Reducing Measurement Error to Increase the Statistical Reliability of Academic Performance Measures

As previously noted, the extent of measurable learning loss related to the COVID 19  pandemic is undeniable and requires new strategies, approaches, and thinking. Fortunately, to accelerate progress for the students who have fallen furthest behind—students with special needs and ELLs—Director Schneider of the Institute of Education Sciences (IES) is advocating for a widescale overhaul of education research, data collection, and analysis. Accountability data that reliably measure school performance is essential for identifying the schools that most need support. However, measurement error impacts the random differences between students’ true abilities and their test scores and thereby can impact a school’s true performance. 

 The Every Student Succeeds Act (ESSA, 2015) requires states to designate schools with low-performing student subgroups for Targeted Support and Improvement (TSI) or Additional Targeted Support and Improvement (ATSI). Measurement error is more likely and impactful to small districts, schools, or student subgroups, whereby random factors affecting fewer students create an outsized impact on the reported average score. Ensuring the reliability of school performance measures is incumbent upon state and local education agencies that must identify and provide support to the districts, schools, and students that need it.

Bayesian Interpretation of Estimates (BASIE) is an innovative framework for using an evidence-based Bayesian approach to interpret traditional impact estimates (Deke, Finucane, & Thal, 2022). Using the BASIE framework, a study of how the Pennsylvania Department of Education (PDE) identifies its schools for TSI and ATSI used Bayesian stabilization to improve the reliability of subgroup proficiency measures. The Regional Education Laboratory Mid-Atlantic study team (Farrow, Starling, & Gill, 2023) applied two statistical models to subgroup-specific proficiency rates. One model aligned with PDE’s accountability rules for ATSI.  The other model aligned with rules for TSI. To assess whether stabilization increased the statistical reliability, the results of the stabilization models were then compared with the un-stabilized proficiency rates that are currently used in accountability calculations.

 A goal of statistical analysis should be is to reduce measurement error and thereby increase the statistical reliability of academic performance measures.  Therefore, the BASIE framework shows promise.  In the 2023 study, Bayesian stabilization improved statistical reliability, showing similar variation across subgroup sizes, indicating more reliable results by reflecting less measurement error. Therefore, as the Regional Education Laboratory Mid-Atlantic study team concluded, utilization of Bayesian stabilization could allow for inclusion of subgroup sizes under 20 because stabilization showed proficiency rates for subgroups with 10–19 students varied less than un-stabilized proficiency rates for subgroups with 20–29 students.

 The 2023 Regional Education Laboratory Mid-Atlantic study suggests that stabilized data using an evidence-based Bayesian approach to interpret traditional impact estimates meets the current reliability requirements. More studies should further test this hypothesis. Improving the reliability of proficiency rates will absolutely benefit interpretation of subgroup proficiency measures and thereby optimize the identification of schools that most need support.

 

To cite:

Anderson, C.J. (February 28, 2023). Reducing measurement error to increase the statistical

            reliability of academic performance measures. [Web log post] Retrieved from

            http://www.ucan-cja.blogspot.com/

 

 

References

Anderson, C.J. (July 31, 2021). Generalizing virtual strategies that worked and planning for

accelerated learning. [Web log post] Retrieved from http://www.ucan-cja.blogspot.com/

 

Anderson, C.J. (January 31, 2023). Understanding the Needs of Struggling Learners 

            in Relation to Post COVID Accelerated Learning Goals. [Web log post] Retrieved from

            http://www.ucan-cja.blogspot.com/

Deke, J., Finucane, M., Thal, D. (2022) The BASIE (BAyeSian Interpretation of Estimates)

            framework for interpreting findings from impact evaluations: A practical guide for

            education researchers. U.S. Department of Education, Institute of Education

            Sciences, National Center for Education Evaluation and Regional Assistance

 

Farrow, L. Starling, J. & Gill B. (2023). Stabilizing subgroup proficiency results to improve the

             identification of low-performing schools. Regional Education Laboratory (REL)

            Mid-Atlantic study team. Retrieved from

            https://ies.ed.gov/ncee/rel/Products/Publication/106926

 

Understanding the Needs of Struggling Learners in Relation to Post COVID Accelerated Learning Goals

 Historically, the very nature of specially designed instruction requires embracing the reality that a diverse learner responds better to differentiated opportunities to access the curriculum.  A goal of No Child Left Behind (NCLB, 2001) was to wipe out ‘below basic,’ which was the lowest possible score on the National Assessment of Educational Progress (NAEP) educational systems collected data to prove the efficacy of this endeavor. Yet, NCLB and subsequently the Every Student Succeeds Act (ESSA, 2015) are simply the latest reauthorizations of the Elementary and Secondary Education Act (1965) that sought to address the achievement gap with the goal to make every student a proficient reader, writer, science learner, and mathematician.   

The extent of measurable learning loss related to the COVID 19 pandemic is undeniable and requires new strategies, approaches, and thinking. Institute of Education Sciences (IES) Director Mark Schneider is advocating for a widescale overhaul of education research and data to accelerate progress for the students who have fallen furthest behind—students with special needs and ELLs.  Leveraging Evidence to Accelerate Recovery Nationwide (LEARN), is one of three new research initiatives geared to pandemic recovery in schools.  It is a $7 million project launched by the IES, the U.S. Department of Education’s primary research arm, to identify and quickly scale up effective practices to help students recover academically from pandemic disruptions.

Certainly, reform is necessary in how teaching and learning research is conducted, educational data is collected, and how research is analyzed.  Therefore, perhaps this is the best time to demand educators and educational researchers widely adopt the Model Code of Ethics for Educators (MCEE).  Given the purpose of the Model Code of Ethics for Educators (MCEE): To serve as a shared ethical guide for future and current educators who are faced with the complexities of P-12 education; who can be righteously offended?

While that opportunity to form consensus on the need to integrate the MCEE with LEARN begins to brew, let’s revisit the ethical need to do no harm to our students.   Post COVID, most educational leaders and teachers struggle with whether their students will benefit more from accelerated learning rather than remediation. As predicted by Mercanti-Anthony (2021),  the broad assumption that students will need to catch up due to learning loss resulted in schools initially defaulting to remediation strategies. However analysis of research from the Fordham Institute, which suggested that the focus should instead be on accelerated learning, in many cases proved prophetic.

The Acceleration Imperative is an open-source, evidence-based document designed to promote four key principles:

1.   Many students—especially the youngest children in the highest-need schools—will require extra help coming out of the pandemic, particularly in the form of extended learning time, high-dosage tutoring, and expanded mental-health supports.
2.  That extra help should complement, but cannot replace, what students need from schools’ core programs, such as high-quality curricula and positive school cultures.
3. To make up for what’s been lost, we need to focus on acceleration, not remediation. That means devoting the bulk of classroom time to challenging instruction at grade-level or higher, and giving all students access to a rich, high-quality curriculum in English language arts, mathematics, social studies, science, the arts, and more.
4. Decisions should be guided by high-quality research evidence whenever possible.

Created with input from dozens of current and former chief academic officers, scholars, and others with deep expertise and experience in high-performing, high-poverty elementary schools, The Acceleration Imperative is designed to be an organic document.  As such, it will continuously evolve.  You are invited to download and use The Acceleration Imperative as a starting point or as an aid for your own planning purposes. Since The Acceleration Imperative is in the public domain, with no rights reserved, you are invited to freely access, utilize, and distribute! Given previous links will age out due to the nature of the document, click here to view and download the latest version of The Acceleration Imperative.

Let’s agree that student engagement is key to sustained learning. Then we can consider approaches to optimizing student achievement by ethically and morally examining if students will benefit more from accelerated learning or remediation. So, let’s consider how we can increase student engagement.  

An educator’s utilization of an intentionally caring, optimistic, respectful, and trusting (ICORT) mindset should optimize feelings of inclusion and promote a positive school climate.  However, an ICORT-driven educator must also be guided by the axiom: ‘A goal without a plan is just a wish.’ Therefore, inclusion and engagement goals should be strengthened by plans that pursue research-based practices to increase awareness of what is relevant, elevate student knowledge, and willingly make better possible regardless of the teaching modality. This approach is wonderfully exhibited by the following strategies and justifications shared by Schwartz (2021):

•         Encourage writing by hand. There is compelling evidence that writing by hand rather than on a keyboard promotes better recall and comprehension of new information.
•       Welcome international visitors. This endeavor invites students to build connections and exhibit empathy between groups of students. Teachers can freely access organizations such as PenPal Schools or ePals, which can connect your class with international classes. Additionally, Narrative 4, is a nonprofit organization dedicated to telling and sharing stories and thereby promoting social-emotional learning opportunities.
•       Incorporate music. Through Burnout: The Secret to Unlocking the Stress Cycle (Nagoski & Nagoski, 2020), suggest engaging in some form of artistic expression.  Their book provides several activities that can help classes move through stressful experiences regardless of the needed modality.

 

To cite:

Anderson, C.J. (January 31, 2023). Understanding the Needs of Struggling Learners in Relation to Post COVID Accelerated Learning Goals. [Web log post] Retrieved from http://www.ucan-cja.blogspot.com/

 

 

References

Anderson, C.J. (July 31, 2021). Generalizing virtual strategies that worked and planning for accelerated learning. [Web log post] Retrieved from http://www.ucan-cja.blogspot.com/

Mercanti-Anthony, M.J. (2021). Using cognitive science to boost learning. Edutopia. Retrieved from https://www.edutopia.org/article/using-cognitive-science-boost-learning 

Purkey, W. W., & Novak, J. M. (2016). Fundamentals of invitational education. (2^nd Ed)         International Alliance for Invitational Education. Retrieved from: http://invitationaleducation.net/product/category/books  

Schwatrz, J. (2021) Virtual Teaching Practices With Staying Power. Edutopia retrieved from https://www.edutopia.org/article/virtual-teaching-practices-staying-power

 

 

An Organization That Makes a Difference: The International Alliance for Invitational Education®

During the last few monthly blog posts, we have examined Elements 1-4 of the Coherence Lab framework.   Element 1 of the framework emphasizes the need for Building Focus and Coordination. Element 2 examines the need to Cultivate Trusting Relationships. Element 3 sets the expectations for stakeholders to Change Behavior at Scale. Element 4 of the Coherence Framework encourages Equitable Ways of Thinking and Working.

Advocates of Invitational Education theory and practices (Purkey & Novak, 2016; Purkey, Novak & Fretz, 2020), readily see the correlation between the Coherence Lab’s framework and Invitational Education (IE) theory and practices. This correlation simply proves again that IE is not something more to add to one’s pedagogical plate. Invitational Education (IE) theory IS the plate!  As evidenced by its lack of attribution to any theoretical foundation, the Coherence Lab might suggest its framework is innovative. 

Yet, for over 40 years proponents of IE theory believed that through intentional invitations for vibrant and active interactions an intentionally, caring, optimistic, respectful, and trusting (ICORT) educational leader can systemically address institutional needs through an inventory of the entire network: People, places, policies, programs, and processes (5-Ps), which influences the potential for success.

Although uncited, the Coherence Lab’s Framework readily integrates tenets of Invitational Education theory and practices (Purkey, 1992; Purkey & Novak, 2016). Frankly, this blog post can focus entirely on organizations that take an established theoretical foundation and repackage or rebrand previous tenets and assumptions as something new.  Although capitalism may be driven by greed, academia should always embrace ethics and integrity.

So, let’s discuss solutions. How can someone stand up for ethical practices and demand integrity?  Leaders can begin by intentionally invite stakeholders to become more knowledgeable.  Then encourage direct support for the institutions, alliances, or groups that exhibit research-based practices and theoretical foundations that make better possible. 

My journey as an educational leader led me to Invitational Education theory and practice, which then brought me to my first International Alliance for Invitational Education®(IAIE) World Conference in 2013. You will find the IAIE is a not-for-profit group of educators and allied professionals from throughout the world, dedicated to the development of positive school, work, and home environments as well as being opposed to those forces that demean and defeat human potential. Through IAIE membership, you are invited to learn how to intentionally create climates based on care, optimism, respect, and trust while networking with IAIE members internationally.  By joining the IAIE, you will receive: 

·         “Fundamentals of Invitational Education” (Purkey & Novak, 2016), 

·         The monthly Alliance newsletter,

·         Access to the Journal of Invitational Theory and Practice and the IAIE Abstracts.

·         Free participation in IE-themed webinars,

·         Discounted rates for the IAIE World Conference,

·         Information for how your school can earn an Inviting School Award,

·         A network of members engaging in Invitational Education research and practice.  

 An annual individual IAIE membership is $35.00.  Here are ways to join the Alliance:

·         MEMBERSHIP | IAIE (invitationaleducation.org) You can join with credit card or PayPal.

·         If you prefer to pay by check, make it payable to IAIE and mail to:

Tammy Baker, IAIE Manager;  PO Box 594.  Nicholasville, KY  40340. 

Email: tammy.baker@invitationaleducation.org

To learn more about Invitational Education theory and practice or the IAIE, please visit: ABOUT | IAIE (invitationaleducation.org)

School reform requires systemic change: A metamorphosis, based on systemic analysis of the people, places, policies, programs, and processes (the Five Ps). This structural analysis of school climate discerns whether any part of the whole is disinviting (Purkey & Siegel, 2013). IE research and documented practices exhibit how IE theory addresses “the total culture or ecosystem of almost any organization” (Purkey and Siegel, 2013, p. 104). While there is no quick fix for educational problems, the IE framework encourages ongoing vigilance before affirming sustained change (Purkey & Siegel, 2013; Strahan & Purkey, 1992). Vigilance is required because changing how a school operates requires transforming its people (Asbill, 1994).

During 2023, be resolute in your endeavor to model and nurture an intentionally inviting stance.  We must intentionally promote IE theory and practice in our demonstrated efforts to encourage the learning for all mission (Lezotte & Snyder, 2011). We must lead others in the “direction and purpose for all Invitational thought and action” (Purkey & Novak, 2016, p 11).

Crucially, we must willingly teach others to extend intentional invitations. As proponents of IE theory, we know others are better served through empowering opportunities for achieving one’s human potential.  Therefore, encourage dialogue that promotes critical thinking and open-mindedness.  Willingly reject any exhibition of contempt, which merely destroys motivation and incites further division.  As champions of IE theory and practices we must always promote intentionality, care, optimism, respect, and trust (I-CORT) in all our educational, leadership, and interpersonal opportunities. 

 

To cite:

Anderson, C.J. (December 31, 2022). An Organization That Makes a Difference: The

            International Alliance for Invitational Education®. [Web log post] Retrieved from 

http://www.ucan-cja.blogspot.com/

 

References

Asbill, K. (1994). Invitational leadership: Teacher perceptions of inviting principal

            practices. Unpublished doctoral dissertation, School of Educational Management,

            New Mexico State University.

 Fullan, M. & Quinn, J (2021). Coherence: The Right Drivers in Action for Schools, Districts,

and Systems (Pages 17-27; 47-53). Retrieved from

https://drive.google.com/file/d/1Mgw1kds313QeA5G9vDSgPRCJqcoIMW1S/view

 Lezotte, L. W., & Snyder, K. M. (2011). What effective schools do: Re-envisioning the

            correlates. Solution Tree Press.

Purkey, W.W. (1992). An introduction to invitational theory. Journal of Invitational theory and Practice 1(1), 5-15.

Purkey, W.W.., & Novak, J.M. (2016). An introduction to invitational theory. https://www.invitationaleducation.org/wp-content/uploads/2019/04/art_intro_to_invitational_theory-1.pdf

Purkey, W.W., Novak, J.M., & Fretz, J.R. (2020). Developing inviting schools: A beneficial framework for teaching. Teachers College Press.

Purkey, W. W., & Siegel, B. L. (2013). Becoming an invitational leader: A new approach   

            to professional and personal success. Humanics. Retrieved from:             http://invitationaleducation.net/featuredbooks.html

Strahan, D., & Purkey, W. W. (1992). Celebrating diversity through invitational

            Education. The International Alliance for Invitational Education.

Element 4 of the Coherence Framework: Equitable Ways of Thinking and Working

           Last month you were invited to reflect upon your teacher education or leadership programs. A guiding question in this regard asked you to consider how effectively did (does) your preparation programs concretely develop intentionally caring, optimistic, respectful, and trusting (ICORT)-driven educators capable (and willing) to embrace systemic models, promote cooperative learning, exhibit high expectations, utilize HOTS, and analyze data to monitor and adjust as needed? This month we examine Element 4 of the Coherence Framework: Equitable Ways of Thinking and Working. 

Reference the Coherence Lab framework chart (below) to review the first three elements needed to promote effective advocacy and systems change. Initially we emphasized Element 1: Building Focus and Coordination. Last month we then examined Element 2: Cultivate Trusting Relationships. Advocates of Invitational Education theory and practices (Purkey & Novak, 2016) appreciate Element 3: Change Behavior at Scale.  Invitational Education (IE) theory and practices believe that through intentional invitations for vibrant and active interactions an ICORT-driven educator systemically addresses institutional needs through an inventory of the entire network: People, places, policies, programs, and processes (5-Ps) that influence the potential for success.

As proponents of the Coherence Framework move practitioners to Element 4, IE theory and practices is reinforced by the need to align our beliefs and values around equity through our mindsets and our actions. To encourage equitable ways of thinking, stakeholders need to reflect on their individual identity, acknowledge and address biases, and design at the margins resulting in a constellation of solutions that ultimately work for all stakeholders.

Equitable ways of working require framing the problem as a defined tool for equity rather than a statement that perpetuates inequity. Subsequent exploration of solutions can then intentionally invite people who most deeply experience the problem so their expertise can drive the solution finding process. Through a circular rather than a linear process, focus is placed upon what is learned as a measure of an initiative’s success.  Equitable systems, tools and culture can be developed despite the potential for risk or fear of failure.

However, when dysfunctional institutional inertia prevails and is consistently exhibited an organization either fails or refuses to take accept where the institution is compared to where its organizational mission states it should be heading. For instance, dysfunctional inertia continues to blame disengaged parents for student failure and poor school climate.  By contrast, strong and effective leadership humbly poises the question: “Is it reasonable to suggest many parents in low SES, urban school districts were previously students in that school district?”  Therefore, the culture of the community is that schools are a place of failure.  Education failed to free them of the bondage of poverty--as promised!  As a result, the opportunity gap chained these parents to the achievement gap.  When that becomes the prevailing cultural reality, then the potential for equity loses to systemic injustice.

The Coherence Framework (below) readily integrates tenets of Invitational Education theory and practices (Purkey & Novak, 2016).  Likewise, Effective Schools Research (Lezotte & Snyder, 2011) readily integrates with Continuous Improvement Theory as a sustainable school improvement framework.  The continuous improvement management approach reinforces Deming’s Total Quality Management (TQM) system, comprised of 14 points posited as “essential for business success” (Davenport & Anderson, 2002, p. 33). 

A skillful educational leader begins developing an effective collaborative culture by understanding the interdependency of the improvement process rather than merely undertaking elemental processes for change. Leaders interested in promoting an equitable and truly collaborative learning culture must embrace this reality: It is not enough to want to change or need to change, to become enculturated within an organization, stakeholders must experience positive change. a culture based on “defined autonomy” (Marzano & Waters, 2010, p. 8) communicates non-negotiable goals to both the internal and external stakeholders.  Otherwise, change can be either slow, inconsistent, or nonexistent.

To cite:

Anderson, C.J. (November 30, 2021). Element 4 of the Coherence Framework: Equitable ways

            of thinking and working. [Web log post] Retrieved from 

http://www.ucan-cja.blogspot.com/

 

References

Davenport, P., & Anderson, G. (2002). Closing the achievement gap: No excuses. APQC.

DuFour, R., DuFour, R., & Eaker, R. (2008). Revisiting professional learning communities at

            work: New insights for improving schools. Solution Tree Press.

Eck, J., & Goodwin, B. (2010). Autonomy for school leaders. School Administrator, 67(1),

24-27.

Fullan, M. & Quinn, J (2021). Coherence: The Right Drivers in Action for Schools, Districts,

and Systems (Pages 17-27; 47-53). Retrieved from

https://drive.google.com/file/d/1Mgw1kds313QeA5G9vDSgPRCJqcoIMW1S/view

Lezotte, L. W., & Snyder, K. M. (2011). What effective schools do: Re-envisioning the

            correlates. Solution Tree Press.

Marzano, R. & Waters, T. (2009). District leadership that works. Solution

            Tree Press

Purkey, W. W., & Novak, J. M. (2016). Fundamentals of invitational education. (2^nd Ed)

            International Alliance for Invitational Education. Retrieved from:

http://invitationaleducation.net/product/category/books

Effective Advocacy for Change: Progress rather than perfection

          As we continue examining how to effectively advocate for inclusive education and the Learning for All Mission, reflect upon your previous efforts to establish non-negotiable goals (NNG) (Marzano & Waters, 2009). As requested last month, how did you rate your efforts to model effective collaboration?  What has been most difficult in removing identified obstacles to needed change? 

An effective leader recognizes when and how staff can work autonomously and collaboratively, thereby developing or removing staff as necessary, which promotes the culture of high expectations within the school (Eck & Goodwin, 2010).  Establishment of non-negotiable goals (NNGs) are a product of earlier collaboration.  Intentional invitations promote staff empowerment (Purkey & Novak, 2016).  Determination to collaborate, time to meet, willingness to ask serious questions, creation of an action plan, and always meeting with an agenda, promotes collaborative communication aligned to the established NNGs. 

Positive change can be the outcome of innovative thinking, willingness, humility, collaboration, and a collective vision grounded in a clearly-defined mission.  Unintended consequences, which often fall into the pool labeled “negative change,” typically ignore the characteristics connected with positive change.  In conclusion, leaders interested in promoting a collaborative learning culture must embrace this reality: It is not enough to want to change or need to change, to become enculturated within an organization, stakeholders must experience positive change.

Let’s return to the Coherence Lab framework chart (below) for envisioning effective advocacy and systems change. Previously we observed that the framework is divided into four elements.   Last month we emphasized Element 1: Building Focus and Coordination. This month we will further examine Element 2: Cultivate Trusting Relationships and Element 3: Change Behavior at Scale.

While building focus and coordination is an initial step toward coherence, lets agree that cultivating trusting relationships strengthens coherence by empowering everyone through choice and decision-making.  This requires profession development.  There are three core sub-elements of Cultivating Trusting relationships:

1.      Engage Authentically: Inviting leaders in education involve local stakeholders with varied experiences, perspectives and beliefs. When engaging with stakeholders, it's important to be transparent about the role and decision- making responsibility of stakeholders. It’s also important to approach each engagement with empathy. Engaging stakeholders with transparency and empathy exhibits intentional understanding of stakeholders’ needs, motivations and interests.

2.      Recognize and Address Power Dynamics: Intentional, empathic listening exhibits understanding when addressing individual identities and power dynamics, This is a key sub-element for building trusting relationships. Effective leaders recognize that power dynamics impact the way we engage with one another and make decisions. Rather than authority alone, power is often attributed due to cultural identity. It is therefore prudent to confront issues of identity and power to comfortably cede power in favor of more equitable and authentic engagements.

3.       Support Inclusion: Intentionally inviting leaders embrace the experiences of stakeholders and honor their expertise resulting from being in proximity to issues or problems needing to be addressed.

When seeking to apply Element 3: Change Behavior at Scale, intentionally inviting leaders believe greater student success is possible when educators utilize an intentionally caring, optimistic, respectful, and trusting (ICORT) mindset. Through intentional invitations for vibrant discussions and active interactions an ICORT-driven educator systemically addresses institutional needs through an inventory of the networks: People. places, policies, programs, and processes (5-Ps) that influence the potential for success. This intentional desire promotes collaboration,  exhibits critical, higher order thinking skills (HOTS), that appeals to emotions.  Well-defined ley outcomes allow valid analyzes through accessible, reliable data.  

Reflect upon your teacher education or leadership programs. How effectively did (does) your preparation programs concretely develop ICORT-driven educators capable (and willing) to embrace systemic models, promote cooperative learning, exhibit high expectations, utilize HOTS, and analyze data to monitor and adjust as needed? Let’s explore these points next month when we examine Element 4 of Coherence: Equitable Ways of Thinking and Working. 

 

 

To cite:

Anderson, C.J. (October 31, 2021). Effective advocacy for change: Progress rather than

    perfection. [Web log post] Retrieved from http://www.ucan-cja.blogspot.com/

 

References

DuFour, R., DuFour, R., & Eaker, R. (2008). Revisiting professional learning communities at

            work: New insights for improving schools. Solution Tree Press.

Eck, J., & Goodwin, B. (2010). Autonomy for school leaders. School Administrator, 67(1),

24-27.

Fullan, M. & Quinn, J (2021). Coherence: The Right Drivers in Action for Schools, Districts,

and Systems (Pages 17-27; 47-53). Retrieved from

https://drive.google.com/file/d/1Mgw1kds313QeA5G9vDSgPRCJqcoIMW1S/view

Lezotte, L. W., & Snyder, K. M. (2011). What effective schools do: Re-envisioning the

            correlates. Solution Tree Press.

Marzano, R. & Waters, T. (2009). District leadership that works. Solution

            Tree Press

 Purkey, W. W., & Novak, J. M. (2016). Fundamentals of invitational education. (2^nd Ed)

            International Alliance for Invitational Education. Retrieved from:

http://invitationaleducation.net/product/category/books