Counting & Realia

OR “Why Counting Collections Should Be In the Toolkit of Every Special Education Math Teacher.”

Over the years it has become clear to me that commitment to good instructional activities (or routines) is the bedrock of any good math class, special education or not.

Magdalene Lampert defines instructional activities (or routines) as “…well designed procedures that have been proven in practice, that take into account the complexity of the goals that need to be accomplished, and that allow the practitioner temporarily to hold some things constant while working on others.  The use of such routine procedures involves not only acquiring the capacity to do the steps in the routine in an actual working environment but also the learning professional norms or “principles” that would enable a practitioner to make appropriate judgments about when and where it is appropriate to use the routines.”

This is especially enticing in a special education classroom where holding constant parts of the classroom (behavior, anxiety, comfort level with the task, familiarity of expectations, etc.) in order to highlight and work on others (mathematical proficiency) is an ideal situation for learning.

One of my favorite instructional routines is called Counting Collections.

If you click the link you’ll be taken to, a site built through the College of Education at the University of Washington.  There you can find more information about Counting Collections and many other fantastic instructional routines like Number Strings, Contemplate then Calculate, and more!

Another resource on discusses ambitious instruction for students who are English Language Learners.  Many of these strategies would also benefit students with disabilities who struggle with receptive and expressive language.  One of my favorite strategies is using visuals and realia.  Visuals are pretty self-explanatory, they are the visual representation of a concept.  Students who struggle reading the English language benefit greatly from visual representations, not only of mathematics content, but also teacher directions and classroom routines.  Here, however, I want to talk about realia, which is defined as

Realia is a term used to describe real-life objects brought into the classroom to help with students’ comprehension of a lesson, concept, idea, and English language development. For example, a teacher doing a unit on the Gold Rush, might bring in a pan, a small pickaxe, an apron, and small pieces of imitation gold nuggets. A teacher who is going to read the book aloud to her students or have her students read independently, might bring in objects that are in the story or that represent key ideas in the story.

The concept of realia is an important one for special educators to become familiar with.  I think many teachers of students with disabilities already use realia out of the necessity to make abstract concepts become more concrete and hands-on.

My Argument: Combining the instructional routine called Counting Collections and the pedagogical concept of realia is one of the most potentially rich contexts for teaching amth to students with disabilities.

Differentiating instruction has long been thought of as the holy grail for working with students with disabilities, unique learning needs, and disparate goals within one classroom.  It is my postulate that counting collections with realia provides the opportunity to naturally differentiate without much extra work for the teacher.  In one classroom different students can be working on 1:1 correspondence and fractions at the same time.

An example would be at our school store.  One class is responsible for counting the inventory of the school store to identify which items need to be replenished.  If there are 16 juice boxes of different flavors, students can work to count the total amount of juice boxes (1:1 correspondence) while others are deciding what part of the whole each flavor represents (fractions).

Counting a collection of juice boxes

Counting a collection of juice boxes

Other contexts in which we have combined the ideas of Counting Collections and realia are counting money from our school play ticket sales and counting produce from our school’s CSA (Community Supported Agriculture).

Counting money from ticket sales for our school play

Counting money from ticket sales for our school play

Counting sunchokes at our school's CSA

Counting sunchokes at our school’s CSA

My Suggestion: If you are a special education math teacher consider integrating Counting Collections with realia into your curriculum!

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