The dynamics of the student population yields no two students who are exactly alike. For this reason, it seems unreasonable to use one form of instructional materials, curriculum delivery, and assessment standards for all students. Educators realize that students learn at different rates and through different avenues. Individualized instruction approaches attempt to make the learning experience suitable for each student in terms of his or her learning needs, interests, and developmental level. Individualized instruction programs focus on objectives that are personal for each child.
The child is an active partner in decision-making in terms of activities, subject matter, and assessment. Because students learn at different rates, individualized instruction is flexible in instructional pacing and the scheduling of class material. Individual instruction should be varied for each student in order to provide a variety of learning modalities best suited for the student. Teachers must be dedicated to curriculum planning and instructional decision-making, and encourage students to be responsible for their learning and take an active role in the learning process.
Individualized instruction is not just a philosophy, but rather is comprised of a specific plan for meeting every student’s educational needs. Individualized instruction begins with a system to diagnose student strengths and weaknesses. Teachers use this pre-assessment to define goals for the student and understand their academic interests. The next step is to determine the best possible arrangement to group students for instruction, whether it is by needs, interests, or developmental levels.
Once the teacher has determined student needs and organized the students into groups for effective instruction, the teacher must decide how to instruct the students to produce maximum benefits for each individual student. This includes instruction delivery, course content, integrated activities, and a learning time frame. In order to evaluate the student’s progress, a design for record keeping and a variety of assessment techniques must be must be made. The purpose of this paper is to design a plan for implementing an individualized instruction program in mathematics education.
The plan will focus on mathematics content in 4th to 5th grade. The content area for this plan is geometry, and will include components of measurement and fractions. Geometry is one of the five content areas outlined by the National Council of Teachers of Mathematics. A relational understanding of geometry incorporates aspects of measurement for determining properties such as area, volume, perimeter, etc. Fractions are used in geometry for understanding geometric equations such as the area of a triangle (A= b*h) and in determining ratios between various geometric objects or shapes.
Van Heile levels, meeting students where they are at Diagnosing strengths and weaknesses Many people believe that individualizing instruction means adapting learning for students experiencing academic difficulties or cognitive delays. This could not be further from the truth. Individualizing instruction means engaging students in learning content, processes, and attitudes that are most appropriate for the individual. This means the needs of all students must be met for the program to be effective. The needs of students experiencing difficulty, students who right on track, and students who far exceed academic expectations must be met.
As educators, we provide opportunities for every student to maximize his or her individual potential. It is impossible to look at a student and understand the needs of that child. Teachers must create a thorough plan for diagnosing students’ abilities and interests, as well as determining objectives and goals for each student. Diagnosing student strengths and weaknesses can be a stressful process for students because it often involves diagnostic testing. For this reason, students must understand the purpose of an individualized instruction program in order to truly benefit from it.
Explain to the students that the testing will not be used for grading purposes, but instead will be used to allow the student to work at a pace and on a level that they feel comfortable at and that they will be successful at. A pre-assessment process will be used to determine student needs in mathematics. As previously mentioned, it is important to meet the students where they are at in terms of geometrical understanding. The van Heile levels break geometric understanding into three levels; 3 levels. The students progress through all of the levels, and in the same order.
In order to maximize student achievement, the teacher must be aware of what level the student is at, so that the student can be appropriately challenged. There are many ways to conduct the pre-assessment. You do not want to rely on simply one form of pre-assessment because a variety of assessments will eliminate testing biases and more effectively reveal student needs. One popular form of pre-assessment is a diagnostic test. The diagnostic test will reveal what students already know and what their strengths and weaknesses are.
The diagnostic test allows students to focus in areas that they have weaknesses in (such as lower level students) and omit areas that they already have an understanding in and move on to more challenging work (as in higher level students). Students who demonstrate prior mastery in a unit’s objectives can participate in a Curriculum Compacting program to eliminate instructional time and practice in the mastered content. The students will use their learning time to participate in enrichment options or acceleration programs. In addition to diagnostic testing, observations of student behavior can reveal student needs.
The area of geometry is special because it is a very hands-on, manipulative subject, especially in elementary school. There are an abundance of commercially made and personally made materials that students can interact with. Teacher observation with a checklist can reveal if students have little understanding, a functional understanding, or superior understanding, of geometry content or skills. In these observations, use geometric constructivists activities such as learning centers and mathematics games and manipulatives to reveal the students’ van Heile level.
The student might even be able to diagnose their strengths and weaknesses better than the teacher. Use student journals, questionnaires, and interest inventories to determine what the student feels confident or hesitant about doing, what his or her interests are, and what kind of goals they have for themselves. As a teacher, use the diagnostic testing, real-setting observation, and personal reflections to place the student into the appropriate van Heile level. This is not to say that each student falls onto one of three categories and will receive the same instruction as other members of the group level.
However, it will allow you as a teacher to generally classify students according to a level of understanding so that you can meet them where they are at for instructional purposes. After the teacher has determined what the needs are of each child from an educator’s standpoint, it is important to conduct individual conferences, both with the student and the parents. Together the student and the parents should define goals for the child. Determine what each party wants the student to get out of the unit. Students need to have something to work towards; otherwise they will never see the purpose of the learning in their lives.
Use the conference period to outline 5 to 6 meaningful, behavioral objectives for the student. Compile the diagnostic test results, observation checklist, student reflections, educational goals and objectives, and overall teacher reflections into a file. This will allow the teacher, student, and parents to revisit the pre-assessment at the conclusion of the unit do determine academic progress made, objectives accomplished, and effectiveness of the individualized program. See appendix for an example a diagnostic test, observation checklist, and interest inventory. Grouping of Students
When using an individualized instruction program, organization on the part of the teacher is essential. Meeting the needs of all students, differentiating assignments, and supervising the class are issues that must be addressed. Dividing students among different groups makes it easier for the teacher to adapt instruction for individual differences. However, a teacher must be careful when deciding on a system for grouping students. Students must work in many different groups based on a variety of characteristics. For example, having students work in the same ability group for every project becomes a problem.
Students become tracked on a certain level and have trouble reaching their potential, in addition to limiting their interactions with all classmates. Grouping by ability level is often very beneficial. Lower ability students will often require personal interaction with the teacher. Working at a small-group table with four to five students allows the teacher to meet the needs of a few students who are experiencing similar difficulty. The students who are having trouble will not feel embarrassed like they would if they were grouped with students whose ability far exceeded their own.
Students who are progressing at a normal rate can benefit from small group instruction as well. The teacher can take the opportunity to challenge these students at a higher level through hands-on interaction and application exercises. Students who are at the highest level can be grouped for curriculum compacting after passing the pre-assessment. These students participate in enrichment activities like self-selected projects, independent study, or learning centers designed to accelerate the curriculum. These three levels will likely correspond to the van Heile levels of understanding.
A second way to group students is by separating students by preferred learning modality. Teachers should provide opportunities to for students to work with other students who learn in ways similar to their own. This makes it easier for students to teach each other because they have a similar reference for explaining concepts or skills. Some students are visual learners and may be grouped as such. These students might prefer to learn from workbooks, videos, or by observing other students or the teacher work out a problem.
Other students may be auditory learners and would prefer to work at a learning station with audio equipment to guide them through a learning process as they manipulate objects or work out problems. These students may wish to work together as one student explains how a problem is carried out, while the other listens to follow the process. Still a third type of learning modality is the tactile kinesthetic. These students learn best from manipulating objects and completing activities that encourage them to use their hands. These students will benefit from exploratory learning centers, creating projects, and using manipulatives.
A third way to group students is by interests. Some students may enjoy problem-solving activities, while others enjoy mathematical games, and still others prefer construction or creative activities. Students should be encouraged to work in areas that they feel comfortable about and that they enjoy learning about. The student will gain a more meaningful learning experience because he or she enjoys the mathematics content and processes they are engaged in, and will feel like they are an important factor the decision-making process of their education.
Group work should not be selected simply for the purpose of having group work. The goals for instruction should be specific and personalized for each student, and these factors will determine the appropriate way to group students for any given lesson. Group size and number of groups is important. When you first assign students to work in groups, the number of children per group should be small. Students should feel comfortable working with a small number of students so that everyone feels like they can offer relevant input to the group.
The larger the group, the less influence every child has on the learning that takes place. When the teacher decides to assign the students to groups, the number of groups in the classroom must not bee too overwhelming for the teacher. The teacher must be able to circulate around the room and spend an acceptable amount of time observing student interactions and academic progress. If the class is divided into 10 groups, it will be very difficult for the teacher to devote enough time to each of the groups. Some students are natural teachers and this makes it possible to group students into tutoring relationships.
This does not mean that gifted student should be placed with students experiencing difficulty. There must be a purpose for each child and the decision must be individualized for the situation. For example there are a few students in every class who enjoy helping lower-ability students. These tutors do not miss out on more advanced instruction, but instead solidify their understanding by relating it to other students. Additionally, there are some students who enjoy personal attention from peers and who prefer to learn from a child’s explanation, rather than from that of an adult.
Unfortunately for the teacher, he or she cannot be in more than one place at a time. When students are working on different tasks, at different stations, and on different levels, the teacher must devise a system for organizing students and managing both the students’ time and that of the teacher. Depending on how the students are grouped on any given day, the teacher should make it possible to personally meet with every student every day. This may include meeting with a small group of students, observing students at centers, or one-on-one assistance.
If a teacher is working with a small group of students, every other student in the class must have something to do. The student should work on an activity that is challenging and promotes positive learning for the student. The students should not simply be sitting at their seats or playing games with no educational purpose. There are many approaches to grouping students for instruction. The chosen lesson, the students’ needs and interests, and student learning preferences will dictate how the teacher will separate students for instruction. Prescribing Enabling Activities
Materials Management A major component of an individualized program is self-discovery of concepts through hands-on manipulation of geometric objects and shapes, and the use of other games and activities to reinforce concepts. The notion that mathematics is an abstract, textbook approach subject is simply untrue. Mathematics should be as engaging as science tools and as entertaining as the books in the class library. Building a bank of materials, whether it be commercially made or personally made, is vital to the implementation of the program.
Most schools also have a mathematics resource room for using materials that are unfeasible for supplying in every classroom. Mathematics materials should not be thought of as games for reward and free time activities, but instead should be used in conjunction with instruction as a major part of the curriculum. It is beneficial for teachers to select an area of the room for storing mathematics materials. Organize the materials in large see-through bins with clear labels.
This way, students will be able to find the materials they need and return them without misplacing them in a location where they will be difficult to find. Along with typical mathematics materials, supple the storage center with paper and crayons or chalkboards and chalk so students can make charts, graphs, or draw at any time. The organization of tables and chairs, learning centers, activity tables, and materials storage containers will allow for smoother transitions between learning at the student’s seat and moving about the classroom.
In supplying your materials, provide duplicates of popular items. Excess materials reduce arguments about sharing, increase cooperation, and keep students on task. Another important stocking concern is the introduction of new materials. This sustains student interest and maintains a challenge for the students. Because materials are sometimes hard to come by or time consuming to make, rotate materials in and out so that they will seem fresh, even if they have been previously used. Keep in mind that mathematics materials should be used with a purpose in mind.
The materials are not supplied just to keep the students busy. Each game or activity should have clear directions with it and contain all possible materials that go with the activity so that the students use the material properly and understand its purpose. The activities and materials that the teacher selects should be built into lessons and also be effective for independent use. The selected materials should promote mathematical reasoning and emphasize skills such as comparing, recognizing and extending patterns, hypothesizing, spatial sense and measurement, and statistics and probability.
Because geometry, measurement, and fractions can be very hands-on orientated, there are a wealth of materials that can be used in learning centers, with instruction, and individually. Examples of math materials As with all instructional activities, document student use with mathematics materials. Students can document and evaluate their use with materials. They can keep a record of the activities they participate in and any modifications they make to the activity. Keep these evaluations near the storage center and periodically transfer the evaluation to the student’s portfolio.
Obstacles to Individualized Instruction Individualizing instruction is no easy task. Individualized instruction is a large undertaking because it requires great effort. A teacher must research individualized instruction ad develop a plan for implementation. Teachers who see the importance of individualized instruction but feel they can wing it will find the program unsuccessful. However, teacher patience, extensive planning, and belief in the program will prove beneficial for students and teachers.
A common characteristic of many great teachers is the ability to be creative and bold and attempt new things. Teachers who lack energy and creativity for the program will relay this attitude to their students. Additionally, individualized instruction might not be widely practiced in a particular school and the teacher may feel like he or she is alone in the process. Solicit the help of fellow teachers and lobby for support form administrators. As previously mentioned, teachers must be patient with the individualized program and not expect immediate successes.
As with behavior modification plans and implementation of new curriculum, a new instructional format will require adjustment on the part of the teacher. Most importantly, believe in the program, have a system for implementing the program, and encourage the students to see the value of the program. Record Keeping Because of the nature of an individualized instruction program, student progress is not measured along the same continuum. Student achievement goals, learning activities, and rate of learning are all specific for each individual student.
For this reason, teachers cannot assess student progress using identical methods for all students. Again, how records are kept and the nature of assessments must be strategies that are appropriate for each student in order effectively meet the needs of the individual. Record keeping is as important for the student as it is for the teacher. The goals that were outlined by the teacher, parent, and student at the beginning of the unit should be the guide for all assignments and activities. These goals should be kept in a portfolio for easy reference and as a way to self-monitor the progress for the student.
The portfolio should also be a means to keep assignments and self-assessments. The teacher can use the portfolio when meeting with the student, parent, or both. Individualized instruction requires that students play an active role in both the learning process and the evaluation process. However, there is also a place for teacher evaluation. Rubrics can be decided on for the student at the beginning of the unit. While the performance indicators can be specific for each child, it seems practical for the teacher to design a rubric for each van Heile level, with modifications for any students that require it.
These rubrics allow the teacher to assess in context, rather than assign an arbitrary grade. The teacher should place the rubric in a file folder. Activity checklists allow the teacher to make observations of a child’s skill proficiency in geometric tasks such as construction and manipulation of objects. Checklists can be used to evaluate students at learning centers, during group work, and on teacher-designed tasks. By nature, individualized instruction programs require a great deal of accountability. Parents and administrators want to know that the student is learning and will require proof.
Using an effective record keeping system including rubrics allows the teacher to assess learning and report it to those concerned. Most students do not enjoy tests, and many teachers do not enjoy giving them, however, testing is inevitable. Assessments should be individualized for each student, however, the test should be challenging to every student, regardless of level. Teacher-developed tests and standardized tests tell us a great deal about what the child has learned. If a student scores a 70% on a math test at the end of the geometry unit, it can mean many things and must be looked at in context.
If the student scored 20-30% on the tests at the beginning of the unit, then it is clear that the student has made great personal gains (although there is much more to be mastered). If a student scored a 70% at the end of the unit and scored 65% on the tests at the beginning of the unit, it is clear that the student has made no real academic gains. The student’s program should be reevaluated to determine a plan that will maximize the student’s potential. A good way chart a child’s progress is with record keeping programs like databases and spreadsheets.
Databases allow the teacher to analyze student progress, while spreadsheets can convert data into graphs to give a visual representation of the student’s progress. While it would be nice to give every student an A, it is impractical. A system for reporting grades is necessary for the teacher to decide how to evaluate mathematics skills and processes, attitudes and dispositions, and student progress and efforts within the unit. Much of the evaluation process will be described later, however the evaluation is based on this system of record keeping. Student Assessment
Student assessment involves much more than assigning letter grades to students in each subject area. Instead, an assessment is an overall evaluation of student achievement, progress, and attitudes, as well as teacher evaluation of instructional practices and effectiveness of learning programs. Assessment makes it possible for students to be accountable for their learning and teachers to be accountable for their teaching. One of the most important things to remember about assessment is that the student should be aware of what and how they will be evaluated.
Assessments should also take on various forms to account for student differences and evaluation preferences. Most students to not like to take exams because they are stressful and are often a poor example of what students actually know. However, student assessments are important and students should be held accountable for what they have learned. With this unit, performance tests help students demonstrate what they can do, rather than recall of obscure facts like many tests do. Students must show that they can apply their learning to novel places and demonstrate a technique for using mathematical strategies.
These performance tests will be beneficial for problem solving tasks, manipulation of objects, construction activities, and identifying patterns and relationships. Performance tasks can be evaluated in real-learning situations or learning centers through teacher observation using a rubric with performance indicators. This way, the teacher can describe the mathematical processes that the student is capable of doing, rather that simply assigning an arbitrary letter grade, which only compares a student with his or her peers.
Achievement tests have their place in the evaluation process. While the process is nearly as important as the product, as educators, we want students to be solving problems appropriately. Parents, administrators, and school board officials (as well as teachers) want to know that students are learning skills that follow the curriculum. Additionally, students need to know that they are solving problems correctly, and if they are not, the teacher needs to determine why that is the case.