Gradient of a distance function Let P01a, b, c2 be a fixed point in _3 and let d1x, y, z2 be the distance between P0 and a variable point P1x, y, z2. a. Compute _d1x, y, z2. b. Show that _d1x, y, z2 points in the direction from P0 to P and has magnitude 1 for all 1x, y, z2. c. Describe the level surfaces of d and give the direction of _d1x, y, z2 relative to the level surfaces of d. d. Discuss lim PSP0 _d1x, y, z2.
Notes for the week of 4/11 Management 300 Key Terms: Management – Guiding employees to complete their various roles and tasks. Leadership – The ability to influence employees to voluntarily pursue organizational goals. Managerial Leadership – The process of influencing others to understand and agree about what needs to be done and the process of facilitating individual and collective efforts to accomplish shared objectives. Authority – The right to perform or command that comes with a given job. Power – The extent to which a person is able to influence others so they respond to orders. Readiness – The extent to which a follower possesses the ability, skills, and willingness to complete a task. Management – Guiding employees to complete their various roles and tasks Providing reward and punishments contingent on performance Best stable situations Planning Organizi8ng Directing Controlling Leadership – The ability to influence employees to voluntarily pursue organizational goals Can and should be present at all levels in an effective organization Roles: Passionate enthusiast Visionary Cheerleader Coach Investing trust and love Managers vs. leaders Managers A. Coping with complexity B. Planning, organizing, directing, and controlling C. Executing plans and delivering goods and services D. Being conscientious E. Acting responsibly F. Putting customers first Leaders A. Coping with change B. Being visionary C. Being inspiring, setting the tone and articulating the vision D. Managing people E. Being inspirational / charismatic F. Acting decisively G. Putting people first – responding to and acting for followers Managerial Leadership – The process of influencing others to understand and agree about what needs to be done and the process of facilitating individual and collective efforts to accomplish shared objectives. Authority – The right to perform or command that comes with a given job. Power – The extent to which a person is able to influence others so they respond to orders. Personalized power – power directed at helping oneself Socialized power – Power directed toward helping others Legitimate power – results from formal positions within the organization Reward power – results from authority to reward their subordination Coercive power – results form an authority to punish their subordinates Expert power – results from expertise Sophisticated knowledge develops over time Results from specialized information Mundane knowledge acquired through experience Referant power – derived from personal attraction Relationship or connection power – results from social alliances or influence Information power – access to and control over important information Generic influence tactics Rational persuasion – using reason, logic, or facts Inspirational appeals – building enthusiasm or confidence by appealing to other’s emotions, ideals, or values. Consultation – getting other to participate in the decisions Ingratiating tactics – acting humble or friendly or making someone feel good or important before they make a decision Personal appeals – drawing on friendship and loyalty Exchange tactics – swapping favors Coalition tactics – building support by amassing followers Pressure tactics – using demands threats or intimidation Legitimating tactics – basing requests on one’s authority, organizational rules and politics, or implied support from superiors Possible responses to generic influence tactics: A. Enthusiastic commitment B. Grudging compliance C. Outright resistance 5 approaches to leadership 1. Trait approaches 2. Behavioral approaches 3. Contingency approaches 4. Fullrange approach 5. Four additional perspectives Trait approach – an attempt to identify the distinctive characteristics that account for the effectiveness of leaders Organizations may incorporate personality and leadership traits into selection and promotion Aspiring leaders should invest in cultivating adaptive leadership traits Traits play a central role in how people view/perceive leaders Key positive leadership traits (Ralph Stogidll’s) 1. Dominance 2. Intelligence 3. Selfconfidence 4. High energy 5. Taskrelevant knowledge Kouzes and Posner’s five traits 1. Honesty 2. Competent 3. Forwardlooking 4. Inspiring 5. Intelligent Bass and Bass’s 6 traits 1. Task competence – Intelligence, knowledge, problemsolving skills 2. Interpersonal competence – ability to communicate and ability to demonstrate caring and empathy 3. Intuition 4. Traits of character – conscientiousness, discipline, moral reasoning, integrity, honesty 5. Biophysical traits – physical fitness, hardiness, energy level 6. Personal traits – selfconfidence, sociability, selfmonitoring, extraversion, self regulating, selfefficiency. Gender studies Women tend to have more leadership traits than men, but hold fewer leadership positions Old assumption: Women do not want to aspire to top positions New thinking on women in management careers Women have traits that make them better than men in some instances and vice versa Areas where women score higher than men Producing high quality work Goalsetting Mentoring Teamwork/being collaborative Mentoring Teamwork/being collaborative Seeking less personal glory Being motivated less by selfinterests Less turf conscious Recognizing trends Generating new ideas Engaging in participative management Social leadership Women tend to be more unwilling to complete or sacrifice Kids and family are too important Modesty Women tend to give credit to others rather than taking it for themselves Lack of a mentor Less likely than males to have access to a supportive mentor because they can be excluded from important social networks Starting out lower and more likely to quit Because women start lower, they lack significant general management experience, and have not been around long enough to be selected. Project GLOBE (Global Leadership and Organizational Behavior Effectiveness) Ongoing attempt to develop an empirically based theory to describe understand and predict the impact of specific cultural variables on leadership and organizational processes and the effectiveness of these processes Surveyed 17000middle managers from 951 organizations across 62 countries Developed a list of universally liked and disliked leader attributes The behavioral approach – Behavioral leadership – approach attempt to determine the distinctive styles used by effective leaders Leadership style – the combination of traits, skills, and behaviors that leaders use to interact with others University of Michigan’s leadership model Job centered behavior – close attention to job and work procedures with the principal concerns being achieving production efficiency, keeping costs down and meeting schedules Employee – centered behavior – managers pay more attention to employee satisfaction and making work groups cohesive Ohio State’s leadership model Initiating structure – focuses on getting things done and performing behavior that organizes and defines what group members should be doing Consideration – focuses on building trust, supporting feelings, and establishing a warm friendly, supportive climate Peter Drucker’s Tips for improving leadership effectiveness 1. Determine what needs to be done 2. Determine the right thing to do for the welfare of the entire enterprise or organization 3. Develop action plans that specify desired results, probable restraints, future revisions, check0ins points, and implications for how one should spend his or her time 4. Take responsibility for decisions 5. Take responsibility for communication action plans and give people the information they need to get the job done 6. Focus on opportunities rather than problems. Do not sweep problems under the rug and treat change as an opportunity rather than as a threat 7. Run productive meetings. Different types of meetings require different forms of preparations and different results. Prepare accordingly. 8. Think and say “we” rather than “I” consider the needs an opportunities of the organization before thinking of your opportunities and needs 9. Listen first speak last Contingency leadership model 2 leadership orientations Diagnosed with the least preferred coworker scale up 1. Taskoriented – concerned with the task as hand (best in high or low control situations) 2. Relationshiporiented – concerned with people (best in midlevel control situations) Three dimensions of situational control (how much influence do you have in the situation) Diagnosed by answering the questions in parenthesis 1. Leadermember relations – (Do employees accept me) 2. Task structure – (Do employees know exactly what to do) 3. Position power – (Do I have power to reward or punish) PathGoal leadership Model Pathgoal leadership model – holds that the effective leader makes available to followers desirable rewards in the workplace and increases their motivation by clarifying the paths or behavior in the workplace and increase their motivation by clarifying the paths or behavior, that will help them achieve those goals providing them with support Recommendations: The meaningful rewards to goalaccomplishment Promote intrinsic motivation Through empowerment Share leadership Key lessons Use more than one leadership style Help employees achieve their goals Modify leadership style to fit employees and task characteristics Pathgoal leadership 1. Leader behaviors a. Pathgoal clarifying (directive) b. Achievementoriented c. Work facilitation d. Supportive e. Interaction facilitation f. Grouporiented decision making (participative) g. Representation and networking h. Valuebased 2. Employee characteristics a. Locus of control b. Task ability c. Need for achievement d. Experience e. Need for pathgoal clarity 3. Environmental factors a. Task structure b. Work group dynamics 4. Leadership effectiveness a. Employee motivation b. Employee satisfaction c. Employee performance d. Leader acceptance e. Interaction facilitation f. Workunit performance Situational leadership theory – leadership behavior reflects how leaders should adjust their leadership style according to the readiness of the followers Readiness – The extent to which a follower possesses the ability, skills, and willingness to complete a task. Situational leadership in action 5 steps to applying situational leadership theory 1. Identify important outcomes 2. Identify relevant leadership behavior 3. Identify situational condition 4. Match leadership to the conditions at hand 5. Determine how to make the match The fullrange model Fullrange leadership – leadership behaviors vary along a full range of leadership styles Fullrange model: transactional leadership Transactional leadership – focuses on clarifying employees’ roles and task requirements and providing rewards and punishments that are contingent on performance Key management behaviors: Setting goals and monitoring progress Best is stable situations Motivates people to do ordinary things Prerequisite to any effective leadership style Transformational leadership: Transforms employees to pursue organizational goals over selfinterests Good in rapidly changing situations Motivates people to do exceptional things Encourage higher levels of intrinsic motivation, trust, commitment, and loyalty Excite passion, inspiring passion Factors that can influence transformational leaders 1. Individual characteristics a. Best characteristics include: extroverted, agreeable, proactive, open to change 2. Organizational culture a. Best characteristics include: adaptive and flexible 4 key behaviors of transformational leaders 1. Inspirational motivation – “Let me share a vision that transcends us all” i. Charismatic leadership using interpersonal attraction to inspire motivation, acceptance, and support 2. Idealize influence – “We are here to do the right thing” i. Inspire trust by acting ethically with consistency and integrity 3. Individualize consideration – “You have the opportunity here to grow and excel” i. Actively encourage employees to grow by giving them challenging work and more responsibility ii. Act as mentors 4. Provide intellectual stimulation – “Let me describe the great challenges we can conquer together” i. Clearly communicate the organization’s strengths, weaknesses, opportunities, and threats ii. Encourages employees to view problems as personal challenges and develop a sense of purpose Positive outcomes of transformational leadership 1. Greater organizational effectiveness 2. Greater leadership effectiveness and employee job satisfaction 3. More employee identification with their leaders and with their immediate work group 4. Greater commitment to organizational change 5. Higher levels of intrinsic motivation, group cohesion, work engagement, setting of goals consistent with those of the leader, and proactive behavior Key considerations It can improve results for both individuals and groups It can be used to train employees any level It requires ethical leaders Things managers should do to be effective transformational leaders Employ a code of ethics – the company should create and enforce a clearly stated code and ethics Choose the right people – recruit, select, and promote people who display ethical behavior Make performance expectations reflect employees treatment – develop performance expectations around the treatment of employees these expectations can be assessed in the performanceappraisal process Reward high moral conduct identify, reward, and publicly praise employees, exemplify high moral conduct. 4 additional perspectives 1. Leadermember exchange (LMX) – emphasizes that leaders have different sorts of relationships with different subordinates a. Ingroup exchange (Trust, respect, liking, sense of common fate) i. Partnership relationships b. Outgroup exchange (no trust and no respect) i. Overseen relationships 2. Servant leaders a. Focus on providing increased service to others – meeting the goals of both followers and the organization – rather than to one’s self b. Require a longterm transformational approach to life and work 3. Leadership a. Can involve onetoone, onetomany, withingroup, betweengroup, and collective interactions via information technology i. Ebusiness – interaction within and between organizations ii. Ecommerce – interaction with customers and suppliers 4. Shared leadership a. Leaders and followers need each other, and the quality of the relationship determines how they behave b. Research show that followers seek and admire leaders who create feelings of significance, community, and excitement c. Followers vary in compliance from helpers (most compliant) to independents (least compliant) Characteristics of servant leaders Focus on listening Ability to empathize with other’s feelings Focus on healing suffering Selfawareness of strengths and weaknesses Use of persuasion rather than positional authority to influence others Broadbased conceptual thinking Ability to foresee future outcomes Belief they are stewards of their employees and resources Commitment to the growth of people Drive to build community within and outside the organization