Thursday, December 18, 2014

The Language Of Math, The Language in Math, and Math as a Foreign Language

The math anxieties and math phobias so many people experience result from a lot of misconceptions about mathematics.  Many people simply consider themselves not mathematically inclined, as if there is a dreaded gene responsible for being bad at math, or some sort of Mathematics Deficiency Syndrome (probably caused by drinking blue Kool-Aid as a kid, or eating those Pop Tarts with the red sprinkles).

Sadly, many people have convinced themselves they are bad at math because when they were a child, an adult told them so.  Sometimes it was a teacher that bore the bad news:

"Some people just aren't math people, and based on your grade in my class, that some people is YOU."

Other times it was a parent:

"Don't worry, son/ daughter, you just happen to come from a long, proud line of good people who are very bad at math.  Just remember that we love you anyway."

What compounds the problem of anyone mistakenly believing he or she is hopeless at math is that it is commonly accepted and shrugged off, or even worn like a badge!  It has become cool in some middle school and high school circles to be "mathematically challenged."

There is no doubt that we all learn in different ways, and some of us excel in areas where others struggle.  But math is such a large and vague category of something to be good at or bad at; while about 7% of the population are born with dyscalculia, the math equivalent of dyslexia, this does not mean such individuals cannot excel in problem solving, or geometry, or even advanced mathematics. Math is a great many subjects in one, and almost all barriers to success in each can be overcome.

There are all sorts of learning disabilities out there, including dyslexias and dyscalculias, but we do not dismiss them as conditions we can do nothing about.  When a child has a reading disability, we work diligently with the child to make sure he or she can read.  Likewise, if a child has a learning disability related to numeracy, we work just as hard.  These learning challenges affect a small percent of our students, yet far more adults and teenagers gleefully proclaim they are no good at math.

What we are experiencing in our classrooms is not a great video game induced increase of Mathematics Deficiency Syndrome, or an increase in the number of children borne with the bad-math-gene.  What is far more likely is that our students today are coming from a wider variety of math backgrounds.  Important learning experiences may or may not have impacted their brains at that crucial stage of child development where kids have huge capacities for learning language and mathematics.

That's right!  Language and mathematics.  Many parents remember when their children began soaking up words and phrases like a sponge, and those of us who are not parents get to see examples of this every day posted on facebook.  "Watch this video of our Junior reciting the French alphabet backwards!"  Brain research has determined we gain huge amounts of language knowledge between the ages of 3 and 9.  And that also happens to be when children learn a lot of number sense and become fluent with their facts.  That is, unless they don't.

Just like a foreign language, math is a language that is best introduced at an early age, and not just with flashcards, but with actual verbal intercommunicating.  We don't learn to speak a foreign language by memorizing long lists of vocabulary words alone, and children do not learn to become fluent in math by memorizing long lists of facts.   We learn new languages by speaking them.  Beginning Spanish students learn how to respond to "Como estas?" before they knew how to spell it, so they can gain an understanding of how the language works and what it sounds like.  Likewise, we often teach the word "half" before we teach what a denominator and a numerator are, and how to even write fractions, so we can introduce the concept for our students to understand.

A criticism of the earlier editions of Everyday Math and other broad math curriculum programs is that they tried to squeeze too many topics into one school year, and sometimes did not give children deep enough understandings of the concepts being introduced to them.  Some students, especially those who for one reason or another may have missed out on important early childhood mathematical learning experiences, advanced through the grade levels with less than stellar understandings of basic operations and concepts.

What we are seeing more and more of with modern mathematics instructional resources and curriculum materials is an effort to teach mathematics more for understanding, and less for procedural memorization.  Even the Common Core features fewer content standards per grade level, with the expectation that math curricula will be constructed to allow for deeper exploration into math concepts.  In addition to the content standards, the Common Core also includes Standards for Mathematical Practice, which are guidelines not for what math should be learned, but how that mathematics learning should occur.  There is a tremendous effort to incorporate a wide variety of learning experiences into mathematics curricula nationwide.

While this is seen by many as a big step toward increasing math proficiency, it also presents challenges.  Students are being asked to problem solve, express their thinking on paper and share strategies with peers not only more often, but at a younger age (see previous post in this blog from November 20, Everyday Math, Cognitive Development, and "Explain..").

Learning mathematics relates to language learning, and today students are also being asked to use language more often in mathematics.  This is hard for students who struggle with language learning, and students who might not be learning in their first language to begin with.

In Lewiston, Maine, nearly 20% of all students are learning English as their second language.  When I taught in Lewiston, I often found it difficult to determine whether my ELL (English Language Learner) students were struggling with the mathematics of a particular lesson or unit, or with the language itself.  I quickly learned to slow my delivery in the classroom, and to check for understanding with greater frequency, but I still found it to be one of the most difficult challenges of my teaching career. I wanted to be able to speak in their first language.  Progress in math can come more slowly for students who have difficulties with reading, and for students who have had fewer experiences playing with numbers and quantities in pre-school.  Now consider a student who is just beginning to master the English language after being raised to speak one or more other languages.

Jessica Sturges shared with me some important pieces for teachers to incorporate into their instruction when there is an ELL student on board (in fact, I would recommend these practices even if there are no ELL students in the class):

#1:  Speak slowly and clearly

#2:  Provide students with vocabulary lists that pertain to the current unit to take home and study before the unit is taught.

Here is a sample Everyday Mathematics graphic organizer Ms. Sturges shared with me that shows how she presents unit vocabulary to some of her students:



In this example, there are some words listed in the student's first language, but that is not always an option, and it is not always necessary.  A word bank used in this manner could be helpful to any student learning new concepts.

Finally, an important thing to remember both with ELL students and other students who have trouble showing their thinking on paper, is that the language of mathematics can be confusing.  Upper elementary, middle school, and even high school students can still be heard using words like "times" or "timesed" when they really mean multiply or multiplied.  Early elementary is a time to encourage all students to use "add" and "plus" appropriately, as well as "subtract" and "minus."  Add is the verb and plus is a conjunction.  Subtract is a verb and minus is the conjunction ("take away" is often used in kindergarten and first grade in place of "minus," but by second grade, we should be encouraging the use of minus as the proper conjunction).  And likewise, multiply is the verb and times is the conjunction.  Division has some challenges as well... Remember guzinta?  6 guzinta 42 how many times??  Division all too often represents a great void of essential understanding.  I think we'll save that for a separate post.

It is hard for struggling students.  Minus, subtract, take-away, what is the difference, how many more than, how many less than, how many are left... The list goes on.  It is ok to use and encourage all of these representations of subtraction, but it is also important to check for understanding frequently.

There have been entire books written on the language connection to mathematics, but for now let's just remember that as we present new ways of learning mathematics, we are trying to tap the natural hunger for learning that occurs in a child's developing brain, in order to build a greater foundation for understanding as they tackle more complex mathematics concepts in the future.  This is why we use the word fluency in mathematics (more on that topic in a future post!).  The more fluent we are in a language, the less it actually hurts our brains to use that language.   The same is true of math.  With greater "fact-fluency" and overall mathematical fluency, complex problem solving becomes less painful, and potentially enjoyable and engaging.

For further reading on math and the brain, and the links between mathematics learning and language learning, here are a couple online resources:

http://www.pbs.org/wgbh/misunderstoodminds/mathbasics.html

http://www.mathematicalbrain.com/dysclink.html

http://www.ascd.org/publications/books/105137/chapters/Mathematics-as-Language.aspx

http://www.doe.virginia.gov/instruction/esl/resources/strategies_teach_math.pdf

And here is a highly informative series of links from PBS' "Child Development Tracker," for several age levels relating to learning mathematics:

http://www.pbs.org/parents/childdevelopmenttracker/five/mathematics.html

http://www.pbs.org/parents/childdevelopmenttracker/six/mathematics.html

http://www.pbs.org/parents/childdevelopmenttracker/seven/index.html

http://www.pbs.org/parents/childdevelopmenttracker/eight/index.html

And relating to language learning:

http://www.pbs.org/parents/childdevelopmenttracker/five/language.html

http://www.pbs.org/parents/childdevelopmenttracker/six/language%20.html

http://www.pbs.org/parents/childdevelopmenttracker/seven/language.html

http://www.pbs.org/parents/childdevelopmenttracker/eight/language%20.html