Modifications and Best Practices to
Accommodate Diverse Learners


 How do I make sure I leave the math in the modifications?


It is important that ALL STUDENTS LEARN MATH.  Modifications are necessary, at times, to accommodate some learners; however, modifications should not result in students not learning essential math vocabulary and content.  The following procedure is recommended for developing modifications of content (The curriculum guide and mathematics standards should be the primary resources for designing modifications of content.)


1.    Identify essential vocabulary or terminology from the verbiage in the curriculum map or mathematics standards.  The vocabulary list generated will probably contain fewer terms than may be found in the textbook.  Efforts should be made to use these terms while teaching, explaining, and developing activities.  Hold students accountable for these basic terms when designing assessments.


2.    Identify the essential content or knowledge


3.    Identify essential mathematics principles and concepts for the lesson.


4.    Based on the learning and the learner, decide the best way for the student to learn the content and to develop understanding of the concepts.


5.    Plan hands on activities (group activities, organizers, games, labs, etc.) that directly relate to the concept being taught to avoid confusion and to support understanding the mathematics, vocabulary, and written and verbal communication about the concept.


6.    Plan varied developmentally appropriate assessments to determine understanding and knowledge of the essential vocabulary, content, and principals identified for the lesson.


The curriculum pacing charts should be used to identify what and when content and skills should be addressed.  Lessons should be planned knowing where students are in their understanding and skills.  Modifications in materials, instructional design, and assessments should be made to accommodate each studentŐs learning style and abilities.  A studentŐs Individual Education Plan (IEP) accommodations should be utilized in planning lessons. 


What strategies can I use to help ELL students learn math?


1.    All students benefit from activities and inquiry that engage him/her in the learning.  Authentic investigations, hands-on experiences, and demonstrations should directly relate to the concept being taught to avoid confusion and to provide a basis for understanding the math, vocabulary, and written and verbal communication about the concept.


2.    A peer partner can be assigned to work with an ELL student during math activities.  The peer can assist or show what is being discussed or expected.


3.    Technology support such as appropriate software and interactive online student activities can enhance learning opportunities.  Use Nettrekker ( or another meta-search engine to locate a variety of online resources such as video shorts, pictorials, charts, etc. that illustrate math concepts and content.  A variety of modified math lessons and activities in Spanish and other languages can also be located using these tools. 






4.    Visuals should accompany instruction to illustrate the learning and to help students understand. Students also benefit from learning to use and create their own visuals such as graphic organizers, concept maps, webs, diagrams, storyboards, charts and graphs to help them to understand, to organize information, and to illustrate what they know and understand.


a.     Pictorials are visual representations of a concept on paper to describe, for example, various mathematical concepts or processes.  Pictorials can be used while teaching throughout a lesson to help students focus on or visualize things.  Visual representations can be used to provide background knowledge, to support hands on activities or procedure, or to extend learning.  Transparencies in the Glencoe/McGraw-Hill teaching resources are excellent visuals that support instruction.


 b.     Poster boards, bulletin boards, and word walls using pictures to illustrate abstract concepts or vocabulary help build working vocabulary and understanding.  


c.     Picture file cards (http:/ can be used to provide a visual bank for student or teacher use.  See the online bank of picture cards.


d.     The online McGraw-Hill Science Glossary provides pictures to accompany mathematics definitions.


e.      Movies, quizzes, links, games, worksheets and more are available at point of use online at the McGraw-Hill Math teacher and pupil edition sites.


5.    Video cams, computers, and other technology should be made accessible to students as well as used by the teacher as tools for teaching and learning.


What approaches can be used for the above average math student?


1.  Above Average Learners (i.e. APEX, Gifted) ( should be given the opportunity to expand and deepen their science knowledge and skills.  However, it is important not to assume what students know and understand. To develop rigorous learning experiences for these students:


a.     Conduct informal pre-assessments to reveal what students know, understand, and can do.  Pre-assessment can also reveal misconceptions or gaps in a studentŐs learning. Curious, bright students often seek to make sense of events and phenomena that they have observed. At times they form their own explanations resulting in misconceptions (Project Universe).


b.     Use curriculum maps vertically and horizontally to identify content and skills to plan for instruction. Activities and lessons that address specific math content coupled with new independent discoveries should be enriching for these students.


2.  Encourage students to tackle Essential Questions.  Questions can be assigned for students to explore collaboratively over time. These explorations can be challenging, add to studentsŐ content knowledge and skills, and engage students in open-ended inquiry.


3.  Engage students in investigations that require practical application of their skills and knowledge as well as utilization of their interdisciplinary knowledge and process skills (An Equity Dilemma-Teaching Gifted and Talented Students, enc Focus, Volume 7, No. 4, 2000).


4.  Provide opportunities for students to engage in community-based (and beyond) and collaborative problem-solving projects.  Many online projects are available for independent and small group students.  Students should be encouraged to participate in math and technology fairs, NCTM competitions, etc.



How and why must I vary assessments?


Special attention should be given to developing varied assessments that match the learner and the learning.  (See the Assessment component). Assessment should be on going, varied, and appropriate for the student.  In addition to using modified versions of traditional subjective and objective test formats to meet the needs of diverse learners, consider that:


a.     Pictures, graphic organizers, and other visuals can illustrate what a student knows and understands (Use rubrics to set criteria for performance and evaluation).

b.     Conferences or interviews can be conducted to determine what a student knows and understands.  Responses should be recorded.

c.     Test items can be read orally and written and/or oral responses can be accepted.  Responses should be recorded.

d.     Use Glencoe Exam View Test Generator to design paper and pencil or electronic tests to meet the individual needs of students.

e.     Portfolio of student work is an important tool for teacher, student, and others.  Among the benefits is that it is a means for setting individual criteria, personalizing evaluation of student progress overtime, and providing authentic documentation of student learning.


See Assessment for additional strategies.