HRD Resources

Concrete Math Instruction

Students that lack a firm foundation built on conceptual knowledge may experience barriers to learning and assimilating new math skills. One method to increase conceptual knowledge is to use the Concrete-Representational-Abstract sequence of instruction (CRA Instruction). In this method, students begin with multiple opportunities to explore, experiment, and solve problems with concrete objects. Objects might include chips, base-ten blocks, pattern blocks, or fraction tiles. Real-world objects, like M & Ms, food cartons, and floor tiles also provide opportunities for students to explore concepts such as patterns and shapes, measurement, and more. During the representational phase, students approach and solve problems through drawings, pictures, or visual maps relative to the concrete items. In the Abstract phase, students solve problems using numbers and symbols associated with concrete items and representations.

More information and online resources:
Strategies for Teaching Elementary Mathematics
Concrete-Representational-Abstract Instructional Model YouTube Video
Concrete-Representational-Abstract: An Instructional Strategy for Math


Calculators allow students to simplify tasks and spend more time understanding concepts and solving problems. Calculators can also increase student engagement by serving as scaffolds for lost or deficient math skills in related topics, thus allowing students to focus their time on grade-level standards. Calculators available as mobile apps, software downloads, and online versions often have features that can eliminate barriers such as voice output, customizable layouts, size, and color.

Example calculators:

  • Meta Calc – Online calculator with adjustable sizes, including fullscreen
  • Calculatoria – Online basic and advanced calculators with printable paper tape display and comments
  • Alcula – An extensive array of free online calculators for a variety of purposes, including:

Virtual Manipulatives and Simulations

Virtual manipulatives and simulations can provide the platform for representational instruction in a CRA sequence of instruction as well as take the place of concrete objects when materials are not readily available in a classroom when materials are not accessible by students with disabilities, or increase student engagement. Virtual representations and simulations are often graphic-rich and interactive resources can be customized by the user, such as size and color and can be paired with a student’s assistive technology such as alternative mouse controls.

Example Resources:
National Library of Virtual Manipulatives – Online math manipulatives and simulations for grades PK-12
Illuminations – Collection of online, standards-based virtual manipulatives and lessons
Explore Learning – Interactive mathematic simulations for grades 3-12
MathBlaster – Interactive virtual world math games
Algodoo – Physics sandbox that allows the user to create, explore, and experiment

Microsoft Virtual Learning Resources

Microsoft has released a collection of special education and accessibility resources for remote learning, to help support educators working with students in virtual or eLearning settings.

These resources are intended for all educators, but will be especially helpful for educators and support staff who work in the following areas:

  • special education,
  • assistive technology,
  • blind and visually impaired,
  • deaf and hard of hearing,
  • occupational therapy, physical therapy,
  • speech language pathology,
  • early childhood special education,
  • behavior,
  • counseling,
  • school psychology,
  • language interpretation,
  • literacy,
  • autism,

and many other areas that assist students who need specially designed instruction.

State Tuition Support Program

The Tuition Support Programs for Exceptional Student Educators (ESE) provide financial support to ESE teachers earning an endorsement in autism, severe/profound, or prekindergarten disabilities; paraprofessionals earning a bachelor’s degree in special education; and educators earning a master’s degree in speech/language pathology. Upon completion of the program, recipients must fulfill a service obligation.

Math Comprehension

Acquiring and utilizing math vocabulary is an essential skill for students. Having a robust math vocabulary allows students to think about, talk about, and interact with their math environment. To increase math vocabulary development consider:

  • Pre-teaching mathematics vocabulary.
  • Modeling vocabulary when teaching new concepts.
  • Using appropriate labels clearly and consistently.
  • Integrating vocabulary knowledge in assessments.
  • Using graphics-rich and interactive games that reinforce or teach vocabulary.

Some examples include:
A Maths Dictionary for Kids – Interactive math dictionary from A to Z with sample problems
Math is Fun – Illustrated math dictionary
Graphic Organizers – Collection of printable graphic organizers useful for planning, organizing, and solving
Visuwords – Word relationship graphic organizer with dictionary and thesaurus
Wordle – Online tool for creating word clouds

Additional information and resources


MathTV is an online site that provides over 10,000 video tutorials covering topics from basic math through calculus. In each video tutorial, a student or adult math teacher explains, demonstrates, or solves a specific example. Multistep problems are written out step-by-step using traditional math logic. Most videos are a couple of minutes long and users can select which tutor they want for each lesson. Other features include:

  • Multiple videos by different tutors for each example.
  • Video tutorials available in closed captioning.
  • Video tutorials available in Spanish.

Find more information and videos at MathTV.