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Stephanie Burroughs, Ed.D.

Curriculum Leader, K-12 Education

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Why Inquiry? Understanding the differences between traditional instruction and "New Math"

For the same reason that Shakespeare is not as important as Reading and Writing, the Quadratic Formula is not as important as developing a student's ability to break down problems into solvable parts, follow the logic of those individual steps, and assess the reasonableness of their answer. Learning should be relevant and transferable to other contexts. 

The true purpose of mathematics instruction is helping students to develop problem solving and logical thinking skills that are transferable to any of their future pursuits. To achieve this, we must understand the nuances between traditional instruction and this supposed "new math" brought about by the Common Core and its Standards for Mathematical Practice. 

 

What does a traditional mathematics class look like? 

In a traditional mathematics classroom a teacher would direct the class from the front of the room on a particular process and then have their students rehearse that process at their seats. There is always some scaffolding done here, building on prior learning, and talking through the reason why we use this particular process to solve this particular type of problem. Students are receiving information that justifies this one set process and immediately move toward memorizing these steps so that they can replicate it. 

In a traditional setting students are missing the purpose of mathematics and instead seeing mathematics as simply practicing structure and rules. This is the equivalent of only addressing grammar and sentence structure in English class; we all know that there is more to English than the ability to write a sentence. Without a conceptual conversation, our students are made to believe that mathematics is a set procedure with very little flexibility. 

 

What does "new math" instruction look like?

It's certainly not the case that all instruction pre-dating the Common Core was traditional. But, for me, this supposed "new math" is the first time I have seen a cohesive plan to understand Mathematics and be able to apply mathematical thinking to the real world. For clarity, there is nothing new about math, but there are very clear distinctions between a student-centered, inquiry based instructional approach and traditional, teacher-driven instruction.

Inquiry based learning and questioning techniques are the secret sauce to shifting instruction to a student-centered, conceptual conversation on the purpose of mathematics. They force our focus away from answer-getting and support a discussion on sense-making. I believe that structuring class with these in mind can solve the STEM career crisis, opening up the study of Mathematics for students who would otherwise not have seen the beauty and flexibility of the subject. 

Everything does not have to be inquiry based (for me, blended is always best), but if we as Math teachers can ask more questions and give less answers to start this process, we just might begin to shift the way that our students perceive mathematics class while also supporting a deeper conceptual conversation. Mathematics is more than a routine and our students need to see that.

 

How do I incorporate inquiry and questioning techniques?

Start with asking questions and establishing a classroom where discussions are valued over lectures. You don't have to change everything, Math is not new, but the way that we talk about it is. Try the following questions to get you started:

 

Before the LessonDuring the Lesson

What do I want my students to understand?

What theme does this concept connect to?

What conversation do I want my students to be having?

How can I connect this with prior knowledge?

How can I connect this with the real world?

How would this discussion look in another course?

What question should I ask first?

What questions can I ask to support student discovery?

Can you find a pattern?

How does this look different than previous concepts?

How does this look similar?

Can you develop a rule?

Why do you think this is happening?

What real world situation could this apply to?

Why do you think you got a different answer?

Why do you think this Mathematics was needed?

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