Thinking like a Mathematician: Helping Students Meet Higher Math Standards

When we think of challenging grade level texts that align to high standards, our minds tend to gravitate towards Reading/English Language-Arts classes and finding ways to increase our student’s literacy competency.  However, my students – and even my honors level students – have more difficulty reading in math class then they do in reading class. If I give my math students a page of computational problems to complete, I know that most of them will do well.  However, when I give them a word problem or an extended mathematical task to complete that is surrounded by words, the results are not so great.

Many students give answers that don’t make sense and some students won’t even attempt the task. Just as we challenge students to read complex text, we also need to provide them with skills to increase their mathematical literacy, which is key to helping them meet higher standards. It’s as equally important that we teach our students strategies that will help them solve complex word problems that require the use of higher-level thinking skills.

What is math literacy and why is it different? We usually think that math literacy is consists of understanding math vocabulary.  However, even if my students can read and identify math vocabulary, my most fluent readers often still have difficulty reading and knowing what to do when working with word problems. There is undoubtedly more to math literacy than vocabulary.

My big “Ah Ha” moment came recently when I read about a teaching technique called, “Three Reads.”  The technique is one of a set of math classroom routines designed to increase mathematical thinking and reasoning skills.  It is described in the book, Routines for Reasoning, by Grace Kelemanik, Amy Lucenta, and Susan Janssen Creighton.  Math literacy is not just about vocabulary, but more about the structure of a problem. I realized that the skills students learn in other subject areas actually backfires on them when they apply the skills to reading a math problem.

If you look at the typical math problem and compare it to an average paragraph of a text, you will notice that the structures are completely opposite from each other.  A paragraph of text usually begins with a topic sentence that lets the reader know what the paragraph will be about.  The first sentence sets up our thinking and helps us collect the reasons and details that support the topic.  However, math problems are written with a reversed structure – the reader is presented with a lot of details and only at the end of the problem do they read the actual question that tells them what to pay attention to.

I realized that many of my students who are frustrated with problem solving are the ones who try to solve a problem after only reading it one time. The same students often try to solve the problem by looking for keywords and numbers, making calculations based on those keywords and numbers and often coming up with a wrong answer that makes no sense. A successful problem solver needs to read a problem more than once.  Sorting through details before getting to the purpose is too hard to do with only one read of the problem.

So how is the “Three Reads Routine” helping to change problem solving in my classroom?  The most important change has been that my students no longer stare after one read and immediately say, “I don’t get it.”  They now have a specific routine to follow. Once they’ve gone through the steps to in the routine, they have a more clear idea of how to solve the problem.

We begin with the first read just to get the context.  What is the problem about?… peaches? zebras? money? Numbers in an equation?  Students think on their own, share with a partner, and then record the information as a class.

The purpose of the second read is to interpret and understand the question.  Students restate the question in their own words individually, share with a partner, and then record the restated question as a class.

The third read is for the details.  What information is given? What is important to this problem? What information is important?  What are the numbers?  Do the numbers stand for quantities? Or… do the numbers show relationships between quantities? Is there a unit involved? Are there any other clues or hidden numbers?

In between each of the Three Reads, my students turn and talk with each other.  They work in pairs or groups and we collect information together as a class. More students participate and when it’s time to begin solving after the third read, more students are coming up with answers that make sense.

The Three Reads” Routine is helping my students think more critically, and meet the high expectations set for them by the state standards. Like any good routine, it is becoming automatic.  I know that it has made a difference in the way my students approach math problems and I am excited to see how it will make a difference in my students’ academic performance.

Cindy Evarts is a teacher at Martinsburg South Middle School in Martinsburg, West Virginia. She teaches math and English/Language Arts. Cindy is a National Board Certified Teacher and 2014 winner of the Presidential Award for Excellence in Mathematics and Science Teaching. She has been teaching for over 30 years and has worked with students in age groups ranging from pre-school to 8th grade.