Collaboratively Developing Students’ Understanding of the Learning Goals (Part 2)

Recently we heard from a concerned educator, “I display the learning goals at the beginning of each lesson, every day, but learners just ignore them. How can I get my students to pay attention to the learning goals and use them to improve?”

“Teachers should continually help students clarify the intended learning as lessons unfold – not just at the beginning of a unit of study”.


(Chappuis & Stiggins, 2002)

Simply telling students the daily learning goal or even posting it on the wall is not a particularly effective way to get learners to engage with the goal. Learners need to come to a deep understanding of how that goal connects to what they already know and are able to do, and what ‘lies between’ their current conceptual understanding and the next level of understanding that the goal represents. That’s why the curriculum, developmental continua and scope and sequence documents are so helpful to educators – they lay out a ‘learning map’ of the knowledge, skills and concepts that learners need to develop and understand. Learning goals result when educators translate that information into manageable chunks of learning in language that is meaningful to learners.

In Part 1 of this post, we outlined a number of collaborative and autonomy-supportive ways to share the learning goals with students. In this post, we’ll provide a detailed example of one of the strategies, analysing the curriculum expectations with learners. This example relates to a cluster of expectations from the 2005 Ontario Mathematics Curriculum for Grade 8 Measurement that focuses on:

  • relationships among measurable attributes of 3D shapes, specifically the volume of a cylinder;
  • developing the processes of reasoning and proving.

While planning, the educator has identified the expectations to be addressed and crafted the following learning goals and success criteria:

 

LG: We are learning about relationships among the measurable attributes of a cylinder.

SC:

  • I know how to find the volume of other 3-D shapes – rectangular prism, triangular prism, and generalize to find volume of prisms with other polygon bases.
  • I know what area is.
  • I can find the area of a circle.
  • I know what volume and capacity are, and how they are different.
  • I know what it means for two attributes to have a ‘relationship’.
  • I can identify and measure the attributes of various figures and shapes (e.g. height, radius, circumference).
  • I can calculate the volume of a cylinder.
  • I can explain how changing the radius and the height of the cylinder affects the volume.
  • I know and can use a formula for finding the volume of a cylinder.

LG: We are learning to think mathematically.

SC:

  • I know what it means to generalize.
  • I know what a conjecture is.
  • I know what ‘inductive reasoning’ means.
  • I know and use several strategies to prove a conjecture.
  • I can explain my thinking, step-by-step, so that others can understand.
  • I use reasoning and evidence to justify my conclusions.

Analyze the Curriculum with Learners

One way to engage learners to think deeply and actively about the learning goals is to share the curriculum expectations, and ask questions to elicit from learners what they already understand about this learning, and what they are wondering about. For educators who are not familiar with this practice, it’s helpful to determine the questions in advance. Once this practice becomes routine, you will find it becomes part of the flow of the instruction and assessment decisions you make with automaticity. Questioning and the ensuing discussion to elicit learners’ thinking will lead to collaboratively identifying the learning goals (and even some success criteria).

Sometimes, you may decide to modify the curriculum statements that you share with learners to focus their attention on certain aspects of learning. In this case, we would modify both the overall and specific expectations that we share:

Overall Expectation:

  • determine the relationships among units and the measurable attributes, including the area of a circle and the volume of a cylinder.

Specific Expectation:

  • determine, through investigation using a variety of tools and strategies (e.g., generalizing from the volume relationship for right prisms, and verifying using the capacity of thin-walled cylindrical containers), the relationship between the area of the base and height and the volume of a cylinder, and generalize to develop the formula (i.e.,Volume = area of base x height);

Modifications to the overall expectation focus the learning on the volume of a cylinder. For the specific expectation, leaving out the strike-through portions ensures that we don’t compromise the students’ investigations with the information provided in the expectation. We don’t want to give them the formula that they are supposed to develop!

Here are some pre-planned questions to ask learners about these expectations, in the hope that they will elicit the learning goals, and perhaps some of the success criteria. (At this early stage of the learning, the focus is on having the learners identify the learning goals.)

Broad questions:

  • What do you think this curriculum expectation means?
  • What do you think we’re supposed to be learning (about)?
  • Are there concepts or ideas here that you have seen before?
  • What are you wondering about, or what don’t you understand?

Specific questions relating to the knowledge and skills in the expectations:

  • What do you already know about area? volume? a cylinder? a relationship? reasoning? proving?
  • What knowledge or skill do you think is involved?
  • What do you think it means to ‘reason’?
  • What do you already know about inductive reasoning? Can you give an example?
  • What is a conjecture?
  • What do we need to prove a conjecture?

Determining when to Identify the Learning Goals with Students

It may not be optimal to introduce the expectations at the very beginning of the learning; rather, waiting to discuss the expectations until after an initial investigative task involving volume will give learners an opportunity to revisit their thinking and recall what they already know about volume as well as make connections to the process of reasoning. It will also give the educator an opportunity to observe and gather information about prior knowledge and skills, and to draw attention to important aspects of the new learning that may emerge.

Having gathered some assessment information about their current knowledge and skills as you observe and talk with learners during the first investigation, you’ve laid the groundwork to share and discuss the expectations. Depending on your observations from the prior learning experience, you could choose to have learners:

  • answer questions orally;
  • discuss their thinking first with a partner using a “Think-Pair-Share” approach, then answer questions;
  • incorporate some of these questions into an ‘entrance card’ so that you have a written record of their thinking.

Map the Learning Goals with Learners

When educators share single learning goals at the beginning of each day’s lesson, it is difficult for many learners to see how these discrete goals connect and build to an understanding of a concept. By recording the goals visually as a ‘learning map’, we can help learners see how knowledge and skills connect, so they can start to monitor their progress. How do we do that?

As students contribute their ideas in response to the above question prompts, record their thinking on chart paper large enough to display and be seen by the class for discussion. Use the responses to the questions,

  • What do you think this curriculum expectation means?
  • What do you think we’re supposed to be learning (about)?

to guide the development of learning goals. If you have the learning map clear in mind, you can guide students development of the map through questioning and discussion. Here’s an example:

Educator: What do you think we’re supposed to be learning (about)?

Student1: I think we’re learning about cylinders.

Student2: And something about measurable attributes, although I don’t know what that means.

Educator: That is definitely mathematical language. (Student3), what do you think it could mean…any ideas?

Student3: Well, measurable…maybe it’s what you can measure in a cylinder?

Educator: That’s exactly it. So could we say we’re learning about the measurable attributes of a cylinder? Let’s write that down…Anything else? Is it just about measuring ‘attributes’?

Student4: It says something about relationships.

Discussion continues about the idea of ‘relationships’, what it means, and where students have seen examples of relationships in their math learning.

Educator: So we are also learning about relationships among the attributes we can measure. Let’s add that to our learning goal? How would we do that?

Student 5: We’re learning about the measurable parts of a cylinder and the  relationships.

Educator: …among them? (Writing down the learning goal.)

Student1: I know that the base of a cylinder is a circle.

Student2: And we know how to find the area of a circle.

Educator: Would the area of the base be something we could measure on a cylinder?

Student3: Yes, because we know how to find the area of the circle. We just measure across the bottom for the diameter.

Educator: Now, Student1 and Student2, you mentioned that you know the base of a cylinder is a circle, and you know how to find the area. Would being able to find the area of the circle that is the base of the cylinder be important for us to know how to do?

Students: Yes!

Educator: Then why don’t we add those as success criteria for our learning goal.

By recording ideas on separate pieces of chart paper, they can be moved around and reorganized over the course of the learning, so that the learners’ understanding of the big idea, overall goal, specific goals and success criteria can be displayed as it emerges and grows.

Possible responses from learners related to these questions,

  • What do you think this curriculum expectation means?
  • What do you think we’re supposed to be learning (about)?

might include:

We’re learning:

  • how to investigate to learn mathematics.
  • how to reason and prove mathematical ideas.
  • how to find the volume of a cylinder.
  • a formula for calculating the volume of a cylinder.

These responses become the basis for our learning goals as we progress together through the learning.

As they experience the learning tasks and conduct investigations, additional learnings, criteria and questions will be generated and can be added to the list. Eventually, with the your guidance over the course of the unit, the map will include all the necessary learning goals (based on content and processes), success criteria, and big ideas.  

Realize that it is unlikely that all these responses will be generated after the learners’ first interaction with the expectations – and that’s ok. At the beginning of the learning, learners may contribute only a few of the possible responses, or different ones.  Further, different groups of students will vary in what they identify as what they already know, and what they are learning. As such, the development of each classes’ learning map will be unique.

Here’s an example of a series of learning experiences relating to these expectations.

One last thought – and a call to action! The approaches outlined in this post can work with any age and any subject. Want to see it in action? Watch Segment 3 of the video series, Assessment for Learning with Young Learners. Why not give it a try, and share in the comment box below what happened? We’re hoping to hear from you!

Chappuis, S., & Stiggins, R. (2002). Classroom assessment for learning. Educational Leadership, 60(1), 40–43.

 

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