerian opera, which would have a lasting impact on his work. Debussy, like many young musicians of the time, responded positively to Richard Wagner’s sensuousness, mastery of form, and striking harmonies. Wagner’s extroverted emotionalism was not to be Debussy’s way, but the German composer’s influence is evident in La damoiselle élue and the 1889 piece Cinq poèmes de Charles Baudelaire . Other songs of the period, notably the settings of Verlaine— Ariettes oubliées , Trois mélodies , and Fêtes galantes —are all in a more capricious style.
Around this time, Debussy met Erik Satie, who proved a kindred spirit in his experimental approach to composition and to naming his pieces. Both musicians were bohemians during this period, enjoying the same cafe society and struggling to stay afloat financially.
In 1889, at the Exposition Universelle in Paris, Debussy first heard Javanese gamelan music. He incorporated gamelan scales, melodies, rhythms, and ensemble textures into some of his compositions, most notably Pagodes from his piano collection Estampes.
Music Style
Rudolph Reti points out the following features of Debussy’s music, which “established a new concept of tonality in European music”:
- Glittering passages and webs of figurations which distract from occasional absence of tonality;
- Frequent use of parallel chords which are “in essence not harmonies at all, but rather ‘chordal melodies’, enriched unisons,” described by some writers as non-functional harmonies;
- Bitonality, or at least bitonal chords;
- Use of the whole-tone and pentatonic scale;
- Unprepared modulations, “without any harmonic bridge.”
He concludes that Debussy’s achievement was the synthesis of monophonic based “melodic tonality” with harmonies, albeit different from those of “harmonic tonality.”
The application of the term “Impressionist” to Debussy and the music he influenced is a matter of intense debate within academic circles. One side argues that the term is a misnomer, an inappropriate label which Debussy himself opposed. In a letter of 1908 he wrote: “I am trying to do ‘something different’ — an effect of reality . . . what the imbeciles call ‘impressionism’, a term which is as poorly used as possible, particularly by the critics, since they do not hesitate to apply it to [J.M.W.] Turner, the finest creator of mysterious effects in all the world of art.” The opposing side argues that Debussy may have been reacting to unfavorable criticism at the time, and the negativity that critics associated with Impressionism; it could therefore be argued that he would have been pleased with application of the current definition of Impressionism to his music.
Contributors and Attributions
- Claude Debussy. Provided by : Wikipedia. Located at : http://en.Wikipedia.org/wiki/Claude_Debussy . License : CC BY-SA: Attribution-ShareAlike


27.3.9: Java Examples
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Overview
The following examples demonstrate data types, arithmetic operations, and input in Java.
Data Types
// This program demonstrates variables, literal constants, and data types. public class Main { public static void main(String[] args) { int i; double d; String s; boolean b; i =<PHONE_NUMBER>; d = 1.23456789012345; s = "string"; b = true; System.out.println("Integer i = " + i); System.out.println("Double d = " + d); System.out.println("String s = " + s); System.out.println("Boolean b = " + b); } }
Output
Integer i =<PHONE_NUMBER> Double d = 1.23456789012345 String s = string Boolean b = true
Discussion
Each code element represents:
-
//
begins a comment -
public class DataTypes
begins the Data Types program -
{
begins a block of code -
public static void main(String[] args)
begins the main function -
int i
defines an integer variable named i -
;
ends each line of Java code -
double d
defines a double floating-point variable named d -
string s
defines a string variable named s -
boolean b
defines a Boolean variable named b -
i = , d = , s =, b =
assign literal values to the corresponding variables -
System.out.println
calls the standard output print line function -
}
ends a block of code
Arithmetic
// This program demonstrates arithmetic operations. public class Main { public static void main(String[] args) { int a; int b; a = 3; b = 2; System.out.println("a = " + a); System.out.println("b = " + b); System.out.println("a + b = " + (a + b)); System.out.println("a - b = " + (a - b)); System.out.println("a * b = " + a * b); System.out.println("a / b = " + a / b); System.out.println("a % b = " + (a % b)); } }
Output
a = 3 b = 2 a + b = 5 a - b = 1 a * b = 6 a / b = 1 a % b = 1
Discussion
Each new code element represents:
-
+, -, *, /, and %
represent addition, subtraction, multiplication, division, and modulus, respectively.
Temperature
// This program converts an input Fahrenheit temperature to Celsius. import java.util.*; public class Main { private static Scanner input = new Scanner(System.in); public static void main(String[] args) { double fahrenheit; double celsius; System.out.println("Enter Fahrenheit temperature:"); fahrenheit = input.nextDouble(); celsius = (fahrenheit - 32) * 5 / 9; System.out.println(Double.toString(fahrenheit) + "° Fahrenheit is " + celsius + "° Celsius"); } }
Output
Enter Fahrenheit temperature: 100 100° Fahrenheit is 37.7777777777778° Celsius
Discussion
Each new code element represents:
-
private static Scanner input ...
defines an object to read from standard input -
input.nextDouble()
reads input as a double floating-point value
References
- Wikiversity: Computer Programming


5.5: The Kinetic-Molecular Theory
- State the postulates of the kinetic-molecular theory
- Use this theory’s postulates to explain the gas laws
The gas laws that we have seen to this point, as well as the ideal gas equation, are empirical, that is, they have been derived from experimental observations. The mathematical forms of these laws closely describe the macroscopic behavior of most gases at pressures less than about 1 or 2 atm. Although the gas laws describe relationships that have been verified by many experiments, they do not tell us why gases follow these relationships.
The kinetic molecular theory (KMT) is a simple microscopic model that effectively explains the gas laws described in previous modules of this chapter. This theory is based on the following five postulates described here. (Note: The term “molecule” will be used to refer to the individual chemical species that compose the gas, although some gases are composed of atomic species, for example, the noble gases.)
- Gases are composed of molecules that are in continuous motion, travelling in straight lines and changing direction only when they collide with other molecules or with the walls of a container.
- The molecules composing the gas are negligibly small compared to the distances between them.
- The pressure exerted by a gas in a container results from collisions between the gas molecules and the container walls.
- Gas molecules exert no attractive or repulsive forces on each other or the container walls; therefore, their collisions are elastic (do not involve a loss of energy).
- The average kinetic energy of the gas molecules is proportional to the kelvin temperature of the gas.
The test of the KMT and its postulates is its ability to explain and describe the behavior of a gas. The various gas laws can be derived from the assumptions of the KMT, which have led chemists to believe that the assumptions of the theory accurately represent the properties of gas molecules. We will first look at the individual gas laws (Boyle’s, Charles’s, Amontons’s, Avogadro’s, and Dalton’s laws) conceptually to see how the KMT explains them. Then, we will more carefully consider the relationships between molecular masses, speeds, and kinetic energies with temperature, and explain Graham’s law.
The Kinetic-Molecular Theory Explains the Behavior of Gases, Part I
Recalling that gas pressure is exerted by rapidly moving gas molecules and depends directly on the number of molecules hitting a unit area of the wall per unit of time, we see that the KMT conceptually explains the behavior of a gas as follows:
- Amontons’s law. If the temperature is increased, the average speed and kinetic energy of the gas molecules increase. If the volume is held constant, the increased speed of the gas molecules results in more frequent and more forceful collisions with the walls of the container, therefore increasing the pressure (Figure \(\PageIndex{1a}\)).
- Charles’s law. If the temperature of a gas is increased, a constant pressure may be maintained only if the volume occupied by the gas increases. This will result in greater average distances traveled by the molecules to reach the container walls, as well as increased wall surface area. These conditions will decrease both the frequency of molecule-wall collisions and the number of collisions per unit area, the combined effects of which balance the effect of increased collision forces due to the greater kinetic energy at the higher temperature.
- Boyle’s law. If the gas volume is decreased, the container wall area decreases and the molecule-wall collision frequency increases, both of which increase the pressure exerted by the gas (Figure \(\PageIndex{1b}\)).
- Avogadro’s law. At constant pressure and temperature, the frequency and force of molecule-wall collisions are constant. Under such conditions, increasing the number of gaseous molecules will require a proportional increase in the container volume in order to yield a decrease in the number of collisions per unit area to compensate for the increased frequency of collisions (Figure \(\PageIndex{1c}\)).
- Dalton’s Law. Because of the large distances between them, the molecules of one gas in a mixture bombard the container walls with the same frequency whether other gases are present or not, and the total pressure of a gas mixture equals the sum of the (partial) pressures of the individual gases.
Molecular Velocities and Kinetic Energy
The previous discussion showed that the KMT qualitatively explains the behaviors described by the various gas laws. The postulates of this theory may be applied in a more quantitative fashion to derive these individual laws. To do this, we must first look at velocities and kinetic energies of gas molecules, and the temperature of a gas sample.
In a gas sample, individual molecules have widely varying speeds; however, because of the vast number of molecules and collisions involved, the molecular speed distribution and average speed are constant. This molecular speed distribution is known as a Maxwell-Boltzmann distribution, and it depicts the relative numbers of molecules in a bulk sample of gas that possesses a given speed (Figure \(\PageIndex{2}\)).
The kinetic energy (KE) of a particle of mass ( m ) and speed ( u ) is given by:
Expressing mass in kilograms and speed in meters per second will yield energy values in units of joules (J = kg m 2 s –2 ). To deal with a large number of gas molecules, we use averages for both speed and kinetic energy. In the KMT, the root mean square velocity of a particle, u rms , is defined as the square root of the average of the squares of the velocities with n = the number of particles:
The average kinetic energy, KE avg , is then equal to:
The KE avg of a collection of gas molecules is also directly proportional to the temperature of the gas and may be described by the equation:
where R is the gas constant and T is the kelvin temperature. When used in this equation, the appropriate form of the gas constant is 8.314 J mol -1 K -1 (8.314 kg m 2 s – 2 mol -1 K –1 ). These two separate equations for KE avg may be combined and rearranged to yield a relation between molecular speed and temperature:
\[u_\ce{rms}=\sqrt{\dfrac{3RT}{m}} \label{RMS}\]
Calculate the root-mean-square velocity for a nitrogen molecule at 30 °C.
Solution
Convert the temperature into Kelvin:
\[30°C+273=303\: K \nonumber\]
Determine the mass of a nitrogen molecule in kilograms:
\[\mathrm{\dfrac{28.0\cancel{g}}{1\: mol}×\dfrac{1\: kg}{1000\cancel{g}}=0.028\:kg/mol} \nonumber\]
Replace the variables and constants in the root-mean-square velocity formula (Equation \ref{RMS}), replacing Joules with the equivalent kg m 2 s –2 :
\[ \begin{align*} u_\ce{rms} &= \sqrt{\dfrac{3RT}{m}} \\ u_\ce{rms} &=\sqrt{\dfrac{3(8.314\:J/mol\: K)(303\: K)}{(0.028\:kg/mol)}} \\ &=\sqrt{2.70 \times 10^5\:m^2s^{−2}} \\ &= 519\:m/s \end{align*} \]
Calculate the root-mean-square velocity for an oxygen molecule at –23 °C.
- Answer
-
441 m/s
If the temperature of a gas increases, its KE avg increases, more molecules have higher speeds and fewer molecules have lower speeds, and the distribution shifts toward higher speeds overall, that is, to the right. If temperature decreases, KE avg decreases, more molecules have lower speeds and fewer molecules have higher speeds, and the distribution shifts toward lower speeds overall, that is, to the left. This behavior is illustrated for nitrogen gas in Figure \(\PageIndex{3}\).
At a given temperature, all gases have the same KE avg for their molecules. Gases composed of lighter molecules have more high-speed particles and a higher u rms , with a speed distribution that peaks at relatively higher velocities. Gases consisting of heavier molecules have more low-speed particles, a lower u rms , and a speed distribution that peaks at relatively lower velocities. This trend is demonstrated by the data for a series of noble gases shown in Figure \(\PageIndex{4}\).
The gas simulator may be used to examine the effect of temperature on molecular velocities. Examine the simulator’s “energy histograms” (molecular speed distributions) and “species information” (which gives average speed values) for molecules of different masses at various temperatures.
Summary
The kinetic molecular theory is a simple but very effective model that effectively explains ideal gas behavior. The theory assumes that gases consist of widely separated molecules of negligible volume that are in constant motion, colliding elastically with one another and the walls of their container with average velocities determined by their absolute temperatures. The individual molecules of a gas exhibit a range of velocities, the distribution of these velocities being dependent on the temperature of the gas and the mass of its molecules.
Key Equations
- \(u_\ce{rms}=\sqrt{\overline{u^2}}=\sqrt{\dfrac{u^2_1+u^2_2+u^2_3+u^2_4+…}{n}}\)
- \(\mathrm{KE_{avg}}=\dfrac{3}{2}RT\)
- \(u_\ce{rms}=\sqrt{\dfrac{3RT}{m}}\)
Summary
- kinetic molecular theory
- theory based on simple principles and assumptions that effectively explains ideal gas behavior
- root mean square velocity ( u rms )
- measure of average velocity for a group of particles calculated as the square root of the average squared velocity
Contributors and Attributions
-
Paul Flowers (University of North Carolina - Pembroke), Klaus Theopold (University of Delaware) and Richard Langley (Stephen F. Austin State University) with contributing authors. Textbook content produced by OpenStax College is licensed under a Creative Commons Attribution License 4.0 license. Download for free at<EMAIL_ADDRESS>).


7.1: The Multiplication Rule for Counting
Apply the Multiplication Rule for Counting to solve problems.
One of the first bits of mathematical knowledge children learn is how to count objects by pointing to them in turn and saying: “one, two, three, …” That’s a useful skill, but when the number of things that we need to count grows large, that method becomes onerous (or, for very large numbers, impossible for humans to accomplish in a typical human lifespan). So, mathematicians have developed short cuts to counting big numbers. These techniques fall under the mathematical discipline of combinatorics , which is devoted to counting.
Multiplication as a Combinatorial Short Cut
One of the first combinatorial short cuts to counting students learn in school has to do with areas of rectangles. If we have a set of objects to be counted that can be physically arranged into a rectangular shape, then we can use multiplication to do the counting for us. Consider this set of objects (Figure \(\PageIndex{2}\) ):
Certainly we can count them by pointing and running through the numbers, but it’s more efficient to group them (Figure \(\PageIndex{3}\) ).
If we group the balls by 4s, we see that we have 6 groups (or, we can see this arrangement as 4 groups of 6 balls). Since multiplication is repeated addition (i.e., ), we can use this grouping to quickly see that there are 24 balls.
Let’s generalize this idea a little bit. Let’s say that we’re visiting a bakery that offers customized cupcakes. For the cake, we have three choices: vanilla, chocolate, and strawberry. Each cupcake can be topped with one of four types of frosting: vanilla, chocolate, lemon, and strawberry. How many different cupcake combinations are possible? We can think of laying out all the possibilities in a grid, with cake choices defining the rows and frosting choices defining the columns (Figure \(\PageIndex{4}\) ).
Since there are 3 rows (cakes) and 4 columns (frostings), we have possible combinations. This is the reasoning behind the Multiplication Rule for Counting , which is also known as the Fundamental Counting Principle. This rule says that if there are ways to accomplish one task and ways to accomplish a second task, then there are ways to accomplish both tasks. We can tack on additional tasks by multiplying the number of ways to accomplish those tasks to our previous product.
Every card in a standard deck of cards has two identifying characteristics: a suit (clubs, diamonds, hearts, or spades; these are indicated by these symbols, respectively: , , , ) and a rank (ace, 2, 3, 4, 5, 6, 7, 8, 9, 10, jack, queen, and king; the letters A, J, Q, and K are used to represent the words). Each possible pair of suit and rank appears exactly once in the deck. How many cards are in the standard deck?
- Answer
-
Since there are 4 suits and 13 ranks, the number of cards must be
Joe’s Pizza Shack offers pizzas with 4 different types of crust and a choice of 15 toppings. How many different one-topping pizzas can be made at Joe’s?
The University Combinatorics Club has 31 members: 8 seniors, 7 juniors, 5 sophomores, and 11 first-years. How many possible 4-person committees can be formed by selecting 1 member from each class?
- Answer
-
Since we have 8 choices for the senior, 7 choices for the junior, 5 for the sophomore, and 11 for the first-year, there are different ways to fill out the committee.
The menu for Joe’s Pizza Shack offers pizzas with 4 different types of crust and a choice of 15 toppings. Suppose that Joe’s also offers a choice of 3 sauces and 2 cheese blends. How many different one-topping pizzas can be made at Joe’s now?
The standard license plates for vehicles in a certain state consist of 6 characters: 3 letters followed by 3 digits. There are 26 letters in the alphabet and 10 digits (0 through 9) to choose from. How many license plates can be made using this format?
- Answer
-
Since there are 26 different letters and 10 different digits, the total number of possible license plates is .
At a certain college, ID cards are issued to all students, faculty, and staff. These cards have unique ID codes for each person: a letter to indicate the person’s status (S for students, F for faculty, and E for staff), followed by 5 digits and finally 3 letters (these letters can be anything). How many different ID codes can be created using this scheme?
Check Your Understanding
- A website that lets you build custom belts has 18 different buckles and 30 different straps. How many different belts can be made using those materials?
- A chain of chicken restaurants offers a combo that includes your choice of 3 or 5 chicken strips, along with your choice of side dish. If there are 7 side dishes, how many different ways are there to build this combo meal?
- When you flip a coin, there are 2 possible outcomes: heads and tails. Let’s say you flip a coin 10 times, and after each you write down the result of the flip (H for heads, T for tails). How many different results (strings of 10 characters, where each is either an H or a T) are possible?
- A T-shirt company allows shoppers to customize their shirts in several ways. There are 5 sizes, 8 shirt colors, 4 designs, and 5 design colors. How many different shirts can be made?
- Josephine is trying to build her class schedule for next semester. Because of her work schedule, she has only 4 class periods that can work for her, and she must take 4 classes. If there are 15 classes that she could take during the first period, 18 during the second, 12 during the third, and 8 during the fourth, how many different schedules could Josephine build?


19.1C: Hardy-Weinberg Principle of Equilibrium
- Use the Hardy Weinberg equation to calculate allelic and genotypic frequencies in a population
The Hardy-Weinberg principle states that a population’s allele and genotype frequencies will remain constant in the absence of evolutionary mechanisms. Ultimately, the Hardy-Weinberg principle models a population without evolution under the following conditions:
- no mutations
- no immigration/emigration
- no natural selection
- no sexual selection
- a large population
Although no real-world population can satisfy all of these conditions, the principle still offers a useful model for population analysis.
Hardy-Weinberg Equations and Analysis
According to the Hardy-Weinberg principle, the variable p often represents the frequency of a particular allele, usually a dominant one. For example, assume that p represents the frequency of the dominant allele, Y, for yellow pea pods. The variable q represents the frequency of the recessive allele, y, for green pea pods. If p and q are the only two possible alleles for this characteristic, then the sum of the frequencies must add up to 1, or 100 percent. We can also write this as p + q = 1.If the frequency of the Y allele in the population is 0.6, then we know that the frequency of the y allele is 0.4.
From the Hardy-Weinberg principle and the known allele frequencies, we can also infer the frequencies of the genotypes. Since each individual carries two alleles per gene (Y or y), we can predict the frequencies of these genotypes with a chi square. If two alleles are drawn at random from the gene pool, we can determine the probability of each genotype.
In the example, our three genotype possibilities are: pp (YY), producing yellow peas; pq (Yy), also yellow; or qq (yy), producing green peas. The frequency of homozygous pp individuals is p 2 ; the frequency of hereozygous pq individuals is 2pq; and the frequency of homozygous qq individuals is q 2 . If p and q are the only two possible alleles for a given trait in the population, these genotypes frequencies will sum to one: p 2 + 2pq + q 2 = 1.
In our example, the possible genotypes are homozygous dominant (YY), heterozygous (Yy), and homozygous recessive (yy). If we can only observe the phenotypes in the population, then we know only the recessive phenotype (yy). For example, in a garden of 100 pea plants, 86 might have yellow peas and 16 have green peas. We do not know how many are homozygous dominant (Yy) or heterozygous (Yy), but we do know that 16 of them are homozygous recessive (yy).
Therefore, by knowing the recessive phenotype and, thereby, the frequency of that genotype (16 out of 100 individuals or 0.16), we can calculate the number of other genotypes. If q 2 represents the frequency of homozygous recessive plants, then q 2 = 0.16. Therefore, q = 0.4.Because p + q = 1, then 1 – 0.4 = p, and we know that p = 0.6. The frequency of homozygous dominant plants (p 2 ) is (0.6) 2 = 0.36. Out of 100 individuals, there are 36 homozygous dominant (YY) plants. The frequency of heterozygous plants (2pq) is 2(0.6)(0.4) = 0.48. Therefore, 48 out of 100 plants are heterozygous yellow (Yy).
Applications of Hardy-Weinberg
The genetic variation of natural populations is constantly changing from genetic drift, mutation, migration, and natural and sexual selection. The Hardy-Weinberg principle gives scientists a mathematical baseline of a non-evolving population to which they can compare evolving populations. If scientists record allele frequencies over time and then calculate the expected frequencies based on Hardy-Weinberg values, the scientists can hypothesize the mechanisms driving the population’s evolution.
Contributions and Attributions
- OpenStax College, Biology. October 16, 2013. Provided by : OpenStax CNX. Located at : http://cnx.org/content/m44575/latest...ol11448/latest . License : CC BY: Attribution
- Evolution. Provided by : Wikipedia. Located at : en.Wikipedia.org/wiki/Evolution%23Mechanisms . License : CC BY-SA: Attribution-ShareAlike
- gene flow. Provided by : Wikipedia. Located at : en.Wikipedia.org/wiki/gene%20flow . License : CC BY-SA: Attribution-ShareAlike
- Boundless. Provided by : Boundless Learning. Located at : www.boundless.com//biology/de...ic-hitchhiking . License : CC BY-SA: Attribution-ShareAlike
- fitness. Provided by : Wikipedia. Located at : en.Wikipedia.org/wiki/fitness . License : CC BY-SA: Attribution-ShareAlike
- mutation. Provided by : Wiktionary. Located at : en.wiktionary.org/wiki/mutation . License : CC BY-SA: Attribution-ShareAlike
- Natural Selection. Provided by : Wikipedia. Located at : en.Wikipedia.org/wiki/Natural_selection . License : CC BY-SA: Attribution-ShareAlike
- genetic drift. Provided by : Wiktionary. Located at : en.wiktionary.org/wiki/genetic_drift . License : CC BY-SA: Attribution-ShareAlike
- natural selection. Provided by : Wiktionary. Located at : en.wiktionary.org/wiki/natural_selection . License : CC BY-SA: Attribution-ShareAlike
- OpenStax College, Introduction. October 16, 2013. Provided by : OpenStax CNX. Located at : http://cnx.org/content/m44575/latest...e_19_00_01.jpg . License : CC BY: Attribution
- Mutation and selection diagram. Provided by : Wikipedia. Located at : en.Wikipedia.org/wiki/File:Mu...on_diagram.svg . License : CC BY-SA: Attribution-ShareAlike
- Random sampling genetic drift. Provided by : Wikipedia. Located at : en.Wikipedia.org/wiki/File:Ra...etic_drift.svg . License : CC BY-SA: Attribution-ShareAlike
- OpenStax College, Biology. October 16, 2013. Provided by : OpenStax CNX. Located at : http://cnx.org/content/m44582/latest...ol11448/latest . License : CC BY: Attribution
- allele. Provided by : Wiktionary. Located at : en.wiktionary.org/wiki/allele . License : CC BY-SA: Attribution-ShareAlike
- Population Genetics. Provided by : Wikpedia. Located at : en.Wikipedia.org/wiki/Population_genetics . License : CC BY-SA: Attribution-ShareAlike
- founder effect. Provided by : Wiktionary. Located at : en.wiktionary.org/wiki/founder_effect . License : CC BY-SA: Attribution-ShareAlike
- gene pool. Provided by : Wiktionary. Located at : en.wiktionary.org/wiki/gene_pool . License : CC BY-SA: Attribution-ShareAlike
- OpenStax College, Introduction. October 16, 2013. Provided by : OpenStax CNX. Located at : http://cnx.org/content/m44575/latest...e_19_00_01.jpg . License : CC BY: Attribution
- Mutation and selection diagram. Provided by : Wikipedia. Located at : en.Wikipedia.org/wiki/File:Mu...on_diagram.svg . License : CC BY-SA: Attribution-ShareAlike
- Random sampling genetic drift. Provided by : Wikipedia. Located at : en.Wikipedia.org/wiki/File:Ra...etic_drift.svg . License : CC BY-SA: Attribution-ShareAlike
- ABO Blood type. Provided by : Wikimedia. Located at : en.Wikipedia.org/wiki/ABO_blo...blood_type.svg . License : Public Domain: No Known Copyright
- Founder effect. Provided by : Wikipedia. Located at : en.Wikipedia.org/wiki/File:Founder_effect.png . License : Public Domain: No Known Copyright
- OpenStax College, Biology. October 16, 2013. Provided by : OpenStax CNX. Located at : http://cnx.org/content/m44582/latest...ol11448/latest . License : CC BY: Attribution
- genotype. Provided by : Wiktionary. Located at : en.wiktionary.org/wiki/genotype . License : CC BY-SA: Attribution-ShareAlike
- phenotype. Provided by : Wiktionary. Located at : en.wiktionary.org/wiki/phenotype . License : CC BY-SA: Attribution-ShareAlike
- OpenStax College, Introduction. October 16, 2013. Provided by : OpenStax CNX. Located at : http://cnx.org/content/m44575/latest...e_19_00_01.jpg . License : CC BY: Attribution
- Mutation and selection diagram. Provided by : Wikipedia. Located at : en.Wikipedia.org/wiki/File:Mu...on_diagram.svg . License : CC BY-SA: Attribution-ShareAlike
- Random sampling genetic drift. Provided by : Wikipedia. Located at : en.Wikipedia.org/wiki/File:Ra...etic_drift.svg . License : CC BY-SA: Attribution-ShareAlike
- ABO Blood type. Provided by : Wikimedia. Located at : en.Wikipedia.org/wiki/ABO_blo...blood_type.svg . License : Public Domain: No Known Copyright
- Founder effect. Provided by : Wikipedia. Located at : en.Wikipedia.org/wiki/File:Founder_effect.png . License : Public Domain: No Known Copyright
- OpenStax College, Population Evolution. October 16, 2013. Provided by : OpenStax CNX. Located at : http://cnx.org/content/m44582/latest...e_19_01_01.png . License : CC BY: Attribution
- Hardy-Weinberg. Provided by : Wikimedia. Located at : en.Wikipedia.org/wiki/Hardy-W...y-Weinberg.svg . License : CC BY-SA: Attribution-ShareAlike
Key Points
- The Hardy-Weinberg principle assumes that in a given population, the population is large and is not experiencing mutation, migration, natural selection, or sexual selection.
- The frequency of alleles in a population can be represented by p + q = 1, with p equal to the frequency of the dominant allele and q equal to the frequency of the recessive allele.
- The frequency of genotypes in a population can be represented by p 2 +2pq+q 2 = 1, with p 2 equal to the frequency of the homozygous dominant genotype, 2pq equal to the frequency of the heterozygous genotype, and q 2 equal to the frequency of the recessive genotype.
- The frequency of alleles can be estimated by calculating the frequency of the recessive genotype, then calculating the square root of that frequency in order to determine the frequency of the recessive allele.
Key Terms
- genotype : the combination of alleles, situated on corresponding chromosomes, that determines a specific trait of an individual, such as “Aa” or “aa”
- phenotype : the appearance of an organism based on a multifactorial combination of genetic traits and environmental factors, especially used in pedigrees