In some classrooms, teachers pre-test students and place them at the appropriate level of instruction for each chapter. Then, they provide some students with grade level assignments and others with above or below grade level assignments. These assignments may be given to students on a daily basis or given as part of a contract or menu of activities that allow students choices.

Many times, teachers are discovering that a concept is new for the entire class. At these times, they find it necessary to present the lesson (s) to the entire class and give the same assignment until it is apparent which students need more challenging problems or which students need more help.

Some teachers have discovered that there are some years where they do not have any students at the beginning of the year functioning at one whole year above grade level math. This has been true in some of the primary classrooms across the district where most of the students are being exposed to many mathematical concepts for the first time. However, on year-end tests, some of our primary students test a year or more above grade level in math. Therefore, there can be quite a bit of growth and a student might end the year well above grade level.

In some classrooms, teachers are using two (or more) grade level textbooks in the same class, teaching two (or more) different math groups. The teacher works with one group at a time while the other is working independently. (It has been suggested that a district test be developed and given at some upper grade levels in order to determine which students need to be placed in a text that is one whole grade level above.)

In some schools, teachers (usually fifth grade) departmentalize and only one teacher teaches math to all students, with one group accelerated, or, each teacher teaches math, but one group is accelerated. Departmentalization can be very helpful in terms of teacher preparation, but can cause scheduling problems and time constraints.

One of the major concerns of teachers has been with the concept of differentiation in the area of math because it is structured, sequential and teacher-directed. It does not need to be a difficult subject to differentiate. Many teachers have found ways to implement good strategies in their classrooms for meeting the needs of students in the area of math.

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Suggestions for Successful Differentiation in the Elementary Math Classroom

Also remember that differentiation needs to be implemented gradually, at a manageable rate for you, the teacher. It does not mean that every lesson, each day, must be differentiated. Just as our students are at various levels in academic skills, we are all at various levels with the concept and process of differentiation.

We also need to remember that we need to know our students well in order to tailor any lesson that we teach to their strengths, weaknesses, and learning styles, which is what differentiation is. We begin the year with some prior knowledge of students’ strengths by using previous assessment records and recommendations from former teachers. Since it takes time to know students better and because they develop at many different rates, differentiation must be an ongoing process throughout the entire year.

Directing lessons toward multiple learning styles is also one effective way to differentiate. Differentiation occurs when teaching strategies appeal to students’ individual learning styles (e.g., linguistic, kinesthetic, interpersonal, etc.) or individual interest areas (e.g., sports, art, reading, construction, games, etc.) The teacher editions and the resources provide many alternative activities, which address multiple learning styles.

Some students demonstrate a great interest or proficiency in math at an early age and are easily recognized. Teachers can provide above grade level worksheets or activities for them whenever necessary.

Evaluating students’ math aptitudes in order to meet their needs requires time and effort on the part of the teacher. This is because it is not always obvious which students are truly advanced or truly in need of support. Developmentally, there is a wide disparity among students. For example, telling time and counting money may not be strengths because the child is not ready to learn the skills until a later time. What does a very able math student look like? First of all, he or she may not be performing above grade level in all areas, but will usually exhibit inductive and deductive reasoning skills, inquisitiveness about math topics, creative problem solving abilities, and pattern recognition. He or she may choose math activities, games and puzzles when given a choice or may demonstrate perseverance with mathematical tasks. Excellent computational skills do not always indicate that a student is accelerated. A mathematically gifted student may not be proficient at computation. Another student may have exceptional computation skills but finds the higher level problem solving activities or applications too difficult. A student should not be refrained from accelerating simply because of a weakness in computation skills, nor should a student be accelerated only because of proficiency with computation skills. However, computation and application and problem-solving skills are ALL important to a student’s success in math.

There are many ways to assess students’ skills AND learning styles throughout the year in addition to giving quizzes and tests. Assessment records are important to have for communications with students and their parents. Use some of the alternative assessments suggested in the teacher’s edition of the text.

1. Observe students’ work by giving them slates to hold up their answers or to show their work. Send groups of 4 or 5 to the board for you to observe while others are working at their seats.

2. Listen to the students’ explanations (during individual, small group, or whole group discussions) of their mathematical thinking or "tricks" they use to solve problems. Sometimes this reveals mathematical ability in a student who does not excel at computation.

3. Evaluate written journal entries, which include diagrams, drawings, and explanations about math topics.

4. Observe children’s strategies while they are working in small groups on an assignment or playing a game. This often reveals math proficiency or learning difficulties.

5. Keep in mind that our new math textbooks challenge students in the area of reading comprehension. A student may be very able in math, but be challenged by the reading content in the math text. This may make it difficult for some students to work independently or at a more advanced level without teacher assistance. A child may be advanced in math but not in reading.

6. Whole group lessons and activities can be very useful in math instruction and can be a basis for valuable discussions for all students about math concepts.

7. You may choose topic. Those who demonstrate proficiency can be moved on to a higher level assignment (perhaps an Enrichment or Problem-Solving sheet) or be allowed to choose another math activity individually or with learning partners. More concept development can then be worked on with the other students.

8. You may prefer to pre-test the whole class on a concept and then using multi-level materials, assign students work at their appropriate level. You may prefer to do whole group lessons on a concept that is new for the class, such as area and perimeter, while they are working on packets of worksheets on computation skills at different grade levels. Many students can do above grade level computation, but need regular direct instruction on other grade level concepts.

9. When you are doing whole or small group problem solving activities, include extensions or extra challenges for those individuals or groups who are ready to move ahead. There are many resources such as web-sites and resource books that contain challenging problems that can be copied and available for students to work on with a moment’s notice.

10. If you choose to have students work in cooperative learning groups, small groups can sometimes be randomly assigned. On other days, you can assign more advanced students to work together, giving them more challenging problems to work on. This prevents the accelerated students from always having to help, teach or wait for others in a group. While research shows that advanced students achieve more when they are grouped together, slower learners do not have the same benefit from working only with each other. It is important that the slower learners are not always grouped together. They also need a lot of experience with higher level problem solving activities even if they are having difficulties with fact mastery or computation. As you get to know your students well, it is easier to make grouping decisions that will benefit all of them.

Although, developing procedures and routines for classroom management is important, varying your format for instruction (e.g., cooperative learning, whole group, ability groups, textbook lessons, hands-on or Investigations (TERC) lessons, etc.) throughout each week can help to keep students engaged in learning.

Daily problem solving (such as Problem of the Day) challenges everyone and, with a few review problems included, it is a very useful way to promote mastery of concepts. Include topics that you have not yet covered, but those that students should have mastered in prior grades. This can turn into a mini-lesson. Integrating math topics throughout the year makes it easier to begin the study of a new unit, because you have introduced or reviewed it already. Followed by a class discussion of the answers, this is a great way to start each day or afternoon.

Many math skills are included in computer programs and games. Choose computer programs that have a wide span of ability levels and that require high level problem-solving skills as opposed to simply drill and practice. Games can be used to increase skills in computation or used to increase thinking skills. Some games, such as Quizmo, Equals, dominoes, flashcard games, etc., are good for increasing skill with basic facts or computation. Games such as Mancala, Othello, Math Pentathlon, Mastermind, Connect Four, Battleship, Set, checkers, chess, dominoes, etc., can require strategic problem solving, increase logical thinking skills and build confidence. These games, and many others, are available in teaching supply catalogs or stores, and also in toy stores.

Materials by Marilyn Burns are excellent resources for classroom problem solving activities, providing challenge at multiple levels and provoking mathematical communication, both verbal and written. These resources do require some reading and preparation, but they do an excellent job encouraging students to talk about their ideas and to describe their thoughts in writing. Actual teacher/student interactions are described. We have received permission to include some of these activities in our Math Resource notebook. Our Staff Materials by Marilyn Burns are excellent resources for classroom problem solving activities, providing challenge at multiple levels and provoking mathematical communication, both verbal and written. These resources do require some reading and preparation, but they do an excellent job encouraging students to talk about their ideas and to describe their thoughts in writing. Actual teacher/student interactions are described. We have received permission to include some of these activities in our Math Resource notebook.