In my years of leading in-person and online professional development, the idea of teaching students that certain “key words” signify a particular operation (e.g. “altogether means add”) often comes up when discussing story problems. People also generally see the power of the story problem routine that Investigations uses to support students in making sense of and solving story problems. This led me to start a conversation in a recent online course about the juxtaposition between the focus of the story problem routine and the strategy of looking for key words. An interesting conversation ensued:
Arusha: I noticed in the discussion forums for Session 2 a lot of people were talking about how the story problem routine can help students slow down and focus on making sense of problem before solving it. You talked about the story problem routine helping students visualize the problem and think about what the problem is really asking. By retelling a story problem, visualizing it in their mind, acting it out, modeling it with materials and thinking about whether there will be more or less in the end, students get a picture of what is happening in the whole problem.
Looking for key words is a strategy that is sometimes promoted to help students make sense of problems. This strategy, however, can prevent students from fully engaging in making sense of a problem as a whole and can be misleading. While some words can sometimes indicate a particular operation, they can also be deceptive, as in this example:
There are 28 students in our class altogether. 13 are wearing sneakers. How many are not wearing sneakers?
Looking for key words also focuses students on searching only for certain words and therefore moves students away from making sense of the problem as a whole. If students are able to visualize or build a model of what is happening in a problem, they are more likely to make sense of what is being asked and apply a sensible strategy for solving it.
Sharon: Arusha, this is a great point to bring up. I agree that it is more important for students to be able to explain and model what is happening in the story problem. I also often find that having students search for key words can end up misleading and confusing. Sometimes these key words are used in a different way and confuses students. I think your example is a great way to show this confusion because my students would read your example and see the word altogether. This key word could show addition, which would not necessarily be used in this problem. I think it is important to help students simplify word problems, but finding key words can become confusing. Maybe there is a way we can teach finding key words to help simplify a confusing story problem, but also allowing students to determine the meaning of the key words not just through memorization or a specific formula?
Ivan: I agree that having children visualize, retell, act out, and model story problems are essential from the very start. So many children get to fifth grade and believe math to be computation, and that their “job” with story problems is to cull the numbers, complete a calculation and move on.
The entire idea that math is a way we represent the real world and a way we can solve real world problems seems foreign to them. Math needs to have a context and a purpose for children right from the start for them to really understand what math is. Just as we read to children and tell them stories beginning in infancy, long before we try to teach them the ABCs, we need to engage them in real math before and during the time we teach them math facts and calculations.
It does look to me like Investigations is more context driven than what I have been using. I am looking forward to seeing how that plays out with successive cohorts of children.
Evie: I have shadowed many teachers who have highlighted “key words” as an often effective form of solving word problems. I even used a set of “keys” a co-teacher of mine made one year, which I found to be, overall, helpful. There was one for each operation: addition, subtraction, multiplication, and division, on a ring.
I see what you are all saying, however. Test culture has almost hailed skimming and quick solutions to meet time limits, or be efficient in different districts’ pressurized climates for learning. And frankly, key words CAN be used in a variety of contexts, and if you’re not fully engaged in the narrative, you may be duped into using the wrong sign to solve, or tricked into using irrelevant/unnecessary data. I love Ivan’s idea of acting out a problem…how engaging! Especially when thinking about problems with tricky bumps or curves, students can see what they need to focus on, and identify exactly what the question is asking of them. I used to work with students with special needs, who were academically at grade level. My former school used a lot of language encouraging students to visualize, such as the prompt, “make a movie in your mind,” etc., which were helpful in our school culture for students to take time to process, rather than rush through based on vocabulary cues.
Priscilla: I really appreciate the thoughtfulness of this thread. While the use of “key words” is a strategy I have seen used, I see now from this conversation how that strategy can prevent students from doing the necessary work to lead to a deeper understanding of a story problem. As with everything we have discussed in Investigations, it seems so important to allow the time for students to practice visualization, whether in the form of a mind movie or acting it out or otherwise being engaged. Thank you all for moving my thinking on this topic.
I really appreciate how this online conversation gave these teachers and me an opportunity to delve into some aspects of math teaching that may have a big effect on how students are approaching and solving problems. Laying out our thoughts and experiences, and hearing others’ thoughts about the story problem routine and key words, gave everyone a chance to consider the purpose and effect of these practices. The conversation seems to have shifted some participants’ thinking about how they might support students as they solve story problems and made others consider more deeply the reasoning behind their teaching practices.