Friday, October 16, 2015

Flexible Language and Everyday Math

In an effort to be developmentally appropriate, the Everyday Math units we teach include some unique terminology within the huge bank of mathematical vocabulary we deliver to our students.  The vast majority of Everyday Math vocabulary terms are universally acknowledged in mathematics, and are emphasized in the Common Core math standards, but some have been substituted by the authors.  Just as we teach a variety of algorithms for adding , subtracting, multiplying and dividing, we also should include standard mathematical terminology alongside Everyday Math terminology, or we risk students running into roadblocks of understanding down the road.
  • Number sentences and number models are terms Everyday math uses to represent expressions, equations and inequalities.  It is especially important to familiarize your students with the word "equation" alongside the Everyday Math terms, as equation does not show up regularly in Everyday Math units until grade 4.  There will be many times when students come across the term equation, including on standardized assessments, and we want them to be prepared and familiar with it.  Does that mean you need to test your students on the meaning of "equation" and "inequality" ?  No it does not.  But taking regular opportunities to use these words when you teach is important.  For example:  "Janet just gave us a nice number model, also known as an equation, to show us a way of writing six plus five equals eleven.  Equations are number models that include an equal sign in them."  Or another example would be:  "Four times three is a number model for that array, because it shows four rows of three, or for groups of three.  'Four times three' is also known as an 'expression,' or an 'operation,' because there is no equal sign, just two factors and a multiplication sign."
  • Number Stories  are word problems.  "Number story" sounds a lot more pleasant to deal with than "word problem," but we want students to know these two terms are the same.  So it is encouraged to introduce your students to the term, "word problem,"and use it from time to time alongside the term "number story."  For example:  "The directions are for you to use the data in the graph to write your own number story for your partner to solve.  Number stories are also called "word problems," as they are like regular math problems that use words as well as numbers to help you understand them."  
  • Turn-around rule is the term Everyday Math uses to refer to the commutative property of addition and multiplication.  It has a lot of syllables, but it is a specific rule of mathematics we cannot allow our students to ignore.  Use it in your instruction when you can.  For example: "Yes, Janet, four times two equals two times four is an example of the turn-around rule, also known as...????  Who can tell me the official mathematical term for the turn-around rule?  Let's all say it together... The Commutative Property!  Well done.  The commutative property of multiplication means you can multiply two factors and as long as you don't change the factors, you will always get the same answer, no matter what order those two factors are in." 
  • Names is the term Everyday Math uses to refer to different representations of the same number.  Directions in the student journal may ask students to "create at least four different names for the number 8,"  and a student might write the word "eight," draw a four by two array, draw eight tally marks, and write the expression/ number model "4 + 4."  It is important for students to know that this use of the word "names" refers to "representations" of the given quantity.  In programs other than Everyday Math, it is unlikely they will ever see representations of quantities referred to as "names."
  • Use your reading and writing terminology in your math lessons.  Susan Dee came to me recently and asked if fifth grade teachers could use the term "think stems" and "thinking prompts" when Everyday Math uses "sentence frames."  These are clauses that help students find ways to introduce an idea or a strategy in their problem solving.  Perfect!  It is really important that our students carry over their reading and writing strategies into their problem solving in math.  Thank you, Susan Dee and Matt Halpern for thinking of our young mathematicians! 
Are there other Everyday Mathematics terms you have encountered that should be addressed?  Are there other words and phrases you use in other classes that are completely relevant to teaching math?Please let me know and I will add them to this list.  Thank you for taking the time to consider this topic.. It really is important that we paint a complete picture of the language of mathematics for our students.


Addendum:  Here are links to a couple articles related to the language we use in mathematics.  When is it appropriate to retire certain terms, phrases, and mathematical shortcuts?  The first link is directly related to elementary mathematics, but it also may be worth your time to check out the second article about middle school.  Not only is there some overlap, but it is also good to know what is in store in your students' next stages of mathematics learning after they leave you.  Here are the articles:




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