Tuesday, February 28, 2017

Scaffolding word problems



Word problems...ugh.

Of course we all know the trope: students can't do them, students hate them, blah, blah, blah.

Today I had a couple of very sincere teachers asking me how to help some of their students who are struggling with word problems. I did my best, but really I was just doing a bunch of hand waving and using big words like "pedagogy", "schema", and "comprehension". The truth is I wasn't entirely sure how to scaffold word problems for struggling students.

 I perused my Google Drive looking for ideas and found these gems, so I thought I'd share them.
Click to view the Google doc

The 8-Step process for drawing the bar model for word problems

I got this many years ago at a Singapore Math training and often find myself reciting it as a mantra while I'm trying to solve a word problem. Interestingly, the same 8 steps are mentioned in Eureka Math Grade 1 Module 6 Lesson 1.

The 8-Steps of  Model Drawing 
1. Read the entire problem.
2. Turn the question into a sentence with a space for the answer.
3. Determine who and what is involved in the problem.
4. Draw unit bars of equal length.
5. Re-read each sentence one at a time and revise the bar(s).
6. Put the question mark in place.
7. Work computations to the side.
8. Write down your answer to the problem.

Step 2 is really important because it verifies early in the problem-solving process whether the student even understands what he is trying to find.

Step 4 is surprisingly important. By starting with bars that are of equal length, the act of modifying the bars in Step 5 provides clues as to what kinds of math will be used to solve the problem. Resist the common urge to skip Step 4 and jump straight to creating the drawing! Once the model is accurately drawn, the necessary calculations practically leap off the page.
Click to view
How would this look for a 2nd grade problem? Check it out...
Brienne has 23 fewer pennies than Alonzo. Alonzo has 45 pennies. How many pennies do Alonzo and Brienne have altogether?



Click to view

A graphic organizer

Long ago I was given a graphic organizer that accompanies the 8-steps. I modified it so that teachers can give the struggling student a sheet for each problem to be solved. The problem goes at the top and then there are work spaces provided along with the 8 steps explicitly listed along side.

What I've learned

Far more important than the calculations is the model drawing. Spend far more time with your struggling students on the model drawing, since it is far more important than the actual calculations. Once the model is drawn, some students will use subtraction to solve the problem, while other students will solve the exact same problem using addition. Using the drawn model to understand the problem is far more profound than simply teaching students to look for key words.

In a nutshell:
Key words? Not good enough.
Drawing a model? Good!
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