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RUNNING HEAD: FOUR TIER DIFFERENTIATION METHODA Four Tier Differentiation Model: Engage All Students in the Learning ProcessSeptember 7, 2012Janet M. HerrelkoUniversity of Dayton300 College ParkDayton, Ohio 45469-0525937-229-3037 (business)937-427-9002 (home)937-229-3000 (fax)Janet.herrelko@notes.udayton.eduA Four Tier Differentiation Model: Engage All Students in the Learning ProcessAbstractThis study details the creation of a four-tiered format designed to help pre-service teachers write differentiated lesson plans. A short history of lesson plan differentiation models is described and how the Four Tier approach was developed through collaboration with classroom teachers and university faculty. The unifying element for the format came from the Response to Intervention. In-service teachers experimented with the format and identified missing elements. Extensive data were gathered when the method was pilot tested by a pre-service teacher. Further data collections were made when graduate pre-service teachers used the Four Tier Method. This collaborative process helped create a four-tiered format for lesson differentiation designed to help pre-service teachers create lesson plans to engage all students in the learning process. Keywords: differentiation, lesson plans, teachingA Four Tier Differentiation Model: Engage All Students in the Learning ProcessTeacher education systems strive to graduate pre-service teachers with the skills to create lesson plans that can teach diverse populations. It is the responsibility of each classroom teacher to create learning opportunities for all students. The National Research Council in Everybody Counts (1989) and the National Council of Teachers of Mathematics journals in 2000 in their call for “Algebra for All” (Chioke, 2000) put forth the challenge for every teacher to be able to successfully create learning opportunities for all students. These articles were part of the drive to differentiate lesson plans to help all students learn.Teachers create learning opportunities when planning their lessons. While teachers wish for a “one size fits all” format for their lesson planning (Gregory & Chapman, 2007) it is imperative that pre-service and in-service teachers understand that within each classroom, whether the classes are heterogeneous, tracked, leveled, or content specific that limits entrance (such as a calculus class), there is an array of different learning happening within one class. The differentiation needs for single gender, urban, rural, or suburban schools vary greatly in each category. Teachers need to know their students to make appropriate changes to lessons that meet each student at a level that enables that student to actively engage in the lesson and to learn content concepts. As a mathematics educator, helping my pre-service teachers learn how to meet the needs of more than one group of learners has been a challenge. After short field experiences, the pre-service teachers returned asking “How do we differentiate our lesson plans?” It was from this question in 2005, that my research sought a lesson plan format that would assist pre-service teachers not only in their understanding of how to organize a lesson, but how to meet the needs of various groups of students in their classrooms. This study began as a search for a format for pre-service teachers to use to write differentiated lessons. While there have been a multitude of demands for teachers to differentiate their teaching (Hall, 2009; Kronberg, York-Barr, Arnold, Gombos, Truex, Vallejo, & Stevenson, 1997, Tomlinson, 1999), there are few procedures that address how to differentiate lessons. My research led me to gather points of information that contributed to my development of the Four Tier method of lesson differentiation. Once the methodology was established, the case study method was employed to examine this question: When a pre-service teacher uses the Four Tier method of lesson differentiation, does student achievement increase?Collaboration Portfolio evidence provided to the National Board for Professional Teaching Standards (NBPTS) (NBPTS, 2008) for national certification demonstrated that experienced teachers differentiated in their practice, learning how they determined when and how to differentiate would help create a format for pre-service teachers. Working with a university partnership high school, I began my journey to find a differentiation format. I worked with a group of high school teachers who asked for a book study group focused on differentiation. We used Tomlinson and McTighe’s Differentiating Instruction through Understanding by Design (2006) as the basis of our discussions. The group concluded that while differentiation at the high school level was done by the levels of courses, teachers needed to make additional adjustments to lesson implementation within each classroom in order to engage all students. During the book study, these faculty members, from multiple discipline areas, shared their methods and approaches to differentiation. However, the teachers were not able to identify one, specific differentiation format that pre-service teachers could replicate when writing lessons. These discussions reinforced my premise that experienced teachers were able to differentiate within their classes based on their years of classroom experience. Differentiation based on students’ prior knowledge levels was the next area that I examined. Collaborating with a university colleague in the mathematics department, we researched and wrote an article (Driskell & Author, 2007) that walked through a sample fourth grade math lesson plan. The plan identified tiers of student understanding based on the van Hiele levels of geometric understanding to help each student enter the examination of shape at his or her developmentally appropriate level. Definition of RtI TiersFrom intervention specialist colleagues, I learned about the Response to Intervention system, an educational design to prevent students from failing in school by using instructional and behavioral systems (National Center on Response to Intervention (NCRI), 2010). Through research-based testing, the schools place students into three groupings: Tiers 1, 2, 3 (Vaughn, 2003). Tier 1 - the Primary group in which 80% of students are identified (Cheney, 2007) – the majority of students who learn from core instruction (Vaughn, 2003). This is the center group for the lesson being planned. The lesson should present a concept that would address students’ learning preferences appropriate for the age and development of the students. This tier correlates to state curriculum requirements. The presentation of material for this tier represents how a pre-service teacher would conceive and write the original concept presentation to a class before making variations for other tiers. The lesson should address the state standards, and should be challenging, engaging, and developmentally appropriate. There is no limit to the student-focused strategies that a pre-service teacher could use to present the lesson content. Tier 2 - the Secondary group in which 15% of students are identified (Cheney, 2007) – for whom the instruction for the majority of students is not sufficient. These students need additional support which can take the forms of different strategies or methods, such as the use of additional manipulatives to reach curriculum benchmarks (Vaughn, 2003). Those students who are still rooted in concrete learning or who need to physically use manipulatives to construct a concept have needs that should be addressed in this tier. While use of manipulatives is beneficial for all learners (Sowell, 1989), additional models or materials are needed by this group. The lesson can be modified by “content, process, or product according to the students’ readiness, interests, or learning style” (NCTM, 2009). This tier is to have the teacher recognize and prepare ahead of time to have specific manipulatives available, or to have additional activities prepared when students do not grasp the concept of the lesson. Tier 3 - the Tertiary group in which approximately 5% of students are identified (Cheney, 2007) – the instruction for these students is strategic, intense, and usually longer in duration than the first two tiers (Vaughn, 2003). Students with an Individual Educational Plan (IEP) that addresses specific content are usually identified as part of the Tertiary group in the RtI program. Those students whose needs are not met in Tier 2 may need more time to master a concept, or more interactions with the teacher, or more examples at the concrete level, or additional work to grasp the concept reside in this tier. The teacher needs to know who these students are and what difficulties they have when learning math. The modifications for these students must be conducted within the presented lesson, remain within the parameters of the IEP, and be conducted within the class. Any additional time needed would happen during additional mathematics periods while the other tiers are doing deeper applications of the same content. In-service teachers use RtI in lesson plans. During a summer institute for professional development in 2007, I assigned in-service teachers to write lesson plans that included the three RtI levels of tiering as a differentiation method. In addition to differentiating a lesson by finding multiple entry points to a lesson, the teachers in the summer institute were to address how they would assess each differentiated level. The teachers wrote lesson plans using tiers to achieve their lesson objectives that were aligned with state standard requirements. The teachers quickly observed that the format left out one group of students – those students who achieved at a very high level – the accelerated students.When instruction is differentiated, the assessment of that learning needs to accommodate the variations of entry to the content. Alignment between lesson instruction and how that content is assessed is called for by the Ohio Mathematics and Science Coalition in Finding the Solution: A Call to Collaboration (2001). Matching the instruction with how to assess for learning (Black, Harrison, Lee, Marshall, & Wiliam, 2003) is a stumbling block for pre-service teachers who may have experienced only summative assessment in their four years of college courses. Identifying and creating tiered instructional modifications that support the lesson objectives might help focus pre-service teachers’ skills to identify how to use assessment for learning.Using the information collected during the research and collaboration work from 2005 to 2008, I developed a format for pre-service teachers to differentiate a lesson plan. The format adds a tier to the RtI approach to address a wider array of students. While RtI focused on early intervention, and formal, institutional, long-term grouping of students in tiers, this proposed format would help pre-service teachers to address the needs of all learners within a classroom on a daily basis. I added a tier for accelerated students resulting in a Four Tier differentiation model. Four Tier MethodThe Four Tier method of differentiation utilizes the three tiers of RtI with an additional tier to help pre-service teachers plan for all students: Tier 0 – the Accelerated Group of students grasps the lesson concept with ease. These students are able to complete the actions, plans, assignments, and activities presented to them within a few minutes of being given the assignment. Tier 0 lesson adaptations must meet the needs of students who absorb a lesson concept with such speed that they complete their requirements shortly after the work is assigned. Additional challenges - not busy work, but intellectually challenging material - should be assigned to these students. This would address approximately 1-3% of the class.Four Tier Differences from RtIA major element in the Four Tier approach to differentiation that is not in the RtI program should be stressed: this is a fluid system. Students can be moved from one tier to another on a daily basis. To determine what tier a student occupies on a given day, pre-service teachers should use as many formative assessment techniques as possible. To provide a pre-service teacher with evidence for tier placement decisions, the pre-service teacher could use daily short cycle assessment methods, prior knowledge questions, quizzes, homework evaluations, or written responses to questions at the start of the lesson. Examples of assessment for learning might include exit slips from the previous day, knowledge of students’ backgrounds, student interest inventories, or conversations with the students that reveal prior knowledge of the lesson content. These formative assessment methods are just some of the ways to determine which tier level a student may need to achieve the lesson objective (Black, et al., 2003). Tier placement is not a permanent position and need not be established by committee or made a permanent part of a student’s record. Student tier grouping can change daily as the pre-service teacher employs good assessment strategies to identify the needs and achievements of students. While the percentages from the RtI model help the pre-service teachers start their placement identification of students into tiers, the RtI percentages are not strict limitations for the Four Tier method. For example, a class may have no Tier 0 students or no Tier 3 students. Each class will have a Tier 1 as this is the population for whom the lesson is created.Literature Review The educational community heard the call to address diverse learning skills of all students. Educators saw the use of differentiating instruction as the means to engage all students in content learning while recognizing the diverse learning abilities of students. What did educators mean when they differentiated lessons in order to engage all students? One of Merriam-Webster’s (Mish, 2008) definitions noted that differentiation was to “make different by modification.” Tomlinson (1999) advanced the educational definition by noting that teachers should discover multiple student interests and use multiple learning modalities as avenues to engage students. Tomlinson’s view of differentiated instruction in which teachers proactively plan varied approaches to how students will learn content is key to the Four Tier method. NCTM’s Current Collection of Tips (2009) electronic communication on differentiated learning noted that teachers should “Focus on the differences that exist, value the diversity, and allow each student the opportunity to shine.” (NCTM, 2009).Addressing the needs of all students in a classroom is a key element of the responsibility of being a professional educator. Being informed about the background knowledge, experiences, and learning preferences of students enables teachers to select learning techniques, strategies, and environments that engage students in active learning. The National Board for Professional Teaching Standards (NBPTS) identifies as its Core Proposition #1 that teachers should know their students’ individual differences and accommodate for those differences in their practice (NBPTS, 2008). The first criterion of Domain A – Organizing Content Knowledge for Student Learning – requires that teachers should know their students (Danielson, 2007). Differentiating lessons to meet the needs of all students in a classroom is a teaching skill that master teachers are able to do smoothly based on their years of classroom experience. Experienced teachers who apply for National Board Certification (NBPTS, 2008) demonstrate these skills in their portfolio submissions. These teachers can observe a student struggling with a concept and respond with variations and/or modifications to the lesson requirements, adjust the challenges, alternate the implementation, or provide additional information in the middle of a class. These changes keep students on track and learning. How many years does it take to master this skill? That would depend on the teacher, the diversity of the student population, the curriculum demands, and the academic freedom allowed by the school district. Many experienced teachers are learning through professional development opportunities just how to differentiate using multiple student characteristics such as intellectual preferences (Tomlinson & McTighe, 2006), gender, socio-economic background, location (urban, suburban, rural), or by learning or religious preferences (Scott & Spencer, 2006). Each of these differences requires teachers to use a variety of modalities in their classrooms. With the new requirements for teachers to be able to add value to their students’ knowledge base from the moment that the teachers are hired, developmental time for teachers to master their pedagogical content knowledge has been reduced dramatically. The pedagogical skills that have previously been developed over several induction years of teaching in a school system now must be part of a newly hired teacher’s portfolio of skills.In the 1980s, educators embraced discoveries in cognitive science that found students processed information in multiple modes, usually favoring one modality. One of the first systems used to identify learning preferences was based on which sensory mode the student preferred such as auditory, visual, or kinesthetic methods (Dunn, Beaudry, & Klavas, 2002). Teacher educators required that pre-service teachers include one lesson element for each of these learning preferences in their planning. This was a useful beginning to differentiation. Further advances in cognitive approaches to learning occurred with the introduction of the theory of hemispheric brain dominance. McCarthy (1987) proposed that pedagogical methods could be designed to address the left brain or right brain learning preferences. In her 4 MAT method of lesson plan design, McCarthy says that those students who were logical, analytic, sequential, and took a part-to-whole point of view were identified as left brained and had lesson elements that utilized those skills at the start of McCarthy’s format. The students who were intuitive, holistic, random, and whole-to-part thinkers or right brained had elements that utilized those learning preferences in the second part of the format. By creating lesson plans using the 4 MAT method, left-brain and right-brain learning preferences were accommodated in one lesson.Psychologists advanced cognitive theories beyond hemispheric preferences. Gardner (1983) originally proposed that there are seven different learning intelligences and that combinations of these intelligences are what distinguish each person. His recent research expanded the seven into nine categories of intelligences (Gardner, 2009). These learning preferences now include: bodily/kinesthetic, musical, verbal/linguistic, visual/spatial, logical/mathematical, interpersonal, intrapersonal, existentialist, and naturalist. Gardner noted that when a student employed his or her learning preferences, he or she usually was successful, felt successful and could competently work in other modes as long as his or her preferences were bining the cognitive developments with teaching strategies, Tomlinson teamed with McTighe (2006) and created an action plan for educators that included differentiation in multiple modes. They prescribed how lesson differentiation could be accomplished when designing the content for understanding. They introduced the term, Responsive Teaching, to describe the modifications to help students access major ideas and skills and to help students make sense of concepts that are big ideas about content.While not precisely identifying specific levels of student learning, RtI has teachers planning for multiple levels of entry to the content. This approach appears to have some potential as the outline for a tool for pre-service teachers to learn lesson differentiation. Using the information gathered from past research, in-service teachers’ experiences, and working with pre-service teachers, the Four Tier method of differentiating lessons was composed. The next step was to determine: when a pre-service teacher uses the Four Tier method of lesson differentiation, does student achievement increase?MethodologyAfter the years of research, I constructed the Four Tier method to help pre-service teachers construct differentiated lesson plans that addressed four levels of learners. A case study format was used to examine the reliability of using the Four Tier method. A case study method provides an examination of the relationship between a dilemma and a possible solution (Johnston, 2011). This longitudinal case study examined how pre-service teachers use of the Four Tier method affected student achievement. Participants The data was collected from three groups of pre-service teachers over three years as they implemented the Four Tier method. In year one, a pre-service undergraduate, male student seeking Adolescence to Young Adult (AYA) licensure was the focus. In year two, there were ten graduate pre-service teachers: four seeking AYA licensure in mathematics; six seeking the Middle Childhood (MC) level. There were 3 males and 7 females in this group. During the third year of testing, graduate pre-service teachers were the focus group. This third group consisted of nine initial license graduate pre-service teachers in both AYA and MC licensure groups. There was one female seeking AYA mathematics licensure. The other eight pre-service teachers were two males and 6 females seeking MC licensure. The participants in year one included the male undergraduate pre-service teacher and a mathematics class of 22 high school students. This pre-service teacher volunteered to be the subject of this case study to ensure that the Four Tier method was effective and should be taught to pre-service teachers or eliminated from the mathematics methods curriculum, The pre-service teacher was earning licensure in AYA (grades 7-12) in the student teaching semester (final term) of his four year university experience. The 22 high school students were from a lower-middle income school district in a Midwestern state. The pupil population of the school district is 83% Caucasian, 10% African American, 3% Multiracial, 2% Hispanic, and 2% Asian. The percentage of the population that is economically disadvantaged is 25%. The pupil attendance rate is 93%. The average number of pupils per teacher is 19 to one. The district spends $8,635 per pupil annually (, n.d.). In the second and third years, data was collected from a cohort of ten graduate pre-service teachers and a cohort of nine graduate pre-service teachers. They were placed in an urban school district. The urban district has a student population of approximately 14,174 students. That student number is subdivided into 25% white, 68% African American, 7% Hispanic or Asian. The economically disadvantaged percentage is 93% of the student population. The district is in continuous improvement status based on how many indicators it met in the state requirements listing - it met 2 out of 26 indicators (State Department of Education – Report Cards, 2012).ProcedureThe basic procedure followed by each group and in each year of the study, started with a unit of content taught by the pre-service teacher using the cooperating teacher’s method. A test was administered at the end of the unit instruction. This was the first point of collected data. The pre-service teacher taught a second unit of content using the Four Tier method of differentiating the unit. A test was administered at the end of the unit of instruction. This was the second point of collected data used to compare the results of the two units.Mathematics teachers are aware that mathematics content continually builds upon the knowledge learned in the prior unit taught (Freudenthal, 1981). This is a confounding factor to this study. For instance, the students in the first year of the study learned about the laws of sine in the first unit and the laws of cosines in the lesson that was differentiated. It is standard practice among secondary educators to compare testing results and this study does that to test the impact of the differentiated approach to teaching.First year. The AYA undergraduate pre-service teacher did his student teaching with a pre-calculus class of 22 students. The pre-service teacher determined that there were only three identifiable tiers of students in the class. He identified the students as belonging to three tiers: Tier 0, Tier 1, and Tier 2 based on their class work, test scores, and collaboration with his cooperating teacher. He did not identify any students with severe learning disabilities in the class, thus, there were no Tier 3 students.The pre-service teacher presented the two units of lessons using the inquiry-based model. He first presented lessons on the law of sines for one week, conducted a review of the content and then tested the students, recording the test scores as the first set of data. Each student was identified on his data report as a number to protect the anonymity of the students and for purposes of matching this test with the second test. The pre-service teacher taught a second unit of lessons on the law of cosines. During the review of the content, he created three review sheets each focused on a specific tier set of skills. The Tier 0 students received worksheets with review questions that were more abstract and challenged the students to solve laws of cosines problems that had a high degree of difficulty/abstraction. The Tier 1 students were given problems similar to those in the textbook. The Tier 2 students were presented with worksheets that had visual representations, used specific shapes for the students to manipulate, and were focused on the link between the shapes and use of the law of cosines. The next day, all students were administered the same test on the law of cosines and the test scores were recorded as the second set of data.The second and third years. Graduate pre-service teachers seeking initial teaching licensure carried out the research process in the following two years. These pre-service students focused on discovering if the Four Tier Method increased student achievement. They taught a unit using their cooperating teacher’s method and tested the students for the first data points, then taught a unit using the Four Tier Method and tested the students for the second data points.Data CollectionData to evaluate the effectiveness of the Four Tier format for differentiation by a pre-service teacher were collected from the tests administered as summative assessments. The first data points came from the test scores achieved after the students were taught using the pedagogical methods of the cooperating teachers. The second data points were the test scores achieved on a test administered to the students after a unit in which differentiated methods were provided to the students. Data AnalysisDuring the first year of data collection, in depth analysis of the data points were carried out. The two sets of test scores were recorded on Excel spreadsheets and displayed in a bar graph. The student test scores were compared from test one to test two. The differences between the scores were compared and examined for the changes of the test scores. The score differences were compared for each student. The scores were aggregated by test and according to tier. Increases and decreases in student scores were noted. Paired t-tests were conducted on the test scores of test one and test two. The t-tests were calculated on the whole class and on each tier to determine the comparison if the test scores between the two methods of presenting lessons were significantly different.The comparison of the test scores in the following years was done on a broader scale. The two tests were compared for whole class differences, examining the impact of the Four Tier Method on the whole class since the data that examined individuals was done extensively in year one.ResultsThe first year of the study had detailed results reported as test scores, by student, and by tier into which the pre-service teacher placed the students. The comparison of the two tests revealed data that were examined as individual measures, aggregated measures, and increases or decreases in student achievement.The pre-service teacher placed the students into tiers based on grades achieved in the class on work accomplished prior to this study. The tier populations revealed an almost even distribution of students between tiers 0 – 2 with six students in tier 0, eight students in tier 1, and eight students in tier 2 . These percentages do not follow those identified by Cheney (2007) and used by RtI. This represents another of the fluid elements of the Four Tier method where the groups do not need to be categorized by the RtI percentages. There were no students who needed to have the additional planning needed for Tier 3.The first and second test results were recorded and displayed in a bar graph to compare the increase or decrease of student performance. All scores fluctuated by several points of increase or decrease. Six of the students’ scores were lower on the second test, while 16 student scores increased with the implementation of the differentiated review (See Figure 1). (Figure 1)When aggregating the test score results for each tier, all tiers increased scores after the differentiated review was implemented. The aggregated total of Tier 0 scores increased from the prior test by 30 points or 5 points per student. The aggregated total of Tier 1 scores increased from the prior test by 64 points, or 8 points per student. Tier 2 aggregated scores increased by 114 points, or 14.25 points per student. Of the students whose scores increased when a differentiated review was used, 16 students representing 73% of the class improved their performance on the second test. There were students who did not improve their scores on the second test when the differentiated review took place. Six students’ scores decreased, representing 27% of the class. The most noteworthy drop came in Tier 0 where one student lost 22 points from the first test to the second test. Three students in Tier 1 dropped scores of 2, 4, 8 points each. Two students from Tier 2 dropped their scores by 12 points each. When the second test scores were compared with the first test scores, it was noted that increases varied by tier. Tier 0 individual test scores rose from a low increase of 2 points to the highest increase of 18 points. Tier 1 individual test scores increased from 2 points to as much as 26 points. The largest increase in individual scores was found in Tier 2 scores where the lowest increase was 10 points to the highest individual increase of 34 points. In addition to the one individual student who had a dramatic score increase in Tier 2, two other students within Tier 2 improved their test performances by 26 points each.The results of the paired t-tests found that for the whole class (n = 22), the grades were significantly different when this Four Tier Method of instruction was used. The whole class two-tailed p value was 0.0135. There were mixed results when the individual tiers were examined. The small populations in the individual tier analyzes were problematic, but the same two-tailed analysis of paired t-tests were conducted. The results of the paired t-tests done on Tier 0 test scores found that the differences were not significantly different, with a p value of 0.4291. The results of the paired t-tests done on Tier 1 test scores found that the differences were significantly different with a p value of 0.0276. The results of the paired t-tests done on Tier 2 test scores found that the differences were not quite significantly different with a p value of 0.0573.In year two and three, the data collections came from the graduate pre-service teachers. They taught the two lesson units as required. The mean differences between the scores varied. Seventeen (89.5%) pre-service teachers had student scores that achieved an average of five or more points higher student scores when using the Four Tier Method compared to two (10.5%) pre-service teachers with lower student mean scores by 2 and 5 points.The post pre-service teaching interviews provided additional information. While the pre-service teachers were nervous about being on their own creating lesson plans, they knew what was expected of them for the Four Tier differentiation and were able to compose lessons that were student centered activities.The graduate pre-service teachers noted that even with the student scores varying, they witnessed classes that were engaged with the mathematical activities, students tried to complete the work in the designated time period, and reported how successful the students were. The graduate pre-service teachers witnessed that the students now had the mental picture of themselves as successful mathematicians. DiscussionThe results of this case study demonstrate that collaboration between researchers and practicing educators can produce new models that can assist pre-service teachers to increase student achievement starting in the internship experience in a classroom when they differentiate their lessons using the Four Tier format. The resultant data from the first year pre-service teacher test scores showed increased student achievement for 73% of the class when compared to a content unit taught by the same pre-service teacher presenting non-differentiated content. The issue in mathematics education that content builds upon each prior unit is a confounding factor to this study. Having other pre-service teachers in multiple content areas use this method to teach non-sequential content would be a next step to examine the impact of the Four Tier method. In the first year of the study, a pre-service teacher took great pride in his ability to bring the Tier 2 students into evaluation ranges that were much higher than their normal testing achievement levels. While the Tier 2 test scores were not quite significant in the differences from the first test scores, the increases made by individual students were exciting to the pre-service teacher.Of the six students whose scores dropped in the second test, one student’s dramatic drop of 22 points merited additional inquiry. When I interviewed the pre-service teacher about this Tier 0 student, the pre-service teacher noted issues with keeping that student engaged in class work. The pre-service teacher’s reflection on his lesson identified two means that he could try in the future to keep that student involved in the work of the class. The strategies he noted were to have this student work as a mentor with a Tier 2 student explaining the work of the class, or to have the student create a problem to present to the group that would model the law of cosines. These responses demonstrated the pre-service teacher’s ability to examine his practice and develop meaningful alternatives that would meet the needs of a challenging student.The pre-service teacher’s notions of how content should be presented to students were a concern to him. At the time of the experiment, the pre-service teacher held a negative self-efficacy regarding his teaching. After the data analysis, the pre-service teacher was amazed at the improvement of the Tier 1, 2, and 3 students. He feared that differentiating activities within one class would cause the students to protest and object to their assigned activity. This was a fear noted by all subsequent pre-service teachers. He noted that “The students never asked why one group of them was doing one activity while the others were doing different activities. That surprised me. Seeing the data results helped me grasp how important it is to address student strengths if I want to be a successful math teacher.” (pre-service teacher, 4/30/08). Now, the pre-service teacher believes he can create lesson plans that address all students by focusing on their tiered level of understanding of the content being taught. During this case study, tiering helped the pre-service teacher understand the importance of ongoing assessment for learning methods. He realized the importance of continually assessing his students to know what the students were achieving and to understand in which tier each student needed to be in order to grasp the lesson content. The pre-service teacher reported that learning to use the link between planning and assessment for learning was a difficult challenge, but he noted that it was the most helpful pedagogical skill that he learned. At the start of the student teaching experience, both the graduate and undergraduate pre-service teachers saw themselves lecturing and presenting examples of the mathematics to their students as many of the university faculty still do. Using a differentiation model meant that they needed to know more than the mathematics in order to teach. Working with a format that could change daily, the pre-service teachers were challenged to know their students’ background knowledge and meet the needs of each student to increase student achievement. Case studies of pre-service teachers working with students in all four tiers over the student teaching field experience are a recommended extension of this work. Additionally, action research by practicing teachers using the Four Tier method is another research route to examine. Issues Implementing Lesson Differentiation with Pre-service TeachersDuring the 2008 school year, the first year of implementing the Four Tier method of differentiation in my math methods course, pre-service students found writing tiers of instruction extremely difficult. Even after all their research, readings, theoretical reviews, classroom work, practice, and discussions, their notion of helping students enter a lesson was to have the Tier 0 students do all the problems in that section of the textbook rather than the alternate problems assigned to the rest of the class. The Tier 1 students followed the prepared lesson plan. The Tier 2 group was to stay after school and get additional attention. The pre-service teachers’ Tier 3 plan was to have the intervention specialist work with these students. After reading sample lesson plans, I needed to stress that the differentiation instruction of the Four Tier method should be accomplished within the timeframe of the mathematics class. The activities assigned to each Tier should recognize the skill level and knowledge of that group. If Tier 3 needs additional time, challenging extensions should be created for the upper tiers. This element of professional practice, and being responsible for each student in the classroom, remains a challenge for each new cohort of new pre-service teachers. The Four Tier method of lesson differentiation is regularly taught to pre-service teachers at my university. This model does not prepare the pre-service teachers for all learners, but the method does start them examining how students think. After pre-service teachers learn how to diversify their teaching, their lessons can reach more than the average student. When students’ learning needs are met and they can be successful, these students can pursue additional educational opportunities without multiple remedial courses. Using the Four Tier model of differentiation, pre-service teachers and in-service teachers can meet the needs of the whole class room of students.ReferencesBlack, B., Harrison, C., Lee, C., Wiliam, D. (2003). Assessment for Learning: Putting it into Practice. Berkshire, England, UK: Open University Press.Chioke, J. (2000). Teaching strategies for “Algebra for all.” Mathematics Teacher, 93(7), 556-560.Cheney, D. (2007). Response to intervention in the social domain. Retrieved on Jauary 3, 2011 from http: //ies.director/conferences/07ies_conference/ppt/cheney.ppt.Danielson, C. (2007). Enhancing professional practice: A framework for teaching (2nd ed.). Alexandria, VA: Association for Supervision and Curriculum Development.Dunn, R., Beaudry, J., & Klavas, A. (2002). Survey of research on learning styles. California Journal of Science Education. 2(2), 75-98.Driskell, S. & Author. (2007). Using tiers to differentiate instruction on properties of two-dimensional shapes. 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Differentiated teaching and learning in heterogeneous classrooms: Strategies for meeting the needs of all students. Minneapolis, MN: Institute on Community Integration, University of Minnesota.McCarthy, B., (1987). The 4-MAT system: Teaching to learning styles with right/left mode techniques. Barrington, IL: EXCEL, Inc.Mish, F. (Ed.). (2008). Differentiation. Merriam-Webster online dictionary. Retrieved September 6, 2008, from Board for Professional Teaching Standards. (2008). The five core propositions. Retrieved May 15, 2008, from Center on Response to Intervention. (2010). What is RtI? Retrieved Dec. 20, 2010, from Council of Teachers of Mathematics. (2009). Differentiated learning. Retrieved April 15, 2009, from Research Council. (1989). Everybody counts. Washington, DC: National Academy Press.Ohio Mathematics and Science Coalition. (2001). Finding the solution: A call for collaboration. Cleveland, OH: Author.Ohio Department of Education – Report Cards. Dayton City Schools. Retrieved on April 12, 2012 from Scott, W., & Spencer, F. (2006). Professional development for inclusive differentiated teaching practice. Australian Journal of Learning Difficulties. 11(1), 35-44.Sowell, E. J. (1989). Effects of manipulative materials in mathematics instruction. Journal for Research in Mathematics Education. 20 (5), 498-505.Tomlinson, C. A., (1999). The differentiated classroom: Responding to the needs of all learners. Alexandria, VA: Association for Supervision and Curriculum Development.Tomlinson, C. A., & McTighe, J. (2006). Integrating differentiated instruction & understanding by design. Alexandria, VA: Association for Supervision and Curriculum Development.Vaughn, S. (2003, December). How Many Tiers Are Needed for Response to Intervention to Achieve Acceptable Prevention Outcomes? Paper presented at the National ResearchCenter on Learning Disabilities Responsiveness-to-Intervention Symposium, KansasCity, MO.Figure 1. Comparison of Test 1 and Test 2 Student ScoresAuthor Reference:Driskell, S. & Herrelko, J.. (2007). Using tiers to differentiate instruction on properties of two-dimensional shapes. Association of Teachers of Mathematics in New England Journal, 39(2), 36-44. ................
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