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Story problems in math

10/28/2018

Kaitlyn has 6 boxes of pencils with the same number of pencils in each box. All together she has 24 pencils. How many pencils are in each box?
What was your strategy for solving this problem? Did you look for a key word/phrase? Did you skip over the story and go straight to the numbers to help you solve? If you answered "yes" to either or both of these questions, I want to explain why this approach causes problems for students in math. According to the research of Clement & Bernhard (2005), the key word strategy sends a terribly wrong message about doing mathematics. The most important approach to solving any contextual problem is to analyze it and make sense of it. What I have discovered is that the key word approach encourages students to ignore the meaning of the problem. When this happens students don't take the time to think about what's being presented in the story; instead they look for an easy way out of persevering through a problem based on the information presented.
If you are a teacher reading this post, please don't feel guilty because I did the same thing for many years when teaching my students how to solve word problems. I had posters with specific key words displayed on poster boards and I even encouraged students to use those posters as a reference when they needed to. I did it that way because that was the way my teachers taught me, it worked, and I would do the same for my students. Over the years as more research has surfaced and math programs have been revamped in a way that is now designed to provide opportunities to develop students conceptual understanding of mathematics. My philosophy has definitely shifted as well. Before leaving the classroom a few years ago, I really found myself enjoying teaching math lessons that allowed my students to find several ways of tackling problems.
Now as a Math Coach, I especially love listening to children's mathematical thinking. I also appreciate hearing them explain their approach to making meaning of numbers; this concept of math reasoning is part of what is known as Cognitively Guided Instruction (CGI). My challenge for you this week is to read the article in the Intentional Toolkit titled "What is CGI and what does it look like in a classroom?" This short article outlines some specifics of how this type of instruction transforms teaching and learning in the classroom. I'm also sharing an article titled "Key Word Strategy". This article list four ideas that teachers often overlook when introducing story problems to students.
As always, I hope you find this information useful, perhaps your school is currently using the CGI framework and if so, feel free to comment on its impact in your classroom. Until next time...go out there and be GREAT!

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Great Conversations

10/12/2018

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One of the things I've learned about people is that given a topic that sparks their interest, they will spend time talking for hours...what I've also learned is that the same thing goes for children. This week I was invited to visit a 5th grade class to watch a math lesson. For the lesson, students were asked to find the volume of the space inside their classroom. The teacher assigned students to work in groups of 4-6 based on the measuring tool used for the lesson. Teams had the option of measuring the classroom in cubic inches, cubic centimeters, cubic feet, and cubic meters. Before sending students off to work, the teacher reviewed the standard units of measurement. She also explained that when all the units were built, they would look at them together to discuss why some units would work better than others for measuring a large space.
As students went off to work in small groups, both the teacher and I walked around to listen in and observe. Although the teacher did not assign a specific task, you could see the students who stepped to the plate to lead the activity. In one group, I noticed a girl who was insistent that the yard sticks be taped correctly so her groups measurements would be as close to accurate as possible. As she watched her team place yard sticks together to build a large cube, she sent others on her team off to tear pieces of tape and hang them on the edge of the board so the people in charge of tapping could simply pull a piece from the board. Other groups used inch rulers to build their cube and had similar ideas for team work. As the children were actively engaged in the lesson, both the teacher and I asked questions to help them make their plans for their model more explicit (e.g., what they planned to measure, what measurement tools they intended to use, and how they would use their measurements to determine the volume of the classroom).
Prior to the lesson, the teacher was intentional about making sure students understood the meaning of specific math words that would be used in this lesson and she also encouraged them to use that vocabulary when working in teams. Students posed questions to one another and even used mathematical reasoning when building their cube. I especially enjoyed hearing them laugh as they made connections between the lesson they were doing and what they had seen before that was like this activity. One boy commented "I knew there was a reason I watched all those Bob The Builder Shows when I was little"!
Great conversations can certainly make a huge difference in the learning process. As students wrapped up their lesson by sharing their plans for carrying out this activity, I told them that I will come back to their class to hear what their findings are! Below are some pictures that I wanted to share from the work that 5th graders were doing in class.
This week in the Intentional Toolkit, I have shared information that focuses around team building activities in math. I hope you find these resources helpful. Until next time...go out there and be GREAT!