Authentic Lessons for 21st Century Learning

Walking the Line: The Math Spectrum

A Mathematical Growth Mindset

Brittany VanCleave, Brittany VanCleave, Teresa Kavanaugh | Published: November 18th, 2022 by K20 Center

  • Grade Level Grade Level 6th, 7th, 8th, 9th, 10th, 11th, 12th
  • Subject Subject Mathematics
  • Course Course Algebra 2, Geometry, Middle School Mathematics, Precalculus
  • Time Frame Time Frame 1-2 class period(s)
  • Duration More 90 minutes

Summary

This lesson focuses on eliminating the emotional fear of mathematics by allowing students to evaluate where they are on the math spectrum and identify their goals moving forward. Students explore math concepts taught in past years and analyze their math knowledge to assess their relationship with mathematics. By allowing students to understand their emotional relationship with mathematics, set goals, and identify barriers, the lesson fosters a growth mindset moving forward. This lesson can be implemented at many different grade levels ranging from middle school through high school. This lesson includes optional modifications for distance learning. Resources for use in Google Classroom are included.

Essential Question(s)

What is the relationship between students’ mathematical knowledge and their perception of mathematics? How can this perception be used to develop a growth mindset?

Snapshot

Engage

Students reflect on a video and place their initial self-assessment of their mathknowledge on a spectrum line.

Explore

Students research mathematical concepts learned in previous courses to expand theirknowledge on the topic.

Explain

Students present their findings to a peer and then to the whole class.

Extend

Students create a plan with strategies to promote individual growth and success in the math classroom in the coming school year. Students also identify their past barriers in order to overcome them in thefuture.

Evaluate

Students assess their newfound relationship with math through an Exit Ticket.

Materials

  • Lesson Slides (attached)

  • Math Goal Setting handout (attached)

  • Math Concepts Research and Presentation handout (attached)

  • Brain Dump handout (attached)

  • Exit Ticket handout (attached; optional)

  • Spectrum line (tape, string, interactive whiteboard, etc., or whatever you choose)

  • Student devices with internet access

  • Sticky notes

  • Markers

Engage

Math Spectrum Line Sample #1: Does not have any standards associated with it and is created using rope or string and displayed in your room. During the Engage, students will place a sticky note where they think they belong.
Math Spectrum Line Sample #2: Lists various math standards in a more straight-line spectrum. During the Engage, students will place a sticky note or their name where they think they belong.

Begin the lesson by showing students the “With Math I Can" video found on slide 5. Links are available here and in the slide presentation. The full URL of the video can also be found in the Resources at the end of the lesson.

Give students a couple of minutes to reflect on the video and introduce a modified Collective Brain Dump strategy. Distribute the Walking the Line Brain Dump handout (attached) and ask students to write down a takeaway they got from the video. The cloud on the handout will be a place for them to write down thoughts they have throughout the lesson.

Transition to slide 6. After students have written their takeaway on the Brain Dump handout, use an Elbow Partner strategy to facilitate student conversations. Give students time to reflect on the video by discussing their takeaway with an elbow partner.

Next, display slide 7 and ask students, “How much mathdo you know?” If your math spectrum line is physically on display in your classroom, instruct the students to take a sticky note, write their name on it, and placeit where they believe they lie on the math spectrum that you've created for the class. If you chose to make your math spectrum line on an interactive whiteboard, instruct the students to write their names on the line using the interactive whiteboard pens. In the slide graphic, the far left side represents being not very knowledgeable and the far right side is a master at the subject.

Explore

Display slide 9. After students have analyzed where they are on the math spectrum, ask them to return to their Brain Dump Handout and list every math concept they can remember learning in elementary and middle school. Once they have written down a list of math concepts, have them to select two to start exploring online.

Distribute the Math Concepts Research and Presentation handout (attached) and Introduce a Stop and Jot strategy to guide students in taking key notes while they are researching their topics. The students will read through different resources, stop to process the information, and then jot down any key terms on their Math Concepts handout. Inform the students that they will be explaining the topics they research to another student, so it is important to take good notes.

Explain

Display slide 11. Once the exploration is completed, have students find a partner who did not research the same topic as them. Give the students roughly five minutes to pair-share their findings with a partner. In doing so, they will explain the math concepts they researched. A space is provided on the Math Concepts handout to take notes about their partner's presentation. Once each person has shared, ask students to use the box at the bottom of the Math Concepts handout to write one summary statement that describes a connection between one of their concepts and one of their partner's concepts. Finally, have students share their summary statement with the class.

This activity will allow students to recall previous knowledge and help them to realize that they remember more concepts than they may have initially thought.

Extend

After each pair presents the summary statement, display slide 13 and ask students, "How much math do know NOW?" The students will reevaluate their position on the math spectrum by moving their name if they deem it appropriate. The students will more than likely move their name to the right (towards mastery) after they hear different presentations about math concepts they had previously learned.

Transition to slide 14 and distribute the Math Goals handout (attached). After allowing students to move their name, continue to promote a growth mindset by giving students the opportunity to write a math plan for the school year. The plan will include a reflection of past successes and failures and goals moving forward. This is important for the student to create a vision for their learning.

Display slide 15. Once everyone has created a math plan, students will identify barriers they believe could stand in the way of their success. On a separate sheet of paper, have students write down the barriers that have stopped them from reaching their full potential in math in the past. If students feel comfortable, have them share out some of their barriers.

Once everyone who wishes to do so has shared, transition to slide 16. Tell the students to raise their paper on which they've written their barriers, rip it up, and toss the remains in the trash. This will symbolize that their past barriers can no longer hinder their future.

Evaluate

To end the activity in reflection, have the students complete an Exit Ticket on a piece of paper or on the attached Exit Ticket handout. Have students respond to the following question and statement:

  1. What did you learn about your relationship with math today?

  2. This year in math will be a success if…

The Exit Ticket question will give students time to reflect and the statement will give them a focus for future success. Both will give you a starting point to understand where the students are emotionally so you can help them break down their barriers and misconceptions throughout the year.

Resources