Linear Inequalities Review and Graphing Practice

Linear Inequalities Review and Graphing Practice
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Linear inequalities through a series of exercises involving determining solutions, graphing, and writing inequalities based on given scenarios. Practice your skills and deepen your understanding of linear inequalities with these guided examples. Discover how to represent relationships between variables in a clear and visual way.

  • Linear Inequalities
  • Graphing
  • Solutions
  • Writing Inequalities
  • Practice

Uploaded on Feb 27, 2025 | 0 Views


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  1. 'Argyll and Bute Headteachers: Focus on Leadership' Inveraray, 3rdSept. 2015 The Personal Qualities (Personality Traits, Dispositions and Attributes) Associated with High- Performance Leadership of Schools* Clive Dimmock University of Glasgow clive.dimmock@glasgow.ac.uk * based on Dimmock, C. (2012). Leadership, Capacity building and School Improvement. London: Routledge.

  2. Aims of session to address 2 questions 1. What do school leaders need in terms of personality traits, dispositions, and attributes to be high performing - as opposed to mediocre - leaders? 2. Are successful leaders born or made? The answer to Q1. helps us answer Q2. What are your own experiences and ideas in addressing the above questions?

  3. Structure of session Definition of high-performing leadership Background the nature of headteachers work Definition of Qualities personality traits, dispositions and attributes Introduction to the research of - - Zaccaro on personality and leadership - Cave and Wilkinson on basic and higher-order abilities of leadership - McKinsey & Co. on successful leader traits, dispositions and attributes Are HPLs born or made? Q & A

  4. Definition of high-performance leadership (HPL) HPL is a social influence process guided by moral purpose that builds capacity by optimizing human and other resources in successfully achieving shared and desired individual and organisational goals Dimmock, C. (2012). Leadership, capacity building and school improvement. London: Routledge.

  5. Background to study of leadership sociological more than psychological Research and literature in Educational leadership in last few decades dominated by sociological perspectives the field of educational leadership had its roots in sociological theory and this is still perpetuated Yet the psychological and socio-psychological factors, personality and individual characteristics that underlie much of what we do, think and practice as leaders, have been relatively ignored Exceptions personality tests - 16 PF Inventory, Myers-Briggs etc. and work on emotional intelligence (eg. Goleman et al.)

  6. Nature of head-teachers work Logistics Huge number of interactions each day Fragmented and interrupted day, multi-tasking Networking with large and diverse number of interest groups and individuals teachers, students, parents, LAs, peer heads, unions, universities, business, police, etc. Large array of tasks from sorting personal problems, departmental issues, whole school policies and goals, accountabilities, quality performance and social justice Decision making Deciding priorities and use of time Deciding what requires in-depth knowledge as opposed to just awareness Cognitive dexterity and flexibility to switch quickly Memorising and ability to recall relevant facts and details of people, events, problems Processing experiential learning and making best judgements tacit knowledge Right timing is crucial immediate, delayed/considered, or no decision

  7. Personality Traits, Dispositions and Attributes Definitions No clearly agreed definitions of/distinctions between these key terms My definitions are below, boundaries are blurred, and I argue that all three interact Personality traits or characteristics mainly genetic at core, pre-ordain our ways of acting, reacting and interacting, changeable only at margins Dispositions determine the formation of deeply-held beliefs and values, formed from interaction of personality and a mix of personal experiences and social influences change is possible Attributes knowledge, skills, surface beliefs wholly socially acquired, influenced by education, our peer group, and life experiences most malleable of all (Dimmock, 2012)

  8. Personality traits that impact on leadership The Big Five personality factors influencing successful leadership Emotional stability (inc. emotional intelligence) Extroversion outgoing, sociable Openness to experience welcoming new challenges, willingness to take risks Agreeableness pleasing, likeable, willingness to engage Conscientiousness careful and persistent in attending to tasks, wanting to do one s best (Zaccaro et. al)

  9. According to Zaccaro et al. successful leaderspossess and demonstrate higher levels of - social and emotional intelligence (Goleman) good listeners, understand others, good interpersonal relations, sense of humour (psychological traits) self-efficacy, confidence, social engagement, optimism, proactivity, internal locus of control, and nurturance (part psychological traits dispositions) motivation high on need for dominance and power and/or responsibility and achievement needs (but not affiliation needs); passion about their work, enthusiasm, commitment, persistence, resilience, industriousness (part psychological traits part dispositions) cognitive abilities high on intelligence, greater problem-solving expertise, flexible and creative thinking capacity (mostly psychological traits with some elements of attributes) domain-specific knowledge and skills relating to education, leadership and curriculum (attributes).

  10. Emotional Intelligence (EI) Daniel Goleman People who can solve problems involving emotions, or problems requiring the use of emotions, can better: Communicate effectively with staff and clients Identify and respond to others' emotions Manage their own and others' emotional reactions Be less likely to suffer negative emotions Make them more likely to achieve goals. These personality characteristics make EI necessary but not sufficient conditions for high-performing leadership.

  11. Cave and Wilkinson Study 1990s English Headteachers Experiential Evidenceon the qualities needed for H-PL Group of Heads met over extended time to consider: What knowledge and capabilities are needed for high effectiveness in the role?

  12. IDENTIFIED 2 LEVELS OF, AND 3 COMPONENTS TO, KNOWLEDGE AND SKILLS 2 levels of knowledge and skills BASIC and HIGHER-ORDER BASIC 1. Professional knowledge from literature, programs etc. social, legal, educational (curriculum, pedagogy, assessment) Skills and techniques from formal training, mentoring and most importantly, from practical experience on the job (tacit knowledge) 2. Nb. i) A lot of the above are attributes that can be acquired...BUT.. ii) We know some heads have higher propensity to learn from tacit knowledge than others which is (f) personality (intelligence, cognitive processing and insight) and dispositions which suggests HIGHER-ORDER CAPACITIES

  13. HIGHER-ORDER CAPACITIES These are what really distinguish high-performing leaders generally cognitive abilities (and some dispositions eg values) that promote and optimize the effective use of basic level knowledge and skills 4 higher-order capacities (largely personality traits/dispositions): - Reading situations receptive, evaluative, timeliness - Making balanced judgements decision making, whether to take action and what action, combination of rational and intuitive - Having good intuition hunch plus stored memory and ordered experience - Possessing political-social acumen skills to bargain, persuade, manage information, networking etc. Remember Zaccaro s research also suggests the following personality traits/dispositions are crucial confidence, optimism, resilience and reflection.

  14. Main argument 1.Higher-order capacities are what distinguishes high- performing leaders from mediocre; they not only enable leaders to apply their basic knowledge and skills more effectively, but add a higher dimension of insights and intuition to how they work 2.Tacit knowledge accounts for 90% plus of what heads learn to do and how they do it - higher-order capacities enable heads to more effectively learn and apply the lessons from practical experience it makes them better leaders 3. Higher-order capacities are mostly shaped by personality characteristics and dispositions

  15. McKinsey & Co. (2010) The Leadership Premium - recently identified traits, dispositions and attributes of successful leaders focused on student achievement, student welfare ahead of politics (dispositions) resilient and persistent in goals, but adaptable to people and context (personality traits and dispositions) willing to develop a deep understanding of people and context (personality traits/dispositions) willing to take risks, and challenge accepted beliefs and behaviours (personality traits/dispositions) self-aware and willing to learn (personality traits and dispositions) optimistic and enthusiastic (personality traits and dispositions).

  16. Future research We need to - combine studies of personality traits that is, cognitive abilities, motives, social skills, expertise and problem solving skills look at patterns and integrations of multiple traits and dispositions distinguish those traits, dispositions and attributes that are not malleable from those that are bounded/influenced by situational contexts understand how combinations of malleable/fixed traits/dispositions and attributes connect to fit with type of school and context.

  17. Question Undertaking a self assessment 1. Which personality traits, dispositions and attributes do you feel you possess sufficiently to enable you to be a high-performing leader? 2. Which do you feel you particularly need to develop?

  18. Are leaders born or made? Nicholson (2007) London Business School the most important pre-requisite for leadership is DESIRE TO LEAD 3 types of people, those - with strong drive to lead irrespective of situation, or field small minority my hunch - maybe c.5% or less? with no desire to be leaders (content, unambitious, priority to family, hobbies etc)- large proportion maybe 45% to 50%? persuadable to be leaders, but only under specific conditions (eg. where they feel a good match with school, salary, location etc.) maybe 40 to 50%? Cont .

  19. Drive is a basic personality trait, therefore mostly genetic, rather than socially influenced; to the extent that drive is a personality trait/disposition, it can be (marginally) changed Group 1 (above) needs few inducements to seek promotion to the top echelons of leadership Group 2 some may be potentially good leaders, but they have eschewed leadership in preference for other life goals Group 3 have some drive and propensity for leadership but need encouragement and right opportunities, training and experiences to be committed to leadership. They are usually particular about the level of leadership to which they aspire HoD, VP etc. and the context city/rural, large/small school SES catchment etc

  20. Besides Drive, good leaders need Capability DRIVE + CAPABILITY= HPL Capability = the right person, doing the right things, in the right place 2 things follow high performing leaders read situations well, and how they change over time have willingness, resilience, values and abilities to complete what needs to be done. When these are all aligned = high-performing leaders

  21. Nicholson concludes BORN or MADE? Many leadership capabilities are inborn (eg. core personality traits inc. drive ) They are often mediated by dispositions and values (socially acquired in part) The rest (attributes) is learned provided there is motivation ( drive ) and willingness Hence a lot of our leadership attributes (largely learnt) depend on, and are programmed by, our personality and dispositions eg. seeking knowledge, finding out the facts of a situation, furthering experience etc. The less inborn an individual s leadership capabilities, the more the aspirant leader needs to develop and rely on dispositions and attributes to compensate but higher-order capacities will be harder to develop

  22. Conclusions 1. Outstanding leaders possess higher-order capacities and personal/social skills that raise them above the mediocre, and enable them to successfully manage complex situations in which poor and mediocre leaders flounder 2. We can explain the effectiveness of high performing leaders by considering the key personality traits, dispositions and attributes that differentiate them from the rest 3. While the relationships between personality traits, dispositions and attributes have multiple iterations, personality traits combine with social factors to determine dispositions, and both of these in turn exert powerful effects on attributes 4. Serving head teachers can improve their performance levels by focusing on developing their higher-order capacities, personal (including cognitive) and interpersonal skills which improve their tacit knowledge (practical wisdom) Cont ..

  23. Cont 5. In future, spotting, nurturing, training and selecting leaders MUST take greater account of the qualities (personality traits, dispositions and attributes) required of potential high-performing leaders 6. We also need to get smarter in how we train leaders to improve their learning through tacit knowledge 7. Greater use of system leadership is needed where outstanding leaders at headteacher-, middle- and teacher-levels are deployed to other schools across local, regional and national boundaries ..to maximise benefits to all students.

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