Do our students make sense of tasks and persevere in solving them? Are they able to look for and make use of structure? Look for and express regularity in repeated reasoning. How might we help them focus on developing their mathematical practices? What if we offer structure and listen to learn, teach, and facilitate?

What if we establish mathematical goals to focus learning?

As a team, we selected the following essentials to learn over the course of the entire school year. If you follow the links, you can see how we established mathematical goals for these throughlines.

#LL2LU SMP-1:  I can make sense of problems and persevere in solving them.
#LL2LU SMP-3: I can construct a viable argument and critique the reasoning of others.
#LL2LU SMP-7: I can look for and make use of structure.
#LL2LU SMP-8: I can look for and express regularity in repeated reasoning.

And what if we ask our students about their progress?

Below are students’ reflections on their progress. (I’ve removed the name of the student.) Each student has different strengths and needs. What if we intentionally group students so that they grow as practitioners of mathematics?

I am proud of my work on ______, because ______.

Zero product property because I can reason through and persevere through challenging problems with this method.

I can improve my work on ______ because _______.

I can improve my work on utilizing the Square root method because it is still a bit confusing to me, and difficult to use in complex quadratic equations.

I am proud of my work on ______, because ______.

This last unit because I was having a hard time figuring out how everything fit together, but after some practice, I started to understand the algebraic reasoning for how to solve these problems.

I can improve my work on ______ because _______.

Solving problems that are slightly more difficult than others because oftentimes, I can get stuck when solving problems that involve a fraction or require a slightly varied method to complete.

I am proud of my work on ______, because ______.

I am proud of my work on the quadratic formula because I really feel like I understand it well.

I can improve my work on ______ because _______.

I can improve my work on completing the square because I sometimes get mixed up when I am adding and subtracting things on each side.

From Taking Action: Implementing Effective Mathematics Teaching Practices in Grades K-5: In ambitious teaching, the teacher engages students in challenging tasks and collaborative inquiry and then observes and listens as students work so that she or he can provide an appropriate level of support to diverse learners. The goal is to ensure that each and every student succeeds in doing meaningful, high-quality work, not simply executing procedures with speed and accuracy. (Smith, 4 pag.)

From Principles to Actions: Ensuring Mathematical Success for All: Effective teaching of mathematics establishes clear goals for the mathematics that students are learning, situates goals within learning progressions, and uses the goals to guide instructional decisions.

To strengthen our understanding of using mathematics goals to focus learning, we make the learning goals visible to learners, ask assessing and advancing questions to empower students, and listen and respond to support learning and leveling up.

How might we listen and respond?

How will we listen and respond?

Listen and respond.

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Gough, Jill, and Jennifer Wilson. “#LL2LU Learning Progressions.” Experiments in Learning by Doing or Easing the Hurry Syndrome. WordPress, 04 Aug. 2014. Web. 11 Mar. 2017.

Leinwand, Steve. Principles to Actions: Ensuring Mathematical Success for All. Reston, VA.: National Council of Teachers of Mathematics, 2014. (p. 21) Print.