Find: The Problem

Karen Wootton, Director of Assessment

My new mission, along with changing the perception of mathematics and math teaching in the U.S. within my lifetime, is to eradicate the use of the word “find” from mathematics. This mission formulated slowly; in fact, I spent the first 20 years of my career using the term freely. “Find x” was definitely part of my lexicon as was “Find the width,” “Find the area,” “Find the distance”. I used it all the time.

Maybe it was the well-circulated comic that had me questioning my practice and pushed me towards this mission. At first I just made it a personal goal to not use the “F” word in math problems that I wrote, but now I have formulated my opinion on why I must rid the math world of “find.” Some people might dismiss the comic as just the response of a smart aleck student, and not worthy of extra clarification. I strongly disagree with that and will now explain why we must be more clear with our language.

This is a bigger problem than thwarting smart alecks. Let’s remind ourselves of one of our Standards of Mathematical Practice: attend to precision. Is it really precise to say “Find x”? What does that ask the student to do? In particular, what does that tell the struggling student to do?

The definition of “find” is “to discover or perceive by chance.” Is that how you want your students to think that is how we do math? Do you want them to think of solving math problems as random, or by chance? For many students, and in particular, struggling students, most of their confusion stems from not seeing the connections, and think that most of math is random. To many struggling students, math is for the lucky who are good guessers of what to do next, or for those people with the elusive math gene that enabled them to be “math people.”

Let us explicitly ask students what it is we want or expect. Rather than “Find the intercepts” which implies that there is some way to just have them appear before you, change this to “What are the intercepts?” Asking the question at least implies there is something for the reader to do rather than rely on chance. Better yet, “Calculate the intercepts” or “Determine the intercepts.” If we ask “Find the intercepts” we must give full credit to the student that draws arrows pointing to the intercepts on the graph because the student has accomplished exactly what was asked. But, if that is what you want students to do, why not say “Point to the intercepts on the graph”? If we expect our students to attend to precision, we must model what that looks like. Even if we are asking something that might have an element of luck, we can do better than “find.” “Find a strategy” can be replaced with “Develop a strategy” or “Create a strategy” which implies there could be creative work, but work none the less.

So here is your challenge: whenever you are writing a math problem and are about to type the “F” word, reconsider. Can you turn a find-statement into a more precise question? Can you write the question as precisely as possible, to be sure your expectations are clear? Let us stop the perception that math is done by chance.

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Algebra Tiles Blue Icon

Algebra Tiles Session

  • Used throughout CPM middle and high school courses
  • Concrete, geometric representation of algebraic concepts.
  • Two-hour virtual session,
  •  Learn how students build their conceptual understanding of simplifying algebraic expressions
  • Solving equations using these tools.  
  • Determining perimeter,
  • Combining like terms,
  • Comparing expressions,
  • Solving equations
  • Use an area model to multiply polynomials,
  • Factor quadratics and other polynomials, and
  • Complete the square.
  • Support the transition from a concrete (manipulative) representation to an abstract model of mathematics..

Foundations for Implementation

This professional learning is designed for teachers as they begin their implementation of CPM. This series contains multiple components and is grounded in multiple active experiences delivered over the first year. This learning experience will encourage teachers to adjust their instructional practices, expand their content knowledge, and challenge their beliefs about teaching and learning. Teachers and leaders will gain first-hand experience with CPM with emphasis on what they will be teaching. Throughout this series educators will experience the mathematics, consider instructional practices, and learn about the classroom environment necessary for a successful implementation of CPM curriculum resources.

Page 2 of the Professional Learning Progression (PDF) describes all of the components of this learning event and the additional support available. Teachers new to a course, but have previously attended Foundations for Implementation, can choose to engage in the course Content Modules in the Professional Learning Portal rather than attending the entire series of learning events again.

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Building on Instructional Practice Series

The Building on Instructional Practice Series consists of three different events – Building on Discourse, Building on Assessment, Building on Equity – that are designed for teachers with a minimum of one year of experience teaching with CPM instructional materials and who have completed the Foundations for Implementation Series.

Building on Equity

In Building on Equity, participants will learn how to include equitable practices in their classroom and support traditionally underserved students in becoming leaders of their own learning. Essential questions include: How do I shift dependent learners into independent learners? How does my own math identity and cultural background impact my classroom? The focus of day one is equitable classroom culture. Participants will reflect on how their math identity and mindsets impact student learning. They will begin working on a plan for Chapter 1 that creates an equitable classroom culture. The focus of day two and three is implementing equitable tasks. Participants will develop their use of the 5 Practices for Orchestrating Meaningful Mathematical Discussions and curate strategies for supporting all students in becoming leaders of their own learning. Participants will use an equity lens to reflect on and revise their Chapter 1 lesson plans.

Building on Assessment

In Building on Assessment, participants will apply assessment research and develop methods to provide feedback to students and inform equitable assessment decisions. On day one, participants will align assessment practices with learning progressions and the principle of mastery over time as well as write assessment items. During day two, participants will develop rubrics, explore alternate types of assessment, and plan for implementation that supports student ownership. On the third day, participants will develop strategies to monitor progress and provide evidence of proficiency with identified mathematics content and practices. Participants will develop assessment action plans that will encourage continued collaboration within their learning community.

Building on Discourse

In Building on Discourse, participants will improve their ability to facilitate meaningful mathematical discourse. This learning experience will encourage participants to adjust their instructional practices in the areas of sharing math authority, developing independent learners, and the creation of equitable classroom environments. Participants will plan for student learning by using teaching practices such as posing purposeful questioning, supporting productive struggle, and facilitating meaningful mathematical discourse. In doing so, participants learn to support students collaboratively engaged with rich tasks with all elements of the Effective Mathematics Teaching Practices incorporated through intentional and reflective planning.