Post # 21 Math Made Real When They Hold It In Their Hands

As I prepared a new presentation for educators working with English Language Learners, students who have missed class time in their home countries, I thought about the dual difficulties they encounter: content and language.  In this program we have students who are disadvantaged because they – through no fault of their own- have missed instructional time in their native countries AND now must attempt grade level content in a new language.  How does an educator even begin to think about ways to reach these students?

Many of us may encounter older students who will all too soon be in the work force and for all our talk about “career and college readiness” are at an extreme position on that scale.  These youngsters will confront an impossible time table to gain basic skills which will form a foundation for district level content mandates.  Thankfully these students are in a unique program that does attempt to address their needs.  I will also soon be working with educators in an adult education program whose students missed gaining fluency in math for other reasons.  It inspires me to think about those students who are too often pushed too quickly or are simply left behind.  

One of the features of this multisensory approach is a focus on instructional language.  It must be concept based, memorable and retrievable.  Another feature of this approach is what I call vertical thinking.  With a core set of fluent facts, complex concepts can be taught. 

There is no getting around the meaning behind the math.  A student must understand what operations mean.  Calculators are no substitute for conceptual understanding.  Technology is an essential element of today’s math, a tool for expanding competence beyond fact recall; but it is no substitute for reasoning. 

So as I prepare for my ELL presentation, I am focused on an algebra mandate.  These students who may just be learning to be competent at basic operations may be thrust into a more advanced curriculum.  Their conceptual understanding of pre-algebra must be rock solid.  We must decide which concepts form the conceptual underpinnings  and focus intently on student comprehension. 

We will begin with language and constructions.  Simple language paired with concrete manipulatives forms a bridge for many gaps.  As a student constructs solutions to applications involving integers, linear functions, ratios, square numbers and roots, meaning can be extracted while visual and tactile memories take root.  In constructing solutions the language input is enhanced.  The student sees the meaning behind the math take shape as he holds it in his hands. 

Simultaneous processing is a major key here.  The student struggling with language is the language made real, concrete and observable.  Then we can move to the representational:  number lines, graphs and the like.  For the student struggling with language for any reason, the concrete level of experience is essential, communal and explicit.  It is an elegant blend of math made real and meaningful as we read the math concepts with our hands.  

Here a student models the creation of an "improper" number in order to subtract. Composing or decomposing (formerly known as regrouping)  involves either the simplification of an improper number OR the creation of one in order to subtract. Newer math programs use only the terms composing and decomposing. Parents and those of us who came of age in the past are admonished to banish the words "borrow and carry." Teachers need to thoroughly understand the linkages between older terminology and newer descriptions that may be in use.  Our language matters.  The words we choose must be mathematically accurate and make sense to a child who is reasoning through a problem. We may need to conference with parents to illustrate connections between these terms and the older "borrow and carry" terms parents know and which remain largely procedural in nature.