25 simple steps to solving Word Problems

I'm surprised you even clicked on this blog, after reading a title like that. Seriously though, who wants to learn (or has time, let alone mental capacity to absorb) 25 whole steps (which is NOT simple, by the way) to solve word problems?

But this is the type of absurd pressure we place on our students in Elementary schools in efforts to cram comprehension down their throats, get them to pass their annual accountability assessments, or convince them that they have some false level of mastery. You know what i'm talking about. All of the colorful, cute posters that we spend endless minutes dressing up and hanging confidently on our walls for students to reference when we leave them to solve word problems in isolation! Let me jog your memory...

Any of these look familiar to you!? I can honestly say I used that last one (RUBIES) one year, after seeing it at a local conference. I was duped into believing that my students who had 1-2 years of gaps, were struggling in ELA and read on levels lower than their current grade would be able to take a few doses of this poster medicine and magically make growth or passing grades in math.

Think about the title of this blog and how silly that sounded...that's just how silly that RUBIES acronym proved to be to my students. Some of them came from other districts where they had been exposed to (through drill and kill) various other Acronym posters forced upon them and here I was saying, "Forget that smut and learn this NEW-TRIED-AND-TRUE method!" At that rate and under those conditions, by the time a 3rd grader exited elementary, they could have easily been exposed to 25 "simple" steps to solving word problems!

I tutor this 5th grader (weekly) who attends school in a different district than the one I currently work in. This student has been the sad victim of several teachers who were inexperienced and/or had crumbled under the pressures of being a teacher, leading to their quitting in the middle of the school year. After weeks of re-teaching concepts from a conceptual and representational standpoint, I tested the waters with introducing him to abstract learning through the lens of word problems. I had him read (and re-read) the word problem and tell me what he thought was going on in the problem.

I had him talk me through the meaning of each sentence and then I asked the question that caused me to fall out of my chair:

"What do you think the problem is asking you to do? How do you know?"

To which he replied, "I think we are dividing because it says 'which'." 

*crickets...blank stare*

I could have screamed! Why did he think "which" meant to divide? Perhaps it had something to do with those posters? After some brief investigating, I uncovered that his teacher had taught him the following:

"Which" means divide

"How much" means to add

"How many" means to subtract

...and so on. 

I stopped him and mentally scolded that teacher. I was up against a much bigger giant than just closing his years of math concept gaps, and firming up his ability to comprehend word problems...now I also had to break his bad habits and train him in new ones. 

This is an example of the gaps we can create and the ultimate fate of giving students cute-sy short cuts and fast food feaux learning tricks rather than helping them understand how to think through a problem. 

John Van de Walle (as if I could write a blog without quoting my Mathematical boyfriend) says its profitable for students to draw pictures, act out and model (with objects) word problems as early as Kindergarten so they (in true slow cooker form) grow up into a deeper, more solid foundation of how to think through and solve word problems. The TEKS even make provisions in their explicit wording that yearly building on students' developmental abilities should suffice in regard to word problems. 

Model the action of joining and separating... 

(K.3A)

Solve Word problems using objects and drawings...

(K.3B)

Explain the strategies used to solve problems...using spoken words, concrete and pictorial models... 

(K.3C)

Use objects and pictorial models to solve word problems involving joining, separating and comparing... 

(1.3B)

Represent word problems involving addition and subtraction...using concrete and pictorial models... 

(1.5D)

Explain strategies used to solve problems...using spoken words, objects, pictorial models... 

(1.3E)

Represent and solve addition and subtraction word problems... 

(2.7C)

Not to mention the explicit use of strip diagrams in 3rd-5th for multi-step problem modeling. 

Let's commit (for the NEW YEAR) to cut the tricks out of our lesson plans and get down to supporting student thinking. This means that among the other numerous hats we wear, we must also be reading teachers! Guided Math and Math Workshop are great vehicles through which we can foster such conversations with students. We have that small teacher to student ratio (uninterrupted time) to have a two-way conversation with students about thinking through each sentence of a word problem, providing them manipulatives and scratch paper to model and draw out their thinking. I can guarantee this method is NOT simple. But for my class of 22 (full of students with severe gaps and low reading levels) this proved successful as I watched my students gain confidence and make significant steps in growth. 

If you have ideas of innovative and non-cliche methods that have worked in YOUR classroom, drop your ideas, videos and/or pictures in the comments. Or follow me on Twitter @kloneal2 and leave me a comment! 

Kindergarten Numeracy Activities

        In Kindergarten, when considering the notion of comparing numbers (and even if we back up to the ideal of magnitude of numbers), we tend to jump ahead of the development process for students. Donna Boucher talks about how “Alligators are for swamps, not for comparing numbers” and this is completely accurate. However, we lean towards this animation of a numeracy concept simply because we don’t know how to help students retain the understanding of comparing two numbers.

Our state standards address, very directly, the method with which we can support students development in comparing numbers. John Van de Walle encourages this approach in his book, Teaching Student Centered Mathematics. Kinder students should focus heavily on not only building numbers (to support their one-to-one correspondence) but also have exposure to multiple representations of numbers (to support their perceptual and conceptual subitizing skills) while comparing such models with words. I would even highly suggest that students use two comparison statements so they are acclimated to the notion of “fewer” and “less” as critical comparisons.

A member of my PLN (Professional Learning Network) on Twitter shared these cards and I found them quite helpful in supporting the idea of students using them to compare numbers. They are multiple representations of numbers and can be used for various reasons. 

Here are a few:

            
          Comparing numbers. Have students shuffle the deck and place them face down. Then with two players, each player turn over one card and build (with linking cubes) their number and then express the comparison(s) using words.

          More Less or Equal. Have students shuffle the deck and place them face down. Have them spin a spinner that has options for “More, Less and Equal”. Once pulling a card and spinning the spinner, have students build (with linking cubes) a number more, less or equal (based on the results from the spinner) to the number they pulled from the deck.

         Build the number multiple ways. Have students shuffle the deck and place them face down. After pulling a card, have students build that number using double sided counters on a five or ten frame. Then have that student build or represent that number as many different ways as possible. (example: if they pull the number eight with fingers five and three, have them build eight as five and three on the ten frame and again as four and four to represent the same number). They might even record all of the ways they built the number.

         Decompose it. Have students shuffle the deck and place them face down. Draw a line down the middle of a plastic bag with a permanent marker. Turn over a card and place that number of beans inside the plastic bag and seal it. Have students slide beans around on both sides of the line to represent different ways to decompose the number. Once the number has been decomposed different ways, pull another card and replace the beans in the bag with the new amount.

Just a few numeracy activities that would support students development if they remained in centers as TEKS based station activities for Kinder! The great thing about these activities are they can be extended and used with numbers 11-20 and reused at the beginning of first grade as scaffolded concepts.

Don't forget to get your set of Deca-Deck Cards

Example of Stations listed above that I created for my District Kinder Teachers from ideas I gathered from reading John Van de Walle and viewing other resources.
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