Close Reading in Mathematics

Ain't that the truth! Take a look at the problem solving strategies below.... Any of them look familiar? You may even be using one of them in your own classroom. You may want to rethink the way you use these -- none of them are necessarily bad, they are simply used too early in the process in many classrooms and often do not create a need for students to think as deeply as they should when entering a problem solving situation. 

Despite our best efforts and best intentions, we still find that students struggle with word problems more than any other type of problem. The strategies above probably work great IF the students understand what the problem is asking in the first place, but that is exactly where problem solving process breaks down for most students - they struggle to understanding what is being asked.

If they don't understand what is being asked, how can they possibly make a plan? If they can't make a plan that works, there is no way they can solve the problem. And if they can't solve the problem, obviously they can't check their work. See the dilemma? Students must FIRST understand what the problem is asking and none of the word problem strategies shown above really help them learn how to do that. 

That is where we can take a lesson from Common Core ELA (English Language Arts) . In ELA classes, students are being taught a process called "Close Reading" -- we can adapt that same process in math class to help students become more proficient mathematical problem solvers.

So, how do we get started in this process, you ask? Well, let's begin with an understanding that this is going to be a PROCESS, not a worksheet that we simply hand students and then "wish them luck". Let's imagine that our students are presented with the following word problem:

The first step in this process is "Read to Make Sense". Remember, this is a process, not just a one shot read. In the classroom, it may look something like this: 

​Teacher: Who would like to read the problem for us?
Student 1: Lindsay has four more baseball cards than Roderick. Lindsay has sixteen baseball cards. How many does Roderick have?
Teacher: Okay, so think about this problem and what it means. Tell me in your own words what is going on in the story.  But you can't use any numbers when you retell the story!
Student 2: Lindsay has some baseball cards and we are trying to figure out how many Roderick has.
Student 3: Lindsay has MORE cards than Roderick and we are trying to figure out how many Roderick has. 

This process may continue through several students either explaining their understanding more deeply or simply rephrasing each other's explanations in their own words. 

At this point, don't solve the problem or even proceed with this specific problem. Students need A LOT of practice time just wrapping their thinking around what the words mean; so instead, present another word problem and, again, have students rephrase the problem in their own words --- this repeated process helps them to MAKE SENSE of the words rather than simply looking for key words and numbers that they may or may not understand. Step 1 will be repeated over and over across several days before moving on to Step 2. Don't get too wrapped up in the idea that you haven't solved the problem; the idea is to practice how to MAKE MEANING of the words. Do this every day until you are convinced that students are fully proficient. Once they "have it", it is time to move on to Step 2. 

Step 2: Now that students have wrapped their thinking around the meaning of the words, it is time to begin looking closer at the details (we're not solving, yet). This is the point in the process that we should help students recognize that there are various problem structure types. Is this an "Addition Structure with Result Unknown"? or perhaps it is really a "Subtraction Structure with Change Unknown"?  We must help our students recognize that not all problems come in the same structure. Students should become accustomed to seeing the many different types of problem structures (click HERE to read more about Problem Structures, also referred to as Situation Types by AchieveTheCore.org).


At this point, we are looking at text features, such as charts and graphs, and perhaps circling the numbers and determining what they mean -- students should always be able to express what the numbers represent -- does that 4 represent 4 cards or 4 packs of cards? In the story about the baseball cards, students may be easily led astray to believe that we are adding 4 to the 16 since it says "4 more" -- Do you see why working to understand the problem structure and the context of the words is SO important before we begin working with the numbers? 


Just like we spent several days on Step 1, we will spend focused time on both Steps 1 and 2 together until students are proficient. Once that happens, it is time to bring out Step 3 in the process.

Step 3 is all about representing the problem. Some students will draw a sketch, some will use tally marks, and many will benefit from physical manipulatives (regardless of their grade level!). At this point, we want students to be able to show that they can create a representation of the problem, for some, this may be a simple equation if they are ready for an abstract representation. (A word of caution here: Be careful not to allow students to spend so much time drawing detailed pictures that they never get to the math or completely forget the purpose of the representation because so much time was invested in the drawing. Remember, we are trying to teach students to be efficient in their calculations, too). 

Steps 4 & 5: Once students understand the first three steps in the process, it is time to move on to Steps 4 & 5 -- this is perhaps the only two steps that can be presented together within the same work session. At this point the focus is on reasonableness and accuracy. Help students to ensure that they have actually answered the question that was asked. It would be a shame to have amazing representations and calculations that do not answer the question being asked.