When In Doubt … Multiply

By January 12, 2020July 1st, 2020Uncategorized

When in doubt multiply or add or…

Is this what your students are doing when given a word problem?  I have noticed that a large amount of students automatically respond to word problems by adding if they are in grades K-2 or by multiplying if they are in grades 3 and up, or they do nothing. They may look up at you with their big beseeching eyes and ask, “What do I do?” Instead of giving students answers, let’s give them a strategy that will serve them for the rest of their lives. Stop and jot.

I believe in setting students up to be as independent and confident as possible.

Stopping and jotting may be a strategy your students use during reading or writing time, but it can also be used during your mathematics instruction. Explicitly teach your students that when they get to a period, stop and jot down the information they think is important. For example:When given a word problem, when you see a period, stop and do something.
When you get to a period quickly jot down what you heard/read.
When you get to the period write a number.
When you get to the period draw a model.
When you get to a period stop and circle an important fact or word.
When given a word problem, Do not read through an entire problem without stopping and jotting information down.
If you do not jot something down the first time, go back and reread it again.

Students are not allowed to get to the end of a word problem and ask if this is adding or multiplying (especially since most problems can be solved with multiple operations).

Last week while working with 2nd, 3rd, 4th and 5th graders I provided explicit instruction on how to use the stop and jot strategy.

“Today we are going to be solving a word problem. One thing mathematicians do when solving a problem is stop and jot down information that they think is important. Today we are going to try that strategy together. I am going to read the problem with you and when we get to the period we will stop and jot.” 

While working with a group of 4th and 5th graders, I read the first sentenced. I stopped and pointed at the period. I looked at the students. They looked back at me. I looked back at them and said, “This is the part where you jot something down. What would make sense to jot?”
The students quickly jotted something down. I read through the next sentence. I stopped when I got to the period and looked at the students. They looked back at me. Once again, I said, “This is the part when you jot something down. What would make sense?” The students jotted something down.

This process went on for 3 different word problems. By the time we got to the third word problem students began to jot something down at the periods with some automaticity. One wouldn’t intuitively think that it requires this much explicit instruction to implement a new strategy, but sometimes it does.

I noticed, however, that the effort was worth it, because while students struggled to solve the first word problem, they did better with the second try, and much better with the third. Plus they were putting a new strategy in their toolbox for solving problems without their teachers ongoing prompting.

I wondered if this strategy would work for multi-step complex problems as well. My 6th grade daughter asked me to help her with her homework (Yay!). As I read through the problem, I actually began to panic a little bit, it was confusing. It was a 5 step problem involving multiple operations and models (addition, multiplication, ratios, ratio tables, fractions, percents, and comparisons). I wondered, “How am I going to solve this problem!?1 And make sure she understands how I solved it.” I reminded myself to go back reread the problem and stop and jot when I got to the period. Guess what? The strategy helped me calm down, organize my thoughts, come up with a plan to solve the problem step by step, and making my thinking clear to my daughter. Is it a perfect strategy? No, nothing ever is, but it can be useful. So next time you get to the period, stop and jot.

Researchers have found that the use of pictures and drawings supports students’ comprehension and concept; understanding of mathematics (Marino et al., 2010; O’Connell et al., 2005)

What do you think about this approach? Can you see it being useful for your students?

We can teach them all of the operations, but we can also teach them how to become lifelong problem solvers.

Sometimes students flail, fail, and flounder. We often instinctively want  to save our students by giving them answers. We can also give students opportunities and strategies they can use to save themselves. If we jump in with answers the moment a student begins to falter, we are teaching students that they do not have to or cannot figure problems out for themselves. However, once students sit down to do homework, take a test, or leave your loving presence, how will they save themselves?