Content: Learning Progression Activities

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In the Unit 8 Introductory Challenge, Jessica became overwhelmed when asked to identify whether a shape had a line of symmetry. The trouble wasn’t that the material itself was too difficult; in fact, one of the Grade 4 Common Core Standards is that students should be able to “identify line-symmetric figures and draw lines of symmetry.” The problem was that Jessica needed a step-by-step learning progression to build up to being able to achieve that standard.
math unit8 illustration1

Figure 1 shows the learning progression for identifying line-symmetric figures suggested by “Ohio’s Academic Content Standards—Extended, Mathematics.” (Here’s the link to the full document: https://education.ohio.gov/getattachment/Topics/Special-Education/Ohios-Learning-Standards-Extended/MathExtStrdsFinal_2_05_19-1.pdf.aspx?lang=en-US) 

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But why is the learning progression arranged in this way? Let’s examine each step of the learning progression in more detail.

Step 1

Understand the definition of line symmetry.

Without knowing the definition of line symmetry, it would be very difficult to identify whether a figure has line symmetry!

Definitions should be the default starting point for new topics in math.

  • A “line of symmetry” is a line that divides a figure into two mirror-image halves.
  • A “line-symmetric figure” is any figure on which at least 1 line of symmetry can be drawn.

Step 2

Decide whether a specific line creates line symmetry.

The next step after a definition is often a direct concrete example of how to use the definition.  Direct Concrete Examples:

Each of the dashed lines shown in 
 is a line of symmetry. Any other line drawn through any of these shapes would not be a line of symmetry.
 

math unit8 illustration2

Step 3

Find a line of symmetry on a shape with line symmetry. Several decades ago, a series of books called “Where’s Waldo?” were published. The idea behind the books was to find a specific man amidst an entire page of elaborate illustrations. Although it was often time-consuming and even frustrating to find Waldo, at least the reader could rely on the fact that Waldo was indeed somewhere on the page.

MOVE FROM EASIER TO MORE CHALLENGING STEPS IN THE LEARNING

 In the same way, it is easier for students to find or identify something when they know that it exists. For this reason, finding a line of symmetry on a line-symmetric figure is placed earlier in the learning progression than identifying whether a shape has line symmetry. 

Step 4

Identify whether a figure has line symmetry. Only after students know what line symmetry is, have classified lines as symmetric or not, and have identified where a line of symmetry is, are students then ready to complete the actual content standard of identifying whether or not a figure has line symmetry. 

 

Activity One:Investigating Learning Progressions 

Purpose 

The purpose of this activity is for you to become more comfortable with the learning progressions related to the math standards in the state of Ohio. The more comfortable you are with the learning progressions, the better you will be able to supports students, particularly students who experience difficulty with math.

Procedures 
  1. Visit the learning progressions document: https://education.ohio.gov/getattachment/Topics/Special-Education/Ohios-Learning-Standards-Extended/MathExtStrdsFinal_2_05_19-1.pdf.aspx?lang=en-US. 
  2. Choose a grade levels (Grades 3-8) or High School.
  3. Read through one of the Learning Standards. Then, read through standards that support that Learning Standard (these are in the same row as the Learning Standard), and these are labeled Complexity a, b, and c. Notice how Complexity c is less complex than Complexity a. See Figure XX for an example.

Figure: Learning Progression from Grade 4.

TAKE NOTES: 

  • How do Complexity a, b, and c build to the Learning Standard. How would you use the standards described in Complexity a, b, and c to support students who are working on the Learning Standard?
  • How might you understand when students are ready to move from Complexity c to Complexity b and so on?
  • If students are experiencing a lot of difficulty in math, can you think of a scenario when you might have to go look at the standards from previous grade levels to fill in gaps in understanding?

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Activity: Going Beyond the Common Core Practice Standards 

Purpose 

The purpose of this activity is for you to familiarize yourself with the Standards for Mathematical Practice. In the webinar, we learning about six of the standards (and did not dig into standards #4 and #8). When you understand the practice standards and other strategies for the practice of mathematics, you will better be able to support your students as they learn math.

See Figure XX for a list of all eight practice standards from the Common Core.

Figure XX: Common Core Standards for Mathematical Practice

TAKE NOTES: 

 

  1. Which of these practice standards might be easiest for you to use with students? Which might be most difficult for you?
  2. When you support students, particularly students who struggle with me, you may also want to know of resources that might talk about practices important for those students as they learn math. Here is one such resource from the What Works Clearinghouse (https://ies.ed.gov/ncee/wwc/PracticeGuide/26).

Figure Below provides an overview of the practices from the guide.