You are searching about What Is The Hardest Math Problem, today we will share with you article about What Is The Hardest Math Problem was compiled and edited by our team from many sources on the internet. Hope this article on the topic What Is The Hardest Math Problem is useful to you.
A Leadership Guide – Developing Curriculum Based Decision Making Teams with Response to Intervention
A new vision and role is emerging in the field of school psychology, demanding a revision of the traditional ‘tester/interpreter’ to that of skilled and knowledgeable facilitator/leader in the area of Curriculum Based Decision Making (CBDM) and Response to Intervention (RTI). Curriculum Based Decision Making and problem solving assessment is a welcome change in education, which may help to address concern in the areas of the psychology/isolation of educators, teacher development, and trust required in order to successfully accomplish real change in an education system, most importantly, school improvement and student learning. In order to fully grasp the concepts required in the facilitation/supervision role, psychologists must have the more broad understanding in the fundamental areas of the historical perspective, problem solving, curriculum based decision making teams, tiered intervention systems, using research and reason in education, and getting started.
Leadership and Vision: A new role for school psychologists
Successful schools fulfill individual needs through organizational goals. Team members are able to brainstorm for alternative teaching and assessment strategies (Glickman, Gordon, and Ross-Gordon, 2004, p. 5) and envision ways to address most, if not all, students within the general education program. Among suggested ethics and professional roles for school psychologists reflected in the literature, two in particular suggest direct involvement and facilitation of the leadership role in Curriculum Based Decision Making and Response to Intervention. “Competent practitioners are committed to a proactive rather than reactive stance in ethical thinking and conduct. They use their broad knowledge of ethical codes, professional standards, and law along with ethical reasoning skills to anticipate and prevent problems from arising,” and “skilled practitioners are able to analyze the ethical dimensions of a situation and demonstrate a well-developed ability to reason about ethical issues. They have mastered and make use of a problem-solving model,” (Jacob & Hartshorne, 1992, p. 4). Based on these premises, it stands to reason that a competent school psychologist would be the best candidate in facilitation, leadership, implementation, and oversight of active and prevalent problem solving teams, able to lend expertise, guidance, leadership, and support to teams in attempting to meet the learning needs of all students.
Effective leaders and school systems have established learning goals for all of their students, which is consistent with the concept of public education in a Democratic society. As such, these schools are “always studying teaching and learning, setting common priorities, making decisions about internal changes and resource allocations, and assessing effects on student learning,” (Glickman, et al., 2004, p. 6). The new vision for school psychologists will include a purposeful vision of what teaching and learning should be and the collaboration with administrators, teachers, and other members of the CBDM team, acting as the glue utilizing knowledge and interpersonal skills, along with consultative, behavioral, and technical skills to help develop and carry out instructional and behavioral improvement plans school-wide, class-wide, and individually (Glickman, et al., 2004, pp. 8-9).
The new role for school psychologists will affect student learning and teacher development through consultation, direct observation and intervention, group professional development, and prereferral activities directly related to the problem solving approach (Glickman, et al., 2004, p. 12). Directly addressing the difficulty of teachers regarding professional and personal isolation, frustration, and (sometimes) inadequate resources, the CBDM team and school psychologist facilitator-leader can improve learning by avoiding the isolation of teachers, and “instead encourage professional dialogue and collaboration.” Since “teaching in effective schools is collective rather than individual enterprise,” (Glickman, et al., 2004, pp. 20-27).
Over the past 25 years, the percentage of students placed in programs for Learning Disabilities has increased to the point that 50% of all students in special education are labeled learning disabled (Fuchs, Fuchs, & Speece, 2002). The debate over the discrepancy model for placement in learning disability programs has been ongoing. Recently, a model utilizing a student’s response to intervention as a replacement model has been studied. This approach to identification utilizing an intervention responsiveness approach (Fuchs, Mock, Morgan, & Young, 2003), attempts to examine levels of student performance, gauge the effects of individual student adaptation to regular education interventions and accommodations, and finally verify the effectiveness of special education programming prior to placement (Fuchs, et al, 2002).
Regular Education Intervention
General education intervention, previously termed “pre-assessment” or “prereferral,” is based on the problem-solving model. CBDM (RTI) teams should be flexible and should be determined by the area(s) of concern including age and needs of the child. In addition to the parents of the child, the team may consist of: building principal, referring teacher, regular education teachers, special education teachers, counselor, transition coordinator, related services personnel, school nurse, Title I or Section 504 coordinator, or others as deemed appropriate by the team.
The team bases their interventions on a child’s strengths and concerns. The team attempts to remediate the child’s concerns through regular education interventions. When a child demonstrates a need for supports or is struggling behind his or her peers, the team meets to discuss potential accommodations and supports needed in order to best meet the child’s needs. A child may not be referred for a comprehensive evaluation until such time that a team has documented the exhaustion of regular education intervention supports utilizing scientifically based interventions, and they suspect that the child has a disability or the parent requests the evaluation and the school agrees that the evaluation is appropriate.
Identification and Placement
USC Sec 300. 308 and 300.540 of the Individuals with Disabilities Education Act (IDEA), mandates that the determination of whether or not a child suspected of having a specific learning disability qualifies for special education be made by the child’s parents and a team of qualified professionals, which must include the child’s regular education teacher, at least one person qualified to conduct individual diagnostic examinations and interpret such information such as a school psychologist, speech language pathologist, or remedial reading teacher. Prior to the most recent reauthorization, the team was required to determine if a suspected student demonstrated a severe discrepancy between ability and achievement. Meaning the child’s achievement in math, reading, writing, or language was significantly different than the child’s measure of ability (commonly referred to as IQ score).
The reauthorization of IDEA, removed the requirement to show a discrepancy between ability and achievement using an IQ test. This does not indicate that ability testing will be banned, but there will be a strong possibility that psychologists will forgo this piece of the comprehensive evaluation in certain circumstances. USC 300.307(a)(2) of the IDEA states, “the criteria adopted by the State must permit the use of a process based on the child’s response to scientific, researched based intervention.”
Response to Intervention Models
Critics of traditional ability testing question the appropriateness of using child-based characteristics for treatment matching rather than classroom accommodation and varied instructional interventions. Response to Instruction models focus on the context of learning and instruction as a potential reason for the child’s difficulties rather than automatically considering the problems to be a “child’s deficit” (Fuchs, et al., 2003).
Over the years we have evolved a process through which we try to find the student entitled for funding first, and then we get around to developing an appropriate educational program to meet her needs. That is backwards! Because need is one criteria for entitlement, finding a solution to the student’s learning problems has to come first, only then can a team brainstorm a solution. A team cannot draw conclusions about need from evidence of a disability (the second criterion for entitlement). This is Curriculum Based Decision Making (CBDM) (Howell, 2005).
Shifting Our View of the Problem: The Problem is not the Disability!
It used to be assumed that recognition of the disability did tell us something about need. That was because, as it developed, the field of special education retained many of the assumptions that go with medical treatment. These included that the: client is ill; cause of the illness must be determined before treatment can be started; evaluation focuses on the client; treatment is directed at the client; treatment often requires modifications in expectations because the; underlying pathology cannot be corrected; and problem is interactive (Howell, 2005).
The central question is not: “What about the learner is causing the performance discrepancy?”
The central question is: “What about the interaction of the curriculum instruction, learner and learning environment should be altered so that the child will learn?” (Howell, 2005)
The emphasis of our inquiry is the target of the educational interaction — learning. And learning is illustrated with measures that show us how the student’s behavior is changing in the areas (academic, social or task-related) in which he or she is being taught (Daly & Glover, 2006).
The Shift in Focus:
We must become immediately interested in measures which directly sample the curriculum and that are sensitive to instruction. That is because the emphasis of our inquiry is the target of . . .
Domains of Influence in Problem Solving:
· Instruction – How we teach what is being taught
· Curriculum – What is being taught
· Environment – Context where learning is to occur
· Learner – Characteristics intrinsic to the individual in relation to the concern (Howell, 2005)
Problem Solving: Shifting the Emphasis from Measurement to Evaluation
Evaluation is a process of comparison that leads ultimately to the drawing of conclusions and the making of judgments. To make good decisions we need to elevate the role of evaluation over measurement. Stressing the dynamic nature of the problem-solving process does this. It is also done by seeing to it that measures (in the form of reviews, interviews, observations and tests) are given to answer specific questions, not as part of a standard menu (Howell, 2005).
Shifting the focus from unalterable to alterable variables:
Moving the focus from unalterable variables to alterable variables allows educators to get information about things that they can do something about (Howell, 2005).
Unalterable Variables-things that cannot be altered through instruction (i.e., IQ, physical/medical status, lives with a single parent, prior knowledge); however, unalterable does not mean unimportant!
Alterable Variable – something that can be altered through instruction. (Howell, 2005)
“Education is a social process. Education is growth. Education is not a preparation for life; education is life itself.”
The Problem Solving Approach (PSA)
The rationale behind the CBDM team, is the process of moving toward problem solving assessment. What is Problem Solving Assessment? Problem Solving Assessment (PSA) is an educational assessment model that seeks to maximize the resources available to schools while at the same time minimizing costs. Many of the resources available to schools reside in the school, in the home, and in the larger community. Traditionally these resources have remained untapped. Lacking are the coordination, organization, and attitude necessary to utilize this pool of potential solutions to learning problems. PSA is an education model that seeks to empower individuals within schools and communities to help provide solutions to the educational problems of our students.
With the greater social and legal stress placed upon schools for increased documentation, this model allows schools to demonstrate greater accountability. Within this model, regular and special educators are seen as partners who cooperate, beginning at the prereferral level and beyond to help children and families. In PSA, students having problems that affect their education are seen in the context of their whole environment. The difficulties they experience are not seen as solely residing in the child. Instead, an ecological view is encouraged. Student identification in terms of disability labeling becomes less of an issue as more emphasis is placed on finding solutions for individual learning problems. These solutions emphasize not only maximizing student strengths and minimizing weaknesses, but also trying to match these strengths with school/district strengths and resources (UNK, professional seminar series).
Problem Solving Process
· Define the Problem (screening and diagnostic assessments)
What is the problem and why is it happening?
· Develop a plan: Goal setting and planning
What are we going to do?
· Implement the Plan (With integrity and fidelity)
Carry out the intervention.
· Evaluate (Progress monitoring and assessment)
Did our plan work?
· Begin the process all over again. (Howell, 2005)
Curriculum-Based Measurement is based on the principle that schools should test students over what is actually taught in the classroom instead of relying solely upon national achievement tests to measure student progress. It can provide performance data regarding which areas of the actual curriculum are being learned. This method should be balanced in combination with nationally normed/standardized testing. CBA may provide a fairer, less culturally biased, easy, cost effective, quick overview of a student’s performance. The results also have more meaning to the teachers and parents as it is directly related to the student, curriculum used, and teaching style of the classroom teacher involved. Standardized tests provided an overview of the student, which will have meaning from state to state across the country (UNK, professional seminar series).
Curriculum-Based Assessment/Evaluation: Shifting the Emphasis from Measurement to Assessment
Assessment/evaluation is a process of comparison that leads ultimately to the drawing of conclusions and the making of judgments. To make good decisions we need to elevate the role of evaluation over measurement. Stressing the dynamic nature of the problem-solving process does this. It is also done by seeing to it that measures (in the form of reviews, interviews, observations and tests) are given to answer specific questions, not as part of a standard menu. For example, starting with the hardest item and going down to the easier ones, if the child doesn’t pass the highest level… i.e.- the child may not be able to ‘produce’ the right letter, they may be able to ‘identify’ the right letter. The definition of a ‘task’ is the objective. The objective could be related to content, behavior, conditions or Criteria for Acceptable Performance (CAP). Fluency – Requires accuracy first. Automaticity – Maintaining fluency and accuracy in context a task is more than content. It’s all of the components above. If a student makes errors in a timed reading, don’t give an error passage just don’t time it. Have them practice it multiple times. PRACTICE is more powerful than FEEDBACK! Caution on giving feedback . . . if you say, “Good, you got the answer right”, the child may have copied the answer from a neighbor so they just received positive feedback for cheating. Place the emphasis on the process rather than the product. A teacher that has to answer the same question over and over, teach them the procedures for figuring out the answer themselves. Relate to wearing a coat at recess, remembering their homework, etc. (Howell, 2005)
Curriculum-Based Decision Making (RTI) TEAMS
In Problem Solving Assessment, an expanded and important role is also envisioned for the CBDM team. Currently, many teams consist of regular educators and are used as a “rubber stamp” to send referred students on for testing. They may lack the procedures, time, or experience to provide meaningful suggestions to one of their peers having problems with an individual student. In PSA, emphasis is placed on providing effective intervention sooner rather than later. After careful analysis on building resources, the team may consist of regular educators, special educators, counselors, school psychologists, behavior interventionists, and the child’s parents.
Each member brings his or her own expertise regarding the child and education, personality, and assessment to the table. Not only does this arrangement have the chance of providing earlier intervention, it may cut the costs of later testing and more importantly, lessen the stigma to students who go through the verification procedures and emerge with a Special Education label. In the PSA model, emphasis is placed on students being helped by interventions in the regular classroom if possible. If not, resources already available to the school can generate much data concerning the student before referral to the Multidisciplinary team.
Analyzing and maximizing the use of building and district resources makes sense in terms of providing quality service to children and their families as well as recognizing the need for affordability. Tapping the resources that are already available is a crucial step in the ecological approach to child-focused decision-making. Utilizing these virtually untapped resources may allow for a more cost-effective approach to interventions, while providing services to the child that may have previously remained unrecognized by the team (UNK, professional seminar series).
Ethically, a child should receive assessment based on the notion, “One score does not a label make.” Assessment should include multiple sources, multiple settings, and multiple methods. The active CBDM team should effectively screen those who do not need a full comprehensive assessment. For those students, who have been determined by the team to be in need of a full comprehensive assessment, every effort should be made to look at the whole picture. Is this truly a behavior problem, or could it be an intolerant adult problem? Is this truly a learning problem, or is it a teaching style/learning style mismatch (Curwin & Mendler, 1988)? Defining the strengths and weaknesses of children through the testing process, and applying this knowledge within the team setting allows for more appropriate interventions to be generated (Daly & Glover, 2006).
The concept of prescriptive teaching assumes that each individual teacher has certain teaching strengths or certain modes of teaching in which they are most comfortable and that each individual student has certain learning strengths or modes in which he or she learns best. The goal of PSA is to discover each of these modes and to be flexible in trying to match teaching style with student learning style. To do this can help students reach their potential and reduce frustration of teachers who are doing their best to help the student learn. Be creative with staff usage! Think “ours,” not “theirs and ours,” (Howell, 2005).
Multi-tier Models of Services Delivery: What Is a Tier of Intervention?
Tiers of Intervention refer to a 3-Tier model in which instruction is varied over time in response to students increasing needs. The 3-Tier Reading Model is designed to meet the instructional needs of all students, including those who are slow starters and those who continue to struggle in the early elementary grades. For students whose response to the first and second tiers of intervention is not adequate, the third tier provides ongoing intervention tailored to meet their specific instructional needs (Vaughn, 2006).
Tier One Instruction
Tier One is designed to provide for the majority of students instructional needs and is comprised of three elements: a research based core program, benchmark testing of students to determine instructional needs at least three times per year, and ongoing professional development (Beebe-Frankenberger, 2006).
Tier Two Intervention
Tier Two intervention is for students for whom Tier One instruction appears to be insufficient. Tier Two is for students falling behind on benchmarks skills, and requires additional intervention to achieve grade-level achievement. Tier Two is small-group supplemental instruction in addition to the time allotted for core reading instruction. Tier Two may include programs, strategies, and procedures designed and employed to supplement, enhance, and support Tier One. Tier Two instruction starts as soon as possible after students have been identified as falling behind grade expectations through benchmark testing. After the first 10- to 12-week round of Tier Two instruction, a decision should be made about the student’s instructional needs by the CBDM (RTI) team (Vaughn, 2006).
Tier Three Intervention
Tier Three intervention is intensive, strategic, supplemental and often considerably longer in duration than the 10 to 20 weeks of supplemental instruction provided in Tier Two. Tier Three is specifically designed and customized small-group reading instruction that is extended beyond the time allocated for Tiers One and Two (Beebe-Frankenberger, 2006).
Using Research and Reason in Education
Schools are now required to demonstrate the use and documentation of scientifically based instruction (NCLB). As professionals, teachers can learn to recognize and identify scientifically based practice by using basic research concepts. Educators are informed by formal scientifically based research via the archival research-based knowledge like that found in peer-reviewed educational journals. Educators may gain continued exposure to scientific research through professional journals, graduate courses, and becoming lifelong learners (Stanovich, & Stanovich, 2003).
The scientific criteria for evaluating a credible source include:
· The publication of findings in refereed journals (scientific publications that employ a process of peer review),
· the duplication of the results by other investigators, and
· a consensus within a particular research community on whether there is a critical mass of studies that point toward a particular conclusion. (Stanovich, & Stanovich, 2003)
Empiricism is considered to be the practice of relying on observation to gain knowledge. However, empiricism alone will not lead to scientific knowledge. Scientific knowledge is gained through introducing theories, which are tested empirically (theory – prediction – testing – theory modification).
Objectivity means “nature speaks for itself.” In other words, experimentation is reported honestly and without bias. Objectivity is, therefore, critical to the process of gaining scientific knowledge. The scientific criteria for peer review and the replication of findings provides the checks and balance regarding the objectivity of the scientific process. In education, it is sometimes difficult to obtain a “cut and dried” outcome regarding the efficacy of a program. Therefore, a professional judgment call is made utilizing the “preponderance of evidence” (the principle of converging evidence). Research is considered “highly convergent” when a series of outcomes consistently supports one theoretical approach to instruction. Clearly there are some areas of educational research lacking in research-based consensus. Even when teachers are well aware of the scientific criteria for evaluating a credible source, the literature often fails to provide clear and convincing direction. Educators will need to utilize their own strong reasoning processes gained through teaching experiences. Looking into an opinion article, an educator might consider if the author used peer-reviewed research on which to base their opinion. Is the author referring to more than one reference for the basis of their opinion? Do the authors cite the works of other researchers or based their opinions solely on their own works? We can use the same evaluative techniques applied towards presenters at workshops or conferences (Stanovich, & Stanovich, 2003).
Teachers may also utilize the “connectivity principle” to a new teaching method. Is it linked to peer reviewed research? Is it based on scientifically proven theories or related to other scientifically based instruction? Even with the total absence of empirical evidence, there could still be a theoretical link to the consensus in the curriculum literature supporting the method (Stanovich, & Stanovich, 2003).
Implementing CBDM requires a shift in thinking from “ours and yours” (general education and special education students) to that of an integrated system designed to serve all students. It is a belief system in which everyone agrees that students’ problems can be defined and changed through scientifically based instruction and intervention. Enabling learning rather than a “rubber stamp” towards special education placement is the goal. Knowing why learning problems occur and figuring how to solve them is the goal. Intervention is derived from gathering data and analyzing the results, and assessments will serve multiple purposes, which will lead to appropriate instructional decisions for children (Allison, 2006).
· Decide what is important for students to know.
· Teach what is important.
· Keep track of how students are doing.
· Make changes according to the results you collect. (Howell, 2005)
Children’s needs should be met in the general educational setting and with the general education curriculum. Proactive instruction should be provided before concerns arise; no “wait to fail.” Teachers need adequate tools, a variety of research-based strategies, support, and resources in order to meet the needs of all students. Quality professional development is essential to effect systemic change and improve student learning. Administrative and teacher leadership teams are needed (Glickman, Gordon, Ross-Gordon, 2004, pp. 208-209). Parents are vital members of the team. Each school has a unique culture, set of resources, and needs requiring a tailored system of decision-making.
Foundational Problem Solving
There is more than one way to implement an RTI model; however, it must be done with integrity and fidelity! Identify and support key people within your school/district, the “movers and shakers,” and develop a plan on the use and/or need for resources (Allison, 2006). School psychologists have an even greater opportunity to make meaningful and lasting impact on student learning by understanding and embracing the new vision for facilitation and leadership in RTI, as the future of our profession. By becoming a leader in CBDM, we have the ability to move beyond the traditional tester, to that of a collaborative, supportive, integrated part of a team dedicated solely to improving the educational experience for all students.
Allison, R. (2006, September). Response to Intervention: Critical components and
important considerations. Professional Development Seminar presented at
Educational Service Unit 8, Neligh, NE.
Beebe-Frankenberger, M. Response to instruction (RTI): A multi-tiered assessment
process to systematically target AYP. Retrieved December 12, 2006 from:
Curwin, R. & Mendler, A. N. (1988). Discipline with dignity resource handbook.
Bellevue, WA: Bureau of Education and Research: Retrieved October 10, 2005 from: [http://www.disciplineassociates.com/dwd.htm]
Daly, E. & Glover, T. (2006). Response to Intervention. Retrieved December 17, 2006
from: [http://www.nde.state.ne.us/SPED/RTI%20Video%20Conference/] Ed%20Daly%20Todd%20Glover%20UNL.pdf
Fuchs, L.S., Fuchs, D., & Speece, D.L., (2002). Treatment validity as a unifying
construct for identifying learning disabilities. Learning Disabilities Quarterly, 25, 33-45.
Fuchs, D., Mock, D., Morgan, P.L., & Young, C.L., (2003). Responsiveness-to-
Intervention: Definitions, evidence, and implications for the learning disabilities construct. Learning Disabilities Research & Practice, 18, 157-171.
Glickman, C.D., Gordon, S.P., & Ross-Gordon, J.M. (2004). SuperVision and
instructional leadership: A developmental approach, 6th ed. Boston, MA:
Pearson Education, Inc.
Howell, K. (2005, October) Response to Intervention and curriculum based decision-
making. Professional Development Seminar presented at Kearney, NE.
Jacob, S. & Hartshorne, T. (1992). Ethics and law for school psychologists. Brandon,
Vermont: Clinical Psychology Publishing Co. Inc.
Pre-referral Intervention Teams, Multidisciplinary Teams, and Section 504: How can we
possibly do it all? Workshop of the Professional Development Seminar Series sponsored by the University of Nebraska @ Kearney, Department of Counseling and School Psychology.
Response to Intervention policy considerations and implementation,
Alexandria, VA: NASDSE, pp. 19-20. Retrieved December 17, 2005 from:
Stanovich, P.J. & Stanovich, K.E. (2003). Using research and reason in education.
Portsmouth, New Hampshire: RMC Research Corporation. Retrieved October 20, 2005 from:
Vaughn, S. (2006). Education for students with reading/learning disabilities: What
makes it ‘special.’ Center on Instruction-Special Education, University of
Texas. Retrieved December 31, 2006 from: [http://www.centeroninstruction].
Vaughn, S. (2006). A three-tier model for preventing/reducing reading disabilities.
Retrieved December 31, 2006 from: [http://www.utsystem.edu/everychild/Present]
Video about What Is The Hardest Math Problem
You can see more content about What Is The Hardest Math Problem on our youtube channel: Click Here
Question about What Is The Hardest Math Problem
If you have any questions about What Is The Hardest Math Problem, please let us know, all your questions or suggestions will help us improve in the following articles!
The article What Is The Hardest Math Problem was compiled by me and my team from many sources. If you find the article What Is The Hardest Math Problem helpful to you, please support the team Like or Share!
Rate Articles What Is The Hardest Math Problem
Rate: 4-5 stars
Search keywords What Is The Hardest Math Problem
What Is The Hardest Math Problem
way What Is The Hardest Math Problem
tutorial What Is The Hardest Math Problem
What Is The Hardest Math Problem free
#Leadership #Guide #Developing #Curriculum #Based #Decision #Making #Teams #Response #Intervention