On Thursday, I’ll be sharing about numberless word problems at the NCTM Annual Conference in Washington, D.C.
In preparation for my session, I reached out to fellow educators on Twitter, asking them, “How have numberless word problems impacted student sense making in your classroom?” I’ll have plenty to say about this in my talk, but I wanted to take this opportunity to let a wider variety of voices share their thoughts and reflections on using numberless word problems.
Macy, Math Interventionist, Arkansas:
“They no longer see two numbers and add. They think about the problem and what a reasonable answer could be.”
Julie Bourke, 2nd grade teacher, Michigan:
“I can actually watch my students shift from plucking out numbers and adding them to reading the problem and visualizing what is happening. This helps them solve and understand exactly what the quantities in the problem represent.
I also saw a shift in my repeated direction of “don’t forget the unit/label” has disappeared because the students aren’t thinking of the numbers as separate from the problem. They are making sense of the context, deciding on the best strategy to solve and the numbers in the problem aren’t really the focus.
This has also improved my own teaching. I was a “circle the number and underline the key words” teacher and I was teaching students to follow directions. Now I am teaching mathematicians who make sense of problems, develop strategies and discuss solutions within a context.
This has been an important shift for my career and my own understanding of teaching math.”
Kristen Mangus, Math Support Teacher, Maryland:
“I have shared these with teachers in my school, K-5. K teachers started using these when they began teaching word problem standards and they instantly noticed a difference in how their students solved problems compared to when they taught problem solving without numberless word problems.
Numberless word problems also reduce “number plucking” because students have time to think about the problem, make connections and ask questions so that they are ready and confident when the numbers are introduced.”
Kjersti Oliver, Middle School Instructional Facilitator, Virginia:
“These are great for MIDDLE SCHOOL TOO! Especially students that are EL or struggle with word problems! They can work for equation word problems, systems, proportions, etc.! Great entry point for students!”
Carrie DeNote, Math Interventionist, Florida:
“The student Notice/Wonder about everything now. I’ve seen N/W t-charts on their assessments where they have used it to help them make sense of a question.”
Jana Byrd, K-2 Elementary Specialist, Alabama:
“The very first time I used numberless story problems, I was amazed at the amount of math vocabulary that naturally surfaced during the discussion; greater than, less than, the same, equal, etc.
Without the numbers in the problem, I noticed that students focused on finding the relationship between the quantities even though they weren’t there. That prevented them from just grabbing numbers and doing something with them.
When the numbers were presented within the story problem, they did what made sense to them. They were able to decide on a strategy and discuss their thinking in a more clear manner. I’m sold on numberless word problems, especially when introducing new situations to students.”
Jordan Hill, 2nd grade teacher, Alabama:
“It has allowed the students to stop and make sense of the situation before attacking the problem.”
Wendy Wall, Mathematics Support Teacher, Virginia:
“Thank you! You have created an opportunity for students to talk and reason. You have created a resource teachers love!”
Deepa Bharath, Math Coach, Florida:
“Focus is on understanding the context, considering what is asked and possible strategies – students can notice structures and similarities, this is like the other one we did, when numbers are shown students tend to think less and just compute. Also helped students to be less afraid of fractions and large numbers – we solved the same problem with whole numbers before working with fractions, almost like a number string estimating first how the answer would be affected.”
Nicole Grygar, 1st grade teacher, Texas:
“When solving word problems, they are not jumping to conclusions. They are working all the way through the problem to make sure they are solving the right question.”
Christine Mauer, Special Education Resource & Inclusion Instructional Assistant, Texas:
“Taking the numbers out of the questions has allowed them to become immersed in the story first.”
Jenna Laib, K-8 Math Specialist, Massachusetts:
“Students are willing to think deeper and slower about world problems; they don’t shy away from a block of text as much, and they have a greater awareness of problem types (CGI style) which helps them determine their strategy. I have noticed the biggest change in students with disabilities, especially students with language-based disabilities like dyslexia.”
Melanie Tindall, Elementary Math Specialist K-5, New Jersey:
“Numberless word problems help students think about and visualize the problem. They help students think about what information they know and what information they need in order to solve the problem. They also help students think about what question(s) can be answered with the given information.”
Kristine Venneman, Elementary Mathematics Specialist, Middletown:
“Students are essentially forced to consider the context to begin their solution path without simply adding or multiplying.”
Rose Scullion, K-5 Mathematics Specialist, New Jersey:
“Before numberless word problems became part of regular instruction students would take the numbers they saw in the problem, cross their fingers, have a hope and a prayer, and perform some type of procedure or algorithm, with no sense if they were correct or not. Now, students are relying more on visualizing the mathematical context, planning out their solutions, and choosing strategies to solve.”
Anonymous, Math Coach, Connecticut:
“The use of them have increased students focusing on the context and sense making.”
Shawna Velt, Special Education Math Consultant, Michigan:
“I share this strategy with special education teachers to support students in understanding word problems. We use cubes to model along with each step”
Brian Buckhalter, K-4 Math Coach, Mississippi:
“Traditionally, the “goal” of math class is to find the answer. Numberless word problems take the attention away from finding the (usually) one correct solution. Instead, they open the door for discussion among students to share their interpretations and reasoning about problems. Then the focus shifts from following steps or other procedures to reasoning, examining relationships, extending patterns, doing what “just makes sense” (as my students would say) and other hidden beauties of truly understanding mathematics.”
Thank you to everyone who took the time to share their feedback and experiences! It was so heartwarming to read how numberless word problems have impacted other classrooms across the country. As someone whose mission it is to help students develop identities as mathematical sense makers, it means a lot that this strategy has helped so many of you foster that with your own students.
And to those of you able to join me at the NCTM Annual Conference in D.C., I look forward to seeing you in a couple days!