Reflection: Complex Tasks Writing in Math Classroom, Part 3: Comparing and Contrasting Arithmetic and Geometric Sequences - Section 4: Collaborative Work: Comparing and Contrasting Arithmetic and Geometric Sequences


Having students create their own example (student work: Arithmetic Sequence 2 and Geometric Sequence 2) of a function or sequence is a powerful tool to assess understanding. I also have found that having students explain their creations with their peers is a great way to get students to identify their own misconceptions and to challenge classmates with misconceptions. 

During this activity, one of the biggest challenges was in that the task was open ended. Students struggled initiating the task on their own, and I found myself providing a number of cues and starters to get each student going on the task. 

The end result of the task was well worth the time invested. It was interesting in the different ways students represented linear sequences. For example, in Arithmetic Sequence 1 the student defined the sequence recursively, while the student in Geometric Sequence 1 created a sequence both recursively and in function notation. The variety of work samples attached to this resource reflects the variety of conversations that students were engaged in during this interesting activity on comparing and contrasting sequences.

  Complex Tasks: Challenging Misconceptions through Collaborative Work
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Writing in Math Classroom, Part 3: Comparing and Contrasting Arithmetic and Geometric Sequences

Unit 5: Exponential Functions
Lesson 10 of 10

Objective: SWBAT compare and contrast arithmetic and geometric sequences. SWBAT construct equations in 2 variables to model sequences as functions. SWBAT construct clear arguments and critique the reasoning of others.

Big Idea: Students work collaboratively to teach each other the similarities and differences between arithmetic and geometric sequences!

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