As I did with I, We, You, today I am going to analyze one of my favorite strategies – 3 Reads – by answering ten questions.
Where did I hear about this strategy?
Source: OUSD Instructional Toolkit for Mathematics p. 27-28
Also see: Dan Meyer’s Post that led me to it
I should note that I found this strategy one day after brainstorming modeling/word problem strategies in my PLC. (Intellectual Vindication again.)
What preparation does this strategy require?
Find a word problem, and omit the question.
An acidophilus culture containing 150 bacteria doubles in population every hour.
It is quick and easy, and I will be using it every Monday as a Do Now.
What content is this strategy trying to teach?
This strategy works with any content that has word problem applications, so … pretty much anything.
How does the strategy work?
Students read the problem three times, each time using a different lens.
Read 1: Students familiarize themselves with the the context and ask questions to clarify any unfamiliar vocabulary, often as a result of an unfamiliar context.
Read 2: Students focus on the quantities in the problem and analyze the relationship between these quantities. In doing so, students might:
- underline the quantities and key words
- define variables
- analyze or apply a formula/equation, and determine which parts of the question corresponding parts of the formula/equation
- draw a diagram of the situation, and use the diagram to write an equation
- make a table, and analyze the table
Read 3: Students brainstorm as many mathematical questions for the situation as possible. Students might:
- ask an obvious question that is implied by the missing quantities
- define the quantity for one variable in order to ask for the value of the other variable
- ask mathematical questions that are uninteresting or nonsensical in this context, and should discuss why these questions are unreasonable
- ask interesting and creative mathematical questions
Sequel (optional): Answer one of the student-generated questions.
Will my students want to do it?
In comparison to traditional word problems, this strategy is extremely engaging. In particular, there are two reasons I think this strategy hooks students.
Does this strategy make math accessible by allowing for a low-floor, high-ceiling, language support, and accommodations/modifications?
1. Most word problems are closed-ended. In other words, they have an answer. Many students read the problem and give up because they doubt they will be able to find that answer. A few students solve it quickly – often using a strategy that avoids the targeted content altogether – and either give away the answer or become a distraction. Some students need more time to parse the language or struggle to decode it at all. 3 Reads goes a long way in changing these results.
- Read 1 helps students access the language as its own step. Read 1 also helps overcome any cultural bias written into the problem.
- By asking students to read it again, the teacher sends a message of perseverance: “It’s okay not to understand what to do after reading it once; in fact, you aren’t expected to. This is hard, and it takes time to process and figure out what’s going in this problem.”
- Read 3 opens-up the problem and introduces all sorts of interesting extensions, challenging students to find all relevant questions, to find questions the teacher didn’t think of, to find silly questions that make the class laugh, and perhaps even to answer some of these questions.
How does this strategy create a need for this content?
2. Most word problems ask students to use the appropriate procedure to compute an answer. In “3 Reads,” students meet the same procedural/computational needs during the sequel. But Read 3 also asks students to grapple with the structure of a problem and make connections between different parts of the problem and different mathematical content/skills. For instance, in the bacteria example above, students could come up with a question that (1) provides a number of hours and asks for the number of bacteria or (2) provides the number of bacteria and asks for the number of hours. By considering these two questions concurrently, students grapple with exponents, logarithms, and the inverse relationship between them. Most word problems would ask them to apply exponents or logarithms.
How deep of an understanding do my students need or demonstrate in this activity?
Word problems are traditionally at the end of the chapter because students need to understand the content before they can apply it. Procedural and conceptual mastery is not a prerequisite with 3 Reads; content and application can develop concurrently, which hopefully instills a deeper understanding.
How will my students be thinking mathematically?
MP1, MP2, MP4, MP7. Modeling shines here, but perseverance and reasoning play a role as well.
Can I pull this off? What are students saying about it?
In short, yes. Students love asking questions. Usually, they ask me about my personal life or about what color something is (I’m colorblind). Getting students to ask academic questions is a wonderful feeling and having a curious class is extremely powerful. That’s one of the reasons I love running a philosophy club: students come to philosophy overflowing with curiosity. But in math class, it has been much harder than expected to get students asking good mathematical questions. I tried the Ferris Wheel 3 Act, and I was blown away by how difficult for my students to ask the desired question. 3 Reads presents asking questions as a low-stakes brainstorming activity, helps them practice that skill, and helps make curiosity part of the class culture.