The Common Core State Standards, that are now referred to as the Washington State K-12 Learning Standards include the Standards for Mathematical Practice. The math practices “describe the ways effective math doers think and the kinds of actions they take when engaged in mathematical problem-solving.” (Routines for Reasoning, Fostering the Mathematical Practices in All Students, G. Kelemanik, A. Lucenta, S.J. Creighton, 2016, pg. 2)
As I’ve observed teachers work in classrooms and in professional development opportunities that across, I’ve learned how important it is to implement routines that help students examine how they think mathematically, to understand that mathematics looks at patterns, and to know that mathematicians use structures to help in problem-solving. Routines can build capacity so that ALL students have access to exploring rich mathematics.
The routine, Three Reads, supports students to make sense of problems and persevere in solving them (Math Practice 1). When using the Three Reads routine, mathematicians read a problem more than once. Let me repeat, mathematicians read a problem more than once. In language arts, Read Aloud –Think Aloud is a routine which models how good readers engage in and construct meaning as they read. Three Reads is designed to help math students make sense of problems and persevere in solving them.
Have you ever seen a problem like this?
A prince picked a basketful of golden apples in the Enchanted Orchard. On his way home, the prince came to a troll who guarded the orchard. The troll stopped him and demanded payment of one-half of the apples plus 2 more, so the prince gave him the apples and set off again. A little further on, he encountered a second troll. The second troll demanded payment of one-half of the apples the prince now had plus 2 more. The prince paid him and set off once more. Just before leaving the Enchanted Orchard, a third troll stopped him and demanded one-half of the remaining apples plus 2 more. The prince paid him and sadly went home. He had only 2 golden apples left. How many apples had he picked?
(Routines for Reasoning, Fostering the Mathematical Practices in All Students, G. Kelemanik, A. Lucenta, S.J. Creighton, 2016, pg. 128)
Reading a math problem is not like reading a regular text. In a math problem, students read text containing lots of information and finally, at the end, the question or task is finally presented. We aren’t able to make sense of any of the information till the end, so we have to read again. When reading a math problem, you have to read for the math inside the context or narrative. This means it is important to read a math problem multiple times “with a different focus each time so that the reader can understand the situation, identify the question to be answered, and decide what mathematically important information given in the problem statement will be useful in solving the problem.” (Routines for Reasoning, Fostering the Mathematical Practices in All Students, G. Kelemanik, A. Lucenta, S.J. Creighton, 2016, pg. 132). As the name implies, in the Three Reads routine students will read the math problem three times with a different focus each time. The routine looks like this:
Introduction: Articulate the purpose of the routine. “Learn to read like a mathematician.”
First Read: Read for context. What is the problem/story about?
Second Read: Read for the question. Interpret what the question is asking; put it into your own words.
Third Read: Read for information. What are the values and quantities in the problem? What is mathematically important information?
Important aspects of this routine are the specific teacher actions to encourage dialogue and reflection. Students think individually, then share in pairs, and finally share as a group. This deep thinking, scaffolding, and use of dialogue supports learning for students with disabilities, English learners, and gifted students.
I’ve learned that Three Reads and other “Routines for Reasoning” are unique in that they are designed to support a growth mindset in students by helping them identify practices of mathematical thinking which will support them in learning through the grade levels. I encourage you to learn more about Three Reads and other routines that encourage mathematical thinking by visiting FosteringMathPractices.com.