## The paths to "Eureka" moments: Teaching Mathematics in Secondary Education

### Student Diversity Honored in Design of Application Activity

P-1 Practice intentional inquiry and planning for instruction.

Teacher-candidates plan and/or adapt standards-based curricula that are personalized to the diverse needs of each student.

As a student teacher, I create curricula based on standards and the readiness levels of my students.

Savings Problem

In my 8th grade honors classes with Algebra students, we continued to work on recursive sequences using contextual problems to relate the concept to real life scenarios. I created a savings account activity and word problem where students were asked to determine how long it would take them to save \$500 under different circumstances. Previous to this lesson, we had worked on recursive sequences for about 5 class periods and I had determined student readiness levels through formative assessments. In the activity, students were separated into 6 different groups and asked to solve one of two word problems. The two word problems were formulated for different readiness levels. The first problem was for those who were not quite proficient in finding explicit formulas and the second problem was for those who were proficient.

This activity was based on the standard:

A1.7.C Express arithmetic and geometric sequences in both explicit and recursive forms, translate between the two forms, explain how rate of change is represented in each form, and use the forms to find specific terms in the sequence.

Students were asked in both problems to find the explicit formula of the savings scenario they were given and then find the term when the balance reached \$500. Those who were not proficient received additional aid in interpreting the problem as well as steps to finding the explicit formula. The sequence they were given was arithmetic and thus was less challenging mathematically than the second geometric sequence. In this way, students in the first readiness group were able to focus more on interpretation and application of their skills rather than the more complex mathematics operations.

Creating this activity provided me the experience of using formative assessment and knowledge of students’ readiness levels to plan for instruction which challenges students appropriately. I was able to isolate specific learning objectives and provide the opportunity for diverse students to be individually and collaboratively successful.

This activity allowed students to build on their prior understanding of recursive sequences through contextual examples. Additionally, students were able to collaborate in their groups, creating a learning community, and using their peers as resources for their academic growth.

Finally, this activity is exemplary of future lessons that I will plan to challenge diverse students. While this lesson was generated to meet student readiness levels, in the future, I will use similar strategies to fit diversity in learning styles, learning profiles, and multicultural backgrounds.