This is a common sight in many of the classrooms I visit:
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Whether on a poster...
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...or displayed on a bulletin board.
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Students are taught to use these strategies
in order to help them make sense of what they read...
in reading class.
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| Their independent reading books have post-it notes sticking out all over the place. |
Every math teacher knows that many students have trouble solving word problems. Looking at these displays day in and day out got me thinking: might these active reading strategies be useful
in math class? Curious to find out, I enlisted Shannon and her third grade class in a little experiment.
In your typical series of lessons on solving number stories, at least as presented in our curriculum, the kids are given the following:
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This is of dubious value.
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They are provided with some information:
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Animals are a favorite of elementary curriculum writers. All kids like animals, right?
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And then asked to solve some related number stories:
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This is sure to kill any interest you may have had in the animals.
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We decided to try something different. We provided the kids with the animal information, and asked them to use their active reading strategies:
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Shannon created the sheet. The boxes are intended to resemble the post-its the kids stick to the pages of their independent reading books. In the top right corner they indicate the strategy they've employed.
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It's really quite similar to noticing and wondering:
Next, we asked the kids to write questions for their classmates to solve.
Shannon and I vetted them, and threw in some of our own. We typed them up and taped them to index cards. Students got to choose which problems they wanted to solve, and each had a sheet where they had to record both an active reading strategy and a solution:
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This was a student generated question.
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This student used the questioning strategy. Shannon and I felt that this showed good insight into a curious turn of events for the crocodile.
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This was one I wrote.
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| I think this question came from the book. |
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| A clutch is a nest. |
I tried it out with a fourth grader who has particular problems with number stories.
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| She predicted, visualized, clarified, and made a text-to-self connection. Unfortunately she got the wrong answer due to a computation error. |
Some comments, reflections, and questions:
- Treating number stories as texts similar to those encountered in reading class could be one way to demystify these often intimidating and challenging tasks.
- This strategy can help kids with the first step in solving number stories: making sense of the problem.
- One advantage was that the kids didn't have to be taught these strategies. They already knew them.
- Integrating reading and math builds curricular coherence. It's second nature for them to "post-it" up their books. Why not their number stories? Why can't math have what reading's having?
- I haven't followed up, although I'd like to revisit this activity with Shannon's class before the year is out. There's a lot happening in the MTBoS surrounding the issue of math and literacy. How do we help kids make sense of number stories? What strategies can we provide to help them make sense of text-heavy problem solving scenarios? Noticing and wondering and numberless word problems are two that have been offered up and that have proven benefits. Could this be another? Fire away.
Joe this a great idea. We often talk about combining these strategies in the schools I work with. This question always comes up. Is it the math they do not understand or is it the reading that stumps them? I am going to share this blog post with my teachers if that is OK with you. One question, I notice the a student used the traditional algorithm for the subtraction problem. Is this something you are still seeing a lot of? My schools have really been increasing their number talks and we are seeing less and less of it and more of the students using efficient mental strategies. What do you think?
ReplyDeleteThanks for your comments Mark. Absolutely it's OK to share the post! I'd love to hear the feedback you get from your teachers.
DeleteRegarding the traditional algorithm, great question. For the long answer, see the previous post (When Bad Things Happen to Good Algorithms), the comment thread, and also the response Marilyn Burns published on her blog. The short answer is that yes, we still see it. I admit that we are behind in our implementation of number talks, and the fact that you are seeing an increase in efficient mental strategies only reinforces my belief that the routine needs to become a non-negotiable part of what we do in our math classes.
"But math is about sums. They do reading anyway". This is a common attitude, and not only does it not help kids with the redong of "word" problems, it discourages or even prevents the seeing of algebra as a vey cryptic language, in which statements have meaning outside of the coding or symbols. Kids don't know what "y = mx + c" is saying, and it sure isn't "whyequalsemexpluscee".
ReplyDeleteThanks Howard. Would applying reading strategies help students decode the meaning of y = mx + c? Is there a narrative encrypted there that an active reading strategy might help decode? I never thought of algebra that way! Maybe that's why I was so bad at it.
DeleteIf there are strategies for dealing with the classic confusion "Fruit flies like an apple" and "Time flies like an arrow" then yes is the answer. basically interpreting y = mx + c involves asking questions like "What is m doing in there?". Before that it is necessary to accept some mathematical conventions, such as "x and y are variables, m and c are constants". Then a student might be able to tell you what happens to the value of y if the value of x increases by 1. It is also useful to see x, y and c as representing quantities, and m as being a number (a multiplier). Of course, some non algebraic representations (graphs) should come or be brought to mind as well.
DeleteI've also thought a lot about literacy in the math classroom. Here is a typical exchange I've experienced when students are working independently:
ReplyDeleteS: raises hand and then says "I don't know what to do."
Me: "Can you read the problem for me?"
S: "I already did."
Me: "Read it out loud for me."
Student reads the text out loud.
Me: "What do you think you should do?"
Student tells me the EXACT thing they should do.
Now, I don't know if it's hearing the problem that helps them make better sense of it. Or, if it's the security blanket of me standing there with them...but it's happened often enough (with middle schoolers) that I think it could be a thing.
I think that when students read the problem silently, they are not actively thinking about the words they are reading.
I definitely think applying reading strategies in the math classroom is something that needs to be explored by all math teachers.
Thanks! I agree that when students read the problem they are not actively thinking about the meaning. They are focused on the numbers, and I suspect that many understand that the entire (often painfully contrived) scenario has been created for the sole purpose of seeing if they can do something with those numbers. So the tail is wagging the dog.
DeleteDuring reading class, when a student is at their seats reading a book, they don't ask, "Can you read it to me?" They read, and at regular intervals get out their post-its, and "stop and jot". They should be able to follow the same protocol with the number stories they read in math class. Even if they don't arrive at the correct solution, at least it's a way they can start on a solution pathway.
Great ideas thanks. A couple of years ago I was thinking about this exact topic in my own practice and I found the text Building Mathematical Comprehension by Laney Sammins helped me to think more about how I could easily integrate the strategies I used in my literacy lessons within our math lessons.
ReplyDeleteI spent more time also unpacking tricky and important vocabulary as I would have done within a guided reading activity.
Reading this reminded me that my students would benefit from more work around this, thanks for the re-inspiration!
Thanks Rebecca for your kind words, comments, and for steering me towards Building Mathematical Comprehension. I've read Laney Sammons's book on Guided Math and I'll have to check this one out.
ReplyDeleteI think this kind of integration is easier for primary grade teachers who are self-contained and teach both subjects. It's more of a challenge for those teachers who are departmentalized. That's why I tried this out with a third grade teacher, because in my school starting in fourth grade the kids switch teachers for reading and math.
Vocabulary is a tricky issue. I think sometimes we do a disservice to the kids when we introduce vocabulary too soon, before the concept itself has had a chance to take hold.
It's not just vocabulary, it's the rush to symbols. This is one reason that the kids can't "read" the math. Do 10 + 3 = 13 and 13 = 10 + 3 mean the same or not?
Delete(I am not going to answer that question). Math has a weakness for overloading some of the symbols (the - sign particularly) and so context matters.
I would love to meet you someday Howard! Math is so symbolic that the notion that symbols could be overloaded is almost counter-intuitive, but it makes sense to me. Your example couldn't be more timely: our first graders are really struggling right now completing equations like 5 = 9 - _____. Sometimes I shake my head and think: what must they make of something that looks like that?
DeleteHello Joe
DeleteSo not only are there word problems, but symbol problems as well. I am not surprised ! I guess that the instructions are not very helpful, does it say "What number makes the equation true?"
I've been teaching math related stuff to college and university kids for years and years, and many of them have problems with the symbolism. In all that time I have never seen a false equation !!!!!
One problem is the current obsession with "algebraic thinking", something which the CCSSM lists for every grade from K to 5 but NEVER explains what is meant. I think that they mean "writing equations".
How do I read 5 = 9 - ______ ?? With difficulty.
When the symbols get in the way of understanding the problem then they are not doing the job they were designed for.
Anyway, I am in Mayaguez, Puerto Rico, a short plane ride from Newark to Aguadilla (BQN).
Here's my email: howard+at_58@yahoo.co.uk
and here's my blog site:
howardat58.wordpress.com
Pretentiously called "Saving School Math".
There are numerous posts on Common Core horrors.
Hi Joe-
ReplyDeleteI have recently begun reading your blog-
I am a Math Specialist also located in Dobbs Ferry, NY.
This is very interesting what you have tried here.
I would like to try it.
One of the barriers to students solving word problems is that they are answering the wrong question, in my opinion.
The question shouldn't be what do I do, but rather it should be "What is happening here?" "What is this about?" Asking kids to wonder, speculate, and theorize before going into what calculation is to be done is a more effective approach in my experience.
Thanks for stopping by and taking the time to comment. Noticing and wondering, removing the question and even the numbers, employing these active reading strategies; we need to try anything and everything to make number stories more accessible. Asking, "What is happening here?" seems to me to be less a mathematical question than a reading comprehension question, but maybe it's equal parts both? I think that if we accustom our students to mathematize their worlds, then the transition to answering "What is happening here?" through a mathematical lens will be that much easier.
DeleteI think the question "What is happening?" forces the students to attend to what the numbers refer to. Often, students have difficulty attaching the number to what it represents, and this seems to happen particularly with multi-step questions. I think that it is a reading comprehension strategy that leads toward the students seeing the mathematics. It is very rare student that is a weak reader that doesn't have difficulty with word problems. Thanks for the posts.
ReplyDeleteI occasionally post on my blog mathman287.blogspot.com
It's nice to connect with other like minded folks.
Josh
Your comment that,"It's a rare student that is a weak reader that doesn't have difficulty with word problems" has really got me thinking. If that's true, then the opposite would hold; that good readers should have little difficulty with word problems. But I know from personal experience that that's not the case. I've always loved the printed word, been an avid and very careful reader, but always struggled with word problems (as I struggled with most everything in math.) Yes, seeing the numbers and knowing I was going to have to do something with them triggered lots of anxiety, but maybe there was more to it than that. Maybe it was the stories themselves. They were (are) so contrived, so devoid of any interesting narrative. Words are supposed to communicate some kind of truth and meaning, not just be a delivery system for an equation or formula. On some level I suppose it made me mad, and it makes me mad today. So now it makes perfect sense why I'm such an easy target for the MTBoS, especially for something like a 3-act task, which allows me to participate in creating a story that has a personal meaning and generate a question I'm interested in finding the answer to.
ReplyDelete