Today, one of my classmates and I completed our planning and preparation for our first “Group-Worthy Task” for use with a Math Analysis class Friday morning. Students in that class just completed a chapter on trigonometric functions. Our group-worthy task serves as an introduction to the next chapter, Inverse Trigonometric Identities. In a perfect world, we would not have selected this particular topic for our class project, however, we are schedule driven so we embraced the challenge of making something fairly esoteric interesting and hopefully exciting, from a student learning standpoint. Time will tell.
For those not familiar with group-worthy tasks, the following excerpt explains their essence. They serve as equitably accessible assignments where students of any status or station are able to contribute to solving the task at hand. Of course, some familiarity with the subject, in our case, trigonometry helps, however, one does not need to be expert, nor the best and brightest since one brings their strengths and insights to the group task.
“Group-worthy tasks are as close as possible to genuine dilemmas and authentic problems. They require students to share their experiences and justify their beliefs and opinions. In such activities, students analyze, synthesize, and evaluate; they discuss cause and effect, explore controversial issues, build consensus, and draw conclusions. By assigning such tasks, teachers delegate intellectual authority to their students and make their students’ life experiences, opinions, and points of view legitimate components of the content to be learned (Lotan, 1997).” Rachel A. Lotan, Group-Worthy Tasks, Creating Caring Schools Pages 72-75, March 2003 | Volume 60 | Number 6
Prior to distributing a group-worthy task, “multiple abilities orientation” usually occurs illustrating various skills helpful to the specific task which no one student typically possesses; hence, the need for students to rely on one another bringing multiple perspectives and diverse skills to the group. Groups usually consist of four students oriented so they are facing each other surrounding a common work space.
Once we complete the multiple abilities orientation, we distribute task cards to the groups. In our case, we plan to have three versions of the following each focusing on a different trigonometric function: sin, cos, and tan.
Task Card: Inverse Trigonometric Identities
Your group needs to discuss and solve the problem below. Pay special attention to the IMPORTANT GUIDELINES on the projector screen before starting to work on, and before handing in, your solution(s) to the problem.
- One sheet of poster paper
- Two sheets of tracing paper
- Colored markers and crayons
The following guidelines are important for each group to complete the project. Rather than overwhelm students on the task card with these guidelines, we opted to keep the task card fairly concise and to project the following slide throughout the task.
For students who hit a roadblock, seem stumped, or are unable to go ahead with the task, we plan to distribute “hint cards.” We have yet to decide on whether we will hand these out at set times through the exercise or on demand. Also, the hint cards have three different hints on them, which when originally conceived were to be cut out into strips and handed out one at a time. Whether we stick with that in the real lesson or not is TBD.
Lastly, upon completion, and as homework, students need to complete the following reflection assignment.
Write a reflection describing what you learned about inverse trigonometric functions. Be as specific as possible, using examples where applicable. One page will suffice; however, feel free to write more if desired.
In your reflection, please address the following:
- State the entire problem you were asked to discuss and solve.
- State your findings and explain the reasons for your findings.
- What you found easy about the task.
- What you found challenging about the task.
- Whether anything would have made it easier to understand the task that could have been provided?
Stay tuned for how this works out! I’ve enjoyed the process, mostly, up until now.