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Are Your Students Receiving a Rigorous Mathematics Education?

Rigor in mathematics teaching and learning requires a balance of conceptual development, procedural fluency, and application. While math instruction in America has been typically focused on procedural fluency, how can school administrators help preK-12 teachers of mathematics assure that students are truly developing their own understandings of mathematical concepts? (I’ll address application in a future post.)

One way for administrators to assure that students are provided the rigor required of current math standards is to do more classroom observations. But don’t watch the teachers. Watch the students!

Let teachers know that you are looking for evidence of student agency, a critical part of student conceptual development. You’ll watch whether or not students are actively engaging in practices, or “habits of mind,” of proficient students of mathematics.

Now you just need to know what to be looking for! Luckily, student behaviors that lead to conceptual development are printed in standards documents and are called Standards for Mathematical Practice (in the CCSS-M), or Process Standards for Mathematics (in the Indiana Academic Mathematics Standards) and are listed here:

  1. Make sense of problems and persevere in solving them.

  2. Reason abstractly and quantitatively

  3. Construct viable arguments and critique the reasoning of others

  4. Model with mathematics

  5. Use appropriate tools strategically

  6. Attend to precision

  7. Look for and make use of structure

  8. Look for and express regularity in repeated reasoning

When students are learning mathematics by actively engaging in these practices, you can bet that students are developing their own understandings instead of just following rote procedures.

If you don’t see evidence of these behaviors, follow up with the teachers to ask them what they think their students need in order for students to engage in these practices on their own. Then, try to provide the support requested. Once those supports are provided, repeat the process. Hopefully, you’ll see a change in student engagement. But if you don’t, ask again what might be needed. Sometimes it takes several cycles to identify an effective intervention that gets students to think critically.

Rigor in the teaching and learning of mathematics is a difficult balancing act for teachers to achieve, but with the right support, it’s entirely possible.


To see student behaviors in action, watch our whiteboard sessions on classroom observation look-fors:


For ideas on effective instructional supports for teachers, check out our professional learning programs:

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