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Wednesday / June 26

3 Guidelines for Mathematics Learning Goals

Teacher clarity is one of the high yield practices for building assessment-capable learners (Frey, Hattie, Fisher 2018). Included in teacher clarity is communicating learning intentions and success criteria, which is also a focus of one of NCTM’s eight effective mathematics teaching practices: Establish mathematics goals to focus learning (NCTM, 2014).

Although the importance of establishing and using learning goals is widely accepted, teachers across the nation share with me the need to improve their implementation of this practice. The following three guidelines are designed to support implementation:

1) Create lesson level learning goals with a balanced set of success criteria

A Learning Intention can be defined as the core mathematical concept students will understand by the end of the lesson. Success criteria are statements that allow the students and teachers to know what they will use as evidence for meeting the learning intention. Together, the learning intention and success criteria are often referred to as the learning goal or target.

Success criteria should include a balance of procedural and higher-level process skills that would provide evidence that a student is on track to meeting the learning intention.

Sample sentence starters for developing

procedural success criteria include:

I can identify . . .

I can solve . . .

I can distinguish between ___ and ___

I can define . . .

I can use ____ to . . .

 

Sample sentence starters for developing higher-level process success criteria include:

I can use a model to . . .

I can explain why . . .

I can design a . . .

I can construct an argument about . . .

I can provide evidence for . . .

 

Teachers indicate their learning goals too often focus only on procedural skills. As you develop and refine a learning intention and success criteria, the following questions can guide your process for creating a balanced learning goal.

  • Is the learning intention focused on the important mathematics concepts in the lesson rather than referring to activities or tasks students will complete?
  • Does at least one of the success criteria describe something students can do or explain how to do (procedural success criteria)?
  • Does at least one of the success criteria describe something students can justify, model or explain at a higher conceptual level? (higher-level process success criteria)?

Samples of Learning Goals with a balanced set of success criteria.

2) Establish and use routines to focus students’ attention on the criteria while learning is underway.

Since success criteria are what both the teacher and students will use to determine the extent to which students are meeting the goal, pausing at key points mid-lesson provides a much-needed opportunity for students to summarize their learning to that point.

Routines can provide structure and purpose to revisiting the goal. Below is a list of examples of such routines:

  • Take Stock is used after the completion of a task or activity. Engage students in a discus­sion using the following series of questions.

1) “Who can describe for me what we’ve done so far with (this math

task)?”

2) “So in our success criteria, we said we would (read criteria to students). Can someone else describe what this means in their own

words?”

3) “In what way did this task help us work toward meeting the success

criteria?”

  • A Picture Tells a Thousand Words is used to highlight the difference between doing and learning. Post a picture of students engaged in a task with manipulative or other materials. Ask:

1) What were we doing?

2) What were we learning?

  • Feedback Focused Group Discourse is a way for teachers to provide whole-group feedback or feedback on selected student responses.

Create a feedback poster or anchor chart displayed in a place visible

to students with the following sentence prompts:

  • You are on track for meeting the learning goal because _________.
  • You haven’t yet met the learning goal because _________.
  • A hint to revise your thinking is _________.

Showcase a student worked example and have students respond to the prompts in partners or small groups. Lead a whole group discussion to debrief. Close the feedback loop by having students revisit their own work.

3) Take appropriate responsive action based on evidence collected.

At any time in a lesson when you elicit and interpret evidence, there are a number of possible responsive actions, whether for an individual or for the whole class. The four most common are:

a. Provide formative feedback. When students show enough understanding or skill that some slight adjustments will allow them to meet the current goal, then provide formative feedback. One method for doing this might be to use the Feedback-Focused Group Discourse routine described above.

b. Provide further instruction. If the evidence suggests that there is a significant gap between a student’s current learning status and the learning goal, the student is unlikely to make progress after receiving formative feedback. This may be because there is a significant barrier or misconception or because there are enough smaller issues that they collectively prevent students from moving on. In such a case, taking a step back to address the issues through further instruction is often an appropriate responsive action.

c. Gather more evidence. In many cases, when a student gives you a response, the information gathered may be inconclusive. You might have gained some insight into student thinking but not enough for you to determine which of the other responsive actions is most appropriate. In this case, you simply need to gather more evidence.

d. Move on. Most often, this is appropriate when your students are on track with where you expected them to be, with regard to meeting the goal. This may be after a task has been completed and you check in to see where students are with a particular success criterion; even if they haven’t met the criterion completely, they might be far enough along that they are ready to continue to the next task in your lesson plan. This also may be at the end of a lesson, when you review the evidence of the entire lesson against the whole set of success criteria.

Following these guidelines can greatly improve student learning. Creating a balanced set of criteria focusing on important higher-level processes supports conceptual understanding of the core mathematics idea.  Revisiting of the learning goal helps solidify its meaning for students, and can serve different purposes in moving students’ learning forward. Asking “to what extent are my students meeting the learning target”, helps determine an appropriate responsive action and differentiation needs.


References

Creighton, S.J., Rose Tobey, C., Karnowski, E., Fagan, E. (2015). Bringing Students into the Formative Assessment Equation: Tools and Resources for Math in the Middle Grades. Thousand Oaks, CA: Corwin.

Frey, N., Hattie, J., Fisher, D., (2018). Developing Assessment- Capable Visible Learners, K-12. Thousand Oaks, CA: Corwin.

Hattie, J., Fisher, D., Frey, N. (2017). Visible Learning for Mathematics, Grades K-12. Thousand Oaks, CA: Corwin.

Keeley, P. and Rose Tobey, C. (2011). Mathematics Formative Assessment Volume 1: 75 Practical Strategies for Linking Assessment, Instruction, and Learning. Thousand Oaks, CA: Corwin Press.

Keeley, P. and Rose Tobey, C. (2016). Mathematics Formative Assessment Volume 2: 50 Practical Strategies for Linking Assessment, Instruction, and Learning. Thousand Oaks, CA: Corwin Press.

National Council of Teachers of Mathematics. 2014. Principles to Actions: Ensuring Mathematical Success for All. Reston, VA: National Council of Teachers of Mathematics.

Written by

Cheryl Rose Tobey is the elementary mathematics specialist for Maine’s Department of Education, having previously developed materials and provided professional development for mathematics educators across the state, region and country through her work for Education Development Center (EDC) and Maine Mathematics and Science Alliance (MMSA). While at EDC and MMSA, she led multiple National Science Foundation (NSF) and state funded grants focused on increasing student achievement for struggling learners. Coupled with her experience in mathematics professional development and her ten years as a classroom educator, Cheryl also has extensive experience coaching elementary teachers.

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