Two trains are heading in the opposite direction…: Teaching problem-solving

I’ve always hated the train problem; you know, the one in the title?  I’m not sure why; I think because I would typically read through it once and become defeated since I couldn’t immediately come up with an equation I could apply. Therefore, it must be hard.  My experience has been that most students feel this way about problem-solving.  The STEMtistic below says it all.

THIS IS A PROBLEM!

Our education standards for mathematics expect that students are engaged in problem-solving.  The National Council of Teachers of Mathematics (NCTM) Principals and Standards for School Mathematics has verified that problem-solving is an integral part of learning.  OK, then how do we rewire students’ brains so that they don’t fear math problems?  How do we help students access the math?

To start, we need to teach our students how to read like a mathematician. 

We need to teach our students how to bring the linguistic and math clues to the surface.

We need to engage students in understanding the problem before they try to solve it – or worse, freeze and dismiss it all together.

Close reading is eduspeak for reading deeply for a purpose. It is more than just skimming. In the literacy world, close reading includes three phases:

  1. Reading for Key ideas
  2. Rereading for craft and structure
  3. Rereading to integrate knowledge and ideas.

I’ve been to several trainings on how to close read science and social studies texts and articles, but I have never been trained on close reading in math; I didn’t think it even applied.

Then came those 5th grade classroom teachers I was privileged to visit last month. During one of those visits, I saw close reading . . .  in math!

The close reading strategy was called the 3 Reads Protocol. In this protocol, students read the problem three times, each with a particular focus. While the strategy was used in a 5th grade classroom, it can be used just as effectively at the middle school and high school levels.

Below was the problem given to the 5th graders:

On the first read, the problem was read chorally (as a class) then covered up and students were asked, “What is the problem about?” Students talked to their study partners about what they remembered of the situation – not the math, just the context. Students answered that the boy in the problem was doing some of his homework before dinner and some after.

Next, students read the problem aloud a second time with their partner and were asked to determine the key quantities and key words from the problem.  After 2 minutes of partner time, the teacher listed the quantities and words on the board.  The students answered with the obvious fractions, then included a smattering of words such as completedbefore, after, remaining, dessert, and the rest. Students were asked why these words were important and how the quantities were related.

The third read,  again with a partner, focused students on the question, What is the problem asking us to find out?  After determining this, students were asked to draw a diagram that included the quantities and their relationship. Some students started with a tape diagram, others with an area model.

Only after these three readings and active thinking did students begin to actually solve the problem in partners. There was a lot of math discourse happening around the room that continued for a good 15-20 minutes.  During this time, the teacher walked around the class, listened in, asked questions about student thinking, and noted which students she would call on during the whole class discussion.

Students were then brought together as a class.  The teacher asked specific partners to share the models they had drawn.  As each model was shown, the teacher asked questions of the class such as:

  • How does _________’s diagram show 3/7?
  • Where is ¼ in ________’s diagram?
  • How are ¼ and 3/7 related in this diagram?

She made sure to ask students who had made models that had taken a divergent path to explain their thinking and asked the same questions she had asked the students with the correct models. Once the teacher went back to the class list of key words, the class came to an agreement about which model (s) made the most sense and the answer that was correct.

IMG_0432

After whole group discussion

We want kids to learn how to solve problems on their own. We need to give them strategies to do it!   Like any skill we want to master, teaching kids how to read closely in math will take time, practice, and coaching – especially if we want to change attitudes about word problems in general.

So, try the 3-reads protocol in your math class! Like most new strategies, it is not likely to go super smooth the first time. Don’t give up! Try it again and get your students out of the bathroom and cleaning up in math instead!

BTW:  I solved the train problem…eventually!

Train Problem - SOLVED!

 

 

 

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One thought on “Two trains are heading in the opposite direction…: Teaching problem-solving

  1. Joe Parvankin

    I love the title of this post

    On Mon, Feb 29, 2016 at 10:16 AM, coaches corner blog wrote:

    > bethandshannon posted: “I’ve always hated the train problem; you know, the > one in the title? I’m not sure why; I think because I would typically read > through it once and become defeated since I couldn’t immediately come up > with an equation I could apply. Therefore, it must be h” >

    Reply

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